comparative study on rcc & steel building

COMPARITIVE STUDY ON MULTI-STOREY REINFORCED CEMENT CONCRETE AND STEEL BUILDING

A PROJECT REPORT ON

COMPARATIVE STUDY ON MULTI-STOREY

REINFORCED CEMENT CONCRETE AND

STEEL BUILDING

A PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

BACHELOR OF TECHNOLOGY

IN

CIVIL ENGINEERING

BY

1. ABDULLAH 08E01A0102

2. MOHAMMED JAWAD HUSSAIN 08E01A0120

3. SUFIAN ASHER KHAN 08E01A0139

4. SYED AAMER HUSSAIN 08E01A0140

5. SYED ABDUL HANNAN 08E01A0141

6. SYED MUSHTAQ HUSSAIN SAJJAD 08E01A0152

7. MOHAMMADABDUL RAHEEM 09E05A0103

Under the Guidance of

MR. S. KHALID HASHMI MR. MIR AHMED ALI MUJAHID ASST VICE PRESIDENT-ENGG B.E (CIVIL); ME (STRUCT)

KIRBY BUILDING SYSTEM H.O.D CIVIL ENGG DEPT

HYDERABAD NIZAM INST OF ENGG AND TECH

DEPARTMENT OF CIVIL ENGINEERING

NIZAM INSTITUTE OF ENGINEERING AND TECHNOLOGY (Affiliated to JNTU Hyderabad)

Near Ramoji Film city, Deshmukhi (V) Nalgonda 508284

2008-2012

ACKNOWLEDGEMENT

I would like to express my sincere gratitude to Mr. Mir Mujahid Ali H.O.D of

Civil Engineering Department for having permitted us to carry out this project work.

Needless to mention that, Mr. S. Khalid Hashmi, Assistant vice-president of

Kirby Building India(P) Ltd, who had been a source of inspiration and for his

timely guidance in the conduct of our project work, I take this opportunity to thank for

his guidance toward us throughout the project period.

I take this opportunity to thank Mr. Syed Muneer Hussain, G.M Associates for

his esteem guidance and support throughout the project period during the program

would be nothing without the enthusiasm and imagination from you.

I acknowledge the untiring of Mr. S. Khalid Hashmi (External Guide) for his

excellent guidance without which the completion of this project would have been

impossible. His continuous encouragement and support has always been an

inspiration and a source of energy for us. We thank him for all of his valuable time,

effort and help. Without which the project could not have been completed.

The Materialization of ideas and views of the project work has been valuable

contributing of numerous friends and academics in the form of selfless criticism, well

wishes and above all words of inspiration. I am deeply indebted to all of them for

their support and guidance and sincerely thank each of them. Also my sincere thanks

to all other people who were directly or indirectly associated with the same in any

other way.

CONTENTS PAGE N0

INTRODUTION 1

MODULE I

1. INTRODUCTION TO DESIGN OF REINFORCED 5

CONCRETE STRUCTURE

2. INTRODUCTION TO LIMIT STATE DESIGN 25

3. ANALYSIS OF REINFORCED 31

CONCRETE STRUCTURE

4. DESIGN OF SLABS 80

5. DESIGN OF BEAMS 96

6. DESIGN OF COLUMNS 132

7. DESIGN OF FOOTINGS 152

8. DESIGN OF STAIRCASE 168

9. DETAILING AND DRAWINGS 178

MODULE II

10. INTRODUCTION TO STEEL STRUCTURES 179

11. LIMIT STATE DESIGN SPECIFICATIONS 185

FOR STRUCTURAL STEEL MEMBERS

12. ANALYSIS OF STEEL STRUCTURE 189

13. DESIGN OF DECK SLABS 205

14. DESIGN OF STEEL BEAMS 215

15. DESIGN OF STEEL COLUMNS 238

16. DESIGN OF STRUCTURAL CONNECTIONS 252

17. DESIGN OF COLUMN BASES 267

18. DESIGN OF STAIRCASE 273

19. DETAILING AND DRAWING 275

MODULE III

20. ESTIMATION OF QUANTITIES OF R.C.C MEMBERS 276

21. ESTIMATION OF QUNTITIES OF 294

STRUCTURAL STEEL MEMBERS

22. CONCLUSION 297

COMPARATIVE STUDY ON MULTI-STOREY R.C.C AND STEEL BUILDING

NIZAM INSTITUE OF ENGINEERING AND TECHNOLOGY 0

If one does not reflect, one thinks oneself master of everything;

But when one does reflect, one realizes that one is a master of nothing.

-Voltaire



INTRODUCTION

Sociological changes, new technology in industry and commerce, new

building codes, other new laws and regulations, inflationary economics of nations,

and advances in building technology place an ever-increasing burden on building

designers and constructors. They need more and more knowledge and skill to cope

demands placed on them.

The public continually demands more complex buildings than in past. They

must serve more purposes, last longer and require less maintenance and repair. As in

past they must look more attractive. Yet, both building construction and operation

cost must be kept within acceptable limits or new construction will cease. To meet

this challenge successfully continual improvement in building design and construction

must be made.

One advance of note to building design is the adaption of operation research,

or system design and comparison of different type constructions. In the past, design of

a new building was mainly an imitation of the design of an existing building.

Innovations were often developed fortuitously and by intuition and were rare

occurrences. In contrast, systems design encourages innovation. It is a precise

procedure that guides creativity towards the best decisions. As a result, it can play

significant role in meeting the challenges posed by increasing building complexity

and costs.

I. PRINCIPLES OF ARCHITECTURE

A building is an assemblage that is firmly attached to the ground and the

ground that provides total or nearly total shelter for machines, processing equipment

performance of human activities, storage of human possessions, or any combination

of these.

Building design is the process of providing all information necessary for

construction of a building that will meet its owner’s requirements and also satisfy

public health, welfare, and safety requirements. Architecture is the art and science of

building design. Building design and construction is the process of assembling

members and materials to form a building.

Architects are persons legally permitted to practice architecture. Engineers

are experts in specific scientific disciplines and are legally permitted to design parts of

buildings; in some cases, complete buildings. Building construction is generally

performed by laborers and crafts people engaged for the purpose by an individual or

organization, called a contractor.

In the design of a building architect should be guided by following principles:



1. The building should be constructed to serve purposes specified by the client

2. The design should be constructed by known techniques and with available

labor and equipment, within an acceptable time.

3. The building should be capable of withstanding the elements and normal usage

for a period of time specified by client.

4. Both inside and outside, the building should be visually pleasing.

5. No part of the building should pose a hazard to the safety or health of its

occupants under normal usage, and the building should provide for safe

evacuation or refuge in emergencies.

6. The building should provide the degree of shelter from the elements and of

control of the interior environment-air, temperature, humidity, light and

acoustics-specified by the client and not less than the minimums required for

safety and health of the occupants.

7. The building should be constructed to minimum adverse impact on the

environment.

8. Operation of the building should consume a minimum of energy while

permitting the structure to serve its purposes.

9. The sum of costs of construction, operation, maintenance, repair, and

anticipated future alterations should be kept within the limit specified by the

client.

The ultimate observation objective of design is to provide all

the information necessary for the construction of a building. This objective is

achieved by the production of drawing, or plans, showing what are to be

constructed, specifications stating what materials and equipment are to be

incorporated in the building, and a construction contract between the client

and a contractor. Designer also should observe construction of the building

while it is in process. This should be done not only to assist the client in

ensuring that the building is being constructed in accordance with plans and

specifications but also to obtain information that will be useful in design of

future buildings.

II. SYSTEMS DESIGN AND ANALYSIS:

Systems design comprises a logical series of steps that leads to the best

decision for a given set of conditions. The procedure requires:

Analysis of a building system.

Synthesis, or selection of components, to form a system that meets

specific objectives while subject to constrains, or variables controlled by

designers.

Appraisal of system performance, including comparisons with

alternatives systems.

Feedback to analysis and synthesis of information obtained in system

evaluation, to improve the design.



A system is an assemblage formed to satisfy specific objectives and

subject to constraints and restrictions and consisting of two or more

components that are interrelated and compatible, each component being

essential to the required performance of the system.

Building components, such as walls, floors, roofs, windows and doors,

are interrelated and compatible with each other. The existence of any of the

three components affects to some extent the performance of the others. And

the required performance of the building as a whole imposes restrictions on

the components. Consequently, a building has the basic characteristics of a

system, and system-design procedures should be applicable to it.

III. TRADITIONAL DESIGN PROCEDURES

System design of buildings requires a different approach to design and

construction than that used in traditional design. Because traditional design

and construction procedures are still widely used, however, it is desirable to

incorporate as much of those procedures in systems design as is feasible

without destroying its effectiveness. The basic traditional design procedure

usually starts when a client recognizes the need for and economic feasibility of

a building and engages an architect, a professional with a broad background in

building design. The architect, in turn, engages consulting engineers and other

consultants.

A Structural engineer is a specialist trained in the application of

scientific principles to the design of load-bearing walls, floors, roof,

foundations, and skeleton framing needed for the support of buildings and

building components.

A Mechanical engineer is a specialist trained in application of

scientific principles to the design of plumbing, elevators, escalators, horizontal

walkways, dumbwaiters, conveyors, installed machinery, and heating,

ventilation, and air conditioning.

An Electrical engineer is a specialist trained in the application of

scientific principles to the design of electric circuits, electric controls and

safety devices, electric motors and generators, electric lighting, and other

electric equipment.

STRUCTURAL SYSTEM, The portion of a building that extends

above the ground level outside it is called superstructure. The portion below

the outside ground level is called the substructure. The parts of the

substructure that distribute building loads to the ground are known as

foundation.

Foundations may take the form of walls. When the ground under the

building is excavated for a cellar, or basement, the foundation walls have the



additional task of retaining the earth along the outside of the building. The

superstructure in such cases is erected atop the foundation walls

Broadly multi-storey buildings have been classified into three types:

i. Load bearing construction

ii. Composite construction

iii. Frame construction which can be either with reinforced concrete or steel

The first method has got the limitation that will be economical only up to 2 to

3 storey's. With composite construction technique, the economy is achieved even if 6

storey's or more has to be necessarily dealt with framed type of construction.

ADVANTAGES OF FRAMED CONSTRUCTION OVER OTHER TYPES

1) Dead load on foundation will be less due to reduction in wall thickness.

2) Rate of construction is faster.

3) Floor area will be more due to reduction in thickness of wall

4) Greater feasibility with respect of:

a) Location and size of window b) Location of glazing area is obtained

5) Interior partition wall can be independent of doors on the floors above or below,

thus permitting their removal to suit varying requirement or change in the tenancy.

IV. CHOICE OF MATERIALS:

i. R.C.C. FRAMES: R.C.C frames are found to be economical up to 25 storey's.

Because of its resistance to corrosion, it is widely favored in cold climates too.

ii. STEEL FRAMES: If the number of floors exceeds twenty five, the

experience of designers, reveals that steel frames are more economical due to

the fact that these frames can be fabricated quickly in the workshop and can be

transported to work spot in convenient parts.

This project work consists of design of a four storied commercial cum

residential and both types of frames are used for the comparison of its choice which is

divided in different modules further.

MODULE I


NIZAM INSTITUTE OF ENGINEERING AND TECHNOLOGY 5

1. INTRODUCTION TO DESIGN OF REINFORCED

CONCRETE

The design of reinforced concrete (RC) structures in India is governed by the

Indian Standard Code of practice for plain and reinforced concrete IS: 456. The fourth

revision of this code IS: 456-2000 incorporates the Limit State Method of design

based on serviceability and safety requirements associated with the design loads and

design strengths of the materials. These design loads and design strengths are obtained

by applying partial safety factors for characteristic loads and strengths of the materials

concrete and steel.

Concrete structures have become very common in civil engineering

construction concrete has established as a universal building material because of its

high compressive strength, its adoptability to take any form and shape and resistant to

fire and carrion with negligible maintenance cost. Concrete is very strong in

compression but very weak in tension. Its low tensile strength is compensated by

introducing steel reinforcement in the tension zone. Thus, the concrete is strengthened

by steel and extensively in construction of buildings, bridges, tanks, dams etc. it is

therefore, necessary that every civil engineer should know the basic principles

involved in the design of Reinforced Concrete Structures.

1.1 CONCRETE:

Concrete is a composite material consisting of cement, aggregate and water in

suitable proportions. The chemical interaction between cement and water binds the

aggregates in to a solid mass. Fresh concrete will be plastic, so that it can be moulded

to any desired shape in the moulds and compacted to form a dense mass. Water has to

be applied for few days over the concrete surface soon after its setting because the

hydration reactions between cement and water continue for a longer period due to

which hardening of concrete takes place. This period when concrete is kept moist

during which concrete gains strength is called curing period. Hence, the strength of

concrete increases with age. The process of solidification of concrete from plastic

stage is called setting while gaining of strength after setting is called hardening.

Usually, setting completes within a maximum duration of 10 hours, while about 90%

of hardening is completed by 28 days.

The properties and quality of cement concrete are influenced by the

properties of its ingredients and quality control maintained during its making and

curing. Hence, it is necessary to study the ingredients of concrete.



1.2 INGREDIENTS OF CONCRETE:

The main ingredient materials in concrete are:

(a) Cement

(b) Aggregates

(c) Water

a) Cement:

Cement is the building material which is obtained by burning

calcareous, siliceous and argillaceous materials together in definite proportions

at high temperatures and grinding the resultant clinker in to a fine powder.

Various types of cements have been developed for the use in different types of

structures under different situations. According to IS: 456-2000, the types of

cements and their suitability for specific situations are given Table below.

Table 1.1 TYPES OF CEMENTS AND THEIR SUITABILITY

S.NO. Types of Cement IS Code Where Used

1.

Ordinary Portland

Cement

33 Grade

43 Grade

53 Grade

(for OPC,

compressive strength

of cement at 28 days

in N/mm2 is called as

grade of cement)

IS: 269

IS: 8112

IS: 12269

All general concreting

works

Multi storey structures

Bridges, Tall structures,

Pre-stressed concrete work.

2. Rapid hardening

cement IS: 8041 Road work and repairs

3. Low heat Portland

cement IS: 12600 Mass concreting-Dams

4. Port land slag cement IS: 455 Marine structures

5. Portland pozzolana

cement IS: 1489

General building works,

Mass concrete,

Marine structures

6. Sulphate resisting

Portland cement IS: 12330

Marine structures

foundations in sulphate

bearing soils

7. Hydrophobic cement IS: 8043 Swimming pools, floors of

food processing plants

8. High alumina cement IS: 6452 Marine structures

9. Supersulphated

cement IS: 6909

Marine structures,

construction of sewers



b) Aggregates:

Around 75% volume of concrete is occupied by the aggregates. Hence, the

structural behavior of concrete is significantly influenced by the type of aggregates

used. The aggregates used for the concrete should be durable, strong, hard, chemically

inert and well graded.

Aggregates whose particle size varies from 0.075 mm to 4.75 mm are called as

fine aggregate. Aggregates with particle sizes more than 4.75 mm are called as

coarse aggregates. Usually sand is used as fine aggregate whereas crushed rock and

gravel is used as coarse aggregate.

Type of

aggregate Size of aggregate

Coarse aggregate Size bigger than 4.75 mm

Fine aggregate 4.75 mm and less

TABLE 1.2

The nominal maximum size of the coarse aggregate shall be as large as

possible but it should be limited to 1/4th

of the maximum thickness of the member.

The various properties of aggregates like specific gravity, strength, toughness,

hardness, soundness, particle size distribution and grading should comply with the IS

code IS: 383- 1979.

c) Water:

Water plays an active role in the chemical process of hydration of cement and

curing concrete. Hence, the water used for mixing and cutting of concrete should be

clean and free from injurious amount of oils, acids, alkalis, salts, organic matter etc.

that may be deleterious to concrete and steel.

Drinking water is generally considered satisfactory for mixing of concrete. Sea

water should not be used for mixing and curing because of presence of harmful salts

in it. The PH values of water should not be less than 6. The physical and chemical tests

for water should be done as per IS: 3025.

d) Admixtures:

Admixture is defined as a material, other than cement, water and aggregates.

Admixture is an ingredient of concrete and added to batch immediately before or

during mixing. Additive is a material which is added at the time of grinding cement

clinker at the factory. Admixture is used to modify the properties of ordinary concrete

so as to make it more suitable for any situation.

Admixtures are added to the concrete before or during mixing, to modify one

or more of the specific properties of concrete in the fresh or hardened states. IS: 9103-



1979 lays down the procedures for evolution of admixtures for concrete. The different

types of admixtures used are given below.

1. Accelerating Admixtures: These are added to concrete to increase the rate of

early strength development, which in turn facilitates earlier removal of

formwork. Common accelerators are calcium chloride, flu silicates and

trietanlamine.

2. Retarding Admixtures: These are added to slow down the rate of setting of

cement. They are useful in hot weather concreting. Common types of retarders

are starches and cellulose products, sugar and hydroxyl-carboxylic acids.

3. Water Reducing or Plasticizing Admixtures: The addition of plasticizer

allows greater workability for given water cement ratio or alternatively retains

the workability while reducing the water content. The basic ingredients of

water reducing agents are either lignosulphonate slats or polyhydroxy

compounds.

4. Air-Entraining Admixtures: These are used to incorporate air in the form of

minute bubbles in concrete usually to increase workability and resistance to

freezing and thawing. Commonly used air-entraining agents are animal and

vegetable oils, natural wood resin and their sodium salts of sulphated and

aulphonated organic compounds.

Action of plasticizers:

Fluidify the mix

Improve the workability of concrete

Reduction in the surface tension of water

Site problems in the use of plasticizers:

Slump of reference mix (i.e. concrete without plasticizer).

Sequence of addition of plasticizer.

Problem with crusher dust and crushed sand.

Compatibility with cement.

Slump loss.

Compaction at site.

Finishing.

Removal of formwork.



GRADES OF CONCRETE

Group

Grade Designation

Specified Characteristic

Compressive Strength of

150 mm Cube at 28 Days

in

N/mm2

Ordinary

Concrete

M 10 10

M 15 15

M 20 20

Standard Concrete

M 25 25

M 30 30

M 35 35

M 40 40

M 45 45

M50 50

M 55 55

High

Strength

Concrete

M 60 60

M 65 65

M 70 70

M 75 75

M 80 80

TABLE 1.3

STRESS STRAIN CURVE FOR DIFFERENT MIXES

(1 : 1 : 2 MIX) (1 : 21/2 : 3 ½ MIX) (1 : 3 : 5 MIX)

Strain x 10-3

FIG1 Stress- Strain Relation



Formwork:

Formwork shall be designed and constructed so as to remain sufficiently rigid

during placing and compaction of concrete. The joints are plugged to prevent the loss

of slurry from concrete.

Stripping time of formwork:

TYPE OF FORMWORK MINIMUM PERIOD BEFORE

STRIKING FORMWORK a. Vertical formwork to columns

walls and beams 16 – 24 hours

b. Soffit formwork to slabs (props

to refixed immediately after

removal of formwork)

3 days

c. Soffit formwork to beams (props

to refixed immediately after

removal of formwork)

7 days

d. Props to slab

Spanning up to 4.5 m 7 days

Spanning over 4.5 m 14 days

e. Props to beam and arches

Spanning up to 6 m 14 days

Spanning over 6 m 21 days

TABLE 1.4

1.3 ADVANTAGES OF CONCRETE:

The following are the advantages of concrete due to which concrete is extensively

used in construction industry.

1. Compressive strength of concrete is very high.

2. Concrete can be moulded to any desired shape.

3. The materials for concrete are easily available.

4. It is easy to make.

5. It is durable.

6. By proper proportioning of mix, concrete can be made watertight.

7. It is fire resistant

8. Its maintenance cost is practically nil.

9. Strength of concrete increases with age.

10. Its monolithic character gives it more rigidity.



1.4 DISADVANTAGES OF CONCRETE:

1. Tensile strength of concrete is very low and hence plain concrete cannot be

used in situations where tensile stresses are developed.

2. Strict quality control has to be maintained during production, placing and

compaction.

3. Curing has to be done far at least 14 days and hence time of construction

increases.

4. Once the members’ caste with concrete, it is very difficult to dismantle it.

1.5 DESIGN CATEGORIES:

It is emphasized that any structure to be constructed must satisfy the

need efficiently for which it is intended and shall be durable for its desired life. Thus,

the design of any structure is categorized into the following main types.

1. Functional design

2. Structural design

1. Functional design:

The structure to be constructed should primarily serve the basic purpose for

which it is to be used and must have a pleasing look.

The building should provide happy environment inside as well as outside.

Therefore, the functional planning of a building must take into account the proper

arrangements of rooms/halls to satisfy the need of the client, good ventilation,

lighting, acoustics, etc.

Bearing all these aspects in mind, the architect/engineer (i.e. Designer) has to

decide whether it should be a load bearing structure or R.C.C. framed structure or a

steel structure. He should also decide the system of covering the structure, whether the

roof shall consist of steel roof trusses and girders or R.C.C. folded plates or R.C. shell

or a beam-slab construction or a grid system or a pre-stressed concrete hanging roof or

combination of above.

After deciding the tentative form of the structure the designer should select

appropriate material for it construction. The properties of the available materials have

to be determined to decide their stability and suitability.

2. Structural Design:

Once the architectural planning task is completed further structural designing

task for all structural components of the building will be proceeded.



‘’Structural design is an art and science of understanding the behavior of

structural members subjected to loads and designing them with economy and

elegance to give a safe, serviceable and durable structure’’.

The principal elements of a R.C. Building frame consists of:

i. Slabs to cover large area ,

ii. Beams to support slabs and walls

iii. Columns to support beams

iv. Footing to distribute concentrated column loads over large area of the

supporting soil such that the bearing capacity of soil is not exceeded.



In a frame structure the load is transferred from slab to beam, from

beam to column and then to the foundation and soil below it

1.6 STAGES IN STRUCTURAL DESIGN:

Structural planning

Action of forces and computation of loads

Methods of analysis

Design of members

Detailing, drawing and preparation of schedules.

Structural planning:

After getting architectural plan of the building, the structural planning of the

building frame is done. This involves determination of the following:

a. Positioning and orientation of columns.

b. Positioning of beams.

c. Spanning of slabs.

d. Layout of stairs.

e. Selecting proper type of footing.



A FLOWCHART ON

INVESTIGATION OF

BUILDING



As a Civil Engineering structures such as a house, worship Centre, Factories

etc. that has a foundation, wall, roof etc. that protect human being and their properties

from direct harsh effect of weather like rain, wind, sun etc.

1.6 BUILDING CONSISTS OF THREE PARTS:

(1) Foundation (Sub-structure)

(2) Plinth

(3) Superstructure

(1) Foundation: It is the lowest artificially prepared part, below the surface of the

surrounding ground, which is in direct contact with substrata and transmits all

the loads coming from super structure to the subsoil.

(2) Plinth: It is the middle part of the structure, above the surface of the

surrounding ground up to the surface at the floor (i.e. floor level), immediately

above the ground.

(3) Superstructure: The part of the structure constructed above the plinth level

(or ground floor level) is termed as superstructure.

Buildings are generally classified as residential, educational, institutional,

assembly, business, and mercantile industrial storage and hazardous.

1.7 BUILDING CLASSIFICATION:

According to National Building Code of India 1970, buildings on the basis of

occupancy are classified into following groups:.

1. Residential Buildings: All those building in which sleeping

accommodation is provided for residing permanently or temporarily

with or without cooking or dining or both facilities are termed as

residential buildings, for e.g. apartments, flats, bungalows, dormitories,

private houses, hostels, hotels etc.

2. Educational Buildings: These include any building used for school,

college or day- care purposes involving assembly for institution,

education or recreation and which is not covered by assembly buildings.

3. Institutional Buildings: These buildings are used for different purposes,

such as medical or other treatment or care of persons suffering from

physical or mental illness, disease or infirmity, care of infants,

convalescents or aged persons and for penal or correctional detention in

which the liberty of the inmates is restricted. Institutional buildings

ordinarily provide sleeping accommodation for the occupants. They



include hospitals, sanatoria, custodia institutions or penal institutions like

jails, prisons and mental asylums.

4. Assembly Buildings: These are the buildings where the groups of people

meet or gather for amusement, recreation, social, religious, political, civil

halls, marriage halls, town halls, auditoriums, exhibition halls, museums,

skating rinks, gymnasiums, restaurants (also used as assembly halls),

places of working, dance halls, club rooms, passenger stations and

terminals of air, surface and other public transportation services,

recreation places and stadia etc.

5. Business Buildings: These buildings are used for transaction of business

(other than that covered by mercantile buildings), for keeping of accounts

and records for similar purposes; offices, banks, professional

establishments, court houses and libraries. The principal function of these

buildings is transaction of public business and keeping of books and

records.

6. Mercantile Buildings: These buildings are used as shops, stores, market,

for display and sale of merchandise either wholesale or retail, office,

shops, storage service facilities incidental to the sale of merchandise and

located in the same building.

7. Industrial Buildings: These are buildings where products or materials of

all kinds and properties are fabricated, assembled, manufactured or

processed, as assembly plants, laboratories, dry cleaning plants, and

power plants, pumping stations, smoke houses, laundries, gas plants,

refineries, dairies and saw mills.

8. Storage Buildings: These buildings are used primarily for the storage or

sheltering (including servicing, processing or repairs incidental to

storage) of goods, wares or merchandise (except those that involve

highly combustible or explosive products or materials) vehicles and

animals, as warehouse, cold storage plants, freight depots, transit sheds,

store houses, truck and marine terminals, garages, hangers (other than

aircraft repair hangars), grain elevators, barns and stables.

9. Hazardous Buildings: These buildings are used for the storage,

handling, manufacture or processing of highly combustible or explosive

materials or products which are liable to burn with extreme rapidly

and/or which may produce poisonous elements or explosives; for storage

handling, manufacturing or processing of highly corrosive, toxic or

noxious alkalis, acids or other liquids or chemicals producing flame,

fumes and explosive, poisonous, irritant or corrosive gases; and for the



storage, handling or processing of any material producing explosive

mixtures of dust which result in the division of matter into fine particles

subjected to spontaneous ignition.

Residential building is one in which people reside permanently or for a

considerable time. It is the venues where all the members of a family live

together and have their various activities as eating, relaxing, sleeping, washing,

cleaning, bathing, easing and share their passions.

These shall include any building in which sleeping accommodation is

provided for normal residential purpose with or without cooking or dining

facility.

It includes one or more multi-family dwellings, apartment houses

(flats), lodging houses, restaurants, hostels, dormitories and residential hostels.

10. Dwelling: A dwelling is a house or a sub place of residence.

11. Detached House: A detached is the choice of every individual, pleasing

effect is achieved if the approach from the main road is kept open and

light and fresh air flow of uninterrupted by fences and walls. If proper

coordination with adjoining house were done, each house would present

aesthetic presentation.

12. Semi-detached House: This type of construction has the advantage of

separate unit as well as reduction in the cost of construction as two

dwelling units have a common entrance and staircase. And additional

advantage is the sense of security that is felt by dwellers.

13. Terrace Housing Unit: The main advantage of terrace is the in space.

This type of construction is an improvement over the semi-detached unit.

A terrace unit is the row of three or more dwelling units in continuity.

14. Flats: A dwelling is separated from another by horizontal division. In

case of conventional group vertical divisions or partitions achieve

housing the separation.

15. Duplex Apartments: These are living spaces at two or more levels.

They can be detached, semi-detached or in multi-storied buildings where

corridors can be provided in alternate floors.



1.8 MULTI-STORIED COMPLEX HAVE BEEN CLASSIFIED

INTO THREE TYPES:

1. Load Bearing constructions

2. Composite constructions

3. Framed constructions, which can be with either Steel or Concrete.

1.9 ENGINEERING STRUCTURE AND STRUCTUTAL DESIGN:

An engineering structure is on assembly of members or elements transferring

the load or resisting external actions and providing a form to serve the desired

function.

The structural design is a science and art of designing with economy and

elegance. A durable structure, which can safely carry the forces and can serve the

desired function satisfactory during its expected service life span.

Object and basic requirements of structural design:-

Serviceability

Safety

Durability

Economy

Aesthetic beauty

1.10 PLANNING:

Once the site is chosen of accepted, the architect’s or engineer’s aim to fix the

direction of plan of building and finally to play the building keeping in view the local

bye-laws, principles of planning and requirements of owner.

Orientation is defined as a method of setting or fixing the direction of the plan

of the building in such a way that it devices maximum benefits from the elements of

nature. The knowledge of orientation is the first prerequisite of a good planning. It

should be noted that poor orientation of the buildings results in uncomfortable

conditions inside the building.

Bye-laws are certain rules and regulations laid down the by the municipalities

or town planning authorities in their jurisdiction. These have to be considered while

planning and designing the layout of buildings.

Building line, which is often known as set back refers to the line up to which

the plinth of a building adjoin a street may lawfully extend. Building line facilities

future widening of street and keeps away the noise and dust of the streets.



Open space requirements should be left inside and around a building to meet

the lightening and ventilation requirements of the rooms. The open space left on front,

rear serve the purpose of future widening of streets.

1.11 DESIGNING:

Designing of structures is an art and science of designing a safe, durable and

elegant structure with economy. This not only requires imaginations but also good

knowledge of science of designing besides practical aspects, like the relevant codes

and local municipal bye-law with experience and judgment.

The architect whereas the requirement of safety, serviceability, durability and

economy are taken care of by the structural engineer looks after the design of structure

of planning of the structure and the aesthetics.

As mentioned earlier stages in structural design

Structural planning

Estimation of loads

Analysis of the structure

Design of the members

Drawings and preparation of schedules

Loading:

This stage involves determination of various types that are acting on the

structures. The values of types of loads are taken from relevant IS-codes.

Types of loads:

Various types of loads on a structure and requiring consideration in design

1. Dead load

2. Live load

3. Wind load

4. Seismic load

1. Dead loads:

Dead loads on structure comprise the self-weight of the member, weight of

finishes and partition walls. These are usually dependent upon the constructional

features and have to be assumed in order to design various structural concrete

members.

The unit weight of some of the commonly used building materials are

compiled in Table 1.1 based on IS: 875(PART I)-1987.



2. Live loads or Imposed loads:

The imposed loads of different types of floors and roofs according to IS:

875(PART II) - 1987 in Table 1.2a and Table 1.2b respectively.

3. Wind loads:

The revised code IS: 875 (PART III) -1987 deals with wind loads that have to

be considered while designing while designing structures. The wind load acting on

structural member is expressed as

𝑭 = (𝑪𝒑𝒆 – 𝑪𝒑𝒊) 𝑨𝑷𝒅

F = wind load acting in a direction normal to the structural element

Cpe = external pressure coefficient

CPI= internal pressure coefficient

A = surface area of structural element or cladding unit

Pd = design wind pressure

The design wind pressure depends upon the design wind velocity which in turn

is insufficient by the type of terrain, height and class of structure.

The external pressure coefficient for different types of buildings and sloping

roofs are presented in IS: 875. The internal pressure coefficient depends upon degree

of permeability of cladding and may be positive or negative depending upon the

direction of air flow in relation to openings in the buildings. In the case of buildings

where claddings permit the flow of air through openings not more than 5% of the wall

area (without large openings) a positive and negative internal pressure coefficient of

0.2 is recommended in design.

4. Earthquake load or Seismic load:

Earthquake loads are horizontal loads caused by earthquake and shall be

computed in accordance with IS: 1893 for monolithic reinforced concrete structures

located in seismic zone ii, and iii with not more than 5 storey high, and importance

factor less than 1, the seismic forces are not critical ( see IS: 13920 sect. 1.1).

DESIGN:

Construction is an ultimate objective of design. An engineer is a key person of

successful completion of any kind of project undertaken. Hence, he should adopt all

means to reduce cost of project to minimum, without reducing serviceability aspect of

project.

An engineering structure is an assemble of members for elements transferring

the load and providing from a space, of enclosure and/or a cover to serve the desired,



function. The objective of structural design is to plan a structure that meets the basic

requirements such as serviceability, safety, durability, economy, aesthetic beauty,

feasibility and acceptability.

1.12 STRUCTURAL PLANNING:

Structural planning is first stage in any structural design. It involves the

determination of appropriate form of structure, material to be used, the structural

system, the layout of its components and the method of analysis.

As the success of any engineering project is measured in terms of safety and

economy, the emphasis today being more on economy. Structural planning is the first

step towards successful structural design.

Structural Planning of Reinforced Concrete Framed Building:

Structural planning of R.C framed building involves determination of

1. COLUMN POSITIONS

Positioning of columns

Orientation of columns

2. BEAMS LOCATIONS

3. SPANNING OF SLABS

4. LAYOUT AND PLANNING OF STAIRS

5. TYPE OF FOOTING

1. COLUMN POSITIONING:

Positioning of columns:

Following are some guidelines principles for positioning of columns

a) Columns should be preferably located at or near of the building and at

intersection of the walls, because the function of the columns is to support

beams which are normally placed under walls to support them. The columns,

which are near to property line, can be exception from above consideration as

the difficulties are encountered in providing footing for such columns.

b) When Centre to Centre distance between the intersection of the walls is large

or where there are no cross walls, the spacing between two columns is

governed by limitations on spans of supported beams because spacing of

columns beside the span of the beams. As the span of the beam increases in

total load is negligible in case of column due to increase in length. Therefore,

columns are generally cheaper compared to beams on basis of unit cost.

Therefore, large spans of beams should be avoided for economy reasons.



Orientation of columns:

Columns normally provided in the building are rectangular, width of columns

not less than the width of support for effective load transfer. As far as possible, the

width of column shall not exceed the thickness of the walls to avoid the offsets.

Restrictions on the width of the column necessitate the other side (the depth) of the

column to be larger to get desired load carrying capacity. This leads to the

problems of orientation of columns.

2. BEAMS LOCATIONS:

Following are some of the guiding principles for the positioning of beams:

a. Beams shall, normally be provided under the walls and below a heavy

concentrated load to avoid these loads directly coming on slabs. Basic

principle in deciding the layout of a component member is that heavy loads

should be transferred to the foundation along the shortest path.

b. Since beams are primarily provided to support slabs, its spacing shall be

decided by the maximum spans of slabs. Slabs require the maximum

volume of concrete to carry a given load (i.e. its volume/load ratio is very

large compared to other components). Therefore the thickness of slab is

required to be kept minimum.

c. Avoid larger spacing of beams from deflection and cracking criteria.

Larger spans of beams shall also be avoided from the considerations of

controlling and cracking. This is because it is well known that the

deflection varies directly with the cube of the span and inversely with the

cube of the depth i.e. L3/D

3. Consequently, increase in D is less than

increase in span L which results in greater deflection for large span.

However, for large spans, normally higher L/D ratio is taken to restrict the

depth from considerations of headroom, aesthetics and psychological effect

( a long, heavy, deep beam creates a psychological feeling of crushing load

leading to a fear of collapse). Therefore, spans of beams which require the

depth of beam greater than one meter should as far as possible be avoided.

3. SPANNING OF SLABS:

Span of slabs is decided by the position of supporting beams of walls. The slab

can be made to span in one direction (one-way) or two directional (two-way),

depending on support conditions aspect ratio that is Lx/Ly, ratio of reinforcement

in the two directions. The designer is free to decide as to whether slab should be

designed as one-way or two-way.

The points to be considered in making a decision i.e. whether slab should be

designed as one-way or two-way.



a. The slab acts as two way slab when (Lx/Ly) < 2, a slab acts as one-way

(Lx/Ly) > 2.

b. A two-way slab is economical compare to one-way slab, because steel

along with directions act as main steel and transfers loads to all the

supports, while in one-way slab, main steel is provided along short

span only and load is transferred to either of two supports.

c. Two-way is advantageous, essentially for large spans (greater than 3m)

and for live loads greater than 3 KN/Sq. m. For short spans and light

loads steel required for two-way slab does not appreciably differ as

compare to steel for one-way slab because of requirement of main

steel.

d. Spanning of slab is also decided by the necessity of continuity to

adjacent slab

e. Canopy or porch: while designing any slab as cantilever slab, it is of

utmost importance to see whether adequate anchorage to the same is

available or not.

f. Decide type of slab

While deciding the type of slab, whether a cantilever or a simply supported or a

continuous slab, loaded by udl it should be borne in mind that the maximum bending

moment in a cantilever (M=wL2/2) is four times that of a simply supported slab

(M=wL2/8), while it is five to six times that of a continuous or fixed slab

(M=wL2/12) for the same span length.

Similarly, deflection of a cantilever loaded by a uniformly distributed load is given

by:

δ = wL4/ 8EI = (48/5) x( 5wL

4/384EI)

Which is 9.6 times that of a simply supported slab ( = 5wL4/384EI) for the

same span and load ( besides, additional reduction in deflection is obtained in simply

supported slab due to partial fixity at supports).

In case of cantilevers, on the contrary, there is a probability of increase in

deflection due to probable rotation of the supporting beam due to lack of adequate end

restraint for the beam.



4. FOOTING:

The type of footing depends upon the load carried by the column and

the bearing capacity of the supporting soil. Even under one small building the soil

may vary from soft clay to a hard morum. The nature and properties of soil may

change with season and weather, like swelling in wet weather. Increase in moisture

content results in substantial loss of bearing capacity in case of certain soils which

may lead to differential settlements. It is necessary to conduct the survey in the areas

for soil properties. For framed structure, isolated column footings are normally

preferred except in case of exists for great depths, pile foundations can be an

appropriate choice. If columns are very closely spaced and bearing capacity of the soil

is low, raft foundation can be an alternative solution. For a column on the boundary

line, a combined footing or a raft footing may be provided.



2. INTRODUCTION TO LIMIT STATE DESIGN

2.1 STRUCTURAL DESIGNING:

The object of reinforced concrete design is to achieve a structure that will

result in a safe and economical solution. Structural designing for framed R.C.C

structures can be done by three methods.

1. WORKING STRESS METHOD.

2. ULTIMATE STRENGTH METHOD.

3. LIMIT STATE METHOD.

1. WORKING STRESS METHOD OF DESIGN:

It is the earliest modified method of R.C.C structures. In this method structural

element is so designed that the stress resulting from the action of service load as

computed in linear elastic theory using modular ratio concept does not exceed a pre-

designed allowable stress which is kept as some fraction of ultimate stress, to avail a

margin of safety. Since this method does not utilize full strength of the material it

results in heavy section, the economy aspect cannot be fully utilized in the method.

2. ULTIMATE STRENGTH METHOD OF DESIGN:

This method is primarily based on strength concept. In this method the

structural element is proportioned to with stand the ultimate load, which is obtained

by enhancing the service load of some factor referred to as load factor for giving

desired margin of safety. Since this method is based on actual stress, strain behavior

of the material, of the member as well as of the structure that too right up to failure,

the values calculated by this method agree well the experiments results.

3. LIMIT STATE METHOD OF DESIGN:

In the limit state method, the structural elements are designed for ultimate load

and checked for serviceability (deflections, cracking etc.) at working loads so that

structures is fit for use throughout its life period.

Philosophy of limit state design:

A structure may become unfit for use not only when it collapses but when it

violate the serviceability requirements such as deflections, cracking etc. The

philosophy of limit state method design is to see that the structure remains fit for use

throughout its life period by assuring safety against strength and serviceability

requirement before failure occurs is called limit state. All the relevant limit states

have to be considered in the design. The loads of strength of materials are to be

estimated by probabilistic approach (characteristic values). The design loads and



strengths are derived from the characteristic values through us e of partial safety

factors.

2.2 LIMIT STATES:

The various limit state to be considered in the design are

1. LIMIT STATE OF COLLAPSE

2. LIMIT STATE OF SERVICEABILITY

1. Limit State of Collapse:

It is the limit state at which the structure is likely to collapse. The structure

may collapse due to rupture of one or more critical sections or loss of overall stability

due to buckling or overturning. This limit state may correspond to

a. Flexure.

b. Compression.

c. Shear.

d. Torsion.

2. Limit State of Serviceability:

Limit state of serviceability relate to the performance of the structure at

working loads. It is the limit state at which the structure undergone excessive

deflection, which adversely affect the finishes causing discomfort to the users and

excessive cracking which effects the efficiency or appearance of structure. This limit

state may correspond to

a. Deflection

b. Cracking.

c. Other limit states (vibrations, fire resistance, and durability)

2.3 DESIGN PRINCIPLE, ASSUMPTION AND NOTATION

ASSUMED:

The notation adopted throughout the work is same as in IS-456-2000.

Materials: The design strength of materials is obtained by dividing the

characteristic strength by a factor known as partial safety factor. The partial safety

takes in to account variation of material strength, local weakness etc.

The design strength of the materials, 𝑓d is given by

𝐷𝑒𝑠𝑖𝑔𝑛 𝑠𝑡𝑟𝑒𝑛𝑔𝑡𝑕 = 𝑐𝑕𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑠𝑡𝑟𝑒𝑛𝑔𝑕𝑡 ÷ 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑠𝑎𝑓𝑒𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟



𝑓d= f / γf

f- Characteristic strength of the material

γf Partial safety factor appropriate to the material and limit state being considered.

Material Limit state of Collapse Limit state of

Serviceability

Steel 1.15 1.0

Concrete 1.5 1.0

TABLE 2.1

2.4 ASSUMPTION IN DESIGN:

1. Using partial safety factors for loads in accordance with clause 36.4 of

IS:456-2000 as γf=1.5

2. Partial safety factor material in accordance with clause 36.4.2 of IS: 456-

2000 is taken as 1.5 for concrete and 1.15 for steel.

3. Using partial safety factor in accordance with clause 36.4 of IS: 456-2000

combination of load.

Load

combination Limit state of collapse Limit state of serviceability

D.L L.L W.L D.L L.L W.L

D.L+L.L 1.5 1.5 --- 1.0 1.0 ---

D.L+W.L 1.5 or

0.9 --- 1.5 1.0 --- 1.0

D.L+L.L+W.L 1.2 1.2 1.2 1.0 0.8 0.8

TABLE 2.2

* This value is to be used when stability against overturning or stress

reversal is critical

* While considering earthquake effects, substitute E.L for W.L.

2.5 DENSITY OF MATERIALS:

S.NO MATERIAL DENSITY

1. Plain concrete 24.0 KN/m3

2. Reinforced concrete 25.0 KN/m3

3. Flooring material 20.0 KN/m3

4. Brick masonry 19.0 KN/m3

5. Fly ash 5.0 KN/m3

TABLE 2.3



2.6 LIVE LOADS:

In accordance with IS: 875 (PART II)

i. Live load on slabs

Roof slab = 1.5 KN/m2

Typical floor slab = 2.0 KN/m2

ii. Live load on passage = 3.0 KN/m2

iii. Live load on stairs = 3.0 KN/m2

2.7 DESIGN CONSTANTS:

Using M20 and Fe415 grade of concrete and steel for beams, slabs, footings,

columns.

Therefore:-

fck = Characteristic strength for M20 Grade concrete – 20 N/mm2

fy = Characteristic strength of steel – 415 N/mm2

2.8 ASSUMPTION REGARDING DESIGN:

i. Slab is assumed to be continuous over interior support and partially fixed on

edges, due to monolithic construction and due to construction of walls over it.

ii. Beams are assumed to be continuous over interior support and they frame into

the column at ends.

2.9 PROPERTIES OF CONCRETE:

1. Grades of concrete:

Concrete is known by its grade which is designated as M15, M20 etc. in which

letter M refers to concrete mix and number 15, 20 denotes the specified compressive

strength (fck) of 150mm cube at 28 days, expressed in N/mm2. Thus, concrete is

known by its compressive strength. M20 and M25 are the most common grades of

concrete, and higher grades of concrete should be used for severe, very severe and

extreme environments.

2. Compressive strength:

Like load, the strength of the concrete is also a quality which varies

considerably for the same concrete mix. Therefore, a single representative value,

known as characteristic strength is used.



3. Characteristic strength:

It is defined as the value of the strength below which not more than 5% of the

test results are expected to fall (i.e. there is 95% probability of achieving this value

only 5% of not achieving the same)

4. Characteristic strength of concrete in flexural member:

The characteristic strength of concrete in flexural member is taken as 0.67 times the strength of concrete cube

5. Design strength (fd) and partial safety factor for material strength:

The strength to be taken for the purpose of design is known is known as design strength and is given by Design strength (fd) = characteristic strength/ partial safety factor for material strength

The value of partial safety factor depends upon the type of material and upon the type of limit state. According to IS code,

Partial safety factor ( fs ) is taken as

1.5 for concrete 1.15 for steel

Design strength of concrete in member = 0.45 fck

6. Tensile strength:

The estimate of flexural tensile or the modulus of rupture or the cracking

strength of concrete from cube compressive strength is obtained by the relations.

fcr = 0.7 fck N/mm2

The tensile strength of concrete in direct tension is obtained experimental y by split cylinder. It varies between 1/8 to 1/12 of cube compressive strength..

7. Creep :

Creep is defined as the plastic deformation under sustain load. Creep strain depends primarily on the duration of sustained loading. According to the code, the value of the ultimate creep coefficient is taken as 1.6 at 28 days of loading..

8. Shrinkage:

The property of diminishing in volume during the process of drying and hardening is termed Shrinkage. It depends mainly on the duration of exposure. If this strain is prevented, it produces tensile stress in the concrete and hence concrete develops cracks.



9. Modular ratio:

Short term modular ratio is the modulus of elasticity of steel to the modulus of

elasticity of concrete. Short term modular ratio = Es / Ec Es = modulus of elasticity of steel (2x10 5 N/mm2)

Ec = modulus of elasticity of concrete (5000 𝑓ck N/mm2)

As the modulus of elasticity of concrete changes with time, age at loading etc.

the modular ratio also changes accordingly. Taking into account the effects of creep

and shrinkage partially IS code gives the following expression for the long term

modular ratio.

Long term modular ratio (m) = 280/ (3fcbc)

Where, fcbc = permissible compressive stress due to bending in concrete in N/mn2

10. Poisson’s ratio:

Poisson’s ratio varies between 0.1 for high strength concrete and 0.2 for weak

mixes. It is normally taken as 0.15 for strength design and 0.2 for serviceability

criteria.

11. Durability:

Durability of concrete is its ability to resist its disintegration and decay. One of

the chief characteristics influencing durability of concrete is its permeability to

increase of water and other potential y deleterious materials. The desired low

permeability in concrete is achieved by having adequate cement, sufficient low

water/cement ratio, by ensuring full compaction of concrete and by adequate curing.

12. Unit weight of concrete:

The unit weight of concrete depends on percentage of reinforcement, type of

aggregate, amount of voids and varies from 23 to 26KN/m2. The unit weight of plain

and reinforced concrete as specified by IS: 456 are 24 and 25KN/m3 respectively.



3 ANALYSIS OF REINFORCED CONCRETE

STRUCTURE

The intermediate structure can be analyzed by the following methods.

1. Moment Distribution Method.

2. Slope Deflection Method.

3. Kani’s Method or Rotation Contribution Method.

4. Column Analogy Method.

5. Strain Energy Method.

6. Matrix Method.

7. Finite Element Method (STAAD PRO)

Out of the above mentioned methods here Finite Element Method is adopted.

3.1 FINITE ELEMENT METHOD:

The finite element method analysis is a numerical technique. In this method all

the complexities of problem like varying shape, boundary conditions and loads are

maintained as they are but the solutions obtained approximately. Some of the popular

packages are STAAD-PRO, GT-SRTUDEL, NASTRAN, NISA, ETABS etc.

The finite element analysis originated as a method of stress analysis in the

design of air craft. Today this method is used not only for the analysis in solid

mechanics, but even in analysis of fluid flow, heat transfer, electric and magnetic field

and many others. Civil engineers use this method extensively for the analysis of

beams, space frames, plates, shells, floated plates, foundation, rock mechanic

problems and seepage analysis of fluid through porous media.

This is a time saving method of analysis, with consideration of shape,

boundary condition and loading.

FEM possess some definite advantages over other methods as follows:

a) In classical method exact equations are formed and exact solutions are

obtained where in FEM exact equations are formed but approximate

solutions are obtained.

b) Solutions have been obtained for few standard cases by classical

method whereas solution can be obtained for all problems by FEM.

c) Whenever the following complexities are faced, classical method

makes the drastic assumptions and looks for the solutions:

Shape

Boundary conditions

Loading

d) when material property is not isotropic the solution for the problem

become very difficult in classical method



e) If structure consists more than one material it is difficult to use

classical method but Fem can be used without difficulty.

f) Problems with materials and non-linearity cannot be handled by

classical method this is no difficulty in FEM.

3.2 ANALYSIS SOFTWARE - STAAD.PROV8i OVERVIEW

INTEGRATED SOFTWARE FOR STRUCTURAL

ANALYSIS & DESIGN:

STAAD.PROV8i is a stand-alone finite-element based structural

program for the analysis and design of civil structures. It offers an intuitive, yet

powerful user interface with many tools to aid in the quick and accurate construction

of models, along with the sophisticated analytical techniques needed to do the most

complex projects.

STAAD.PROV8i is controlled based, meaning that the models are

created with members that represent the physical reality. A beam with multiple

members framing into it is created as a single object; just as it exist in the real world,

and the sub-dividing needed to ensure that connectivity exists with the other members

is handled internally by the program. Results for analysis and design are reported for

the overall object, and not for each sub-element that makes up the object, providing

information that is both easier to interpret and more consistent with the physical

structure.

STAAD.PROV8i follows in the same tradition featuring a very

sophisticated, intuitive and versatile user interface powered by an unmatched analysis

engine and design tools for engineers working on transportation, industrial, public

works, sports, and other facilities.

From its 3D object based graphical modeling environment, to the wide

variety of analysis and design options completely integrated across one powerful user

interface, STAADPROV8i has proven to be the most integrated, productive and

practical general purpose structural program on market today.

The intuitive interface allows to create structural models rapidly and

intuitively without long learning curve delays. Complex models can be generated and

meshed with powerful templates built into the interface.

The advanced analytical techniques allow for step-by-step large

Deformation Analysis, Multiple P-Delta, Eigen and Ritz Analysis, Cable Analysis,

Tension or Compression only Analysis, Buckling Analysis, Blast Analysis, Fast

Nonlinear Analysis for Dampers, base Isolators and support Plasticity, Energy

Methods for Drift Control and Segmental Construction Analysis.

Bridge Designers can use STAADPROV8i bridge templates for

generating bridge models, Automated Bridge Live Load Analysis and Design, Bridge



Base Isolated, Bridge Construction Sequence Analysis, Large Deformation Cable

Supported Bridge Analysis and Pushover Analysis

STAADPROV8i enables users to easily apply loads or assign

restraints/supports in skewed directions from the global axis. Even if you don’t have

skewed restraints/supports, but have sloped beams or bracing, STAADPROV8i

analysis results are reported in local directions, making it easy to interpret the

direction of deflections or forces without having to do time consuming, error prone

transformations.

STAADPROV8i constraint options provide unique capabilities to

rigidly ‘link’ joints which are offset from one another. In addition to rigid

diaphragms, STAADPROV8i also provides additional constraint types which rigidly

transfer forces and moments from one joint to another in all degree of freedom, or in

selected degrees of freedom, while accounting for secondary moments that occur due

to the distance between the joint locations (lever arm effect). This ability to transfer

secondary moments differentiates these constraints from traditional master-slave/rigid

diaphragm type of constraints.

This is particularly important when connecting beams with plate

elements, modeling composite behavior, or joint connections offset from an element

centerline which can cause secondary moments. STAADPROV8i constraint options

become especially critical for accurate reactions in a dynamic analysis.

STAADPROV8i enables users to review analysis results graphically

by clicking on individually members or joints, or generate output reports. Output

reports can be limited by graphically selected areas, or by pre-defined groups, by load

case/combination. Results can be printed, exported to Excel or Access database, as

well as generation of DXF drawings.

3.3 GENERAL CHARACTERISTIC OF STAADPROV8i:

Fully integrated program that allows model creation, modification,

execution of analysis, design optimization, and results review

from within a single interface.

Powerful graphical 3D model generation using plan, elevation and

developed views.

A wide variety of automated templates allow a quick start for almost

any mode.

Object-based physical member modeling allows working with large

members that do not need to be broken up at each joint.

Powerful CAD-type editing features.

Compressive interactive spreadsheet editor.

Fully customized units that can be changed at any time.



Fully integrated section Designer allows definition of complex

sections.

State-of-the-art static, dynamic, linear and nonlinear analysis.

Fully interactive steel, concrete and aluminum frame member deign

for many American, Indian, Canadian and European design codes.

Onscreen results display.

Animated display of deformed shapes, mode shapes, stress contours

and time history results.

User customizable tables that can be displayed on screen or output in

multiple formats.

Context sensitive online help, documentation, tutorials and AVI

movie demonstrations.

3.4 ANALYTICAL OPTIONS:

Static linear analysis

Static Non-linear analysis

Model analysis

Dynamic response spectrum analysis

Dynamic linear and Non-linear time history analysis

Bridge analysis (Moving load analysis)

Buckling analysis

3.5 DESIGN OPTIONS:

Fully interactive and graphical steel, concrete and aluminum frame

member design.

Design for static and dynamic load.

Ductile and non-ductile design.

Member grouping for design envelopes.

Automatic drift optimization for steel and aluminum members.

Compressive, color coded, graphical display of design results on the

model.

Detailed onscreen design information with aright button click.

Concrete column axial load – biaxial load moment interaction diagram.



3.6 STEEL FRAME DESIGN THAT SUPPORTS THE

FOLLOWING:

DESIGN CODES:

AISC ASD 89

AISC LRFD 93

API RP2A WSD 2000

API RP2A LRFD 97

ASCE 10-97

BS59950-90

BSS5950-2000

CISC 95

Euro code 3-1993

Indian IS 800-1987

UBC 97 ASD

UBC 97 LRFD Etc.,

3.7 CONCRETE FRAME DESIGN THAT SUPPORTS THE

FOLLOWING:

DESIGN CODES:

ACI 318-99

BS 8110-89

BS 8110 97

CSA-A23 3-94

Euro code 2-1992

Indian IS 456-2000

Italian DM 14-2-92

Mexican RCDF 2001

NZS 3101-95

UBC 97 Etc.,

3.8 A MULTISTOREY RESIDENTIAL CUM COMMERCIAL

BUILDING:

This thesis portrays the design of an earthquake and wind resistant

structure. The structure taken for this thesis is a multistoried residential cum

commercial building located in the Hyderabad which comes under Zone II.

This building is taken as the reference for the design of against earthquake.

The building which has taken for the resident is prone to be most crowded area

in which Publics are likely to be gathered daily. Hence it is very important to

design building to resist against earthquake.



Type of building Commercial cum residential

Number of storey's G+4 (+STAIR CAP)

Area of the Building 354.783 m2

Total Height of the building 19.2 m

Height of each storey 3.2 m

Number of flats in each floor 2

Number of commercial stores 2

Area of each flat 107.038 m2

Wall thickness External-0.300 m,

Internal- 0.150 m

Beam size 0.400m x 0.300m

Column sizes 0.3m x0.5m & 0.3m x 0.4m

Thickness of slab 0.120 & 0.14m

No. of Restraints/supports 32

TABLE 3.1

3.9 MODELING AND ANALYSIS OF MULTISTORIED

RESIDENTIAL CUM COMMERCIAL BUILDING:

STAADPROV8i is an effective software tool for the analysis and

design of structural members. Hence this software could be used to design a

structure against earthquake. The software follows the matrix stiffness

principle in analyzing the structure. The steps for analyzing a structure using

STAADPROV8i are given below.

1. GENERATION OF NODES.

2. MODELING OF THE STRUCTURE.

3. ASSIGNING OF THE STRUCTURAL MEMBERS.

4. RESTRAINTS.

5. APPLICATION OF LOADS.

6. RUN ANALYSIS.

1. Generation of nodes:

The nodes are generated based on the dimensions of the building. The

building is divided in to equal number of known grids. Then the grid spacing

is given on the STAADPROV8i window. The STAADPROV8i automatically

generates grids with specified spacing.

2. Modeling of the structure:

After the nodes are created they are joined with line elements. Based

on the dimension of the building the nodes are joined. Unwanted nodes could

be deleted.



3. Assigning of the structural elements:

The STAADPROV8i has the facility to assign the structural elements.

The line elements have to be assigned as beams and columns and appropriate

dimensions are given.

4. Application of loads:

There are various loads acting on a structure. Current case study

constitute of the following loads:

a) Self-weight

b) Gravity Load

c) Wind Load

d) Seismic Load

The loads are applied on the structure as gravity loads (Dead & Live

Loads), Joint Loads (Seismic Load), Nodal Loads (Wind Load). After the

application of different load cases, combination of loads has to be specified as

mentioned in IS: 456 – 2000.

5. RUN ANALYSIS:

This is the last step in the analyzing of a structure using

STAADPROV8i software. When the run analysis is executed it shows

“ANALYSIS COMPLETE”, which indicated the termination of analysis

process.

3.10 INPUT COMMANDS IN STAAD PRO EDITER:

STAAD SPACE

START JOB INFORMATION

ENGINEER Students of Nizam Institute of Engineering and Technology

DATE 29-Feb-12

JOB NAME comparative study on multi-storey RCC & STEEL Building

END JOB INFORMATION

INPUT WIDTH 79

UNIT METER KN

JOINT COORDINATES

1 0 0 0; 2 3 0 0; 3 6.7 0 0; 4 10.25 0 0; 5 11.9 0 0; 6 13.8 0 0; 7 17.5 0 0; 8 20.5 0 0; 9

6.7 0 2; 10 11.9 0 2; 11 13.8 0 2; 12 0 0 3.65; 13 3 0 3.65; 14 6.7 0 3.65; 15 10.25 0



3.65; 16 13.8 0 3.65; 17 17.5 0 3.65; 18 20.5 0 3.65; 19 0 0 7.15; 20 3 0 7.15; 21 6.7 0

7.15; 22 10.25 0 7.15; 23 13.8 0 7.15; 24 17.5 0 7.15; 25 20.5 0 7.15; 26 0 0 11.3; 27

3 0 11.3; 28 6.7 0 11.3; 29 10.25 0 11.3; 30 13.8 0 11.3; 31 17.5 0 11.3; 32 20.5 0

11.3; 33 0 1.5 0; 34 3 1.5 0; 35 6.7 1.5 0; 36 10.25 1.5 0; 37 11.9 1.5 0; 38 13.8 1.5

0;39 17.5 1.5 0; 40 20.5 1.5 0; 41 6.7 1.5 2; 42 11.9 1.5 2; 43 13.8 1.5 2;44 0 1.5 3.65;

45 3 1.5 3.65; 46 6.7 1.5 3.65; 47 10.25 1.5 3.65; 48 13.8 1.5 3.65; 49 17.5 1.5 3.65;

50 20.5 1.5 3.65; 51 0 1.5 7.15; 52 3 1.5 7.15; 53 6.7 1.5 7.15; 54 10.25 1.5 7.15; 55

13.8 1.5 7.15; 56 17.5 1.5 7.15; 57 20.5 1.5 7.15; 58 0 1.5 11.3; 59 3 1.5 11.3; 60 6.7

1.5 11.3; 61 10.25 1.5 11.3; 62 13.8 1.5 11.3; 63 17.5 1.5 11.3; 64 20.5 1.5 11.3; 65

6.7 3.1 0; 66 6.7 3.1 2; 67 0 4.7 0; 68 3 4.7 0; 69 6.7 4.7 0; 70 10.25 4.7 0; 71 11.9 4.7

0; 72 13.8 4.7 0; 73 17.5 4.7 0; 74 20.5 4.7 0; 75 6.7 4.7 2; 76 11.9 4.7 2; 77 13.8 4.7

2; 78 0 4.7 3.65; 79 3 4.7 3.65; 80 6.7 4.7 3.65; 81 10.25 4.7 3.65; 82 13.8 4.7 3.65;

83 17.5 4.7 3.65; 84 20.5 4.7 3.65; 85 0 4.7 7.15; 86 3 4.7 7.15; 87 3.85 4.7 7.15; 88

6.7 4.7 7.15; 89 10.25 4.7 7.15; 90 13.8 4.7 7.15; 91 16.65 4.7 7.15; 92 17.5 4.7 7.15;

93 20.5 4.7 7.15; 94 0 4.7 11.3; 95 3 4.7 11.3; 96 3.85 4.7 11.3; 97 6.7 4.7 11.3; 98

10.25 4.7 11.3; 99 13.8 4.7 11.3; 100 16.65 4.7 11.3; 101 17.5 4.7 11.3; 102 20.5 4.7

11.3; 103 6.7 6.3 0; 104 6.7 6.3 2; 105 0 7.9 0; 106 3 7.9 0; 107 6.7 7.9 0; 108 10.25

7.9 0; 109 11.9 7.9 0; 110 13.8 7.9 0; 111 17.5 7.9 0; 112 20.5 7.9 0; 113 6.7 7.9 2;

114 11.9 7.9 2; 115 13.8 7.9 2; 116 0 7.9 3.65; 117 3 7.9 3.65; 118 6.7 7.9 3.65; 119

10.25 7.9 3.65; 120 13.8 7.9 3.65; 121 17.5 7.9 3.65; 122 20.5 7.9 3.65; 123 0 7.9

7.15; 124 3 7.9 7.15; 125 3.85 7.9 7.15; 126 6.7 7.9 7.15; 127 10.25 7.9 7.15; 128

13.8 7.9 7.15; 129 16.65 7.9 7.15; 130 17.5 7.9 7.15; 131 20.5 7.9 7.15; 132 0 7.9

11.3; 133 3 7.9 11.3; 134 3.85 7.9 11.3; 135 6.7 7.9 11.3; 136 10.25 7.9 11.3; 137

13.8 7.9 11.3; 138 16.65 7.9 11.3; 139 17.5 7.9 11.3; 140 20.5 7.9 11.3; 141 6.7 9.5 0;

142 6.7 9.5 2; 143 0 11.1 0; 144 3 11.1 0; 145 6.7 11.1 0; 146 10.25 11.1 0; 147 11.9

11.1 0; 148 13.8 11.1 0; 149 17.5 11.1 0; 150 20.5 11.1 0; 151 6.7 11.1 2; 152 11.9

11.1 2; 153 13.8 11.1 2; 154 0 11.1 3.65; 155 3 11.1 3.65; 156 6.7 11.1 3.65; 157

10.25 11.1 3.65; 158 13.8 11.1 3.65; 159 17.5 11.1 3.65; 160 20.5 11.1 3.65; 161 0

11.1 7.15; 162 3 11.1 7.15; 163 3.85 11.1 7.15; 164 6.7 11.1 7.15; 165 10.25 11.1

7.15; 166 13.8 11.1 7.15; 167 16.65 11.1 7.15; 168 17.5 11.1 7.15; 169 20.5 11.1

7.15; 170 0 11.1 11.3; 171 3 11.1 11.3; 172 3.85 11.1 11.3; 173 6.7 11.1 11.3; 174

10.25 11.1 11.3; 175 13.8 11.1 11.3; 176 16.65 11.1 11.3; 177 17.5 11.1 11.3; 178

20.5 11.1 11.3; 179 6.7 12.7 0; 180 6.7 12.7 2; 181 0 14.3 0; 182 3 14.3 0; 183 6.7

14.3 0; 184 10.25 14.3 0; 185 11.9 14.3 0; 186 13.8 14.3 0; 187 17.5 14.3 0; 188 20.5

14.3 0; 189 6.7 14.3 2; 190 11.9 14.3 2; 191 13.8 14.3 2; 192 0 14.3 3.65; 193 3 14.3

3.65; 194 6.7 14.3 3.65; 195 10.25 14.3 3.65; 196 13.8 14.3 3.65; 197 17.5 14.3 3.65;

198 20.5 14.3 3.65; 199 0 14.3 7.15; 200 3 14.3 7.15; 201 3.85 14.3 7.15; 202 6.7 14.3

7.15; 203 10.25 14.3 7.15; 204 13.8 14.3 7.15; 205 16.65 14.3 7.15; 206 17.5 14.3

7.15; 207 20.5 14.3 7.15; 208 0 14.3 11.3; 209 3 14.3 11.3; 210 3.85 14.3 11.3; 211

6.7 14.3 11.3; 212 10.25 14.3 11.3; 213 13.8 14.3 11.3; 214 16.65 14.3 11.3; 215 17.5

14.3 11.3; 216 20.5 14.3 11.3; 217 6.7 15.9 0; 218 6.7 15.9 2; 219 0 17.5 0; 220 3

17.5 0; 221 6.7 17.5 0; 222 10.25 17.5 0; 223 11.9 17.5 0; 224 13.8 17.5 0; 225 17.5

17.5 0; 226 20.5 17.5 0; 227 6.7 17.5 2; 228 11.9 17.5 2; 229 13.8 17.5 2; 230 0 17.5

3.65; 231 3 17.5 3.65; 232 6.7 17.5 3.65; 233 10.25 17.5 3.65; 234 13.8 17.5 3.65;



235 17.5 17.5 3.65; 236 20.5 17.5 3.65; 237 0 17.5 7.15; 238 3 17.5 7.15; 239 3.85

17.5 7.15; 240 6.7 17.5 7.15; 241 10.25 17.5 7.15; 242 13.8 17.5 7.15; 243 16.65 17.5

7.15; 244 17.5 17.5 7.15; 245 20.5 17.5 7.15; 246 0 17.5 11.3; 247 3 17.5 11.3; 248

3.85 17.5 11.3; 249 6.7 17.5 11.3; 250 10.25 17.5 11.3; 251 13.8 17.5 11.3; 252 16.65

17.5 11.3; 253 17.5 17.5 11.3; 254 20.5 17.5 11.3; 255 6.7 20.7 0; 256 10.25 20.7 0;

257 11.9 20.7 0; 258 13.8 20.7 0; 259 11.9 20.7 2; 260 13.8 20.7 2; 261 6.7 20.7 3.65;

262 10.25 20.7 3.65; 263 13.8 20.7 3.65;

MEMBER INCIDENCES

1 33 1; 2 34 2; 3 35 3; 4 36 4; 5 37 5; 6 38 6; 7 39 7; 8 40 8; 9 41 9; 10 42 10; 11 43

11; 12 44 12; 13 45 13; 14 46 14; 15 47 15; 16 48 16; 17 49 17; 18 50 18; 19 51 19;

20 52 20; 21 53 21; 22 54 22; 23 55 23; 24 56 24; 25 57 25; 26 58 26; 27 59 27; 28 60

28; 29 61 29; 30 62 30; 31 63 31; 32 64 32; 101 33 67; 102 34 68; 103 65 69; 104 35

65; 105 36 70; 106 37 71; 107 38 72; 108 39 73; 109 40 74; 110 66 75; 111 41 66;

112 42 76; 113 43 77; 114 44 78; 115 45 79; 116 46 80; 117 47 81; 118 48 82; 119 49

83; 120 50 84; 121 51 85; 122 52 86; 123 53 88; 124 54 89; 125 55 90; 126 56 92;

127 57 93; 128 58 94; 129 59 95; 130 60 97; 131 61 98; 132 62 99; 133 63 101; 134

64 102; 201 67 105; 202 68 106; 203 103 107; 204 69 103; 205 70 108; 206 71 109;

207 72 110; 208 73 111; 209 74 112; 210 104 113; 211 75 104; 212 76 114; 213 77

115; 214 78 116; 215 79 117; 216 80 118; 217 81 119; 218 82 120; 219 83 121; 220

84 122; 221 85 123; 222 86 124; 223 88 126; 224 89 127; 225 90 128; 226 92 130;

227 93 131; 228 94 132; 229 95 133; 230 97 135; 231 98 136; 232 99 137; 233 101

139; 234 102 140; 301 105 143; 302 106 144; 303 141 145; 304 107 141; 305 108

146; 306 109 147; 307 110 148; 308 111 149; 309 112 150; 310 142 151; 311 113

142; 312 114 152; 313 115 153; 314 116 154; 315 117 155; 316 118 156; 317 119

157; 318 120 158; 319 121 159; 320 122 160; 321 123 161; 322 124 162; 323 126

164; 324 127 165; 325 128 166; 326 130 168; 327 131 169; 328 132 170; 329 133

171; 330 135 173; 331 136 174; 332 137 175; 333 139 177; 334 140 178; 401 143

181; 402 144 182; 403 179 183; 404 145 179; 405 146 184; 406 147 185; 407 148

186; 408 149 187; 409 150 188; 410 180 189; 411 151 180; 412 152 190; 413 153

191; 414 154 192; 415 155 193; 416 156 194; 417 157 195; 418 158 196; 419 159

197; 420 160 198; 421 161 199; 422 162 200; 423 164 202; 424 165 203; 425 166

204; 426 168 206; 427 169 207; 428 170 208; 429 171 209; 430 173 211; 431 174

212; 432 175 213; 433 177 215; 434 178 216; 501 181 219;502 182 220; 503 217

221; 504 183 217; 505 184 222; 506 185 223; 507 186 224; 508 187 225; 509 188

226; 510 218 227; 511 189 218; 512 190 228; 513 191 229; 514 192 230; 515 193

231; 516 194 232; 517 195 233; 518 196 234; 519 197 235; 520 198 236; 521 199

237; 522 200 238; 523 202 240; 524 203 241; 525 204 242; 526 206 244; 527 207

245; 528 208 246; 529 209 247; 530 211 249; 531 212 250; 532 213 251; 533 215

253; 534 216 254; 601 255 221; 602 256 222; 603 257 223; 604 258 224; 605 259

228; 606 260 229; 607 261 232; 608 262 233; 609 263 234; 1001 33 34; 1002 34 35;

1003 35 36; 1004 36 37; 1005 37 38; 1006 38 39; 1007 39 40; 1008 42 43; 1009 44

45; 1010 45 46; 1011 46 47; 1012 47 48; 1013 48 49; 1014 49 50; 1015 51 52; 1016



52 53; 1017 53 54; 1018 54 55; 1019 55 56; 1020 56 57; 1021 58 59; 1022 59 60;

1023 60 61; 1024 61 62; 1025 62 63; 1026 63 64; 1027 35 41; 1028 37 42; 1029 38

43; 1030 33 44; 1031 34 45; 1032 36 47; 1033 39 49; 1034 40 50; 1035 41 46; 1036

43 48;1037 44 51; 1038 45 52; 1039 46 53; 1040 47 54; 1041 48 55; 1042 49 56;1043

50 57; 1044 51 58; 1045 52 59; 1046 53 60; 1047 54 61; 1048 55 62; 1049 56 63;

1050 57 64; 1051 65 66; 2001 67 68; 2002 68 69; 2003 69 70; 2004 70 71; 2005 71

72; 2006 72 73; 2007 73 74; 2008 76 77; 2009 78 79; 2010 79 80; 2011 80 81; 2012

81 82; 2013 82 83; 2014 83 84; 2015 85 86; 2016 86 87; 2017 87 88; 2018 88 89;

2019 89 90; 2020 90 91; 2021 91 92; 2022 92 93; 2023 94 95; 2024 95 96; 2025 96

97; 2026 97 98; 2027 98 99; 2028 99 100; 2029 100 101; 2030 101 102; 2031 67 78;

2032 68 79; 2033 69 75; 2034 75 80; 2035 70 81; 2036 71 76; 2037 72 77; 2038 77

82; 2039 73 83; 2040 74 84; 2041 78 85; 2042 81 89; 2043 84 93; 2044 85 94; 2045

87 96; 2046 88 97; 2047 89 98; 2048 90 99; 2049 91 100; 2050 93 102; 2051 103

104; 3001 105 106; 3002 106 107; 3003 107 108; 3004 108 109; 3005 109 110; 3006

110 111; 3007 111 112; 3008 114 115; 3009 116 117; 3010 117 118; 3011 118 119;

3012 119 120; 3013 120 121; 3014 121 122; 3015 123 124; 3016 124 125; 3017 125

126; 3018 126 127; 3019 127 128; 3020 128 129; 3021 129 130; 3022 130 131; 3023

132 133; 3024 133 134; 3025 134 135; 3026 135 136; 3027 136 137; 3028 137 138;

3029 138 139; 3030 139 140; 3031 105 116; 3032 106 117; 3033 107 113; 3034 113

118; 3035 108 119; 3036 109 114; 3037 110 115; 3038 115 120; 3039 111 121; 3040

112 122; 3041 116 123; 3042 119 127; 3043 122 131; 3044 123 132; 3045 125

134;3046 126 135; 3047 127 136; 3048 128 137; 3049 129 138; 3050 131 140; 3051

141 142; 4001 143 144; 4002 144 145; 4003 145 146; 4004 146 147; 4005 147 148;

4006 148 149; 4007 149 150; 4008 152 153; 4009 154 155; 4010 155 156; 4011 156

157; 4012 157 158; 4013 158 159; 4014 159 160; 4015 161 162; 4016 162 163; 4017

163 164; 4018 164 165; 4019 165 166; 4020 166 167; 4021 167 168; 4022 168 169;

4023 170 171; 4024 171 172; 4025 172 173; 4026 173 174; 4027 174 175; 4028 175

176; 4029 176 177; 4030 177 178; 4031 143 154; 4032 144 155; 4033 145 151; 4034

151 156; 4035 146 157; 4036 147 152; 4037 148 153; 4038 153 158; 4039 149

159;4040 150 160; 4041 154 161; 4042 157 165; 4043 160 169; 4044 161 170; 4045

163 172; 4046 164 173; 4047 165 174; 4048 166 175; 4049 167 176; 4050 169 178;

4051 179 180; 5001 181 182; 5002 182 183; 5003 183 184; 5004 184 185; 5005 185

186; 5006 186 187; 5007 187 188; 5008 190 191; 5009 192 193; 5010 193 194; 5011

194 195; 5012 195 196; 5013 196 197; 5014 197 198; 5015 199 200; 5016 200 201;

5017 201 202; 5018 202 203; 5019 203 204; 5020 204 205; 5021 205 206; 5022 206

207; 5023 208 209; 5024 209 210; 5025 210 211; 5026 211 212; 5027 212 213; 5028

213 214; 5029 214 215; 5030 215 216; 5031 181 192; 5032 182 193; 5033 183 189;

5034 189 194; 5035 184 195; 5036 185 190; 5037 186 191; 5038 191 196; 5039 187

197; 5040 188 198; 5041 192 199; 5042 195 203; 5043 198 207; 5044 199 208; 5045

201 210; 5046 202 211; 5047 203 212; 5048 204 213; 5049 205 214; 5050 207 216;

5051 217 218; 6001 219 220; 6002 220 221; 6003 221 222; 6004 222 223; 6005 223

224; 6006 224 225; 6007 225 226; 6008 228 229; 6009 230 231; 6010 231 232; 6011

232 233; 6012 233 234; 6013 234 235; 6014 235 236; 6015 237 238; 6016 238 239;



6017 239 240; 6018 240 241; 6019 241 242; 6020 242 243; 6021 243 244; 6022 244

245; 6023 246 247; 6024 247 248; 6025 248 249; 6026 249 250; 6027 250 251;6028

251 252; 6029 252 253; 6030 253 254; 6031 219 230; 6032 220 231; 6033 221 227;

6034 227 232; 6035 222 233; 6036 223 228; 6037 224 229; 6038 229 234; 6039 225

235; 6040 226 236; 6041 230 237; 6042 233 241; 6043 236 245; 6044 237 246; 6045

239 248; 6046 240 249; 6047 241 250; 6048 242 251; 6049 243 252; 6050 245 254;

7001 255 256; 7002 256 257; 7003 257 258; 7004 259 260; 7005 261 262; 7006 262

263; 7007 255 261; 7008 256 262; 7009 257 259; 7010 260 258; 7011 260 263;

DEFINE MATERIAL START

ISOTROPIC CONCRETE

E 2.17185e+007

POISSON 0.17

DENSITY 23.5616

ALPHA 1e-005

DAMP 0.05

END DEFINE MATERIAL

MEMBER PROPERTY INDIAN

3 4 6 14 16 20 21 23 24 27 28 30 31 103 TO 105 107 116 118 122 123 125 126 129

130 132 133 203 TO 205 207 216 218 222 223 225 226 229 230 232 233 303 304 TO

305 307 316 318 322 323 325 326 329 330 332 333 403 TO 405 407 416 418 422 423

425 426 429 430 432 433 503 TO 505 507 516 518 522 523 525 526 529 530 532

533 601 602 604 607 609 PRIS YD 0.5 ZD 0.3

1 2 7 8 12 13 15 17 TO 19 22 25 26 29 32 101 102 108 109 114 115 117 119 TO 121

124 127 128 131 134 201 202 208 209 214 215 217 219 TO 221 224 227 228 231

234 301 302 308 309 314 315 317 319 TO 321 324 327 328 331 334 401 402 408

409 414 415 417 419 TO 421 424 427 428 431 434 501 502 508 509 514 515 517

519 TO 521 524 527 528 531 534 608 PRIS YD 0.3 ZD 0.5

5 9 TO 11 106 110 TO 113 206 210 TO 213 306 310 TO 313 406 410 TO 413 506

510 TO 513 603 605 606 1001 TO 1051 2001 TO 2051 3001 TO 3051 4001 TO 4051

5001 TO 5051 6001 TO 6050 7001 TO 7011 PRIS YD 0.4 ZD 0.3

CONSTANTS

MATERIAL CONCRETE ALL

SUPPORTS

1 TO 32 FIXED



DEFINE 1893 LOAD

ZONE 0.1 RF 3 I 1 SS 2 ST 1 DM 5 DT 1.5

SELFWEIGHT 1

MEMBER WEIGHT

1001 TO 1050 2001 2002 2005 TO 2008 2011 2012 2023 2024 2026 TO 2028 2030

2031 2036 TO 2038 2040 2042 2044 2047 2050 3001 3002 3005 TO 3008 3011 3012

3023 3024 3026 TO 3028 3030 3031 3036 TO 3038 3040 3042 3044 3047 3050 4001

4002 4005 TO 4008 4011 4012 4023 4024 4026 TO 4028 4030 4031 4036 TO 4038

4040 4042 4044 4047 4050 5001 5002 5005 TO 5008 5011 5012 5023 5024 5026

5027 TO 5028 5030 5031 5036 TO 5038 5040 5042 5044 5047 5050 6003 TO 6005 -

6008 6011 6012 6033 6034 6036 TO 6038 UNI 16

2009 2010 2013 TO 2022 2032 TO 2035 2039 2045 2046 2048 2049 3009 3010 3013

3014 TO 3022 3032 TO 3035 3039 3045 3046 3048 3049 4009 4010 4013 TO 4022

4032 TO 4035 4039 4045 4046 4048 4049 5009 5010 5013 TO 5022 5032 TO 5035

5039 5045 5046 5048 5049 UNI 8

6001 6002 6006 6007 6023 TO 6031 6040 6041 6043 6044 6050 7001 TO 7003 7005

7006 TO 7007 7010 7011 UNI 2

1051 2051 3051 4051 5051 UNI 20

FLOOR WEIGHT

YRANGE 4.7 20.7 FLOAD -4.125 XRANGE 0 20.5 ZRANGE 0 3.65

YRANGE 4.7 20.7 FLOAD -4.125 XRANGE 0 20.5 ZRANGE 7.15 11.3

ONEWAY LOAD

YRANGE 4.7 20.7 ONE -4.125 XRANGE 0 20.5 ZRANGE 3.65 7.15

CHECK SOFT STOREY

DEFINE WIND LOAD

TYPE 1

INT 0.67 HEIG 19.2

EXP 1 JOINT 33 TO 263

LOAD 1 LOADTYPE None TITLE EQ XP

1893 LOAD X 1



LOAD 2 LOADTYPE None TITLE EQ XN

1893 LOAD X -1

LOAD 3 LOADTYPE None TITLE EQ ZP

1893 LOAD Z 1

LOAD 4 LOADTYPE None TITLE EQ ZN

1893 LOAD Z -1

LOAD 5 LOADTYPE None TITLE WL XP

WIND LOAD X 1 TYPE 1

LOAD 6 LOADTYPE None TITLE WL XN

WIND LOAD X -1 TYPE 1

LOAD 7 LOADTYPE None TITLE WL ZP

WIND LOAD Z 1 TYPE 1

LOAD 8 LOADTYPE None TITLE WL ZN

WIND LOAD Z -1 TYPE 1

LOAD 9 LOADTYPE None TITLE DEAD LOAD

SELFWEIGHT Y -1 LIST 1 TO 32 101 TO 134 201 TO 234 301 TO 334 401 TO

434 501 502 TO 534 601 TO 609 1001 TO 1037 1040 1043 TO 1051 2001 TO 2051

3001 TO 3051 4001 TO 4051 5001 TO 5051 6001 TO 6050 7001 TO 7011

FLOOR LOAD

YRANGE 4.7 20.7 FLOAD -4.125 XRANGE 0 20.5 ZRANGE 0 3.65 GY

YRANGE 4.7 20.7 FLOAD -4.125 XRANGE 0 20.5 ZRANGE 7.15 11.3 GY

ONEWAY LOAD

YRANGE 4.7 20.7 ONE -4.125 XRANGE 0 20.5 ZRANGE 3.65 7.15 GY

MEMBER LOAD

1001 TO 1026 1028 TO 1034 1036 TO 1050 2001 2002 2005 TO 2008 2011 2012

2023 2024 2026 TO 2028 2030 2031 2036 TO 2038 2040 2042 2044 2047 2050 3001

3002 3005 TO 3008 3011 3012 3023 3024 3026 TO 3028 3030 3031 3036 TO 3038

3040 3042 3044 3047 3050 4001 4002 4005 TO 4008 4011 4012 4023 4024 4026 TO

4028 4030 4031 4036 TO 4038 4040 4042 4044 4047 4050 5001 5002 5005 TO 5008



5011 5012 5023 5024 5026 TO 5028 5030 5031 5036 TO 5038 5040 5042 5044 5047

5050 6003 TO 6005 6008 6011 6012 6036 TO 6038 UNI GY -16

1027 1035 2009 2010 2013 TO 2022 2032 TO 2035 2039 2045 2046 2048 2049 3009

3010 3013 TO 3022 3032 TO 3035 3039 3045 3046 3048 3049 4009 4010 4013 TO

4022 4032 TO 4035 4039 4045 4046 4048 4049 5009 5010 5013 TO 5022 5032 TO

5035 5039 5045 5046 5048 5049 6033 6034 UNI GY -8

6001 6002 6006 6007 6023 TO 6031 6040 6041 6043 6044 6050 7001 TO 7003 7005

7006 TO 7007 7010 7011 UNI GY -2

1051 2051 3051 4051 5051 UNI GY -20

LOAD 10 LOADTYPE None TITLE LIVE LOAD

FLOOR LOAD

YRANGE 4.7 20.7 FLOAD -2 XRANGE 0 20.5 ZRANGE 0 3.65 GY

YRANGE 4.7 20.7 FLOAD -2 XRANGE 0 20.5 ZRANGE 7.15 11.3 GY

ONEWAY LOAD

YRANGE 4.7 20.7 ONE -2 XRANGE 0 20.5 ZRANGE 3.65 7.15 GY

LOAD COMB 11 SERVICE (DL+LL)

9 1.0 10 1.0

LOAD COMB 12 ULTIMATE 1.5 (DL+LL)

9 1.5 10 1.5

LOAD COMB 13 1.2 (DL+LL+WL XP)

9 1.2 10 1.2 5 1.2

LOAD COMB 14 1.2 (DL+LL+WL XN)

6 1.2 9 1.2 10 1.2

LOAD COMB 15 1.2 (DL+LL+WL ZP)

9 1.2 10 1.2 7 1.2

LOAD COMB 16 1.2 (DL+LL+WL ZN)

9 1.2 10 1.2 8 1.2

LOAD COMB 17 1.2 (DL+LL+EQ XP)

1 1.2 9 1.2 10 1.2



LOAD COMB 18 1.2 (DL+LL+EQ XN)

9 1.2 10 1.2 2 1.2

LOAD COMB 19 1.2 (DL+LL+EQ ZP)

3 1.2 9 1.2 10 1.2

LOAD COMB 20 1.2 (DL+LL+EQ ZN)

4 1.2 9 1.2 10 1.2

LOAD COMB 21 1.5(DL+EQ XP)

9 1.5 1 1.5

LOAD COMB 22 1.5(DL+EQ XN)

2 1.5 9 1.5

LOAD COMB 23 1.5(DL+EQ ZP)

3 1.5 9 1.5

LOAD COMB 24 1.5(DL+EQ ZN)

4 1.5 9 1.5

LOAD COMB 25 1.5(DL+WL XP)

5 1.5 9 1.5

LOAD COMB 26 1.5(DL+WL XN)

6 1.5 9 1.5

LOAD COMB 27 1.5(DL+WL ZP)

7 1.5 9 1.5

LOAD COMB 28 1.5(DL+WL ZN)

9 1.5 8 1.5

LOAD COMB 29 0.9DL+1.5 EQ XP

9 0.9 1 1.5

LOAD COMB 30 0.9DL+1.5 EQ XN

9 0.9 2 1.5

LOAD COMB 31 0.9DL+1.5 EQ ZP



3 1.5 9 0.9

LOAD COMB 32 0.9DL+1.5 EQ ZN

4 1.5 9 0.9

LOAD COMB 33 0.9DL+1.5 WL XP

9 0.9 5 1.5

LOAD COMB 34 0.9DL+1.5 WL XN

9 0.9 6 1.5

LOAD COMB 35 0.9DL+1.5 WL ZP

9 0.9 7 1.5

LOAD COMB 36 0.9DL+1.5 WL ZN

8 1.5 9 0.9

PERFORM ANALYSIS

LOAD LIST 11 TO 36

PERFORM ANALYSIS PRINT ALL

PRINT SUPPORT REACTION

FINISH



3.11 ANALYSIS OF THE MULTISTORIED RESIDENTIAL CUM

COMMERCIAL BUILDING FOR GRAVITY LOADS:

The structure is a residential building which comes under the category of

residential cum commercial building. Hence it has taken care of different types of

dead loads. The dead loads could be of its own self weight, furniture's, some

equipments, machineries, computers, store keeps, etc. Hence the building has to be

designed in such a way that it has to take care of all the loads imposed on it. The

easiest way to withstand these loads is by providing proper beams and columns. The

live load of the building could be taken from the standards.

FLOOR LOAD:

Floor load slab is distributed on the adjoining members as trapezoidal &

triangular loads depending on the length of the sides, as shown in figure. Internally

these loads are converted to multiple point loads. The loads are applied as area loads

over the building. These loads would be transferred to beams and columns.

FORMULAE FOR CALCULATING GRAVITY LOAD:

Area of triangle =1

2 𝑋 (𝑏 𝑋 ℎ)

Area of trapezoidal =A + B

2 𝑋 ℎ

Weight of ceiling plastering = area X 0.012 X 20

Weight of flooring = area X 0.02 X 20 + (area X 0.02 X 26.7)

Total dead load = weigth of ceiling plastering + weight of flooring

Live Load = 2.000 KN (As per IS code book)

Total load = Total Dead Load + Live Load

Factored load = 1.5 X Total load



FIG3.1. DISTRIBUTION OF LOAD FROM FLOOR/SLAB TO BEAMS

TABLE 3.2 FOR FINDING AREA OF SLAB

SLAB

No A B H B

Area of

triangle

Area of

trapezoidal

1. 0.65 3.65 1.5 3.0 2.25 3.225

2. 0.05 3.70 1.825 3.65 3.331 3.421

3. 0.1 3.65 1.775 3.55 3.151 3.328

4. 6.75 10.25 1.75 3.50 3.0625 14.875

5. 0.3 4.15 1.925 3.85 3.71 4.283

6. 0.45 4.15 1.85 3.70 3.422 4.578

7. 0.6 4.15 1.775 3.55 3.151 4.215

slab.No Wt. c.p

(tri)

Wt.

floor

(tri)

T.D.L

(tri)

L.L

(tri) T.L (tri) F.L (tri)

1. 0.54 2.10 2.64 2.00 4.64 6.96

2. 0.799 3.11 3.90 2.00 5.90 8.85

3. 0.756 2.94 3.696 2.00 5.696 8.544

4. 0.735 2.86 3.595 2.00 5.595 8.393

5. 0.890 3.465 4.355 2.00 6.355 9.533

6. 0.821 3.196 4.017 2.00 6.017 9.026

7. 0.756 2.943 3.699 2.00 5.699 8.548

TABLE 3.3 FINDING FACTORED LOAD FOR TRIANGULAR

AREA



TABLE 3.4 FOR FINDING FACTORED LOAD FOR

TRAPEZOIDAL AREA

Slab.

No

Wt. c.p Wt. floor T.D.L L.L T.L F.L

1. 0.774 3.012 3.786 2.00 5.786 8.679

2. 0.821 3.195 4.016 2.00 6.016 9.024

3. 0.798 3.108 3.906 2.00 5.906 8.859

4. 3.57 13.893 17.463 2.00 19.463 29.194

5. 1.027 4.00 5.027 2.00 7.027 10.541

6. 1.098 4.275 5.373 2.00 7.373 11.061

7. 1.012 3.936 4.948 2.00 6.948 10.423



FIG3.2 DEFORMED SHAPE OF THE BUILDING UNDER

GRAVITY LOADS



FIG3.3 BENDING MOMENT DIAGRAM FOR GRAVITY LOADS



FIG3.4 MAXIMUM BENDING MOMENT DIAGRAM FOR BEAM

NO 5021 UNDER GRAVITY LOAD

FIG3.5 MAXIMUM BENDING MOMENT VALUES FOR

GRAVITY LOAD



3.12 ANALYSIS OF THE MULTISTORIED RESIDENTIAL

CUM COMMERCIAL BUILDING FOR WIND LOADS:

WIND LOADS:

Buildings and their components are to be designed to withstand the

code-specified wind loads. Calculating wind loads is important in design of the wind

force-resisting system, including structural members, components, and cladding,

against shear, sliding, overturning, and uplift actions.

DESIGN WIND LOADS:

The wind pressure on a structure depends on the location of the

structure, height of structure above the ground level and also on the shape of the

structure.

The code gives the basic wind pressure for the structures in various

parts of the country. Both the wind pressure viz. including wind of short duration and

excluding wind of short duration have been given. All structures should be designed

for the short duration wind. For buildings up to 10 m in height, the intensity of wind

pressure, as specified in the code, may be reduced by 25% for stability calculations

and for the design of framework as well as cladding. For buildings over 10 m and up

to 30m height, this reduction can be made for stability calculations and for design of

columns only.

The total pressure on the walls or roof of an industrial building will

depend on the external wind pressure and also on internal wind pressure. The

internal wind pressure depends on the permeability; the internal air pressure may be

neglected. In the case of buildings with normal permeability the internal pressure

can be ± 0.2p. Here ‘+’ indicates pressure and ‘_’ suction, ‘p’ is the basic wind

pressure. If a building has openings larger than 20% of the wind pressure. If a

building has openings larger than 20% of the wall area, the internal air pressure will

be ±0.5 p.

WIND PRESSURE ON WALLS:

The wind pressure per unit area ‘p’ on the wall is taken as 0.5p

pressure on the windward surface and 0.5p suction on leeward surface. When the

walls form an enclosure, the windward wall will be subjected to a pressure of 0.5p

and leeward wall to a suction of 0.5p. The total pressure on the walls will depend on

the internal air pressure also.

For buildings with small permeability, design pressure on wall = 0.5p

For buildings with normal permeability, design pressure on wall = 0.7p

For buildings with large openings, design pressure on wall = p



If the wind blows parallel to the ridge of the roof, the average external wind

pressure of the roof may be taken as -0.6p on both slopes of the roof over a length

from the gable end equal to the mean height of the roof above the surrounding ground

level and as-0.4p over the remaining length of the roof on both slopes.

When the wind blows parallel to a surface, a wind force acts on the

surface in the direction of the wind. This force is called the ‘Wind Drag’. In the case

of industrial buildings, when wind blows normal to the ridges, the wind drag is equal

to 0.5p measured on plan area of roof and when the direction of wind parallel to the

ridge, wind drag is equal to 0.025p measured on plan area of roof.

Fig3.6 wind drag

In the multi-span roofs with spans, heights and slopes nearly equal, the

windward truss gives shelter to the other trusses. For general stability calculations and

for the design columns, the windward slope of wind-ward span and leeward slope of

leeward span are subjected to the full normal pressure of suction as given in table and

on all other roof slopes, only wind drag is considered (see fig. ). For the design of

roof trusses however, full normal pressure or suction is considered on both faces,

presuming that there was only one span.

The wind pressures given above are the average pressures on a roof slope. For

designing the roof sheeting or the fastenings of roof sheeting, we may take a larger

wind pressure because these pressures may considerably exceed the average value on

small areas. For designing roof sheeting and its fastenings, the values given in Table.

May be increased numerically by 0.3p. In a distance equal to 15% of the length of the

roof from the gable ends, fastenings should be capable of resisting a section of 2.0p

on the area of the roof sheeting them support.

THE WIND LOAD GENERATOR:

The STAAD Wind Load generator is capable of calculating wind loads on the

structure from user specified wind intensities and exposures factors. Different wind

intensities may be specified for different height zones of the structure. Openings in the



structure may be modeled using exposure factors. An exposure factor is associated

with each joint of the structure and is defined as the fraction of the influence area on

which the wind load acts. Built-in algorithms automatically calculate the wind load on

a SPACE structure and distribute the loads as lateral joint loads.

GENERATION OF WIND LOADS:

The built in wind load generation facility can be used to calculate the wind

loads based on the parameters defined. The following general format should be used

to perform the wind load generation. Note that areas bounded by beam members only

(and ground), and exposed to the wind, are used to define loaded areas(plates and

solids are ignored). The loads generated are applied only at the joints at vertices of the

bounded areas.

BASIC WIND PRESSURES FOR A CITY

S.NO HEIGHT IN METRES PRESSURE IN Kg/m2

1. UPTO 30 200

2. 40 209

3. 45 217

4. 50 222

5. 57 228

TABLE 3.5: BASIC WIND PRESSURES FOR A CITY

For intermediate heights, interpolated values may be adopted.

Calculation of wind loads:

The wind speed in atmospheric boundary layer increases with height

from zero at ground level and to a maximum at a height called gradient height.

Design wind speed:

From IS 875-(PART -III) the Design wind pressure at any height

above mean ground level shall be obtained from the following relationship between

wind pressure and wind velocity.

Pz = 0.6Vz2

Where,

Pz = Design wind pressure in N/m2

at a height of z, and

Vz = Design wind velocity in m/s at a height of z.

Design wind speed:



The Basic wind speed (Vb) for any site is obtained from Fig no 1 of IS 875-

(PART-III) and shall be modified to include the following effects to get a design

wind velocity at height.

Height of the building above ground level h= 19.2 m

Lateral dimensions of Building = 20.8m x 11.6 m

Design wind speed Vz = Vb.K1.K2.K3

Vb = Basic wind speed

For Hyderabad as per IS 875-(PART-III) is 44 m/sec

K1= Probability factor (Risk coefficient) (5.3.1 of IS 875-III)

= 1

K2= Terrain, Height and Structure size factor (5.3.2 of IS 875-III)

Category-4

Class -B

From Table no 2 of IS-875(PART-III) K2= 0.76

K3= Topographic factor (5.3.3 of IS 875-III)

= 1

Design wind speed Vz = 44x1x0.76x1

= 33.44 m/s

Design wind pressure (Pz) = 0.6Vz2

= 0.6 x 33.442

= 670 N/m2

= 0.670 KN/m2



FIG3.7 WIND LOAD ACTING ON THE BUILDING FROM X-

POSITIVE DIRECTION



FIG3.8 WIND LOAD ACTING ON THE BUILDING FROM Z-

POSITIVE DIRECTION

FIG3.9 MAXIMUM BENDING MOMENT DIAGRAM FOR COLUMN NO 117

WIND LOAD ACTING FROM Z +VE DIRECTION



TABLE 3.6

A TABLE FROM STAAD OUTPUT SUMMARY OF MAXIMUM BENDING

MOMENT FOR WIND LOAD



3.13 ANALYSIS OF MULITSTORIED RESIDENTIAL CUM

COMMERCIAL BUILDING FOR SEISMIC LOADS:

Reinforced concrete buildings have become more common in India. These

structures mainly consist of beam-column frames with slabs and walls and are

supported by foundation that rest on the ground. The RC frame participates in resting

the earthquake forces and the earthquake shaking generates inertia forces in the

building, which are proportional to the building mass. Since most of the building mass

is concentrated at floor levels. These forces travel downwards to reach the foundation

from where they are dispersed in to the ground. The structural elements, beams,

columns, slabs, and walls at lower storeys experience higher earthquake forces and

hence are designed to be stronger than those at higher levels.

Buildings are mostly provided with Shear walls in lower storey levels to resist

the earthquake loads.

Earthquake Design Consideration:

The building will be designed for horizontal seismic force only.

The structure in analyzed as an earthquake static approach employing the

use of a seismic coefficient Method.

EARTHQUAKE: An earthquake is vibration of earth surface by waves emerging

from the source of disturbance in the earth by virtue of release of energy in the earth’s

crust. It is essentially a sudden and transient motion or series of motions of the earth

surface originating in a limited under ground motion due to disturbance of the elastic

equilibrium of the earth mass and spreading from there in all directions.

REASONS FOR HIGH CASUALITY:

1) Urbanization is rapidly increasing and due to increase in land cost,

many multi storied buildings are being constructed.

2) Code is not mandatory.

3) Construction as such is governed by municipal bye-laws.

4) Seismic provisions are not incorporated.

5) Non enforceation of elaborated checks proper ways.

6) No checks even for simple ordinary design.

GENERAL GUIDE LINES:

DRIFT: It is the maximum lateral displacement of the structure with respect to

total height or relative inter-storey displacement. The overall drifts index is the ratio

of maximum roof displacement to the height of the structure and inter-storey drift is



the ratio of maximum difference of lateral displacement at top and bottom of the

storey divided by the storey height.

Nonstructural elements and structural non seismic members

primarily get damaged due to drift. Higher the lateral stiffness lesser is the likely damage.

The storey drift in any storey due to minimum specified design lateral force with partial

safety factor of unity shall not exceed 0.004 times the storey height.

Separation between adjacent units or buildings:

Two adjacent buildings or two adjacent units of the same

building with separation joint in between shall be separated by distance equal to the

amount R times the sum of the calculated storey displacements as specified above of

each of them to avoid damaging contact when the two units deflect towards each

other.

Soft storey:

Soft storey or flexible storey is one in which the lateral stiffness is less than

70% of that in the storey above or less than 80% of the average lateral stiffness of the

three storey's above. In case of buildings with a flexible storey such as ground storey

consisting of open spaces for parking i.e. stilt buildings, special arrangements are

need to be made to increase the lateral strength and stiffness of the soft storey.

For such buildings, dynamic analysis is carried out including the

strength and stiffness effects of infill s and inelastic deformations in the members

particularly those in the soft storey and members designed accordingly. Alternatively,

the following design criteria are to be adopted after carrying the

earthquake analysis neglecting the effect of infill walls in other storey's. When the

floor levels of two similar adjacent buildings are at the same elevation levels, factor R

can be taken as R/2.

a) The columns and beams of the soft storey are to be designed for 2.5 times the

storey shear and moments calculated under seismic loads specified.

b) Besides the columns designed and detailed for calculated storey shears and

moments, shear walls placed symmetrically in both feasible to be designed

exclusively for 1.35 times the lateral storey shear calculated.

Foundation:

The use of foundations vulnerable to significant differential settlement due to

ground shaping shall be avoided for structures in seismic zones-III, IV & V.

individual spread footings or pile caps shall be interconnected with ties except when

individual spread footings are directly supported on rock. All ties shall be capable of

carrying in tension and in compression an axial force equal to Ah/A times the larger

of the column or pile cap load in addition to the otherwise computed forces where Ah

is the design horizontal spectrum value.



Projections:

a) Vertical projections: Tanks, towers parapets, chimneys and other vertical

cantilever projections attached to buildings and projecting the

above roof shall be designed and checked for stability for 5 times the

design horizontal seismic co-efficient Ah. In the analysis of the building,

the weight of these projecting elements will be lumped with the roof

weight.

b) Horizontal projections: All horizontal projections like cornices and

balconies shall be designed and checked for stability for 5 times the

design vertical co-efficient equal to 10/3 Ah. These increased design

forces either for vertical projection or horizontal projection are only

for designing the projecting parts and their connection with the

main structures. This means that for the design of main structure such

increase need not to be considered.

Shape of the building:

Very slender buildings should be avoided. Large overhangs and projections

attract large earthquake forces. Heavy masses like water tanks, etc., at the top shall be

avoided. Small water tanks, if provided, should be properly connected with the

framing system. Building should be sufficiently be away from steep slopes. It should

be built on filled up soil.

Symmetry should be avoided as they undergo torsion and extreme corners are

subjected to very large earthquake forces.

Damping:

Damping is the removal of kinetic energy and potential energy from a

vibrating structure and by virtue of which the amplitude of vibration diminishes

steadily. Some vibrations are due to initial displacement or initial velocity. Due to

damping, these vibrations decay in amplitude.

1. When there are harmonic applied forces and its period is nearly equal to

the natural period of the structure. The vibration will grow from zero

displacement and velocity. Damping limits the vibration maximum

amplitude.

2. More damping less is the amplitude.

3. Negative damping arise while the vibration is small, followed by positive

damping at large amplitude vibrations. The code adopted for design of

multistoried buildings considering a seismic force is IS: 1893 (part I) –

2002. More than 60% area of India is earthquake prone. According to IS:

1893(part I) -2002, India is divided into several zones to their magnitude

of intensities.



NEED FOR SEISMIC ZONATION:

a) There cannot be entirely scientific basis for zonation in view of the

scanty data available.

b) Though the magnitudes are known there is little instrumental evidence

for comparing damage.

c) Hence, magnitudes and epicenters are used.

REVISION OF PAST CODES:

It is very difficult to predict the occurrence time an exact location of

next earthquake. More than 60% area is earthquake prone. Various problems are

generated after an earthquake. The magnitudes of these problems are very severe.

In order to reduce this effective counter measures are to be taken. Enough steps

should be taken by the concerned authorities for code compliance so that the

structures being constructed are earthquake resistant. Especially during the past 15

years there were severe earthquake with a less time gap and high intensity. Based

on the technology advancement and knowledge gained after earthquake

occurrences, the seismic code is usually revised. The fifth revision of IS: 1893

with severe zone was done in 2002 after along gap of 18 years. According to the

present revision, the latest map has only 4 zones.

Fifth Revision in 2002:

Code has been split into 5 parts :-

Part 1: General provisions and buildings.

Part 2: Liquid retaining tanks-elevated and ground supported.

Part 3: Bridges and retaining walls.

Part 4: Industrial structures including stack like structures.

Part 5: Dams and embankment.

Part 1: General provisions and buildings:

Zone map is revised and zone factors changed

Response spectra for three types of founding strata

Empirical expression for fundamental natural period

Concept of response reduction factor

Lower bound for design base shear

Model combination rule is revised

Other clauses revised and redrafted



Design philosophy:

The design approach is IS: 1893 is

To ensure that the structure at least a minimum strength to with hand a

minor earthquake (<DBE) without damage.

To resist moderate earthquake (DBE) without significant structural

damage through some nonstructural damage may occur, and

To withstand a major earthquake (MCE) without Lapse.

3.14 CALCULATION OF SIESMIC BASE SHEAR:

Horizontal seismic co-efficient, Ah = zisa

2Rg

Where,

z- Zone factor

i- Importance factor

sa/ g – Spectral acceleration coefficient

R – Response reduction factor

From clause 6.4 of IS: 1893 – 2002

Time period, T = 0.075 h0.75

= 0.075 x 20.70.75

= 0.72785 sec

The soil is medium soil, hence 5% damping.

From staad pro analysis we have the base shear

TIME PERIOD FOR X 1893 LOADING = 0.72785 SEC

SA/G PER 1893 = 0.934, LOAD FACTOR= 1.000

FACTOR V PER 1893= 0.0152 X 19586.58 = 297.707 KN

TIME PERIOD FOR X 1893 LOADING = 0.72785 SEC

SA/G PER 1893= 0.934, LOAD FACTOR= -1.000

FACTOR V PER 1893= 0.0152 X 19586.58 = 297.707 KN

TIME PERIOD FOR Z 1893 LOADING = 0.72785 SEC



SA/G PER 1893= 0.934, LOAD FACTOR= 1.000

FACTOR V PER 1893= 0.0152 X 19586.58 = 297.707 KN

TIME PERIOD FOR Z 1893 LOADING = 0.72785 SEC

SA/G PER 1893= 0.934, LOAD FACTOR= -1.000

FACTOR V PER 1893= 0.0152 X 19586.58 = 297.707 KN

NOTE : NO SOFT STOREY IS DETECTED.



FIG3.10 DISPLACEMENT OF BUILDING UNDER SEISMIC LOAD FROM

X+VE DIRECTION



FIG3.11 MAXIMUM BENDING MOMENT DIAGRAM FOR SEISMIC LOAD

FIG3.12 MAXIMUM BENDING MOMENT VALUES FOR SEISMIC LOAD.



3.15 MAX BENDING MOMENTS FOR BEAMS:

BEAM

NO.

BEAM

CROSS-

SECTION(M)

BEAM

LENGTH

(M)

MAX MOMENT OF RESISTENCE (KN-m)

@ star support

(-ve)

@mid-span

(+ve)

@end support

(-ve)

1001

1002

1003

1004

1005

1006

1007

1008

1009

1010

1011

1012

1013

1014

1015

1016

1017

1018

1019

1020

1021

1022

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

3.00

3.70

3.55

1.65

1.90

3.70

3.00

1.90

3.00

3.70

3.55

3.55

3.70

3.00

3.00

3.70

3.55

3.55

3.70

3.00

3.00

3.70

32.633

42.931

47.176

35.415

27.417

46.584

38.217

32.145

32.499

43.873

48.911

40.323

47.889

38.558

34.200

48.839

46.786

41.262

48.336

40.932

33.292

48.087

12.755

18.381

17.581

18.726

14.725

19.181

15.495

15.876

15.690

18.733

16.683

16.603

18.800

15.561

15.375

17.834

16.887

16.823

17.897

15.246

15.252

17.954

38.451

49.323

46.029

26.626

34.632

43.995

33.055

28.055

38.837

43.340

40.533

48.598

44.362

32.823

41.380

48.759

41.569

47.103

49.281

34.624

41.749

48.228



1023

1024

1025

1026

1027

1028

1029

1030

1031

1032

1033

1034

1035

1036

1037

1038

1039

1040

1041

1042

1043

1044

1045

1046

1047

1048

1049

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

3.55

3.55

3.70

3.00

3.65

3.65

2.00

1.65

3.65

2.00

2.00

1.65

3.65

3.65

3.50

3.50

3.50

3.50

3.50

3.50

3.50

4.15

4.15

4.15

4.15

4.15

4.15

46.685

42.012

47.744

41.037

47.496

49.395

26.778

24.985

47.104

27.293

29.104

24.795

46.528

48.458

47.051

38.479

33.676

49.624

33.749

39.300

47.974

58.106

52.402

56.028

59.694

55.994

52.929

15.548

16.975

17.867

15.181

19.257

19.338

12.837

15.658

19.794

16.304

17.433

12.282

19.588

19.562

16.230

14.152

14.710

16.748

14.566

14.441

16.487

23.535

25.886

25.938

23.878

25.911

26.020

41.293

45.438

48.969

33.763

51.048

49.154

24.410

26.386

49.502

27.534

25.351

25.963

50.348

52.575

47.764

40.940

43.132

51.377

42.512

41.661

49.310

54.393

44.739

48.960

58.167

47.463

45.073



1050

1051

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2018

2019

2020

2021

2022

2023

2024

2025

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

4.15

2.00

3.00

3.70

3.55

1.65

1.90

3.70

3.00

1.90

3.00

3.70

3.55

3.55

3.70

3.00

3.00

0.85

2.85

3.55

3.55

2.85

0.85

3.00

3.00

0.85

2.85

58.937

44.458

44.777

57.491

42.468

39.687

37.754

64.115

47.533

46.531

43.859

55.686

80.267

60.548

65.963

47.208

45.403

88.301

9.783

65.875

49.543

72.414

9.774

60.260

44.992

69.573

9.440

23.701

30.724

21.253

27.412

22.840

25.887

22.386

27.015

21.009

22.873

21.023

26.349

30.346

28.923

26.551

20.694

19.854

18.140

32.812

23.159

23.055

33.136

18.160

19.559

20.696

18.609

31.847

55.853

45.315

48.630

63.879

41.874

35.022

48.304

57.696

45.748

32.731

47.790

67.464

61.970

78.189

57.008

44.612

60.963

9.784

72.969

50.008

68.584

9.775

89.713

46.144

58.999

9.438

51.178



2026

2027

2028

2029

2030

2031

2032

2033

2034

2035

2036

2037

2038

2039

2040

2041

2042

2043

2044

2045

2046

2047

2048

2049

2050

2051

3001

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

3.55

3.55

2.85

0.85

3.00

3.65

3.65

2.00

1.65

3.65

2.00

2.00

1,65

3.65

3.65

3.50

3.50

3.50

4.15

4.15

4.15

4.15

4.15

4.15

4.15

2.00

3.00

62.004

53.822

70.429

9.448

60.467

70.180

65.620

35.945

46.035

63.504

36.505

42.999

42.703

68.375

71.746

38.700

60.319

40.166

76.690

36.152

61.352

91.337

63.880

37.463

78.020

44.511

46.268

23.731

22.783

31.324

29.151

19.998

27.990

26.092

29.585

22.382

27.080

27.069

28.258

38.899

27.096

28.999

27.031

23.991

29.430

34.407

52.264

40.680

44.480

40.679

55.264

34.553

32.654

20.177

53.353

63.285

9.447

86.157

45.328

66.314

64.743

36.845

33.786

55.150

37.662

37.525

35.313

68.005

68.925

40.014

72.120

42.655

80.259

39.547

66.587

94.345

66.183

39.314

82.853

45.356

45.654



3002

3003

3004

3005

3006

3007

3008

3009

3010

3011

3012

3013

3014

3015

3016

3017

3018

3019

3020

3021

3022

3023

3024

3025

3026

3027

3028

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

3.70

3.55

1.65

1.90

3.70

3.00

1.90

3.00

3.70

3.55

3.55

3.70

3.00

3.00

0.85

2.85

3.55

3.55

2.85

0.85

3.00

3.00

0.85

2.85

3.55

3.55

2.85

56.798

39.836

37.935

38.098

65.218

43.975

46.461

45.119

55.998

83.471

56.403

65.076

44.606

46.416

88.620

9.558

67.217

47.172

70.907

9.548

55.896

45.032

69.076

9.140

63.359

52.675

68.126

27.003

24.131

33.052

27.134

27.143

19.762

31.613

20.023

26.507

30.452

29.011

26.762

19.522

18.980

31.885

31.973

23.368

23.289

32.289

30.745

18.928

19.877

30.018

31.291

22.977

22.686

30.532

64.658

43.900

34.612

43.990

57.669

47.717

27.074

45.586

67.003

58.268

81.434

58.063

46.279

56.710

9.558

71.594

47.818

67.958

9.550

90.227

47.268

55.933

9.139

49.686

51.358

62.902

9.148



3029

3030

3031

3032

3033

3034

3035

3036

3037

3038

3039

3040

3041

3042

3043

3044

3045

3046

3047

3048

3049

3050

3051

4001

4002

4003

4004

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.85

3.00

3.65

3.65

2.00

1.65

3.65

2.00

2.00

1,65

3.65

3.65

3.50

3.50

3.50

4.15

4.15

4.15

4.15

4.15

4.15

4.15

2.00

3.00

3.70

3.55

1.65

9.150

56.452

70.383

65.577

32.698

48.503

68.220

34.009

43.586

43.444

68.309

71.730

39.278

59.195

40.585

77.232

36.012

61.819

89.968

64.652

37.334

78.414

39.013

44.051

54.284

35.363

31.181

27.788

19.114

27.566

25.428

27.174

40.553

28.692

25.656

26.820

37.758

26.399

28.594

28.086

25.121

30.414

33.865

55.884

39.257

43.670

39.257

54.882

34.048

27.093

18.662

26.384

21.481

27.346

86.956

45.950

67.030

64.582

35.342

32.134

50.237

36.889

36.930

33.029

67.938

69.708

39.610

74.234

42.382

80.927

40.115

69.348

97.419

68.250

39.933

83.601

41.106

41.045

61.740

41.824

30.938



4005

4006

4007

4008

4009

4010

4011

4012

4013

4014

4015

4016

4017

4018

4019

4020

4021

4022

4023

4024

4025

4026

4027

4028

4029

4030

4031

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

1.90

3.70

3.00

1.90

3.00

3.70

3.55

3.55

3.70

3.00

3.00

0.85

2.85

3.55

3.55

2.85

0.85

3.00

3.00

0.85

2.85

3.55

3.55

2.85

0.85

3.00

3.65

33.781

62.992

38.913

42.206

42.772

53.929

82.479

50.951

61.506

39.944

42.970

84.948

8.073

64.888

42.484

66.101

8.064

49.202

40.963

64.897

7.585

60.549

48.865

62.778

7.596

49.885

64.988

21.212

26.759

18.846

27.381

18.238

26.579

30.595

29.350

26.875

17.867

18.677

29.420

31.538

23.417

23.350

31.891

28.238

18.666

18.251

27.590

28.895

21.820

21.764

29.148

25.081

17.608

26.256

37.280

55.403

45.931

18.962

41.122

63.660

53.088

80.428

56.463

44.185

49.971

8.073

66.797

43.116

65.579

8.067

86.600

43.793

49.509

7.585

45.008

46.958

59.236

7.593

83.356

42.058

61.232



4032

4033

4034

4035

4036

4037

4038

4039

4040

4041

4042

4043

4044

4045

4046

4047

4048

4049

4050

4051

5001

5002

5003

5004

5005

5006

5007

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

3.65

2.00

1.65

3.65

2.00

2.00

1,65

3.65

3.65

3.50

3.50

3.50

4.15

4.15

4.15

4.15

4.15

4.15

4.15

2.00

3.00

3.70

3.55

1.65

1.90

3.70

3.00

59.346

25.547

46.892

67.440

27.892

39.300

40.712

61.348

65.816

34.604

53.594

35.453

72.047

33.986

57.503

84.811

60.353

35.170

72.815

30.265

38.112

50.657

29.423

19.307

25.689

57.571

33.188

25.553

21.860

37.667

28.555

20.797

21.659

33.635

25.583

26.749

23.221

24.493

24.879

33.940

54.961

39.556

33.780

39.556

54.958

33.914

19.115

17.132

26.463

14.537

19.073

11.592

26.471

16.956

58.989

32.463

26.458

42.537

32.450

33.220

27.283

61.747

63.550

34.237

72.348

36.684

76.186

38.069

65.534

94.726

63.857

37.752

78.527

33.648

36.016

54.747

35.869

24.840

28.653

51.657

40.486



5008

5009

5010

5011

5012

5013

5014

5015

5016

5017

5018

5019

5020

5021

5022

5023

5024

5025

5026

5027

5028

5029

5030

5031

5032

5033

5034

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

1.90

3.00

3.70

3.55

3.55

3.70

3.00

3.00

0.85

2.85

3.55

3.55

2.85

0.85

3.00

3.00

0.85

2.85

3.55

3.55

2.85

0.85

3.00

3.65

3.65

2.00

1.65

34.587

37.235

50.109

77.849

44.271

54.889

34.108

35.652

77.703

5.403

59.030

36.432

58.252

5.396

40.106

32.975

57.765

4.906

53.739

43.592

54.710

4.908

40.958

55.184

49.757

15.534

42.350

19.403

17.655

26.755

30.701

29.721

27.016

17.476

18.684

25.403

31.555

23.461

23.387

31.967

24.286

18.647

17.986

23.178

24.546

21.945

21.357

28.915

20.903

17.047

25.360

25.364

14.669

31.563

9.000

35.622

57.027

46.623

75.860

53.010

38.941

40.636

5.403

58.809

36.886

59.558

5.399

79.206

36.286

39.907

4.906

37.582

41.115

52.385

4.904

76.100

33.817

51.351

49.748

28.846

17.089



5035

5036

5037

5038

5039

5040

5041

5042

5043

5044

5045

5046

5047

5048

5049

5050

5051

6001

6002

6003

6004

6005

6006

6007

6008

6009

6010

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

3.65

2.00

2.00

1,65

3.65

3.65

3.50

3.50

3.50

4.15

4.15

4.15

4.15

4.15

4.15

4.15

2.00

3.00

3.70

3.55

1.65

1.90

3.70

3.00

1.90

3.00

3.70

61.350

18.787

31.786

34.862

50.777

55.462

26.622

44.420

26.968

63.158

30.355

49.977

76.977

52.281

31.285

63.475

18.228

16.864

18.660

40.641

19.806

18.701

29.414

7.964

26.206

19.038

29.858

27.431

14.796

13.822

25.084

25.369

25.383

14.426

21.296

15.345

34.172

54.860

39.168

43.601

39.168

54.855

3.150

12.216

8.389

12.199

23.416

6.237

6.304

13.671

8.484

13.521

13.946

19.652

32.453

25.745

27.277

18.961

51.608

53.005

25.750

66.045

27.578

67.198

34.149

57.224

86.958

55.153

33.619

68.891

25.151

9.912

30.269

54.548

21.137

14.139

20.523

18.330

3.436

20.892

39.189



6011

6012

6013

6014

6015

6016

6017

6018

6019

6020

6021

6022

6023

6024

6025

6026

6027

6028

6029

6030

6031

6032

6033

6034

6035

6036

6037

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

3.55

3.55

3.70

3.00

3.00

0.85

2.85

3. 55

3.55

2.85

0.85

3.00

3.00

0.85

2.85

3.55

3.55

2.85

0.85

3.00

3.65

3.65

2.00

1.65

3.65

2.00

2.00

70.503

39.441

37.182

20.250

18.221

49.153

2.597

40.408

22.633

37.860

2.593

24.976

12.185

34.914

2.285

27.475

14.746

22.254

2.279

16.619

22.963

27.416

6.758

34.073

44.125

7.557

21.499

31.136

30.108

20.325

13.656

14.848

114.921

22.457

17.448

17.531

22.483

14.535

14.841

8.056

13.850

16.439

9.754

10.961

15.709

12.294

8.114

12.394

19.730

9.806

20.634

20.295

11.811

10.437

42.801

71.122

32.218

19.975

25.236

2.598

38.337

22.966

40.576

2.595

49.828

18.452

17.665

2.264

25.753

12.706

22.266

2.277

38.417

13.044

21.781

27.079

26.053

11.753

12.262

19.413

21.095



6038

6039

6040

6041

6042

6043

6044

6045

6046

6047

6048

6049

6050

7001

7002

7003

7004

7005

7006

7007

7008

7009

7010

7011

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

0.300 x 0.400

1,65

3.65

3.65

3.50

3.50

3.50

4.15

4.15

4.15

4.15

4.15

4.15

4.15

3.55

1.65

1.90

1.90

3.55

3.55

3.65

3.65

2.00

2.00

1.65

26.767

27.520

22.940

17.6693

11.360

17.783

27.160

17.313

24.514

32.224

25.930

17.336

27.223

14.656

4.571

9.068

13.668

29.325

4.983

12.701

28.585

1.942

6.852

10.162

14.239

19.875

12.431

5.954

25.230

6.295

18.164

41.062

32.698

27.250

32.697

41.056

18.137

12.971

1.847

4.339

11.256

14.452

12.407

19.062

20.730

9.086

3.226

3.788

10.396

27.827

22.585

16.418

32.006

17.358

28.724

20.635

29.9411

42.507

28.414

20.624

29.659

27.847

12.022

3.742

2.290

6.797

31.235

16.717

17.301

9.953

7.671

3.788



4. DESIGN OF SLABS

4.1 GENERAL:

Slabs are usually supported on two parallel sides or an all the four sides.

Beams or walls are the common supports for slabs. If a slab is supported on two

opposite edges, it bends in only one direction. Hence it needs reinforcements in only

one direction. However distribution steel is to be provided at right angles to main

reinforcement so that load is distributed properly. Apart from this distribution steel

helps in distributing secondary stresses like temperature stresses. Hence slab

reinforcement is provided in both directions. Thus, Slabs supports mainly transverse

loads and transfer them to the supports by bending action in one or more directions.

Beams or walls are the common supports for the slab.

If the slab is supported on all the four sides, it bends in both directions and

needs reinforcement in both directions. In such case the reinforcements are to be

designed in for both directions. However, from the analysis of slabs by plate theory it

is found that if the ratio of larger span to smaller span (ly/lx) is more than 2, the

bending moment in the direction of larger span is very small. The main reinforcement

required works out to be less than that required as distribution steel for one-way slab.

The bending moment in shorter span is almost equal to bending moment in one way

slab and hence the slab may be designed as one-way slab if the ratio of larger span(ly)

to shorter span (lx) is more than 2.

The slabs in which main reinforcement is to be designed in only one direction

is called one-way slab. If main reinforcement is to be designed in both directions, the

slab is called two-way slab. Slabs may be a roof or a floor depending on its location in

the building, the design value of live load on slab panels as per IS: 875 part-II is as

follows:

1) Design L.L for roof slab : 1.5 KN/m

2) Design L.L for typical floor slab : 2.0 KN/m

A slab may be simply supported or continuous or may be cantilever. The

bending moments at critical sections are to be found and reinforcements designed.

Slab is usually designed as a beam of one meter width to carry moment over a strip of

1 meter. Instead of number of bars, spacing of bars is to be found. 8 mm or 10 mm are

commonly used.

A slab may be classified according to the method of support:

a) One-way slabs spanning in one direction.

b) Two-way slabs spanning in both directions.

c) Circular slabs.

d) Flat slabs resting directly on columns with no beams.

e) Grid floor & Ribbed slabs.



Slabs are designed by using the same theories of bending and shear as they are

used for beams. The following methods of analysis are available:

a) Elastic Analysis – idealization into strips or beams.

b) Semi Empirical co-efficient as given in code.

c) Yield line Theory.

General Design Requirements for Slabs as per IS 456: 2000

1. Effective span:

The effective span of a simply supported slab shall be taken as clear

span plus effective depth of the slab or center to center distance between the

supports whichever is less.

The effective span of a cantilever slab shall be taken as its length to the face of

the support plus half the effective depth except where it forms the end of a

continuous slab where the length to the Centre of support shall be taken.

2. Limiting stiffness:

The stiffness of slab is governed by the span to depth ratio. As per

Clause 23.2 of IS: 456 for spans not exceeding 10 m, the span to depth ratio

(basic values) should not exceed the limits given below.

Cantilevers - 7

Simply supported - 20

Continuous - 26

Depending upon the type of steel and percentage of steel, the above

values have to be modified as per fig.4 of IS: 456 – 2000.For two-way slabs,

the shorter span should be used for calculating the span to effective depth

ratio.

3. Minimum Reinforcement:

The reinforcement in either direction of span shall not be less than

0.15% of gross cross-sectional area if mild steel is used. However, this value is

reduced to 0.12% where high strength deformed bars (HYSD) are welded by

fabrics are used. (Clause 26.5.2.1 of IS: 456 – 2000).

4. Maximum Diameter of Bars:

The diameter of bars shall not exceed one eighth of the total thickness

of slab (Clause 26.5.2.2 of IS: 456 – 2000)

5. Spacing of Main Reinforcement:

The spacing of main reinforcement in slabs shall not be more than

three times the effective depth of solid slab or 300 mm whichever is less.

(Clause 26.3.3 of IS: 456 – 2000)



6. Distribution Reinforcement:

The area of distribution reinforcement shall not be less than 0.15% of

gross cross-sectional area if plane bars are used and 0.12% if high yield

strength deformed bars are used. The spacing of distribution reinforcement in

slabs shall not be more than five times of the effective depth of slab or 450

mm whichever is less.

7. Cover to Reinforcement:

Reinforcement shall have concrete cover of thickness as follows:

a) At each end of reinforcement bar not less than 25 mm nor less than

twice the diameter of such bar.

b) The bottom cover for reinforcement shall not be less than 20 mm nor

less than the diameter of such bars.

4.2 DESIGN OF ONE WAY SLABS:

One way slab are those in which the length is more than twice the breadth. A

continuous one-way slab can be analyzed in a similar manner to that used for a

continuous beam. The general recommendation for curtailment of bars is given in

clause 26.2.3 of the code applies for slab also. As stated earlier, if the ratio of longer

span to the shorter span (ly/lx) is greater than 2, is called as one-way slab. One-way

slab bends only in one direction across the span, and acts like a wide beam.

Design Procedure for One-way Slab:

1) Assume the sustainable depth based on the stiffness consideration and

calculate the effective span.

Required effective depth = Span ÷ (Basic value x Modification

Factor).

(Span/depth) ratio safely be selected in range of 25 to 30 for simply

supported slabs.

2) Considering one meter width of slab, calculate the loads acting on the slab.

Find the factored Moment and Shear force. For simply supported slabs.

Mu = wul2/8 Bending Moment

Vu = wul/2 Shear Force

Where l = Length of Shorter span

3) Determine the minimum depth required to resist the bending moment by

equating

Mu = Mu, lim = k. fck.b. d2



b = 1000 mm,

k=0.138 for Fe415 steel & 0.148 for mild steel

Provided depth should be more than this value. Otherwise increase the depth.

4) Calculate the area of steel per meter width of slab by using

Mu = 0.87. Fy.Ast. d {1 – [(fy.Ast)/ (fck.b. d)]}

5) Find the spacing of bars using

S = (ast /Ast) x1000

Where

ast - area of bars used.

Ast - total area of steel required.

Spacing should be not more than 3d or 300 mm whichever is less.

6) Distribution Steel :

Provide distribution reinforcement at 0.12% (for HYSD bars) of gross

cross sectional area and find the spacing of these bars. If mild steel bars are

used, provide 0.15% of gross cross sectional area of distribution steel. Spacing

of distribution steel should not be more than 5d or 450 mm whichever is less.

7) Check for Deflection :

Calculate the Pt % corresponding maximum mid span moment, take

the modification factor (F1) from fig.4 of IS: 456 – 2000

(l/d) provided < (l/d) max = basic value x F1

8) Check for Shear :

Maximum shear force at the edges of one-way slab given by

Vu = wul/2 Shear Force

τv = Vu/ b. d Nominal Shear Stress

Calculate the percentage of main steel at supports

Pt = ast/ S. d

τc = ------- Shear Strength of Concrete

Which is calculated by referring table-19 of IS: 456, shear strength of

concrete for beams

τc = --------



For solid slabs, the shear strength of concrete shall be τc.k. Value of k should

be taken from clause 40.2.1.1 depending depth of slab, which is given below.

Overall

depth

300 or

more

275 250 225 200 175 150 or

less

K 1.00 1.05 1.10 1.15 1.20 1.25 1.30

TABLE 4.1

Also note for slabs, nominal shear stress (τc) shall not exceed 0.5 τc max, where

τc max is as given as table-20 IS: 456. Shear reinforcements in slabs should be

avoided, since they work out cumbersome and expensive. Hence, if τv > τc,

increase the thickness of slab and redesign.

9) Check for Development Length :

Ld ≤ (M1 ÷ V) + Lo

The check for shear and check for development length are mostly

satisfied in all cases of slabs subjected to uniformly distributed loads and

therefore omitted in design calculations

4.3 DESIGN OF CONTINUOUS SLABS:

Continuous slabs are subjected to negative moments at supports and to

positive moments at mid span. Hence design is required for all critical sections.

However to avoid problems in construction, usually design is made for the maximum

bending moment and shear force and the reinforcement is provided.

IS: 456 (table-12 & 13) gives expressions for finding moments and shear

forces at critical sections. These are presented in table- 6.2 & 6.3 also. However it

may be noted that these coefficients are for beams/slabs of uniform cross sections

which supports substantially uniformly distributed loads over 3 or more spans which

do not differ by more than 15 % of the longest span. For all other cases, rigorous

structural analysis is required.

It may be noted that if all spans are equal maximum is at support next to end

support.

Mmax = (wdl2/12) + (wLl

2/9)

And Vmax is at outer of first interior support

Vmax = 0.6wd+0.6wL

Design Procedure:

I. Assume a depth of L/30th

of span.

II. Effective span shall be found as explained in Art. 6.3 (clause 222

IS:456)



III. Find design moment and shear force.

IV. Design for Moment.

V. Check for shear.

VI. Check for deflection.

VII. Design distribution steel.

VIII. Sketch reinforcement details.

4.4 DESIGN OF CANTILEVER SLABS:

Common example of cantilever slabs are chajjas and balcony slabs. These

slabs are free at one end and may be treated as fixed at other ends to lintel beams.

They may be overhanging portions of interior slabs. They need reinforcement to top

since in cantilevers subjected to vertical downward loads, tension in on top. Moment

is maximum at fixed/continuous end. Hence design is for the section at the end. We

know in cantilevers moment reduces to zero at free end. Hence the thickness of

cantilever slab may be reduced gradually towards free end. Hence minimum thickness

of 75 mm is maintained at free end.

In the design the following points are to be noted:

i. For uniformly distributed loads, the bending moment and shear force is

Mu = wul2/8 Bending Moment

Vu = wul Shear Force

ii. Basic value of span to depth ratio for cantilever = 7

To find the trial depth, l/d ratio may be taken as 10 taking the modification

factors in to consideration.

iii. Main bars are to be provided at top and distribution bars are to be provided in

the transverse direction.

iv. There should be check for anchorage length of main bars at the support.

4.5 DESIGN OF TWO WAY SLABS:

When slab is supported on all four sides and the ratio of long span (ly) to short

span (lx) is less than 2, the bending moment developed in both x & y directions is

predominant and hence design should be made for reinforcement in both directions.

For the analysis of such slab various theories have been developed and expressions

for bending moment Mx & My presented. Among all those theories plate theory is

quite precise.

The moment developed depends upon the edge conditions also. In buildings,

we come across the following boundary conditions.

1. All four edge continuous (interior panel)

2. One short edge discontinuous



3. One long edge discontinuous

4. Two adjacent edges discontinuous

5. Two short edges discontinuous

6. Two long edges discontinuous

7. Three edges discontinuous and one long edge continuous.

8. Three edges discontinuous and one short edge continuous.

9. Four edges discontinuous but corners held down by providing torsional

reinforcements.

10. Simply supported slab without torsion reinforcements.

Note: simply supported slabs have tendency to lift at corners due to torsion

moment in the slab. Lifting of corners may be prevented by providing torsion

reinforcement in the form of two mats. If such precaution is taken, the simply

supported slab falls under category 9 otherwise it falls under category 10.

FIG4.1

For uniformly distributed load on entire slab, maximum + ve moment (tension at

bottom) develops and at supports – ve moment developed in slabs with various edge

conditions. The maximum bending moment per unit width in slab are given by

Mx=αx w lx2

My=αy w lx

2 (Clause D.2.1 of IS: 456)

Where Mx & My are the design moments along short and long spans

w = uniformly distributed load on slab

lx & ly are the lengths of short and long spans.

αx & αy are the moment coefficients given in table – 26 of IS: 456.

4

2

3 3

1 4

4

7

5

2

6 6



Bending moment coefficients for rectangular panel supported on four sides with

provision of torsion at corners

(IS 456:2000 Clause D-1.1 and 24.4.1)

Ca

se

No

.

Type of Panel

and Moments

considered

Short Span Coefficients αx

(Values of ly/lx)

Long

span

coefficie

nts αy

for all

values

of ly/lx

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

1

Interior Panels:

Negative

moment at

continuous edge.

Positive moment

at mid span

0.032

0.024

0.037

0.028

0.043

0.032

0.047

0.036

0.051

0.039

0.053

0.041

0.060

0.045

0.065

0.049

0.032

0.024

2

One short Edge

Discontinuous:

Negative

moment at

continuous edge.

Positive moment

at mid span

0.037

0.028

0.043

0.032

0.048

0.036

0.051

0.039

0.055

0.041

0.057

0.044

0.064

0.048

0.068

0.052

0.037

0.028

3

One Long Edge

Discontinuous:

Negative

moment at

continuous edge.

Positive moment

at mid span

0.037

0.028

0.044

0.033

0.052

0.039

0.057

0.044

0.063

0.047

0.067

0.051

0.077

0.059

0.085

0.065

0.037

0.028

4

Two Adjacent

Edges

Discontinuous:

Negative

moment at

continuous edge.

Positive moment

at mid span

0.047

0.035

0.053

0.040

0.060

0.045

0.065

0.049

0.071

0.053

0.075

0.056

0.084

0.063

0.091

0.069

0.047

0.035

5

Two Short

Edges

Discontinuous:

Negative

moment at

continuous edge.

0.045

0.035

0.049

0.037

0.052

0.040

0.056

0.043

0.059

0.044

0.060

0.045

0.065

0.049

0.069

0.052

--

0.035



Positive moment

at mid span

6

Two Long

Edges

Discontinuous:

Negative

moment at

continuous edge.

Positive moment

at mid span

--

0.035

--

0.043

--

0.051

--

0.057

--

0.063

--

0.068

--

0.080

--

0.088

0.045

0.035

7

Three Edges

Discontinuous

(One Long

Edge

Continuous):

Negative

moment at

continuous edge.

Positive moment

at mid span.

0.057

0.043

0.064

0.048

0.071

0.053

0.076

0.057

0.080

0.060

0.084

0.064

0.091

0.069

0.097

0.073

--

0.043

8

Three Edges

Discontinuous

(One Short

Edge

Continuous):

Negative

moment at

continuous edge.

Positive moment

at mid span

0.043

0.051

0.059

0.065

0.071

0.076

0.087

0.096

0.057

0.043

9

Four Edges

Discontinuous:

Positive moment

at mid span.

0.056

0.64

0.072

0.079

0.085

0.089

0.100

0.107

0.056

TABLE 4.2



Recommendation of IS: 456 for Design of Restrained Slabs:

1. The maximum bending moments per unit width in a slab are given by the

following equations.

Mx=αx w lx2

My=αy w lx

2

2. Slabs are considered as divided in each direction in to middle strips and edge

strips. The middle strip being ¾ of the width and edge strip of the 1/8 width

of the slab.

3. The maximum moment applies to only to middle strip.

4. Tension reinforcements provided at mid strip shall extend in the lower part of

the slab to within 0.25l of a continuous edge or 0.15l of discontinuous edge.

5. Over the continuous edges of a middle strip, the tension reinforcement shall

extend in the upper part of the slab a distance of 0.15l from the support and at

least 50% shall extend a distance of 0.3l.

6. Due to imperfection of boundary conditions, negative moment may occur at

discontinuous edges. To take care of such moments, tension reinforcement

equal to 50% of that provided at mid span extending to 0.1l in to the span will

be sufficient.

7. Reinforcement in edge strip, parallel to that edge, shall comply with the

minimum requirement.

8. Torsion Reinforcement:

Torsion reinforcement is to be provided at corners where two adjacent edges

are discontinuously/simply supported. It consists of two layers of

reinforcement mesh at top and other at bottom of slab with required cover. The

area of reinforcement in each of these four layers shall be ¾th

of the area

required for the maximum mid span in the slab and shall be of length 1/5th

of

the shorter span.

4.6 Design Procedure for Two way Slab:

1. Assume the depth of the slab based on the stiffness.

(a) For two way slabs with shorter span less than 3.5 m and L.L < 3

KN/m2, the allowable lx/d ratio is

Type Fe 250 Fe 415

Simply supported slabs 35 28

Fixed or Continuous

slabs

40 32

TABLE 4.3

(b) If lx > 3.5 m and L.L >3 3 KN/m2, the allowable lx/d ratio is same as

that of one-way slabs.

2. Find the effective spans lx and ly



3. Calculate the ultimate load considering 1 m width of the slab.

4. Obtain the design moment coefficients along short and long spans

depending on the boundary conditions given in table – 26 of IS: 456 as

applicable. Calculate the bending moments by multiplying the coefficients

by wlx2.

5. Calculate the minimum depth required to resist the absolute maximum

design moment (Mx and My) which should be less than the depth provided,

otherwise increase the depth.

6. Calculate the area of steel at the mid span (and at support if the slab is

continuous) in both the directions using

Mu = 0.87 FY Ast d {1 – [(FY Ast) ÷ (fck b d)]}

The short span bars are provided in the bottom layer and long span bars are

provided above the short span bars in the mid span regions.

Thus for

short span d = D – clear span – ϕ/2

Long span d1 = (D – clear span – ϕ/2) – ϕ = d – ϕ

The main reinforcement shall be provided in the middle strips of width

equal to ¾ of slab width.

7. Torsion steel:

(a) At corners where slab is discontinuous over both the edges At =

¾ Astx

(b) At corners where slab is discontinuous over one edge At = 3/8

Astx

(c) At corners where slab is continuous over both edges, At = 0,

i.e., no torsion steel is required.

Where Astx = Area of steel for maximum mid span moment.

This area of torsion reinforcement will be provide at corners in the

form of mesh, one at top and the other at bottom for a length of lx/5 in each

orthogonal direction, parallel to the sides of the slab.

8. Check for Deflection:

Calculate the Pt % corresponding maximum mid span moment

Take the modification factor (MF) from figure-4 IS: 456

(l/d) provided < (l/d) maximum = basic value x MF



9. Check For Shear:

Maximum shear force at the edges of two way slab is given by

Vux = wv [r4 ÷ (1 + r

4)] (lx/2), where r = (ly/lx)

τv < τc

10. Check for Development Length:

Ld ≤ (M1 ÷ V) + Lo

The check for shear and check for development length are mostly

satisfied in all cases slabs subjected to uniformly distributed loads and

therefore omitted in design calculations. The general arrangement of

reinforcement in two-way.

4.7 CALCULATIONS:

SLAB PANEL: S1

Length of longer span ( ly ): 3.65 m

Length of shorter span (lx ): 3.00 m

Now ratio of longer span to shorter span i.e.,

𝑙𝑦

lx =

3.65

3.00 = 1.217 < 2

Hence Two way slab should be considered.

Loads acting on the slab:

Live load = 2 KN/m2

Floor finish = 1.5 KN/m2

fck = 20 N/mm2

fy = 415 N/mm2

Thickness of slab:

Assume effective depth d = span

32 =

3000

32= 93.75 𝑚𝑚

Adopt d = 100 mm

Effective Cover = 20 mm

Overall depth D = 120 mm

Loads per unit area of slab

Self-weight of the slab = 0.12 x 25 = 3.0 kN/m2

Live load = 2 N/m2



Floor finish = 1.5 KN/m2

Total load = 6.5 KN/m2

Factor of safety = 1.5

Factored load (wu)= 1.5 x 6.0 = 9.75 KN/m2

Type of panel: Two adjacent edges discontinuous

Moment and Area of Steel calculations:

Mu = α.wu .lx

By using SP 16

Span Moment Mu Mu/bd² Pt Ast

reqd

Min

Ast Dia Spacing Ast pro

Coefficient kN.m N/mm

2 % mm² mm² mm mm mm²

shorter

αx

(-ve) 0.064 5.60 0.56 0.16% 157.04 120 8 200 251.33

αx

(+ve) 0.048 4.20 0.42 0.12% 116.77 120 8 200 251.33

longer

αy

(-ve) 0.045 3.98 0.40 0.11% 110.54 120 8 200 251.33

αy

(+ve) 0.034 2.98 0.30 0.08% 82.42 120 8 200 251.33

TABLE 4.4

Check for deflection:

Basic value of Lx/d ratio = 26

From figure 3 of I.S 456:1978 modification factor is 1.66

Maximum permitted l/d ratio = 1.66 × 26 = 43.16

Lx/d provided = 3000/100 = 30

Lx/d provided > Lx/d required

Hence deflection control is safe.



Design of One way slab

SLAB PANEL: S4

Length of longer span ( l y ) = 10.25 m

Length of shorter span (l x ) = 3.50 m

Now ratio of longer span to shorter span i.e.

𝑙𝑦

lx =

10.25

3.50 = 2.92 > 2

Hence One way slab should be considered.

Loads acting on the slab:

Live load = 2 KN/m2

Floor load = 1 KN/m2

Characteristic strength of concrete ( fck ) = 20 N/mm2

Characteristic strength of steel (fy) = 415 N/mm2

Thickness of slab:

Assume effective depth d = span

28 =

3500

28= 125 𝑚𝑚

Adopt d = 125 mm

Cover = 20 mm

Overall depth = 145 mm

Loads: per unit area of slab

Self-weight of the slab = 0.145 x 25 = 3.3.625 kN/m2

Live load = 2 kN/m2

Floor finish = 1 kN/m2

Total load = 6.625 kN/m2

Load factor = 1.5

Factored load = 1.5 x 6.625 = 9.9735 kN/m2

Max B.M Mu= wl2/8 = 15.22 kN-m



By using SP 16

TABLE 4.5

Mu Mu/bd² Pt Ast

reqd

Min

Ast

Dia of

bar Spacing Ast pro

kN.m N/mm2 % mm² mm² mm mm mm²

15.22 0.97 0.28% 352.46 150 8 140 359.04

Distribution reinforcement:

Minimum percentage of steel as per IS 456 Is 0.12% of gross cross sectional area

Ast = 0.12 x 1000 x 145/100

= 174 mm2

Provide 8 mm dia bars @ 280 mm c/c

Check for deflection:

For simply supported slabs basic l/d ratio is 20

From figure 3 of I.S 456:1978 modification factor is 1.43

Maximum permitted l/d ratio = 1.43 × 20 = 28.6

Lx/d provided = 3500/125 = 28.6

Lx/d provided > Lx/d required

Hence deflection control is safe.



Schedule of slabs (Typical & Roof):

slab Lx

(m)

Ly

(m)

Type of

slab

Reinforcement

Effecti

ve

depth

d (mm)

Along X-direction Along Y-direction

-ve +ve -ve +ve

S1 3.00 3.65 100 Two way

Continues 8 ϕ-200 c/c 8 ϕ-200 c/c 8 ϕ-200 c/c 8 ϕ-200 c/c

S2 3.65 3.70 100 Two way


S3 3.55 3.65 100 Two way


S4 3.50 10.25 125 One way ----- 8 ϕ-140 c/c ----- 8 ϕ-280 c/c

S5 3.85 4.15 100 Two way


S6 2.85 4.15 100 Two way


S7 3.55 4.15 100 Two way


TABLE 4.6

Note :

Effective cover for all slabs is 20 mm

Total depth for two way slabs is 120 mm

Total depth for one way slabs is 145 mm

Diameter of bar and spacing is in mm



5. DESIGN OF BEAMS

5.1 INTRODUCTION:

In a building frame at every floor level, there can be large number of

beams with different spans, end conditions, and loadings. It would not be

practicable to design all beams serially from first to last. It is quite likely

that some of the beams may have the same end conditions, spans, and/or

loadings. Under such circumstances, it is always advisable to categorize

them and group them to facilitate design, and reduce the computational

efforts.

Design of reinforced concrete beams involves sizing and finding

required quantity of steel based on the consideration of strength and

serviceability requirements. It also involves detailing. The major

consideration in the design of beams is bending moment. Hence first

beams are designed for bending moment and then the design for shear is

taken up. Checks are applied for deflection and crack width. If the

requirement for any limit state fails redesign is to be made. The detailing

of reinforcement is to be made with neat sketches/drawings taking into

account bond, cracking and durability considerations.

Concrete is fairly strong in compression but very weak in tension.

Hence plain concrete cannot be used in situations where considerable

tensile stresses develop. If flexural members like beams and slabs are

made of plain concrete their load carrying capacity is very low due to its

low tensile strength. Since steel is very strong in tension, steel bars are

provided to resist tensile stresses at a place where the maximum tensile

stresses are developed.

In case of simply supported beam, tensile stresses are induced in

bottom layers because of positive bending moment (sagging bending moment) and hence steel bars are provided near the bottom of the beam.

In cantilever beams steel bars are placed near the top of the beam to resist

the tensile stresses developed in top layers due to the negative bending moment (hogging bending moment). A

A

FIG 5.1 Reinforcement in simply supported beam

-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -

- NA -

-- -- -

- -- -

- -- --

-- --

-- -- -

- -- -

- -- --

-- --

-- -- -



Positioning of beams:

Some of the guiding principles for the positioning of beams are as

follows:

(a) Beams are generally provided under walls or below heavy

concentrated loads to avoid these loads directly coming on slabs.

(b) The spacing of the beams is governed by the maximum spans of the

slabs.

(c) For larger spans and heavier loads the two-way action is advantageous,

as the steel required is minimum.

(d) For designing the cantilever slabs, availability adequate anchorage

should be checked.

Categorization of beams:

The categorization of beams may be done on the basis of design which

depends on the following factors:

(1) End conditions (EC = 1, 2, 3, 4)

(2) Span

(3) Load type (UDL, point load, triangular/trapezoidal load etc.)

(4) Section type (rectangular/flanged)

(5) Load magnitude.

Since categorization of beams would principally depend upon the end

conditions of beam it is necessary, in the beginning, to take certain

decisions or make suitable simplifying assumptions regarding the

following:

(i) Whether the multi-span continuous beams are to be analyzed and

designed as a whole or as made up of independent beams with

appropriate end conditions

(ii) What will be the end conditions of the beam?

The decision would depend upon the following:

(1) Whether detailed calculations are required by the client (as in

case of public buildings) for future/office record.

(2) Whether the client requires only result in the form of schedules

of members as in case of residential buildings constructed by

private owners or builders.

(3) What is the accuracy required? It depends upon the importance

of the building and magnitude and repetitious nature of work.



For example, if it is to be used for a big residential complex with large number

of such units, then small excess of concrete and/or steel that may occur by using

simplifying assumption in design of one unit can lead to appreciable increase in

overall cost of materials in the entire big scheme.

The decisions regarding the assumptions made for the end conditions of the

beam materially affects the design procedure and designs itself.

Bearing the above points in mind, the decision has to be taken very carefully

whether to use the methods of structural analysis or simplifying assumptions and

approximations. A beam may be assumed as simply supported at discontinuous end

for simplicity on safer side, simultaneously taking care to provide steel at top at least

equal to 1/3rd

the mid-span steel to account for partial fixity developed.

For approximate method, the beams may be categorized on the basis of end

conditions as follows:

5.2 CATEGORY:

(1) Beam simply supported at both ends and carrying only UDL. (2) Beam simply supported at one end and continuous at the other end

and carrying UDL. (3) Beam continuous at both ends and carrying UDL only. (4) Miscellaneous beams such as overhanging beams, beams with any end

condition but carrying unusual loading like UDL over part of the length of beam, continuous beams with abnormally unequal spans etc.

The beams under each category may further be divided into different groups

on the basis of approximate equality of spans and loads. For beams with uniform

cross section and having the same end conditions the equality of spans may be

assumed when they do not differ more than 15% of the longest.

Types of Beams:

Designer has to decide whether the section of the beam is going to act as

rectangular or L or T-beam. A single span beam supported on masonry wall can be

considered as simply supported beam. It has zero moments at ends and sagging (+ve)

moment throughout. If slab is cast over it monolithically, the slab is on compression

side. Hence when beam bends part of slab acts as flange of the beam in resisting

bending moment. If the slab is on both sides, it becomes T-beam and if it is only on

one side it is L-beam.

If the beam is part of a framed structure or is continuous over a number of

supports, it will be having sagging (+ve) moment in mid-span and hogging (-ve)

moment near the supports. If as usual slab is on the top of the beam and is cast



monolithically with beam, the mid-span section of the beam becomes flanged section.

At interior supports, the flange is on tension side and hence will not assist in resisting

moment. In such cases the beam is to be designed as a rectangular section for negative

moment.

The designer has to decide whether the section is to be designed as Singly reinforced or Doubly reinforced. For this the depth of balanced section may be

found. If this depth cannot be permitted from the consideration of head room

requirement or from architectural consideration then the section is to be designed as

doubly reinforced. Otherwise it may be designed as singly reinforced.

Beam Section:

The cross-sectional dimensions of the beam consist of fixing breadth and

depth of the beam. The breadth of the beam is generally kept equal to the thickness of

the wall to avoid offset inside the room. It shall not exceed the width of the column

for effective transfer of load from beam to column. The minimum width of beam shall

be 200 mm to meet the requirements of fire resistance of 0.5 hours. (See fig.1 of IS:

456 – 2000).

FIG5.2

The depth of the beam is taken between L/10 to L/16. The types of beams

having different sections are kept minimum to facilitate reuse work. Even in some

cases, especially in residential buildings, the depth of the beam is provided equal to

the difference between the top of the floor and top of the door/ window. The

advantages are there is no need to provide lintel, the depth of the formwork remains

the same so that they can be reused and the top of the formwork being at the same

level there is considerable saving in labor.



FIG 5.3 Stress - strain Diagrams

5.3 ASSUMPTIONS:

The analysis and design of a reinforced concrete section for flexure is based

on the following assumptions. (IS: 456 – 2000, Clause 38.1)

(i) Plane sections normal to the axis remains plane after bending.

(ii) The maximum strain in concrete at outermost compression fiber is taken as

0.0035 in bending regardless of strength of concrete.

(iii) The tensile strength of concrete is ignored.

(iv) The relationship between stress-strain distributions in concrete is assumed

to be parabolic as shown in fig below. Compressive strength of concrete in

the structure (size effect) is assumed to be 0.67 times the characteristic strength of concrete. The partial safety factor γm equal to 1.5 is applied

to the strength of concrete in addition to it. Therefore, the design

compressive strength of concrete is 0.67 fck/1.5 = 0.446 fck. (v) The stress in reinforcement is derived from the representative stress-strain

curve for the type of steel used as shown in fig. The partial safety factor γm

equal to 1.15 is applied to the strength of reinforcement. Therefore, the

design strength of steel is fy/1.15 = 0.87 FY.

(vi) The maximum strain in tension reinforcement in the section at failure

should not be less than the

(FY/ 1.15Es) + 0.002 Where FY = Characteristic strength of steel

Es = Modulus of elasticity of steel



Analysis of Singly Reinforced sections:

If the reinforcing bars are provided only on tension side in the beam section, it

is called as singly reinforced beams.

Consider a simply supported beam subjected to bending under factored loads.

Since plane sections are assumed to remain plane before and after bending, strain is

proportional to distance from the neutral axis. Above the neutral axis the entire cross

section is in compression and below the neutral axis, the cross section is in tension.

All the tensile stresses are assumed to be resisted by steel bars as the tensile strength

of concrete is ignored. The resultant tensile force, thus acts at the centroid of

reinforcing bars.

Effective Depth:

Effective depth of a beam is the distance between the centroid of tension

reinforcement and the maximum compression fibre, excluding thickness of finishing

material placed monolithically with the member.

Effective depth, d = D – clear cover – ϕ/2 Where D= Gross depth or overall depth.

Φ= Diameter of the bar.

Effective span:

For calculation of bending moment and shear force, effective span is to be

considered. IS: 456 Clause No.22.2 specifies effective span, various cases as given

below:

(i) Simply supported beams or slabs:

Effective span = clear span + effective depth

Or

Centre to centre distance between the supports, whichever is less.

(ii) Continuous beams or slabs:

(a) If width of support, w < 1/12th

of clear span, the effective span

is same as for simply supported case.

(b) For end span with one end simply supported and other end

continuous.

Effective span = clear span + d/2

Or

Clear span + (1/2) x width of simple support.

Whichever is less.

(iii) In case of roller supports:

Effective span = distance between the supports.

(iv) Cantilevers:

Effective span = clear span + d/2



(v) Overhanging portion of continuous beams:

Effective span = centre of support to free end.

(vi) Frames:

(vii) Effective span = centre to centre distance.

Depth of Neutral Axis (xu):

The depth of neutral axis can be obtained by considering the equilibrium of

internal forces of compression and tension.

Force of compression C = Average stress x area of beam in compression

= 0.36 fck b xu

Force of tension T = Design yield stress x area of steel

= 0.87 fy Ast

Force of compression should be equal to force of tension

Xu = (0.87 FY Ast) / (0.36 fck b xu)

Lever Arm (z):

The forces of compression and tension form a couple. The distance between

the lines of action of compression and tension forces is called as lever arm.

Lever arm, z = d – 0.42 xu

5.4 MODES FAILURES / TYPES OF SECTIONS:

A reinforced concrete member is considered to have failed when the strain in

concrete in extreme compression fiber reaches its ultimate value equal to 0.0035.

1. Balanced section: when the maximum strains in steel and concrete reach their

maximum values simultaneously, the section is known as a balanced section.

The percentage of steel provided for balanced section is called as limiting

percentage of steel.

xu = xu, max.

2. Under reinforced section (tension failure or ductile failure): when the amount

of steel in a section is less than that required for a balanced section, the section

is called as under reinforced section.

In under reinforced sections, the strain in concrete does not reach its maximum

value while the strain in steel reaches its maximum value. The position of

neutral axis will shift upwards to maintain equilibrium between force of

compression and tension.



xu < xu, max

So failure of the section is initiated by steel reaching its yield value. Before

failure, beam undergoes substantial deflection excessive cracking of concrete

giving sufficient warning of impending failure. For this reason and from

economy point of view the under reinforced sections are designed. IS code

prefers design of under reinforced sections and at the most it can be a balanced

section (xu ≤ xu, max).

3. Over Reinforced section (compression Failure or brittle failure):

When the amount of steel is more than that required for balanced section, the

section is called over reinforced section.

In over reinforced sections, the strain in concrete reaches its ultimate value

before steel reaches its yield value. Neutral axis shift downwards to maintain

equilibrium

xu > xu, max

hence, in over reinforced sections sudden failure occurs by crushing of

concrete out giving any warning. So this type sections should be avoided. IS

code recommends avoid of over reinforced sections.

Maximum Depth of Neutral Axis ( xu, max):

The maximum depth of neutral axis is limited to ensure that tensile steel will

reach its yield stress before concrete fails in compression, thus brittle failure

(sudden failure with less alarming deflection) is avoided.

From strain diagram of IS: 456

𝑥𝑢 ,𝑚𝑎𝑥

0.0035=

𝑑 − 𝑥𝑢 ,𝑚𝑎𝑥

(087 𝑓𝑦/E𝑠) + 0.02

𝑥𝑢 ,𝑚𝑎𝑥

𝑑=

0.0035

087𝑓𝑦E𝑠

+ 0.0055

It may be noted that 𝑥𝑢 ,𝑚𝑎𝑥 is dependent on grade of steel only.



fy (N/mm2) 𝐱𝐮,𝐦𝐚𝐱

𝐝

250

0.53

415

0.48

500

0.46

Table 5.1 Values of 𝒙𝒖,𝒎𝒂𝒙

𝒅 for different grades of steel

Grade of concrete

Fe 250 steel Fe 415 steel Fe 500 steel

General 0.148fckbd

2 0.138 fckbd

2 0.133 fckbd

2

M20 2.96 bd

2 3.45 bd2 3.33 bd

2

M25 3.7 bd

2 3.45 bd

2 3.33 bd

2

Table 5.2 Limiting Moment of Resistance for Singly Reinforced Rectangular Sections

Limiting Percentage of Steel:

The percentage of tensile reinforcement corresponding to the limiting

moment resistance is known as limiting percentage of steel. It can be

obtained by equating force of tension and compression.

0.87𝑓𝑦𝐴𝑠𝑡 ,𝑙𝑖𝑚 = 0.36𝑓𝑐𝑘𝑏𝑥𝑢 ,𝑚𝑎𝑥

𝐴𝑠𝑡 ,𝑙𝑖𝑚 = 0.36𝑓𝑐𝑘𝑏𝑥𝑢 ,𝑚𝑎𝑥 /0.87𝑓𝑦

Limiting percentage of steel 𝑃𝑡 ,𝑙𝑖𝑚 = 𝐴𝑠𝑡 ,𝑙𝑖𝑚

𝑏𝑑 𝑥100

=0.36𝑓𝑐𝑘0.87𝑓𝑦

𝑥𝑥𝑢 ,𝑚𝑎𝑥

𝑑𝑥100

The limiting values of tensile reinforcement percentage corresponding

to different grades of concrete and steel in a singly reinforced rectangular

beam are given below.



Grade of concrete

Percentage of tensile steel

Fe 250 Fe 415 Fe 500

M15 1.32 0.72 0.57

M20 1.76 0.96 0.76

M25 2.20 1.19 0.94

Table 5.3 Limiting Percentage of steel for Singly Reinforced sections.

5.5 GENERAL DESIGN REQUIREMENTS FOR BEAMS:

1. Effective span: The effective span of a simply supported beam shall be taken as clear

span plus effective depth of the beam or center to center distance between

the supports whichever is less.

The effective span of a cantilever shall be taken as its length to the face

of the support plus half the effective depth except where it forms the end

of a continuous beam where the length to the centre of support shall be

taken.

2. Limiting stiffness: The stiffness of beams is governed by the span to depth ratio. As per

Clause 23.2 of IS: 456 for spans not exceeding 10 m, the span to effective

depth ratio should not exceed the limits (basic values) given below:

Cantilever – 7

Simply supported – 20

Continuous – 26

For spans above 10 m, the above values may be multiplied by 10/span

in m.

Depending on the amount and type of steel, the above values shall be

modified by multiplying with the modification factors obtained from fig.4

& 5 of IS: 456.

3. Minimum Reinforcement: The minimum area of tension reinforcement should not be less than the

following (Clause 26.51 of IS: 456) 𝐴𝑠𝑡

𝑏𝑑=

0.85

𝑓𝑦

This works out only 0.2% for Fe 415 steel and 0.34% for Fe 250 steel.



4. Maximum Reinforcement: The maximum area of tension reinforcement should not exceed 4% of

the gross cross sectional area (Clause 26.51 of IS: 456) Ptmax < 0.04 bD

Where D = gross depth of the beam

5. Spacing of Bars: The horizontal distance between two parallel main reinforcing bars

shall usually be not less than the greatest of the following:

(a) Diameter of the bar if the diameters are equal.

(b) Diameter of the largest bar if the bars are unequal

(c) 5 mm more than the nominal maximum size of the aggregate

When there are two or more rows of bars, the bars shall be vertically in

line and the minimum vertical distance between the bars shall be 15 mm,

two-thirds of nominal maximum size of aggregate or the maximum size of

the bars whichever is greater.

The maximum spacing of bars in tension for beams is taken from

Table-15 of IS: 456 depending on the amount of redistribution carried

out in analysis and fy.

6. Cover to Reinforcement: Reinforcement shall have concrete cover of thickness as follows:

(a) At each end of reinforcement bar not less than 25 mm nor less

than twice the diameter of such bar.

(b) For longitudinal reinforcing bar in beam, not less than 25 mm

nor less than the diameter of such bar.

7. Side Face Reinforcement: Where the depth of the beam exceeds 750 mm, side face reinforcement

shall be provided along the two faces. The total area of such reinforcement

shall not be less than 0.1% of the beam area and shall be distributed

equally on two faces at a spacing not exceeding 300 mm or width of the

beam whichever is less.

Use of SP16 for Design and Analysis of Singly Reinforced Beams:

The Indian standards Institution’s special publication SP16, Design aids for

Reinforced concrete of IS: 456, contains a number of charts and tables for design of

reinforced concrete members.

The following are the data presented in SP16 for design and analysis singly

reinforced beams.



(i) Tables 1 to 4 gives the percentage steel required for various values

of ( 𝑀𝑢

𝑏𝑑2) and fy for concrete grades fck = 15, 20, 25 and 30

(ii) Charts 1 to 18 gives the moment of resistance per meter width for

varying depths (5 to 80 cm) and varying percentage of steel, for

various values of

fck= 15 & 20 using steel grades of fy= 250,415 & 500.

Doubly Reinforced Beams:

Beams which are reinforced in both compression and tension asides are called

as doubly reinforced beam. These beams are generally provided when the dimensions

of the beam are restricted and it is required to resist moment higher than the limiting

moment of resistance of a singly reinforced section. The additional moment of

resistance required can be obtained by providing compression reinforcement and

additional tension reinforcement.

Situations under which doubly reinforced beams are used:

1. When the depth of the beam is restricted due to architectural or any

construction problems.

2. At the supports of a continuous beam where bending moment changes its

sign.

3. In precast members (during handling bending moment changes its sign).

4. In bracing members of a frame due to changes in the direction of wind

loads.

5. To improve the ductility of the beams in earth quake regions.

6. To reduce long term deflections or to increase stiffness of the beam.

Analysis of Doubly Reinforced Beams

Doubly Reinforced section can be considered to be composed of two sections

given below.

(a) A singly reinforced section with Mu,lim

(b) A section with compression steel and additional tension steel to resist

additional moment 𝑀𝑢2 = 𝑀𝑢 − 𝑀𝑢 ,𝑙𝑖𝑚 , i.e., a steel beam without

concrete.

Hence, moment of resistance of doubly reinforced beam.

𝑀𝑢 = 𝑀𝑢 ,𝑙𝑖𝑚 + 𝑀𝑢2

Where, 𝑀𝑢 ,𝑙𝑖𝑚 = Limiting moment of resistance of singly reinforced section.

𝑀𝑢2 = Additional moment of resistance to be resisted by compression steel and

additional tension steel.



The lever arm for the additional moment of resistance 𝑀𝑢2 is equal to the

distance between the centroid of the tension and compression reinforcements,

i.e., d-d,. Hence the additional moment of resistance is given by

𝑀𝑢2 = 𝑓𝑠𝑐 𝐴𝑆𝐶 𝑑 − 𝑑′ = 0.87 𝑓𝑠𝑐 𝐴𝑠𝑡2 𝑑 − 𝑑′

Where,

fsc = stress in compression steel

d’ = Distance of centroid of compression reinforcement from the maximum

compression fiber (effective cover to compression reinforcement)

Asc= Area of compression reinforcement required to resist Mu2

Ast2 = Area of additional tensile reinforcement to balance compression steel

Ast1= Area of tensile reinforcement for a balanced singly reinforced section

1. Neutral Axis: The depth of neutral axis can be calculated by equating total force of

compression to total force of tension. Compression force of concrete 𝐶𝑐 = 0.36 𝑓𝑐𝑘 𝑏 𝑥𝑢

Compressive forces in compression steel 𝐶𝑠 = 𝑓𝑠𝑐 𝐴𝑠𝑐

Tensile force 𝑇 = 0.87 𝑓𝑦 𝐴𝑠𝑐

Equate force of Compression with Tension

𝐶𝑐 + 𝐶𝑠 = 𝑇

Therefore, 𝑥𝑢 = 0.87 𝑓𝑦 𝐴𝑠𝑐 − 𝑓𝑠𝑐 𝐴𝑠𝑐

0.36 𝑓𝑐𝑘 𝑏

2. Ultimate Moment of Resistance:

The ultimate Moment of resistance of doubly reinforced section is

given by:

𝑀𝑢 = 𝑀𝑢1 + 𝑀𝑢2

𝑀𝑢 = 0.36 𝑓𝑐𝑘 𝑏 𝑥𝑢 𝑑 − 0.42𝑥𝑢 + 𝑓𝑠𝑐 𝐴𝑠𝑐 𝑑 − 𝑑′

When xu > xu,max is limited to xu,max

𝑀𝑢 = 0.36 𝑓𝑐𝑘 𝑏 𝑥𝑢 ,𝑚𝑎𝑥 𝑑 − 0.42𝑥𝑢 ,𝑚𝑎𝑥 + 𝑓𝑠𝑐 𝐴𝑠𝑐 𝑑 − 𝑑′

3. Area of Compression steel: Additional moment of resistance 𝑀𝑢2 = 𝑓𝑠𝑐 𝐴𝑠𝑐 𝑑 − 𝑑′

𝐴𝑠𝑐 = 𝑀𝑢2

𝑓𝑠𝑐 𝑑 − 𝑑′

The maximum area of compression reinforcement shall not exceed 0.04 bD

i.e., 4% of gross cross sectional area.



4. Area of Tension steel: The limiting moment of resistance of singly reinforced section is given

by:

M𝑢 ,𝑙𝑖𝑚 = 0.87 𝑓𝑦A𝑠𝑡1(d − 0.42𝑥𝑢 ,𝑚𝑎𝑥 )

A𝑠𝑡1 =M𝑢 ,𝑙𝑖𝑚

0.87 𝑓𝑦(d − 0.42𝑥𝑢 ,𝑚𝑎𝑥 )

Additional area of tensile steel (Ast1) can be calculated by equating the

compressive force in compression steel and tensile force in additional tension

steel.

0.87 𝑓𝑦A𝑠𝑡2 = 𝑓𝑠𝑐A𝑠𝑐

A𝑠𝑡2 =𝑓𝑠𝑐A𝑠𝑐

0.87 𝑓𝑦

Ast2 can also be calculated by using

M𝑢2 = 0.87 𝑓𝑦A𝑠𝑡2(d − d′)

A𝑠𝑡2 =M𝑢2

0.87 𝑓𝑦(d − d′)

Total area of tension steel A𝑠𝑡 = A𝑠𝑡1 + A𝑠𝑡2

Stress in Compression Steel:

If εsc is the strain at the level of compression steel, from the strain diagram at

failure

𝜀𝑠𝑐x𝑢 − 𝑑′

=0.0035

x𝑢

Knowing the strain, the stress in compression steel can be obtained from

stress-strain curve of corresponding steel or from Table-A of SP-16 which is given

below

Stress level Fe415 Fe500

Strain Stress N/mm2 Strain Stress N/mm2

0.80fyd 0.00144 288.7 0.00174 347.8

0.85fyd 0.00163 306.7 0.00195 369.6

0.90fyd 0.00192 324.8 0.00226 391.3

0.95fyd 0.00241 342.8 0.00277 413.0

0.975fyd 0.00276 351.8 0.00312 423.9

1.0fyd 0.00380 360.9 0.00417 434.8



Table 5.4 Salient points on the design stress strain curve for cold worked bars (Table-A SP-16)

Note: Linear interpolation may be done for intermediate values

fyd = Design yield strength = 0.87fy

So fsc and xu are interrelated and cannot be found directly. Trial and error

procedure should be adopted.

For mild steel direct relation can be established between stress and strain since

the idealized stress strain curve is linear up to fy and then it is constant equal to fy

𝑓𝑠𝑐 = starin x E𝑠

Substituting the value of strain and E for steel = 2x105

N/mm2

= 0.0035 (1-d’/xu) 2x105

= 700(1-d’/xu), subjected to a maximum of 0.87fy

Stress in Compression Steel (fsc) based on d’/d :

As per SP-16, in designing doubly reinforced beam (by assuming xu= xu,max)

the following table gives the values of fsc for different values of d’/d.

Grade of Steel d'/d

0.05 0.10 0.15 0.20

Fe415 355 353 342 329

Fe500 424 412 395 370

Table 5.5 Stress in Compression Steel (fsc) N/mm2 in Doubly Reinforced beams with cold worked bars (Table-F in SP-16) when d’/d < 0.2

For d’/d < 0.2, fsc for mild steel is 0.87fy

Use of Design Aids SP-16:

SP-16 design tables 45 to 56 gives the percentage of tension and compression

reinforcement (Pt and Pc) for different ratios of (d’/d) varying from 0.05 to 0.20 and

for various grades of concrete (fck= 15 to 30 N/mm2) and different grades of steel (fy=

250, 415 and 500 N/mm2) covering the moment of resistance factor (Mu/bd

2) varying

from 2.24 to 8.30



5.6 DESIGN OF BEAMS USING SP 16

Design of plinth beams:

Beam no's 1001, 1007, 1009,1014, 1015, 1020, 1021, and 1026

Length = 3000 mm

Cross section = 300x400 mm

Clear cover = 25 mm

Effective depth (d) = 375 mm

Max B.M @ Start support = 41.037 KN-m

Max B.M @ Mid span = 15.561 KN-m

Max B.M @End support = 41.749 KN-m

% of Ast @ Start support(-ve)

Mu

bd2 = 41.037 x 106

300x3752

= 0.97 KN/m2

Limiting moment of resistance

Mu,lim = 0.138x fckxbxd2

= 0.138 x20x300x3752 = 117 KN-m

Xu,max = 0.48 x d = 0.48 x 375 = 180 mm

Actual moment is less than the limiting moment.

Referring to Table no 2 of SP 16 for M20 and Fe415

From linear interpolation we get the actual %pt

𝑀𝑢

𝑏𝑑2 %pt

0.95 0.280

1.00 0.295

0.7822 0.287

Area of steel = pt xbxd

100=

0.287 x 300x 375

100



= 322 mm2

Using 12 mm dia bars

No of bars = 322

x1224π = 2.84 ~ 3 no’s

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 15.561 x 106

300x3752

= 0.37 KN/m2



= 0.138 x20x300x3752 = 117 KN-m

Xu, max = 0.48 x d = 0.48 x 375 = 180 mm



%pt = 0.085

Area of steel = 𝑝𝑡 𝑥𝑏𝑥𝑑

100=

0.085 x 300x 375

100

= 95.625 mm2

Check for Area of steel

As per clause no 26.5.1.1 of IS 456-2000, min reinforcement is given by

𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no’s

% of Ast @End support

𝑀𝑢

𝑏𝑑2 = 41.749 x 106

300x3752



= 0.99 KN/m2



= 0.138 x20x300x3752 = 117 KN-m

Xu,max = 0.48 x d = 0.48 x 375 = 180 mm



From linear interpolation we get the actual %pt

𝑀𝑢

𝑏𝑑2 %pt

0.95 0.280

1.00 0.295

0.92 0.292


100=

0.292 𝑥 300𝑥 375

100

= 328 mm2


No of bars = 328

x1224π = 2.90 ~ 3 no’s

Beam no's 1002,1006, 1010, 1013, 1016, 1017, 1022, and 1025

Length = 3700 mm


Clear cover = 25 mm








Mu

bd2 = 48.839 x 106

300x3752

= 1.16 KN/m2


Percentage of steel = 0.384 %


100=

0.384 x 300x 375

100

= 389 mm2


No of bars = 389

x1224π = 3.44 ~ 4 no's

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 19.181 x 106

300x3752

= 0.45 KN/m2


%pt = 0.128


100=

0.128 x 300x 375

100

= 144 mm2



𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no's




𝑀𝑢

𝑏𝑑2 = 49.323x 106

300x3752

= 1.17 KN/m2


percentage of reinforcement (%pt) = 0.349 %


100=

0.349 𝑥 300𝑥 375

100

= 393 mm2


No of bars = 393

x1224π = 3.47 ~ 4 no’s

Beam no's 1003, 1011, 1012, 1017, 1018, 1023, 1024

Length = 3550 mm


Clear cover = 25 mm






Mu

bd2 = 48.911 x 106

300x3752

= 1.16 KN/m2




100=

0.346 x 300x 375

100

= 389 mm2




No of bars = 389

x1224π = 3.44 ~ 4 no's

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 17.581 x 106

300x3752

= 0.42 KN/m2


%pt = 0.118


100=

0.118 x 300x 375

100

= 133 mm2



𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no's


𝑀𝑢

𝑏𝑑2 = 48.598 x 106

300x3752

= 1.15 KN/m2




100=

0.344 𝑥 300𝑥 375

100

= 387 mm2




No of bars = 387

x1224π = 3.42 ~ 4 no’s

Beam no's 1004, 1030, 1034

Length = 1650 mm


Clear cover = 25 mm






Mu

bd2 = 35.415 x 106

300x3752

= 0.84 KN/m2




100=

0.254 x 300x 375

100

= 276 mm2


No of bars = 276

x1224π = 2.44 ~ 3 no's

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 18.726 x 106

300x3752

= 0.45 KN/m2


%pt = 0.128




100=

0.128 x 300x 375

100

= 142 mm2



𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no's


𝑀𝑢

𝑏𝑑2 = 26.626 x 106

300x3752

= 0.63 KN/m2


percentage of reinforcement (%pt) = 0.182%


100=

0.182 𝑥 300𝑥 375

100

= 204 mm2


𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no’s

Beam no's 1005,1008

Length = 1900 mm




Clear cover = 25 mm






Mu

bd2 = 32.145 x 106

300x3752

= 0.76 KN/m2




100=

0.221 x 300x 375

100

= 249 mm2


No of bars = 249

x1224π = 2.20 ~ 3 no's

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 15.876 x 106

300x3752

= 0.38 KN/m2


%pt = 0.107


100=

0.107 x 300x 375

100

= 120 mm2





𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no's


𝑀𝑢

𝑏𝑑2 = 34.632 x 106

300x3752

= 0.82 KN/m2




100=

0.239 𝑥 300𝑥 375

100

= 269 mm2


No of bars = 269

x1224π = 2.37 ~ 3 no’s

Beam no's 1027, 1028, 1031, 105, 1036

Length = 3650 mm


Clear cover = 25 mm








Mu

bd2 = 49.395 x 106

300x3752

= 1.17 KN/m2




100=

0.350 x 300x 375

100

= 394 mm2


No of bars = 394

x1224π = 3.38 ~ 4 no's

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 19.794 x 106

300x3752

= 0.47 KN/m2


%pt = 0.134


100=

0.134 x 300x 375

100

= 150 mm2



𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no's




𝑀𝑢

𝑏𝑑2 = 52.575 x 106

300x3752

= 1.25 KN/m2




100=

0.374 𝑥 300𝑥 375

100

= 421 mm2


No of bars = 421

x1224π = .3.72 ~ 4 no’s

Beam no's 1044, 1045, 1046, 1047, 1048, 1049, 1050

Length = 4150 mm


Clear cover = 25 mm






Mu

bd2 = 59.694 x 106

300x3752

= 1.41 KN/m2




100=

0.431 x 300x 375

100

= 484 mm2




No of bars = 484

x1224π = 4.28 ~ 5 no's

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 19.794 x 106

300x3752

= 0.47 KN/m2


%pt = 0.134


100=

0.134 x 300x 375

100

= 150 mm2



𝐴𝑠𝑡

𝑏𝑑 =

0.85

𝑓𝑦

Ast = 230 mm2


No of bars = 230

x1224π = 2.03 ~ 3 no's


𝑀𝑢

𝑏𝑑2 = 52.575 x 106

300x3752

= 1.25 KN/m2




100 =

0.431 𝑥 300𝑥 375

100

= 421 mm2




No of bars = 421

x1224π = 3.72~ 4 no’s

Beam no's 1029, 1032, 1051

Length = 2000 mm


Clear cover = 25 mm






Mu

bd2 = 44.458 x 106

300x3752

= 1.05 KN/m2




100=

0.312 x 300x 375

100

= 351 mm2


No of bars = 351

x1224π = 3.10 ~ 4 no's

% of Ast @ mid span

𝑀𝑢

𝑏𝑑2 = 30.724 x 106

300x3752

= 0.73 KN/m2


%pt = 0.211




100=

0.211 x 300x 375

100

= 237 mm2


No of bars = 237

x1224π = 2.03 ~ 3 no's

% of Ast @End support45.315

𝑀𝑢

𝑏𝑑2 = 45.315 x 106

300x3752

= 1.07 KN/m2




100 =

0.319 𝑥 300𝑥 375

100

= 359 mm2


No of bars = 359

x1224π = 3.17~ 4 no’s

Design of Beams (1st, 2nd, 3rd & 4th floors)

Beam no Length (m)

Position of Max B.M

Max B.M (KN-m) Reinforcement

2001, 2007, 2009, 2014,

2015, 2022, 2023, 2030,

3001, 3007, 3009, 3014,

3015, 3022, 3023,3030,

4001, 4007, 4009, 4014,

4015, 4022, 4023, 4030,

50001, 5007, 5009, 5014,

5015, 5022, 5023, 5030

3.00

@ Start

support(-ve) 60.47 #3-Φ16

@ Mid span

(+ve) 21.253 #3 -Φ12

@ End

support(-ve) 60.963 #3-Φ16

2002, 2006, 2010, 2013,

3002, 3006, 3010, 3013,

4002, 4006, 4010, 4012,

5002, 5006, 5010, 5013

3.70

@ Start

support(-ve) 65.963 #3-Φ16

@ Mid span

(+ve) 27.412 #3-Φ12



@ End

support(-ve) 67.464 #3-Φ16

2003, 2011, 2012, 2018,

2019, 2026, 2027, 3003,

3011, 3012, 3018, 3019,

3026, 3027, 4003, 4011,

4012, 4018, 4019, 4026,

4027, 5003, 5011, 5012,

5018, 5019, 5026, 5027

3.55

@ Start

support(-ve) 83.471 #4-Φ16

@ Mid span

(+ve) 30.701 #3-Φ12

@ End

support(-ve) 81.434

#4-Φ16

2004, 2034, 2038,3004,

3034, 3038,4004, 4034,

4038, 5004, 5034, 5038

1.65

@ Start

support(-ve) 48.503

#3-Φ16

@ Mid span

(+ve) 40.553 #4-Φ12

@ End

support(-ve) 35.313 #3-Φ12

2005, 2008, 3005, 3008,

4005, 4008, 5005, 5008

1.90

@ Start

support(-ve) 46.531

#4-Φ12

@ Mid span

(+ve) 31.613 #3-Φ12

@ End

support(-ve) 48.304 #4-Φ12

2016, 2021, 2024, 2029,

3016, 3021, 3024, 3029,

4016, 4021, 4024, 4029,

5016, 5021, 5024, 5029

0.85

@ Start

support(-ve) 88.620 #4-Φ16

@ Mid span

(+ve) 31.885 #3-Φ12

@ End

support(-ve) 90.227 #4-Φ16

2017, 2020, 2025, 2028,

3017, 3020, 3025, 3028,

4017, 4020, 4025, 4028,

5017, 5020, 5025, 5028

2.85

@ Start

support(-ve) 72.414

#3-Φ16

@ Mid span

(+ve) 33.136 #3-Φ12

@ End

support(-ve) 72.969 #3-Φ16

2031, 2032, 2035, 2039,

2040, 3031, 3032, 3035,

3039, 3040, 4031, 4032,

4035, 4039, 4040, 5031,

5032, 5035, 5039, 5040

3.65

@ Start

support(-ve) 71.746 #4-Φ16

@ Mid span

(+ve) 28.99 #3-Φ12

@ End

support(-ve) 67.938 #3-Φ16

2033, 2036, 2037, 2051,

3033, 3036, 3037, 3051,

2.00

@ Start

support(-ve) 44.511

#4-Φ12



4033, 4036, 4037, 4051,

5033, 5036, 5037, 5051 @ Mid span

(+ve) 32.654 #3-Φ12

@ End

support(-ve) 45.356 #4-Φ12

2041, 2042, 2043, 3041,

3042, 3043, 4041. 4042,

4043, 5041, 5042, 5043

3.50

@ Start

support(-ve) 60.319 #3-Φ16

@ Mid span

(+ve) 30.414 #3-Φ12

@ End

support(-ve) 74.234 #4-Φ16

2044,2045, 2046, 2047,

2048, 2049, 20503044,

3045, 3046, 3047, 3048,

3049, 3050, 4044, 4045,

4046, 4046, 4047, 4048,

4049, 4050, 5044, 5045,

5046, 5047, 5048, 5049,

5050

4.15

@ Start

support(-ve) 91.337 #4-Φ16

@ Mid span

(+ve) 55.884 #3-Φ16

@ End

support(-ve) 97.419 #3-Φ16

Design of Roof Beams

Beam no Length (m)

Position of Max B.M

Max B.M (KN-m) Reinforcement

6001, 6007, 6009, 6014,

6015, 6023, 6030 3.00

@ Start

support(-ve) 24.96 #3-Φ12

@ Mid span

(+ve) 14.848 #3-Φ12

@ End

support(-ve) 25.236 #3-Φ12

6002, 6006, 6010, 6013 3.70

@ Start

support(-ve) 37.182 #3-Φ12



@ Mid span

(+ve) 20.325 #3-Φ12

@ End

support(-ve) 39.189 #3-Φ12

6003, 6011, 6012, 6018,

6019, 6026, 6027, 7001,

7005, 7006

3.55

@ Start

support(-ve) 70.503 #3-Φ16

@ Mid span

(+ve) 31.136 #3-Φ12

@ End

support(-ve) 71.122 #3-Φ16

6004, 6034, 6038, 7002,

7011

1.65

@ Start

support(-ve) 34.073 #3-Φ12

@ Mid span

(+ve) 20.634 #3-Φ12

@ End

support(-ve) 21.137 #3-Φ12

6005, 6008, 7003, 7004

1.90

@ Start

support(-ve) 26.206 #3-Φ12

@ Mid span

(+ve) 13.521 #3-Φ12

@ End

support(-ve) 14.139 #3-Φ12

6016, 6021, 6024, 6029 0.85

@ Start

support(-ve) 49.153 #3-Φ12

@ Mid span

(+ve) 14.921 #3-Φ12

@ End

support(-ve) 49.828 #3-Φ12

6017, 6020, 6025, 6028 2.85

@ Start

support(-ve) 37.860 #3-Φ12

@ Mid span

(+ve) 22.483 #3-Φ12

@ End

support(-ve) 38.337 #3-Φ12

6031, 6032, 6035, 6039,

6040

3.65

@ Start

support(-ve) 44.125 #3-Φ12



@ Mid span

(+ve) 20.730 #3-Φ12

@ End

support(-ve) 27.827 #3-Φ12

6033, 6036, 6037, 7009,

7010

2.00

@ Start

support(-ve) 21.499 #3-Φ12

@ Mid span

(+ve) 11.811 #3-Φ12

@ End

support(-ve) 26.053 #3-Φ12

6041, 6042, 6043 3.50

@ Start

support(-ve) 17.783 #3-Φ12

@ Mid span

(+ve) 25.230 #3-Φ12

@ End

support(-ve) 32.006 #3-Φ12

6044, 6045, 6046, 6047,

6048, 6049, 6050 4.15

@ Start

support(-ve) 32.224 #3-Φ12

@ Mid span

(+ve) 41.062 #3-Φ12

@ End

support(-ve) 42.507 #3-Φ12

Design of shear reinforcement:

The Following table shows the summary of all loads under gravity, seismic

and wind forces. Shear force acting on the member along the direction of Global Y.

The maximum shear force is acting on member no 5016 is 130.305 KN under

Ultimate load combination(12) and minimum shear force is acting on beam no 5021 is

-130.764 KN under Ultimate load combination (12).



Table 5.6 Summary of Beam End Forces from staad

Max Shear force (Vu) = 130.305 KN

Nominal shear stress τv= ( Vu)/bd = 1.58 N/mm2

From table no 61 of SP 16

Design shear strength of concrete τc = 0.438

From table no J of SP 16

Max shear stress τc,max = 2.8 N/mm2

Min percentage of tension reinforcement is 0.402%

As τv > τc shear reinforcement has to be designed

Shear resistance of concrete Vuc= τc.bd = 49 KN

Shear to be resisted by shear reinforcement

Vus = Vu- Vuc

= 81 KN

Using 6 mm, 2 legged steel stirrups

Asv = 2 x 𝜋

4 x6

2 = 56.54 mm

2



Sv = 0.87fy .Asv .d

Vus

= 151.1 mm

Max allowed spacing = 0.75d = 281.25 mm

= 300 mm whichever is less

Hence provide 2 legged 6 mm stirrups @ 150 mm c/c at ends and 2 legged 6 mm

stirrups @ 200 mm c/c



6. DESIGN OF COLUMN

6.1 INTRODUCTION:

Concrete is strong in compression and steel is strong in tension. Longitudinal steel

rods are always provided to assist the direct loads. A minimum area of longitudinal

steel is provided in the column, to resist tensile stresses caused by some eccentricity

of the vertical loads. There is also an upper limit of amount of reinforcement in R.C.

columns, because higher percentage of steel may cause difficulties in placing and

compacting of concrete. Longitudinal reinforcing bars are tied laterally by ties or

stirrups at suitable interval, so that the bars do not buckle.

The design of column necessitates determination of loads transferred from

beam at different floors levels. Loads are transferred from slabs to beams and then to

columns. Hence, slabs and beams are normally designed prior to the design of

columns. This method is called as Exact method which enables one to assess the loads

on columns more accurately and thereby the design of columns becomes realistic and

economical.

However, in practice, many times situations arise which require the design of

columns and footings are required to be assessed using judgment based on past

experience and using approximate methods. The loads on the columns can be

determined approximately on the basis of floor area shared by each column. These

loads are normally calculated on higher side so that they are not less than the actual

loads transferred from slabs/beams. In such cases, the design of column is likely to be

uneconomical

The design procedure using both these approaches of column load calculation

has been explained.

6.2 DESIGN PROCEDURE:

Design of columns involves following steps:

(1) Categorization of columns:

(a) Category – I: Internal columns or Axially Loaded Columns.

(b) Category – II: Side columns or Columns subjected to Axial Load

and Uniaxial Bending.

(c) Category - III: Corner Column or Columns subjected to Axial Load

and Biaxial Bending.

(2) Computation of Loads on Columns

(3) Calculation of Moments in Columns

(4) Determination of Effective Length and Type of Column – Short or Long

(5) Grouping of Columns

(6) Design of Column Section



(1) Categorization of Columns:

Categorization of columns is extremely helpful because the procedure for

design of column in each of the three categories is different.

The columns shall be first divided into the following three categories:

(I) Category – I: Internal columns or Axially Loaded Columns.

Internal columns carrying beams either in all four directions or only in opposite

directions are predominantly subjected to axial compression because moments

due to loads on beams on opposite sides balance each other. Judgment should be

used to place a column under this category because if span and/ or loads on

beams on opposite sides vary appreciably the beam moments on opposite sides

may not balance each other and the column will be subjected to bending

moment, and it will be required to be placed under the second category.

Structurally, these columns can be termed as Axially Loaded Columns.

Therefore, they require practically very little or no allowance in axial load.

(II) Category – II: Side Columns or Columns subjected to Axial Compression and

uniaxial bending. Columns along the sides of a building, which carry beams

either in three orthogonal directions or a single beam in one direction, are

subjected predominantly to axial load and uniaxial bending due to unbalanced

opposite directions balance each other provided their spans and loads on them

are approximately equal. If such columns are to be designed as axially loaded

columns using approximate method, the axial load is required to be increased to

account for the effect of uniaxial bending in column. The load thus arrived is

called Equivalent axial load for the purpose of design of column section.

(III) Category – III: Corner Columns or Columns subjected to Axial Compression

and Biaxial Bending. Corner Columns or the columns which carry beams in two

perpendicular directions are subjected to biaxial bending due to beams in

orthogonal directions. They require large increase in axial load to account for

the effect of biaxial bending for obtaining an Equivalent axial load.

A column is an important component of R.C. structures. Columns are

compression member, the effective length of which exceeds three times the least

lateral dimension. A compression member with effective length less than three times

the least lateral dimension is called pedestal.

A column is generally defined as a member carrying direct axial load which

causes compressive stresses of such magnitude that these stresses largely control its

design. A column or strut is a compression member. Difference between columns and

strut is that column transfers the load to footing and strut transfers the load to some

other member as in case of compression members of trusses. A column is considered

as short, if its effective length to least lateral dimension is less than 12. If the ratio



exceeds 12, the column is considered is treated as long or slender. A member

carrying mainly axial load is vertical is termed as column. If the axial load is inclined

or horizontal, it is termed as strut.

Depending upon the structural or architectural requirements columns are

designed of various shapes. Columns positioning completely depends on the

architectural plan. In some cases floating columns are assigned for the architectural

requirements of the plan and to provide the necessary open space depending upon the

requirements of the architectural plan.

Types of columns shapes considered:

Circular

Rectangular

Square

Hexagonal

6.3 LENGTH OF COLUMNS:

The unsupported length of column is taken as clear distance between ends restrains.

1. Flat slab construction:

It is clear distance between the floor and the lower extremity of the capital,

the drop panel or slab whichever is less.

L

Fig6.1 Length in flat slab construction

2. Beam and slab construction:

In this case l is the clear distance between the floor and underside of the

shallow beam framing into the column in each direction at next higher level.

FLAT SLAB

FLAT SLAB FLAT SLAB

C

O

L

U

M

N

C

O

L

U

M

N

C

O

L

U

M

N

Column

capital

Drop

panel



lx ly

FIG6.2 Length in beam and slab construction

3. Columns restrained laterally by struts:

In these cases unsupported length (l) is clear distance between

consecutive struts in each vertical plane, provided that two struts meet column

approximately at the same level and the angle between the vertical planes shall

not vary more than 300 from a right angle.

STRUT Column

L

Strut

COLUMN

FIG 6.3 Elevation Plan

4. Columns restrained laterally by struts using brackets at junctions:

In this case unsupported length l shall be the clear distance between the

floor and lower edge of the bracket, provided that the bracket width equals that

of the beam or strut and at least half of the column.

BEAM BEAM

Strut



BRACKET

COLUMN

l

FIG 6.4 Length of columns restrained laterally using brackets

Functions of longitudinal and transverse reinforcements in a column:

a. Longitudinal reinforcement:

To share the vertical load, thereby reducing the overall size of the

column

To resist tensile stresses caused in the column due to

1. Eccentric load

2. Moment

3. Transverse load

To prevent sudden brittle failure of the column

To reduce the effects of creep and shrinkage due to sustained loading.

b. Transverse reinforcement:

To prevent longitudinal buckling of longitudinal reinforcement

To resist diagonal tension caused due to transverse, moment.

To hold the longitudinal reinforcement in position at the time of

concreting.

To impart ductility to the column.

6.4 TYPES OF COLUMNS:

1. Column with Longitudinal steel and lateral ties.

2. Column with Longitudinal steel and spirals. 3. Composite columns.

4. Based on type of loading. 5. Based on slenderness ratio

BEAM BEAM



a. Columns without ties b. square columns with

lateral ties FIG6.6

FIG6.5

c. Circular column with lateral ties d. Composite column

FIG6.7 FIG6.8



4. Based on type of loading

a. Axially loaded columns: when the line of action of the resultant compressive force

coincides with center of gravity of the cross section of the column, it is called axially

loaded column.

b. Eccentricity loaded columns (uniaxial or Biaxial ) : when the line of action of

the resultant compressive force doesn`t coincide with the center of gravity of the

cross-section of the column. Eccentricity loaded columns have to be designed for

combined axial force and bending moments.

5. Based on slenderness ratio

According to IS 456 clause 25.3 impose the following slenderness limits for columns:

i. The unsupported length ‘ l ’ shall not exceed 60 times the least lateral

dimension of the column ( l ≯ 60b ).

ii. If in any given plane , one end of the column is unrestrained 𝑙 ≯ 100 𝑏2/𝑑

6.5 EFFECTIVE LENGTH OF COLUMN

With the reference from strength of materials Euler`s buckling load for

column with different end conditions works out to be form

𝑃𝑐𝑟 = 𝛼𝜋2𝐸𝐼

𝑙2

Where l is the effective length of column. The buckling load 𝛼𝜋2𝐸𝐼

𝑙2 can be found for

idealized conditions. But when it comes to practice end conditions are never ideal.,

but in case of frame structures it is difficult to idealize ends as fixed, free or hinged.

IS 456 gives a method of determining the effective length for such cases in terms of

stiffness of members meeting at joint.

In normal usage idealized end conditions may be assumed and effective length

determined as shown from table 28 in IS 456.



Degree of end

restraint of

compression

members

Symbol

Theoretical

value of

effective length

Recommended

value of effective

length

Effectively held in

position and

restrained against

rotation in both

ends

0.50 L

0.65 L

Effectively held in

position at both

ends, restrained

against rotation at

one end

0.70 L

0.80 L

Effectively held in

position at both

ends, but not

restrained against

rotation

1.00 L

1.00 L

Effectively held in

position and

restrained against

rotation at one end,

and at other

restrained against

rotation but not

held in position

1.00 L

1.20 L

Effectively held in

position and

restrained against

rotation at one end,

and at other

partially restrained

against rotation but

not held in position

1.50 L



Effectively held in

position at one end

but not restrained

against rotation,

and at other end

restrained against

rotation but not

held in position

2.00 L

2.00 L

Table 6.1 Effective length of compression member

Braced and unbraced columns

Columns are also subjected to horizontal loads like wind, earthquake

etc.

If the lateral supports are provided at the ends of the columns, the

lateral loads are borne entirely by the lateral supports. Such columns

are known as braced columns.

Where the lateral loads have to be resisted by them, in addition to

axial loads and end moments are considered as unbraced columns.

Bracing can be one direction or in more than one direction, depending

on the direction of the external loads.

A braced column is not subjected to side sway because the column is

braced in both the directions i.e. X and Y directions.

An unbraced column is subjected to side sway or lateral drift, i.e.

there is significant lateral displacement between top and bottom ends

of the column.

6.6 ASSUMPTIONS IN LIMIT STATE OF COLLAPSE IN AXIAL

COMPRESSION:

1. The plane section normal to the axis of column before deformation

remains plan after deformation. This means strain at any point is

proportional to its distance from the neutral axis.

2. The relationship between compressive stress distribution in concrete

and strain in concrete is represented by stress-strain curve.

3. For design purpose, the compressive strength of concrete is assumed

to be 0.67 times of the characteristic strength. The partial safety factor

is added γmc = 1.5 is added.

0.67𝑓𝑐𝑘

1.5= 0.446 𝑓ck



4. The stress in reinforcement is derived from representative stress-

strain curve for the type of steel used. Factor of safety 1.15 is applied

for steel

5. The maximum compressive strain in concrete in axial compression is

taken as 0.002, and is uniform in section. Hence maximum

compressive stress in concrete, assumed to be uniform across the

section is taken equal to 0.446*fck according to assumption.

Short column:

A compression member may be considered as short when both the slenderness

ratio lex/D and ley/D are less than 12, where

lex = effective length in bending with respect to major axis ( i.e. x- axis )

ley = effective length in bending with respect to major axis ( i.e. y- axis )

D = depth of the section in respect of major axis.

d = width of the section in respect of minor axis.

6.7 SHORT AXIALLY LOADED MEMBER IN AXIAL

COMPRESSION:

Experiments on columns show that load carrying capacity ( Pu ) of an

axially loaded R.C. member at collapse is made up of ultimate strength of concrete

member (Puc ) at collapse plus the ultimate strength of steel ( Pus ) in compression.

𝑃𝑢 = 𝑃𝑢𝑐 + 𝑃𝑢𝑠 = 𝛼𝑐 𝑓𝑐𝑘 𝐴𝑐 + 𝛼𝑠 𝑓𝑦 𝐴s

αc fck = fc = stress in concrete at failure, at uniform of 0.002

αs fy = fs = stress in steel at failure, at uniform of 0.002

Ac = area of concrete ; As = area of steel reinforcement

When a short column is axially loaded, the strain distribution across

the section will be rectangular. At failure, the strain in concrete will be uniform at a

value of 0.002. When concrete attains a limiting strain of 0.0002, the mild steel

reinforcement may develop full design stress ( fyd = 0.87 fy ) . In general therefore

stress fs in steel reinforcement at strain of 0.002, can be taken equal to αs fy, where

the value of αs will depend upon the type of reinforcement as given below ;



Type of reinforcement Value of (αs ) Stress in steel (fy)

Mild steel 0.87 0.87 fy

Fe 415 0.79 0.79 fy

Fe 500 0.75 0.75 fy

TABLE 6.2

Hence the load carrying capacity of a member, subjected to an axial load only, is

given by

𝑃𝑢 = 0.446 𝑓𝑐𝑘 𝐴𝑐 + 𝛼𝑠 𝑓𝑦 𝐴s

From IS CODE ( IS : 456-2000) adopts only the lowest value of αs ( = 0.75

), which is for steel Fe 500 grade . Also the code has redesigned Pu as Puz in section

39.6 of the code, and has given the following expression in design aids ( SP : 16 –

1980 ).

𝑷𝒖𝒛 = 𝟎. 𝟒𝟒𝟔 𝒇𝒄𝒌 𝑨𝒄 + 𝟎. 𝟕𝟓 𝒇𝒚 𝑨s = 𝟎. 𝟒𝟒𝟔 𝒇𝒄𝒌 𝑨𝒈 + 𝟎. 𝟕𝟓 𝒇𝒚 − 𝟎. 𝟒𝟒𝟔 𝑨𝒔

Ag = gross area of concrete

Ac = net area of concrete = Ag – As

6.8 SHORT AXIALLY LOADED COLUMN WITH MINIMUM

ECCENTRRICITY:

According to IS: 456-2000, compression members are to be designed

for the minimum eccentricity of the load in two principal directions. From the clause

25.4 of the code specifies the following minimum eccentricity emin for the design of

the columns :

𝑒 min =𝑙

500+

𝐷

30 , subject to minimum of 20 mm

Where l = unsupported length of the column in direction under consideration

D = lateral dimension of the column in direction under consideration

Here L is in both x and y direction i.e. lx and ly

If the value of minimum eccentricity is less than or equal to 0.05 D ,

from clause 39.3 of the code permits the design of short axially loaded compression

member by the equation :

𝑃𝑢 = 0.4 𝑓𝑐𝑘 𝐴𝑐 + 0.67 𝑓𝑦 𝐴s = 0.4 𝑓𝑐𝑘 𝐴𝑔 + 0.67 𝑓𝑦 − 0.4 𝑓𝑐𝑘 𝐴𝑠

This equation can be rearranged as



𝑷𝒖 = 𝟎. 𝟒 𝒇𝒄𝒌 𝑨𝒈 −𝒑𝑨𝒈

𝟏𝟎𝟎 + 𝟎. 𝟔𝟕 𝒇𝒚

𝒑𝑨𝒈

𝟏𝟎𝟎

Where,

Ag = gross area of cross section = b * D for rectangular section

= 𝜋

4𝐷2 for circular section

P = percentage of reinforcement = 𝐴𝑠/ 𝐴𝑔 ∗ 100

Compression members with helical reinforcement:

The code permits larger load in short compression members with

helical reinforcement because columns with helical reinforcement have greater

ductility or toughness when they are loaded concentrically or with small eccentricity.

As per code, the strength of the short compression members with helical

reinforcement shall be taken as 1.05 times the strength of similar members with lateral

ties.

Requirement:

The ratio of volume of helical reinforcement ( Vhs ) to the volume of core ( Vk )

shall not be less than 0.36 𝐴𝑔

𝐴𝑘− 1 𝑓𝑐𝑘 ÷ 𝑓𝑦𝑕

Where 𝐴𝑔 = gross area of the section

𝐴𝑘 = area of core of the helically reinforced column measured to the

outside diameter of the helix = 𝜋

4𝐷2𝑎𝑘 − 𝐴𝑠

𝐷𝑘 = diameter of concrete core, measured from outside of helix = D – 2 X clear

cover

𝑓𝑦𝑕 = characteristic strength of helical reinforcement but not exceeding

415 𝑁/𝑚𝑚2

Load carrying capacity of axially loaded short columns:

1. Short column with lateral ties :

The ultimate load on the short column with lateral ties, when the minimum

eccentricity does not exceed 0.005 times the lateral dimensions,

𝑷𝒖 = 𝟎. 𝟒 𝒇𝒄𝒌𝑨𝒄 + 𝟎. 𝟔𝟕𝒇𝒚𝑨𝒔𝒄

Where,

Pu = factored axial load on column

Ac = area of concrete = gross area – area of steel = Ag - Asc

Asc = area of longitudinal reinforcement



𝑓𝑐𝑘 = characteristic compressive strength of concrete

𝑓𝑦 = characteristic strength of steel

2. Short column with helical reinforcement:

The strength of column with helical reinforcement shall be 1.05 times

the strength of similar columns with lateral tie, provided the ratio of volume of

helical reinforcement to the volume of the core shall not be less than

𝟎. 𝟑𝟔 𝑨𝒈

𝑨𝒌− 𝟏

𝒇𝒄𝒌

𝒇𝒚

Ag = gross area of section

Ak = area of the core of helically reinforced column measured to the out-side

diameter of the helix.

Long columns or slender columns:

If the ratio of effective length to its least lateral dimension is more than 12 the

columns are called long columns. A column under the action of axial loads deflects

laterally causing maximum lateral deflection at the center ( ∆ ). This makes the load

eccentric at the central section of the column by a distance∆, subjecting a bending

moment P * ∆

Pu Pu

∆ = DEFLECTION FIG6.11

CURVE. ∆ = 0 (NO DEFLECTION )

According to IS : 456-2000,the additional moments Max and May due to lateral

deflection shall be calculated by

Max = 𝑷𝒖 𝑫 𝒍𝒆𝒙

𝒍𝒆𝒙

𝑫

𝟐𝟎𝟎𝟎



May = 𝑷𝒖 𝒃 𝒍𝒆𝒚

𝒍𝒆𝒚

𝑫

𝟐𝟎𝟎𝟎

𝑃𝑢 = Axial load on member

𝑙𝑒𝑥 = effective length in respect of the major axis

𝑙𝑒𝑦 = effective length in respect of the major axis

D = depth of the cross section at right angles to the major axis

b = width of the cross section

The above values may be multiplied by reduction factor

𝑘 = 𝑃𝑢𝑧 − 𝑃𝑢

𝑃𝑢𝑧 − 𝑃𝑏 ≤ 1

Where

Pu = axial load on member

Puz = 0.45 fck Ac + 0.75 fy Asc

Pu = axial load corresponding to the condition of maximum compressive strain

0.0035 in concrete and tensile strain of 0.002 in outer most layer of tension steel.

6.9 DESIGN REQUIREMENTS FOR COLUMNS (CLAUSE 26.5.3

OF IS 456):

1. Longitudinal reinforcement:

a. The cross sectional area of longitudinal reinforcement shall not be

less than 0.8 % and not more than 6 % of gross sectional area of

column.

b. In any column that has large cross sectional area that required to

support the load, the minimum percentage of steel shall be 0.8 % of

required area and not the area actually provided.

c. Minimum number of longitudinal bars to be provided is 4 for

rectangular columns and 6 for circular columns.

d. Minimum diameter of longitudinal bar is 12 mm.

e. Spacing of longitudinal bars measured along the periphery of the

column shall not exceed 300 mm.



2. Transverse reinforcement :

A reinforced concrete compression member shall have transverse or helical

reinforcement so disposed that every longitudinal bar nearest to the compression face

has effective lateral support against buckling. The effective lateral support is given by

transverse reinforcement either in form of circular rings capable of taking up

circumferential tension or by polygonal links (lateral ties) with internal angles not

exceeding 1350. The ends of the transverse reinforcement shall be properly anchored.

i. Lateral ties:

a. The diameter of lateral ties shall not less than ¼ of the diameter of

largest longitudinal bar and in no case less than 6 mm.

b. The pitch of ties shall not exceed the following

Least Lateral dimension of the column

Sixteen times the smallest longitudinal bar

300 mm

ii. Helical reinforcement :

a. The diameter is same as that of lateral ties

b. The pitch of the helical reinforcement shall not be more the

following

75 mm

1/6 of core diameter of the column

c. And the pitch of helical reinforcement shall not be less than the

greatest of the following

25 mm

Three times the diameter of helical bar.

Cover:

For longitudinal reinforcing bars in a column nominal cover shall in any case

not be less than 40 mm, or less than the diameter of such bar. In case of columns

of minimum dimension of 200 mm or under, whose reinforcing bars do not exceed

12 mm, a nominal cover of 25 mm may be used. Ref (clause 26.4.2.1 of IS: 456-

200)

6.10 DESIGN OF COLUMNS USING SP 16:

SP 16 design charts 24 to 26 shall be used for designing of axially loaded short

columns. These charts cover different grades of steel ( fy =250, 415 and 500 ) and

concrete grades

fck = 15,20,25,30,35 and 40.

In lower section of these charts Pu /Ag has been plotted against percentage of steel

( p) for different grades of concrete. If the cross-section of column is known, Pu -

/Ag can be calculated and reinforcement percentage can be read from the chart.



6.11 DESIGN OF COLUMNS:

Categorizations of Columns:

TABLE 6.3

Category – I(a): (13,14,15, 16, 17, 20, 21, 22, 23, 24)

Axially loaded columns

Factored axial load = 1637 KN

Breadth (B) = 300 mm

Depth (D) = 500 mm

Length (L) = 3200 mm

Gross area (Ag) = 300 x 500 = 150000 mm2

Area of concrete (Ac) = 150000- Asc

For a axially loaded short columns

Pu = 0.4 fck.Ac+0.67.fy.Asc

1637 x 103 = 0.4x20x (150000- Asc) + 0.67x 415x Asc

Asc = 1618.21 mm2

Cate

gory Type Column No’s

Size of

column

Max Ultimate

load

I Internal Column or

Axially Loaded

13,14,15, 16, 17, 20, 21,

22, 23, 24 300 x 500 mm 1637.006 KN

9,10,11 300 x 400 mm 818.406 KN

II

Side Column or

Axially Loaded

with Uniaxial

Bending

2, 3, 4, 6, 7,12, 18, 19,

25, 27, 28, 29, 30, 31

300 x 500 mm

1249.386 KN

5 300 x 400 mm 818.406 KN

III

Corner column or

Axially Loaded

Biaxial

1, 8, 26, 32 300 x 500 mm 790.593 KN



Min reinforcement = 0.8 % of gross area

= 0.008 x 300 x 500 = 1200 mm2

Max reinforcement = 6% of gross area

= 0.06 x300 x500 = 9000 mm2

Provide 10 bars of 16 mm dia.

Lateral ties

Diameter of lateral ties should not be less than

1. one fourth of longitudinal bar = 1

4x16 = 4 mm

2. 6 mm

Hence, adopt 6 mm diameter of bars

Pitch of the lateral ties shall be minimum of:

1. Least of the lateral dimension = 300 mm

2. 16 x dia of longitudinal bar 16 x 16 = 256 mm

3. 300 mm

Provide 6 mm lateral ties @ 250 mm c/c

Category – I(b): (9,10,11)

Axially loaded columns

Factored axial load = 818.406 KN

Breadth (B) = 300 mm

Depth (D) = 400 mm

Length (L) = 3200 mm

Gross area (Ag) = 300 x 400 = 120000 mm2

Area of concrete (Ac) = 120000- Asc

For a axially loaded short columns

Pu = 0.4 fck.Ac+0.67.fy.Asc

818.406 x 103 = 0.4x20x (120000- Asc) + 0.67x 415x Asc



Asc = 1172.67 mm2

Min reinforcement = 0.8 % of gross area

= 0.008 x 300 x 400 = 960 mm2

Max reinforcement = 6% of gross area

= 0.06 x300 x400 = 7200 mm2

Provide 10 bars of 12 mm dia.

Lateral ties

Diameter of lateral ties should not be less than

1. one fourth of longitudinal bar = 1

4x12 = 3 mm

2. 6 mm

Hence, adopt 6 mm diameter of bars

Pitch of the lateral ties shall be minimum of:

1. Least of the lateral dimension = 300 mm

2. 16 x dia of longitudinal bar 16 x 12 = 192 mm

3. 300 mm

Provide 6 mm lateral ties @ 250 mm c/c

Category – III:

Axial load (Pu) = 790.593 KN

Initial Moments

About X

KN-m

About Y

KN-m

15.79

7.12

Eccentric Moments

15.81

18.24

Total Design Moments

15.81

18.24

TABLE 6.4

Mx = 15.79 KN-m

My = 7.21 KN-m

Column size = 300 mm X 500 mm



M20 Fe415

Assume clear cover = 40 mm

Assume dia. Of main steel = 12 mm

Dia. Of link = 8 mm

Therefore effective cover = 40+8+ 12/2 = 54 mm

Assume % steel as p = 1.2 %

Emin.x = L/500 + d/30

= 3200 /500 + 500/30

= 23.066 mm

Emin.y= L/500 + d/30

= 3200/500 + 300/30

= 16.4 mm

P/fck = 1.2/20 = 0.06

P𝑢

𝑓𝑐𝑘 𝑏𝑑 = (790.593)/(20 x 300 x 500) = 0.263

From clause 39.6 from pg. 71 IS: 456

Pux = 0.45fckAc + 0.75 fyAsc

[Ac= Ag - Asc

= [(300 x 500) – (0.012 x 300 x 500)]

=148200 mm2]

= [(0.45 x 20 x 148200) + (0.75 x 415 x 1800)]

=1894.04 KN

P𝑢

P𝑢𝑥 =0.417

From pg. 71 clause no 39.6

αn= 1.36

For bending about X-axis

d' /d = 54/500 = 0.108

Selecting appropriate chart- 44 for d’/d = 0.1 from SP-16

Mu

fck bd 2 = 0.081

Mux1 = 121.5 KN-m

For bending about y-axis



d'/b = 54/300 = 0.18

Selecting appropriate chart from SP-16

Mu

fck db 2 = 0.075

Muy1 = 67.5 KN-m

Mux

Mux 1 ∝

+ Muy

Muy 1 ∝

= 0.11 < 1

Hence the assumed column size and % of steel are O.K.

Reinforcement

Asc = 1800 mm2

Assuming 16 mm bars,

Hence provide # 8-16 mm bars

Lateral ties

Provide lateral ties of dia 6 mm

Provide # 6 mm bars @ 250 mm c/c

Schedule of columns:

category Cross section Longitudinal

reinforcement

Lateral ties

(2 Legged)

I 300 x 500 mm 10-16 ϕ

6ϕ 250 C/C 300 x 400 mm 10-12 ϕ

II

300 x 500 mm 8-16 ϕ

6ϕ 250 C/C

300 x 400 mm 8-12 ϕ

III 300 x 500 mm 8-16 ϕ 6ϕ 250 C/C

TABLE 6.5



7. DESIGN OF FOOTINGS

A Building is generally composed of super structure above the

ground and sub-structure, which forms the foundation below ground. The safe bearing

capacity of the soil must not be exceeded; otherwise settlement may occur, resulting

in damage to building and its facility ex. gas mains, water etc

It is important to have an engineer survey made of soil under a

proposed structure so that variation in strata and soil properties can be determined.

The design of foundation ,the areas of bases in contact with ground should be such

that the safe bearing pressure will not be exceeded ,If these loads are to properly

transmitted ,footing must be designed to prevent excessive settlement or rotation, and

provide safety against sliding, overturning.

7.1 INTRODUCTION OF FOOTING:

Foundation or footing is an important part of the structure which transfer the

load of the superstructure to the foundation soil .It may be shallow or deep footing,

depending upon the load and type of foundation soil.

Example: if the soil with adequate bearing capacity at reasonable depth; then shallow

footing is provided.

If, 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑓𝑜𝑢𝑛𝑑𝑎𝑡𝑖𝑜𝑛 𝑖𝑠 ≤ 𝑡𝑜 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑢𝑛𝑑𝑎𝑡𝑖𝑜𝑛 Shallow foundation

If, 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑓𝑜𝑢𝑛𝑑𝑎𝑡𝑖𝑜𝑛 𝑖𝑠 ≥ 𝑡𝑜 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑢𝑛𝑑𝑎𝑡𝑖𝑜𝑛 Deep foundation

7.2 TYPES OF FOOTING:

Footings are classified as follows;

Isolated footing

Combined footing

Strap footing

Mat footing



1) Isolated footing:

Footing which are provided under each column independently is

called isolated footing. It may be square, rectangle, or circular in plan. Its

comprised of thick slab which may be flat or stepped or sloped as shown in

fig..

P P

P

FLAT Stepped Slopped

FIG7.1 Isolated Footing

2) Combined footing:

Footing that supports two or more columns is combined footing. These

may be rectangular or trapezoidal in shape, as shown in fig. This type of footing

is provided when isolated footing of adjacent columns overlap each other and

when exterior column close to boundary line.

P1 P2 P1 P2

FIG7.2 combined footing



3) Strap footing:

It is also one of the types of combines footing. It consists of an

isolated footing of two columns connected by beam called strap beam.

P1 P2

Connecting beam Cantilever slab

FIG7.3 Strap footing

4) Mat footing:

It is a solid re-in forced concrete slab covering entire area beneath the

structure and supporting all the columns. When the column loads are heavy or the safe

bearing capacity of soil is very low, the required footing area become very large and

the footing of adjacent column may overlap. In such case, for all the columns a

common footing may be provided.

FIG7.4 Mat Footing



7.3 DEPTH OF FOUNDATION:

Rankin’s formula is used to determine the min. depth of foundation which is

given below,

ℎ =𝑝

𝑤

(1−𝑠𝑖𝑛𝛼 )

(1+𝑠𝑖𝑛𝛼 )

2

Where,

h = Min depth

p = Safe bearing capacity

w = Unit weight of soil

α = Angle of friction of soil

Loads for foundation:

For,

a) Dead load + Imposed load case, 1.0 DL + 1.0 IL

b) Dead load + Wind load case, 1.0 DL +1.0 WL

c) Dead + Imposed + Wind load case, 1.0 DL + 0.8 DL + 0.8WL

10% of load from column may take as self-weight of footing for determining

the area of footing required.

In case of multi-storey Building, one should take advantage of allowable

reduction in the live load for residential and office buildings

General design requirements for footing (IS 456-2000):

I. Minimum thickness at edges:-

In reinforcement and plain concrete footing, the min. thickness at the edges shall be

taken as given below.

For footing on soil 150 mm

For footing on piles 300 mm

II. Moments and Forces:-

The bending moment at any section shall be determined by passing through

the section a vertical plane which extends completely across the footing, and

computing the moment of forces acting over entire area of footing on one side of said

plane. The critical section for determination of bending moment shall be as follows.



i. At the face of the column, pedestal or wall, for footing supporting concrete

column, pedestal or wall

ii. Halfway b/w the center-line and edge of the wall, for footings under masonry

walls

iii. Halfway b/w the face of the column or pedestal and the edge of the gusseted

base, for footing under gusseted bases

III. Shear:

The shear strength of footing is governed by the more serve of the

following 2 conditions.

For one way or beam action, the critical section for shear shall be assumed as a

vertical section located from face of the column. i.e. {pedestal or wall at a

dist. Equal to effective depth for footing on soil and dist. equal to half effective

depth in case of footing on piles}.

For 2 way action of the footing, the critical section for shear shall be at a dist.

Of D/2 from the periphery of the column perpendicular to the plane of the

slab.{where d = effective depth of section}

IV. Bond:

The critical section for checking the development length in a footing shall

be assumed at the same planes as those prescribed for bending moment and also at

other planes where minimal changes of section occur.

V. Tensile reinforcement:-

Tension reinforcement should be provided to resist the bending moment

obtained in (II) above. The total tensile reinforcement shall be distributed across

the corresponding resisting section as given below;

a. In One way reinforced footing, the reinforcement shall be distributed

uniformly across the full width of footing.

b. In Two ways reinforced rectangular footing, the reinforcement in the long

direction is placed uniformly across the full width of the footing. For

reinforcement in short direction ,a central band equal to the width of footing

shall be marked along the length of the footing and portion of reinforcement

determined in accordance with the equation given below shall be uniformly

distributed across the central band.

𝑅𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑖𝑛 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑏𝑎𝑛𝑑

𝑡𝑜𝑡𝑎𝑙𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑖𝑛 𝑠ℎ𝑜𝑟𝑡 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 = (

2

𝛽+1)

Where, β = ratio of longer side to shorter side of footing.



The remaining portion of reinforcement is provided uniformly in outer portion of

footing as shown in fig. L

ee

End Band B

Central band

(𝑙−𝑏

2) B (

𝑙−𝑏

2)

FIG7.5 End band

VI. Transfer of Load at the base of column:-

The compressive stress in concrete at the base of the column is

transferred by bearing to the top of the supporting footing. The bearing pressure

on the loaded area shall not exceed the permissible bearing stress in direct

compression multiplied by value equal to (𝐴1)/(𝐴2) but not greater than 2.

P

A1 = supporting area for bearing of footing

Column

A2 = loaded area at the column face.

Footing

A1= Max. Area of supporting surface 2d b

2d

A2

FIG7.6 Load distribution in Footing



VII. Min. reinforcement:-

The Min reinforcement and spacing shall be as per the requirements of

solid slab. Min. dia of bar to be used is 10 mm.

VIII. Nominal cover to reinforcement:-

For, footings Min. cover shall be 50 mm.

Column Bar

Development length of column bars Dowel

Bars

FIG7.7 Reinforcement of column – Footing interface

7.4 DESIGN PROCEDURE OF ISOLATED FOOTING:

The Footing for an axially loaded column is designed as an inverted

cantilever slab projecting from column and loaded with uniform upward soil pressure.

These are usually square or rectangular in shape. They may have uniform thickness

throughout or may have sloping surface.

1) Size of the Footing:

Size of the footing is determined based on service loads or working loads and not

the factored loads. Take 10% of the load as self-weight.

Area of the footing required;

𝐴 = 1.1 𝑃

𝑆𝐵𝐶 𝑜𝑓 𝑠𝑜𝑖𝑙

Where P = working load SBC = safe bearing capacity

2) Determine the upward soil Reaction for the factored load:

𝑄𝑢 = 𝑃𝑢

𝐴 =

1.5 𝑝

𝐴



3) Determine The Min Depth Required to Resist B.M:

Calculate the depth required for bending moment and check the depth

for single shear and double shear. The depth is kept uniform. If the footing size is

small and is made slopping, if the footing is large.

The maximum bending moment is calculate at the face of the column

by passing a section extends completely across the footing as shown in fig.

( 𝐵−𝑏

2)

L B-b / 2

aa

B

Qu

FIG7.8 CRITICAL SECTION OF BENDING MOMENT

Projection of the footing = (𝐵−𝑏)

2

The bending moment about x-x is (as a cantilever slab, 𝑤𝑙2

2 )

Mu = 𝑄𝑢 .𝐵(

𝐵−𝑏

2)2

2

≈ 𝑄𝑢 𝐵(𝐵−𝑏)2

8

Where, Qu = upward soil pressure; B= width of footing; b = width of column

4) Determine the area of reinforcement required in Width B using:

Mu = 0.87 ∗ 𝑓𝑦 ∗ 𝐴𝑠𝑡 (1 −𝑓𝑦 ∗𝐴𝑠𝑡

𝑓𝑐𝑘 ∗𝐵∗𝑑)

Using the bars of dia not less than 10 mm, find the spacing of bars.

Spacing = 𝐵∗𝑎𝑠𝑡

𝐴𝑠𝑡

Where, ast = area of bar used

b

b

b



Ast = total area of steel required

B = width of the footing

D = effective depth of footing

NOTE: - Provide same reinforcement in both directions.

5) Check for one way shear:

The check for one way shear is carried out similar to that of beams or

slabs. The critical section for one way shear is at a distance d from the column

extending the full width of the footing as shown in fig.

B

Vu = soil pressure from the shaded area

= Qu ∗ B B−b

2− d

τυ = Vu

bd< τc , permissible shear stress in concrete. B

FIG7.9

6) Check for Two way shear:

Two way shears is also known as “Punching shear”. if the footing

depth is less, the column may punch through the footing because of the shear

stresses in the footing around the perimeter of the column. As per IS 456-2000,the

critical section for two way shear is at a distance d/2 from the periphery of the

column as shown in the fig.

Perimeter of the punching area = 4(b+d)

Area of concrete resisting punching force = perimeter of punching x depth

A = 4 b + d d

Force of punching S = Qu ∗ shaded area

𝑆 = 𝑄𝑢 [𝐵2 - (𝑏 + 𝑑)2]

Punching shear stress,

τp = 𝑆

𝐴 < permissible value.

Permissible value of punching shear stress is τp =0.25 𝑓𝑐𝑘.

(B-b/2)-d

d b

b



B

B

FIG7.10 Critical section of two way shear

7) Check for bond length:

Since the footing is designed as a cantilever with reinforcement

subjected to deigned strength at the column face, sufficient bond length should be

available from the face of the column.

Ld = 0.87fy∅

4 ∗ τbd

8) Check for bearing stress:

The compressive stress in concrete at the base of the column is

transferred by bearing to the top of the supporting footing; the bearing pressure on

the loaded area shall not exceed the permissible bearing stress.

Actual bearing pressure = 𝑃𝑢

𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑜𝑙𝑢𝑚𝑛< 𝑝𝑒𝑟𝑚𝑖𝑠𝑠𝑖𝑏𝑙𝑒 𝑣𝑎𝑙𝑢𝑒

As per clause 34.4 of IS: 456-2000, the permissible bearing stress is

=0.45 𝑓𝑐𝑘 𝐴1

𝐴2 , in which

𝐴1

𝐴2 should not exceed 2

Where, 𝐴1= supporting area for bearing of column

𝐴2 = loaded area at the column face

b+d

b+d

` d/2

d/2 d/2

d/2



7.5 DESIGN OF RECTANGULAR FOOTING:

In case of rectangular footing, footing is provided when the

boundary line restricts one side of the footing. In such cases the projections of the

footing will be unequal. The dimensions of the footing are proportional in the same

ration of column dimensions. The depth of footing is to be calculated based on longer

projection. Reinforcement has to be designed for both the directions separately. The

reinforcement in the long direction is placed uniformly across the full width of the

footing. But in short direction, the reinforcement is distributed as explained in above

(5).the critical sections for bending and shear.

L L

B B

b

(b)

FIG7.11 critical section for one way shear; FIG7.12critical section for two way shear

Bending moment along longer direction = M1 = Qu B(L−a)2

8

Bending moment along shorter direction = 𝑀2 = 𝑄𝑢 𝐿(𝐵−𝑏)2

8

The maximum B.M shall be taken for calculating the depth of footing. The

depth calculated should be checked for one way shear and two way shear similar to

that of square/isolated footing.

7.6 DESIGN CALCULATION OF FOOTINGS:

The following are the reactions of nodes/columns obtained from

STAAD PRO. Footings of the columns having same sizes and variation of loads of

about 10% are grouped together and designed for the maximum load in that group.

Critical section

For bending B-b / 2

a

L - a / 2

(a)

a+d

d

b+d

d/2

b

a d/2



NODES Fx (KN) Fy (KN) Fz (KN) Mx (KN-

m)

My (KN-

m)

Mz (KN-m)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

16.254

16.191

16.392

15.314

20.698

28.706

12.083

5.696

2.826

16.323

10.261

16.470

16.524

15.173

13.614

17.264

11.970

5.750

17.832

21.037

17.198

13.826

17.147

17.231

6.348

739.600

1046.546

1146.586

834.852

681.782

960.644

1039.918

749.144

770.377

665.521

818.406

838.848

1178.568

1212.995

1637.006

1239.291

1180.815

842.925

903.807

1225.531

1361.846

1586.945

1367.383

1225.577

906.918

24.614

22.836

13.988

23.547

13.669

13.785

22.933

25.288

18.641

8.274

14.191

20.098

15.828

28.885

22.396

21.983

15.879

21.148

23.072

19.100

22.471

26.535

18.648

19.854

24.121

31.044

22.386

16.481

19.712

12.918

14.3

28.382

32.406

16.520

10.354

12.940

29.327

24.937

23.043

33.776

18.184

26.009

31.041

31.145

15.719

19.967

35.947

16.853

16.375

32.666

0.229

0.255

0.193

0.288

0.128

0.170

0.080

0.106

0.153

0.087

0.067

0.129

0.185

0.150

0.065

0.127

0.058

0.092

0.085

0.116

0.162

0.068

0.103

0.398

0.145

9.252

13.294

27.988

33.174

18.742

25.731

15.051

14.775

12.038

14.016

15.740

9.106

12.937

27.362

13.704

26.632

14.999

14.831

9.309

27.221

27.370

13.791

27.433

29.104

15.649



26

27

28

29

30

31

32

17.284

21.470

16.008

14.089

17.391

16.685

6.211

788.709

986.219

1056.792

1249.386

1201.954

1020.677

790.593

7.832

4.293

6.420

10.368

5.169

4.528

8.410

22.196

6.199

9.360

26.330

7.041

6.523

23.730

0.076

0.105

0.268

0.088

0.137

0.343

0.395

9.110

26.112

26.894

13.121

26.234

27.889

15.087

7.7 GROUPING OF FOOTINGS:

Group Column No’s Size of column Max Ultimate

load

I 1, 8, 26, 32 300 x500 mm 790.593 KN

II 2, 3, 4, 6, 7,12, 18, 19, 25,

27, 28, 29, 30, 31

300 x500 mm

1249.386 KN

III 13,14,15, 16, 17, 20, 21, 22,

23, 24

300 x500 mm 1637.006 KN

IV 5,9,10,11 300 x 400 mm 818.406 KN



7.8 Design of footings

Step Design calculations Group I Group II Group III Group IV

1.

2.

3.

4.

General Data

Max column load Pu KN

Design working load (P)=Pu/1.5 KN

Column section (b x D) mm x mm

S.B.C of soil KN/m2

Proportioning of Base size

Area of footing required

Af =Pu/SBC m2

Area of footing provided m2

Length of footing Lf m

Breadth of footing Bf m

Projection from column face (Cx) m

Net upward soil pressure

wu=Pu/ Af KN/m2

Depth of footing required from

B.M consideration

MuL = w𝑢 B𝑓Cx 2

8 kN-m

MuB = w𝑢 L𝑓Cx 2

2 kN-m

Depth d = 𝑀𝑢

0.138.𝑓𝑐𝑘 .𝑏 mm

Assuming clear cover 50 mm

Effective depth d

mm

Total depth

mm

Reinforcement along:

(Ast )y= 0.5 fck

fy 1 −

1 −4.6𝑀𝑢

𝑓𝑐𝑘 .𝐵.𝑑2 xBxd mm2

Min %Pt of Ast as per IS 456-2000

(0.85 x100)/fy

Min Ast mm2

Diameter of bars mm

Spacing of bars, S= (astx B)/Ast

mm

c/c

in both directions

790.593

527.062

300 x 500

200

2.64

2.88

1.80

1.60

0.650

189

17.40

15.46

62.77

360

410

135

0.205

431

12

200

1249.386

832.924

300 x 500

200

4.16

4.83

2.30

2.10

0.90

172

40.16

36.67

121

470

520

242

0.205

557

12

180

1637.006

1091.133

300 x 500

200

5.46

5.75

2.50

2.30

1.00

190

59.31

54.57

147

470

520

361

0.205

554

16

180

818.406

545.604

300 x 400

200

2.64

3.06

1.80

1.70

0.70

178

19.66

18.57

84

360

410

155

0.205

425

12

200



5.

6.

Check for One-way shear: The

critical section for one way shear is

at a distance d from the face of the

column

Factored shear force

Vu = wuBf(Cx-d) KN

Nominal shear stress

τv = V𝑢

Bd N/mm

2

Percentage of steel,

Pt = ast x 100

S x d

Shear strength of concrete τc

τc >τv

Hence it is safe with respect to one

way shear.

Check for Two-way Shear: The

critical section is at a distance of

d/2 from the face of the column.

Perimeter of the critical section

=2{(b+d)+(D+d)}

Area of critical section

(A)=Perimeter x d

Two way shear Vu2= wu x area of

shaded portion= {(LxB-

(b+d)x(D+d)}

Two way shear stress = Vu2/A

Permissible punching shear stress

τp=0.25√𝑓𝑐𝑘

Two way shear is less than the

permissible punching shear stress,

hence, it is safe w.r.t two way shear.

85

0.148

0.157

0.260

safe

3040

1094.4x103

423

0.389

1.118

safe

183

0.162

0.157

0.260

safe

3480

1635.6 x

103

706

0.440

1.118

safe

235

0.221

0.237

0.332

safe

3480

1635.6 x

103

952

0.598

1.118

safe

105

0.174

0.157

0.260

Safe

2840

1022.4 x

103

458

0.459

1.118

safe



7.9 SCHEDULE OF FOOTINGS:

Group Length

Lf m

Breadth

Bf m D mm d mm

Astx Asty Clear

cover

(mm) Dia spacing Dia spacing

I 1.80 1.60 410 360 12 200 12 200 50

II 2.30 2.10 520 470 12 180 12 180 50

III 2.50 2.30 520 470 16 180 16 180 50

IV 1.80 1.70 410 360 12 200 12 200 50

C0MPARATIVE STUDY ON MULTI-STOREY R.C.C AND STEEL BUILDING


8. DESIGN OF STAIRCASE

8.1 INTRODUCTION:

Stairs are provided in a building to afford a means of communication

between the various floors, they are called staircase. Since they have to

perform the very important function, the slab over which the steps rests should

be designed properly to provide maximum comfort, easy and safety.

Staircase provides access for the various floors of the building. The

stair consists of series of steps with landings at appropriate intervals. The

stretch between the two landings is called flight. The room or space where

stairs are provided is called stair case.

The width of stair depends up on the type of building in which it is

provided. Generally in residential buildings, the width of stair is kept as 1 m

and in case of public buildings it may be up to 2 m. to allow free flow of users,

the width of landings should be at least equal to the width of stairs.

Each step has one tread (going) and one rise. Rise and tread are

proportioned so as to provide convenient and easy access. The rise may vary

from 150 mm to 200 mm. the tread is in between 250 mm to 300 mm. as per

IS: 456, the slope or pitch of the stairs should be in between 250 to 40

0.

The most important aspect in providing staircase is its location. The

location of stair should be such as to provide as easy access so that in case of

any causality, e.g. fire break, earth, food etc. occupation should be placed in

the center or to the side of a building. The location depends upon the position

of the rooms’ ant type of approach needed. In residential buildings, it should

be placed centrally so as to:

1. Provide easy access from all rooms,

2. Maintain privacy.

3. In public building, the staircase should be located near the main entrance.

8.2 TYPES OF STAIR CASES:

Depending up on the geometry/shape:

The stair cases are classified into the following categories depending up on the

geometry.



1. Single Flight Stair Case:

This type of stair is used in cellars or where the height between the

floors is small and the frequency of its use is less.

2. Quarter Turn Stair Case:

In this stair case, flights run adjoining the walls and provide

uninterrupted space at the centre of the room. Generally, quarter turn stair

case is used in domestic houses where floor heights are limited to 3 m.

3. Doglegged Stair Case:

The most common type of stair arranged with two adjacent flights

running parallel with a mid-landing. Where space is less, dog legged stair

case is generally provided resulting in economical utilization of available

space

4. Open Well Stair Case:

In public buildings where large spaces are available, open well stair

case is generally preferred due to its better accessibility, comfort and

ventilation due to its smaller flights with an open well at the center.

5. Geometrical Stair Case:

It is aesthetically superior compared to other types and is generally

used in the entrance of cinema theatres and shopping malls.

6. Spiral Stair Case:

In congested locations, where space available is small, spiral stairs are

ideally suited. It comprises a central post with precast treads anchored to

the central column.

Based on Structural Behavior (support condition):

The stirs are classified into the following categories depending up on

the structural behavior.

1. Stairs Spanning Horizontally (with Side Supports):

When the stair slab (waist slab) is supported on sides by side

walls or by a stringer beam on one side and wall on other side, the stars

are said to be spanning horizontally. Hence, each step behaves as an

independent simply supported beam spanning horizontally

Sometimes cantilever steps are used which projects from inclined

beam (stringer beam). Steps may cantilever on only one side or may

both side of supporting inclined beam. In such stairs, design of steps is

done as a cantilever.

2. Stairs Spanning Longitudinally (with supports along sloping line):



In this type, the inclined stair slab together with the landings is

supported (on walls or beams along sloping line) at the top and bottom

of the flight without any support on the sides. Dog legged, open well and

quarter turn stair cases comes under this category.

8.3 REQUIREMENT OF A GOOD STAIR CASE:

A well planned and designed stair should provide an easy, quick and

safe mode of communication between the various floors. The general

requirements of a stair are given below:

1. Location:

It should be so located that sufficient light and ventilation is ensured

on the stair case. If possible it should be located centrally so as to be easy

accessible from the different corners of the building.

2. Width of Stair Case:

Width of stair case varies with the situation and the purpose for which

it is provided. Obviously in a building where there is a regular traffic of

people using the stair case its width should be sufficient while in a

residential building it may be the just minimum. The widths of stair case

for public building normally vary between 1.5 to 2.0 m. For residential

building a width of 900 mm to 1000 mm is considered adequate.

3. Length of Flight:

For the comfortable ascend of a stairway to stair the number of steps

in a flight should be restricted to a maximum of 12 and a minimum of 3.

4. Pitch of Stair:

The pitch of long stair should be made flatter by introducing landing to

make ascend less tiresome and less dangerous. In general the slope of stair

should never exceed 40 degrees and should not be flatter than 25 degrees.

5. Head Room:

The head room or clear distance between the tread and the off it of the

flight immediately above it should not be less than 2.13 m.

6. Materials:

The stair should preferably construct of materials, which possess fire

resisting qualities.

7. Balustrade:

The open well stairs should provide with balustrade so as to minimize

the danger of accidents.



8. Landing: The width of landing should not be less than width of stair.

9. Winders:

The introduction of winders in stairs should be provided as far

as possible. They are liable to be dangerous and involve extra expenses in

construction. They are difficult to carpet and are especially unsuitable for

public buildings. However, where the winders cannot be dispensed with, they

should preferably be provided near the lower end of flight. Thus instead of

quarter space landing three winders may be used and for a half/space landing 5

winders and four radiating risers may be adopted.

10. Step Proportions:

The rise and tread of each step in a stair should be uniform dimension

throughout. The ratio of going and the rise of a step should so proportioned as

to ensure a comfortable access of the stair way.

8.4 DESIGN OF STAIRS SPANNING LONGITUDINALLY:

1. Depth of the Section:

The depth of the section shall be taken as the minimum thickness

perpendicular to the soffit of the stairs.

2. Effective Span:

(a) If supported at top and bottom risers by beams spanning parallel

with risers, the effective span is the distance between the centre to

centre of beams

(b) If landing slab spans in the same directions as the stairs, they shall

be considered as acting together to form a single slab. The effective

span is the distance centre to centre of the supporting beams or

walls, the going being measured horizontally.

(c) When spanning on to the edge of a landing slab, which spans

parallel with the rises, the effective span of the stairs depend upon

the width x and y of landing.



TABLE 8.1

X Y Span

< 1 m < 1m G+X+Y

< 1 m > 1 m G+X+1

> 1m < 1 m G+Y+1

> 1 m > 1 m G+1+1

3. Loads on Stairs:

Live loads:

Stairs are prescribed in IS: 875 which is given per unit horizontal area.

Generally the following values of live loads on stairs may be taken.

(a) 5 KN/m2, if crowded.

(b) 3 KN/m2, if not crowded.

Dead loads:

These are to be calculated per unit horizontal area. If T, R and D are tread, rise

and thickness of waist slab in m, then the dead load can be calculated as given below.

(a) Weight of waist slab per unit horizontal area

𝑤1 = 𝐷 𝑅2 + 𝑇2

𝑇x25 = D 1 + [𝑅 𝑇 ]2 x25

(b) weight of steps per unit horizontal area

w2 = 1

2xRxTx 25

T=

1

2xRx25

Where R in meter

Providing load (0.5 to 1 KN/m2) may be added to the above values

4. Distribution of Loading on the Stairs:

In case of stairs with open wells, where spans cross at right angles, the load on

areas common to any two such spans may be taken as one half in each direction.



8.5 DESIGN PROCEDURE FOR STAIRS SPANNING

LONGITUDINALLY:

1. Determine the effective span of the stairs as explained before

2. Assume the thickness of waist slab based on stiffness. Span/thickness ratio can be

selected in the range of 20 to 25.

3. Determine the load wu per meter length on waist slab, which includes the weight of

waist slab, weight of step and live load.

Weight of waist slab per meter length D 1 + (R T )2 x 25

Weight of step per meter length = 1

2xRx25

4. Determine the maximum bending moment Mu = wu l2

8

5. Determine the minimum depth required to resist the bending moment by equating

Mu = Mu,lim = k fck bd2

b = 1000 mm, k = 0.138 for Fe415 steel & 0.148 for mild steel

Provided depth should be more than this value. Otherwise increase the depth.

6. Calculate the area of steel per meter width of slabs by using

Mu = 0.87 fyAst d[1 − fyAst

fck bd]

7. Finding the spacing of bars using

S = 1000xast

Ast

Where ast = area of bars used

Ast = total area of steel required

8. Providing distribution reinforcement perpendicular to the span direction at 0.12%

(for HYSD bars) of gross cross sectional area find the spacing of these bars. If mild

steel bars are used, provide 0.15% of gross cross sectional area as distribution steel.



8.6 DESIFN OF STAIRS SPANNING HORIZONTALLY:

For stairs spanning horizontally, the waist slab is supported on sides by side

walls or by a stringer beam on one side and wall on other side. Hence, each step

behaves as an independent simply supported beam spanning horizontally. For design

purpose each step is considered as a rectangular beam of width b and effective depth

D/2.

Where, b = R2 + T2

D = Thickness of waist slab + R cosθ = Thickness of waist slab + R.T

𝑏

Main reinforcement is provided along the span direction which generally

consists of one rod in each step and distribution reinforcement is provided

perpendicular to the direction of spanning.

8.7 DESIGN PROCEDURE FOR STAIRS SPANNING

LONGITUDINALLY:

1. Assume the thickness of waist slab based on stiffness.

Span/thickness ratio can be selected in the range of 20 to 25.

2. Determine the dimensions of equivalent beam as follows.

b = R2 + T2, R being rise T being tread.

D = Thickness of waist slab + R.T

𝑏

Effective depth d = D/2

3. Determine the load wu on each step per meter width (span direction), which

includes the weight of waist slab, weight of step and live load.

Weight of waist slab = t.b.25KN/m

Weight of step per meter width = 12 R. T. 25 KN/m

4. Determine the maximum bending moment M𝑢 = w𝑢 l2

8

5. Determine the minimum depth required to resist the bending moment by

equating

M𝑢 = M𝑢 ,𝑙𝑖𝑚 = k. 𝑓𝑐𝑘𝑏𝑑2

Where, k = 0.138 for Fe415 steel & 0.148 for mild steel

Provided depth should be more than this value. Otherwise increase depth.

6. Calculate the area of steel by using

M𝑢 = 0.87𝑓𝑦A𝑠𝑡𝑑[1 −𝑓𝑦A𝑠𝑡

𝑓𝑦𝑏. 𝑑]



7. Provide distribution reinforcement perpendicular to the span direction at 0.12

%( for HYSD bars) of gross cross sectional area and find the spacing of these

bars. If mild steel bars are used, provide 0.15% of gross area as distribution

steel.

8.8 DESIGN OF STAIR CASE:

Width of staircase = 1000 mm

Floor to Floor height (H) = 3200 mm

Live load = 3 KN/𝑚2

Let,

Riser (R) = 160 mm

Tread (T) = 250 mm

sec 𝜃 = 2502+1602

2502 = 1.1877

No. of risers required = 𝐻

𝑅 =

3200

160 = 20

No. of risers in each Flight = 10

No. of Treads per Flight = 10 – 1 = 9

Therefore,

Going = 250 x 9 = 2250 mm

Assuming, width of landing at end = 800 mm

Flight I is supported on beam

a) Mid-landing level

Total span L = 2250 + 800 + 300 = 3350 mm {Horizontally}

Design of Flight I:

Type one way single span simply supported inclined slab.

L = 3350 mm ~ 3.35 m

Trial depth of waist slab

Basic 𝐿

𝑑 ratio 𝑟𝑏 = 20 {for simply supported}

Assuming 𝑃𝑡 = 0.4%



Modification factor 𝛼1 = 1.32, for 𝑓𝑠 = 240 N/m𝑚2 {fig. No. 4 of IS

456:2000}

Required effective depth = d = 𝐿

𝛼1 ∗ 𝑟𝑏 =

3350

1.32 ×20 = 130 mm

Assuming, d = 20 mm for 𝐹𝑒415

D = 130 + 20 = 150 mm

Loads:

S/W = 25 x D x sec Φ = 25 x 0.15 x 1.1877 = 4.45 KN/𝑚2

Weight of steps = 25 R

2 = 25 x 0.16 / 2 = 2 KN/𝑚2

Live load = 5 KN/𝑚2

Floor finish = 1 KN/𝑚2

Total working load = 12.45 KN/𝑚2

Total design load, (𝑊𝑢 ) = 1.5 x 12.45 = 18.68 KN/𝑚2

Design Moments: Consider 1m width of slab

Mu = 𝑊

𝑢 ∗ 𝑙2

8 =

18.68 x 3.352

8 = 26.20 KN.m

Mu max = 0.138 fck . bd2 For Fe415

= 0.138 x 20 x 1000 x 1302

= 46.64 KN-m

Mu max > Mu Safe

Main Steel:

Required area of steel Ast = 0.5 x 20

4.5 1 −

4.6 x 26.20 x 106

20 x 1000 x 1302 x 1000 x 130

= 619.66 m𝑚2



Assuming, 10 mm ø Bars

ast = Π

4 x 102 = 78.57 m𝑚2

Spacing:

Ast

ast X 1000 =

78.57

619.66 x 1000 = 126 mm

Therefore,

Provide # 10 mm @ 120 mm c/c

Ast Provided = 654.762 m𝑚2

Distribution Steel:

For, Fe415 Pt = 0.12%

Ast = 0.12

100 x 1000 x 150 = 180 m𝑚2

Provide # 8 mm @ 275 mm c/c

Ast Provided = 182 m𝑚2

Design of Flight II:

Same as flight I

MODULE II



10. INTRODUCTION TO STEEL STRUCTURES

10.1 Introduction:

Structural steel has been used in the construction of structures for well over a

century. It is perhaps the most versatile of structural materials and has been used

extensively in the construction of multi-storeyed buildings, railways, bridges,

industrial structures, transmission towers, overhead tanks, chimneys, bunkers, silos,

etc.,

In many situations, lighter steel structures are invariably preferred to the

heavier alternatives such as reinforced concrete or pre-stressed concrete. The main

advantages of steel structures are its intrinsic strength, prefabrication and quicker

transportability to the work site and faster erection. Steel structures can be easily

dismantled without loss to the integrity of the original structure. Most structural steel

units are prefabricated in a workshop with superior quality control compared to in situ

construction.

Tolerances specified for steel structural components during fabrication and

erection are small compared to similar reinforced concrete structures. Steel also plays

an important role in composite construction in conjunction with reinforced and pre-

stressed concrete structures.

The advantages of steel members are as follows:

1. The steel members have high strength. Therefore, the steel members can resist

high loads with comparatively light weight and small size of members. The

steel members can be conveniently handled and transported because of their

small size.

2. The steel members are gas and water-tight, because of high density of steel.

3. The steel members have long service life. This is because of high and

homogeneous strength and density properties of steel.

4. The steel members can be used as pre-fabricated members, because of ease of

handling, fabrication and erection.

5. The steel members can be readily disassembled or replaced.

6. The existing steel structures and structural components may be strengthened

by connecting additional sections or planes.

7. The steel structures may be inspected quickly and conveniently.

The disadvantages of steel members are as follows:

1. The steel members are susceptible to corrosion. The corrosion necessitates

their painting or the use of other methods of their protection.

2. The steel members are costly.



Structural Steel:

The structural steel is the steel used for the manufacture of rolled structural

steel sections, fastenings and other elements for use in structural steel works. This

material steel is an alloy of iron and carbon (small percentage) and other elements in

varying percentages. The strength, hardness and brittleness of steel increase and

ductility of steel decreases with the increase of percentage of carbon. Depending on

the chemical composition, the different type of steels are classified as mild steel,

medium carbon steel, high carbon steel, low alloy steel and high alloy steel. The mild

steel, medium carbon steel and low alloy steel are generally used for steel structures.

The copper bearing quality of steel contains small percentage of copper contents. The

corrosive resistance of such steel is increased.

1. Mild steel: The mild steel is used for the manufacture of rolled structural steel

sections, rivets and bolts. Following operations can be done easily on mild

steel :

1. Cutting

2. Punching

3. Drilling

4. Machining

5. Welding

6. Forging when heated

The mild steel cannot be used for manufacture of cutting tools.

All structural steels used in general construction, coming within the

preview of IS: 800-84 shall, before fabrication, comply with one of the

following Indian Standard Specifications.

1. IS: 226- 1975 structural steel (standard quality)

2. IS: 1977- 1975 structural steel (ordinary quality)

3. IS: 2062- 1984 weldable structural steel

4. IS: 961- 1975 structural steel ( high tensile)

5. IS: 8500- 1977 weldable structural steel (medium and high strength

qualities)

10.2 ROLLED STRUCTURAL STEEL SECTIONS:

The steel sections manufactured in rolling mills and used as structural

members are known as rolled structural steel sections. The steel sections are named

according to their cross- sectional shapes. Many steel structures are readily available

in the market and have frequent demand. Such sections are known as regular steel

sections. Some steel sections are rarely used. The special requisition and are known as

special sections.



‘ISI’ Handbook for Structural Engineers ‘I’ gives nominal dimensions,

weight and geometrical properties of various rolled structural steel sections. This

handbook also gives other additional data required by the designers and architects.

The various types of rolled structural steel sections manufactured and used as

structural members are given below:

1. Rolled Steel I Sections

2. Rolled Steel Channel Sections

3. Rolled Steel Tee Sections

4. Rolled Steel Angle Sections

5. Rolled Steel Bars

6. Rolled Steel Tubes

7. Rolled Steel Flats

8. Rolled Steel Sheets and Strips

9. Rolled Steel Plates

10.2.1 ROLLED STEEL BEAM (I)SECTIONS

The rolled steel beams are classified into the following four series as per BIS:

(IS: 808- 1989)

a. Indian Standard Junior Beams-------------------------ISJB

b. Indian Standard Light Beams -------------------------ISlB

c. Indian Standard Medium Weight Beams-------------ISMB

d. Indian Standard Wide Flange Beams-----------------ISWB

The rolled steel columns/heavy weight beams are classified into the following

two series as per BIS (IS: 808-1989)

1. Indian Standard Column Sections--------------------ISSC

2. Indian Standard Heavy Weight Beams---------------ISHB

The cross-section of a rolled steel beam has been given below. The

beam section consists of web and two flanges. The junction between the flange and

the web is known as fillet. These hot rolled steel beam sections have sloping flanges.

The outer and inner faces are inclined to each other and they interest at an angle

varying from 𝟏𝟏

𝟐 to 8

0 depending on the section and rolling mill practice. The angle of

intersection of ISMB section is 80. Abbreviated reference symbols (JB, LB, MB, WB,

SC and HB) have been used in designating the Indian Standard Sections as per BIS

(IS: 808-1989)



FIG 10.1 INDIAN STANDARD I SECTION

10.2.2 ROLLED STEEL CHANNEL SECTIONS

The rolled steel channel sections are classified in the following four series as per

ISI:

1. Indian Standard Junior Channels----------------------------ISJC

2. Indian Standard Light Channels-----------------------------ISLC

3. Indian Standard Medium Weight Channels----------------ISMC

4. Indian Standard Medium Weight Parallel -----------------ISMCP

Flange Channels

The cross-section of rolled steel channel section been shown below. The

channel section consists of web and two flanges. The junction between the flange

and the web is known as fillet.

FIG 10.2 INDIAN STANDARD CHANNEL SECTION

Note: As per IS: 808-1989, following channel sections have also been additionally

adopted as Indian Standard Channel Sections

1. Indian Standard Light Channels with -------------------ISLC(P)

parallel flanges



2. Medium Weight Channels------------------------------ --ISMC

3. Medium weight channels with parallel flanges---------ISMCP

4. Indian Standard Gate Channels---------------------------ISPG

In MC and MCP channel sections, some heavier sections have been

developed for their intended use in wagon building industry. The method of

designating MC and MCP channels is also same as that for IS-channels described

above.

10.2.3 ROLLED STEEL TEE SECTIONS

The rolled steel tee sections are classified into the following five series as per

ISI:

1. Indian Standard Normal Tee Bars------------------ISNT

2. Indian Standard Wide flange Tee Bars-------------ISHT

3. Indian Standard Long Legged Tee Bars------------ISST

4. Indian Standard Light Tee Bars---------------------ISLT

5. Indian Standard Junior Tee Bars--------------------ISJT

FIG 10.3 INDIAN STANDARD TEE SECTION

The cross-section of a rolled steel tee section has been shown above. The tee

section consists of web and flange. The junction between the flange and the web is

known as fillet.

Note: As per IS: 808-1984, following T-sections have also been additionally

adopted as Indian Standard T-sections.

1. Indian Standard deep legged Tee bars---------------------ISDT

2. Indian Standard Slit medium weight Tee bars------------ISMT

3. Indian Standard Slit Tee bars from I-sections-------------ISNT

It is to note that as per IS: 808- 1978 (part II), H beam sections have been deleted.

10.2.4 ROLLED STEEL ANGLE SECTIONS

The rolled steel angle sections are classified into the following three series.

1. Indian Standard Equal Angles---------------ISA

2. Indian Standard Unequal Angles------------ISA



3. Indian Standard Bulb Angles----------------ISBA

FIG 10.4 INDIAN STANDARD ANGLE SECTION

The cross-section of a rolled equal angle section has been shown

above, unequal angle section and that of bulb angle section. The lengths of the legs

in case of equal sections are equal and in case of unequal section, length of one leg

is longer than the other. The thickness of legs of equal and unequal angle sections

are equal. The bulb angle shown in fig consists of web flange and a bulb projecting

from end of web. The thickness of web of bulb angle may or may not be equal tp

the thickness of flange.

Note: As per IS: 808- 1984, some supplementary angle sections have also

additionally adopted as Indian Standard angle sections. However prefix ISA has

been adopted. These sections are designated by the size of legs followed by

thickness.

10.2.5 ROLLED STEEL BARS

The rolled steel bars are classified into the following two series:

1. Indian Standard Round Bars------------ISRQ

2. Indian Standard Square Bars------------ISSQ

FIG 10.5 INDIAN STANDARD SQUARE AND ROUND BAR



10.2.6 ROLLED STEEL TUBES

The rolled steel tubes are used as columns and compression members

and tension members in tubular trusses. The rolled steel tubes are efficient

structural sections to be used as compression members. The steel tube sections

have equal radius of gyration in all directions.

FIG 10.6 INDIAN STANDARD TUBE SECTION

10.2.7 ROLLED STEEL FLATS

The rolled steel flats are used for lacing of elements in built-up

members, such as columns and are also used as ties.

FIG 10.7 INDIAN STANDARD STEEL FLAT SECTION

STRUCTURAL STEEL DESIGN INVOLVES THE FOLLWING STEPS:

1. Choice of materials such as the type and grade of structural steel.

2. Selection of the configuration of the structural system such as trusses, griders,

portal frames, stanchions, grid frames, cable structures, space frames, folded

plates, muti-storey framed structures, mill bents and foundation systems.

3. Computation of various types of loads acting on the structure.

4. Preliminary analysis of forces and moments developed in the structural

elements under the most unfavorable loading conditions using elementary

procedures, followed by rigorous analysis using computer software and other

design procedures.

5. Structural design of elements conforming to the latest national codes.

6. Final evaluation of strength, serviceability and safety of the structure as per the

code requirements.

7. Preparation of detailed structural and architectural drawings using AUTO

CAD programs with suitable specifications.



11. LIMIT STATE DESIGN SPECIFICATIONS FOR

STRUCTURAL STEEL MEMBERS

The recently revised Indian Standard code IS: 800-2007 specifies that

in general structures and elements should be designed by the limit state

method. In case where the limit state method cannot be conveniently adopted,

the working stress method may be used.

Limit state design is a method of designing structures based on a

statistical concept of safety and the associated statistical probability of failure.

Structures designed by this method should satisfy the dual criterion of

(a) Limit state of strength and

(b) Limit state of serviceability.

The limit states of strength are those associated with failure (or

imminent failure), under the action of probable and most unfavorable

combination of loads on the structure using the appropriate partial safety

factors, which may endanger the safety of life and property. The limit sate of

strength includes:

(a) Loss of equilibrium of the structure as a whole or any of its parts or

components.

(b) Loss of stability of the structures (including the effect of sway

where appropriate and overturning) or any of its parts, including

supports and foundations.

(c) Failure by excessive deformation, rupture of the structure or any of

its parts or components.

(d) Fracture due to fatigue

(e) Brittle fracture

The limit state of serviceability comprises the following criteria:

(a) Any deformation and deflection which adversely affect the

appearance or effective use of the structure or may cause

improper functioning of equipment or services or may cause

damages to finishes and non-structural members.

(b) Vibrations in the structure or any of its components causing

discomfort to people, damage to the structures, its contents or

which may limit its functional effectiveness. Special consideration

shall be given to systems susceptible to vibration, such as large

open floor areas free of use and occupancy (Refer to Annex C of

the Code).

(c) Repairable damage or crack due to fatigue.

(d) Corrosion, durability.

(e) Fire.



Use of Relevant IS Codes:

1. For steel:

(a) Structural steel as per

IS: 226, IS: 2062, IS: 3502, IS: 1977, IS: 961, IS: 8500

(b) Steel for reinforced concrete

IS: 432, IS: 1139, IS: 1786, IS: 2090.

(c) Steel for bars, rivets etc.

IS: 1148, 1149, 1570, 2073, 7383, 4431, and 5517.

(d) Steel for tubes and pipes.

IS: 1239, 1914 and 1978.

2. For code of practice for design of steel structures:

IS: 800- 1984, IS: 800-2007

3. For size of weld and stresses in weld

IS: 816- 1969

4. For code of practice for design loads:

IS: 875- 1987

Part I: Dead loads – unit weights of building materials and stored

materials

Part II: imposed loads

Part III: wind loads

Part IV: snow loads

Part V: special loads and load combinations

Permissible Stresses:

Structures shall be designed so that the calculated stresses in the members do

not exceed the corresponding permissible stresses specified by IS: 800-1984

1. Axial Tensile stress (αat) (clause 4.1 of IS: 800):

The permissible stress in axial tension, αat in MPa on the net effective area of

the sections shall not exceed

𝛼𝑎𝑡 = 0.6𝑓𝑦

Where fy = minimum yield stress of steel, in MPa.

2. Axial Compression Stress (αac) (clause 5.1 of IS: 800):

The direct stresses in compression on the gross cross sectional area of axially

loaded compression members shall not exceed 0.6 fy nor the permissible stress,

αac calculated using the formula

𝛼𝑎𝑡 = 0.6 𝑓𝑐𝑐𝑓𝑦

[ 𝑓𝑐𝑐 𝑛 + 𝑓𝑦

𝑛]

1𝑛

Where αac = permissible stress in axial compression, in MPa



fy = yield stress of steel in compression, in MPa.

fcc = elastic critical stress in compression = 𝜋2E

𝜆

E = modulus of elasticity of steel = 2 x 105 MPa

λ = 𝑙

𝑟 = slenderness ratio of the member.

m = a factor assumed as 1.4

3. Bending stress (αbc or αbt) (clause 6.2 of IS: 800):

The permissible compressive or tensile bending stress is given by

𝛼𝑏𝑐 𝑜𝑟 𝛼𝑏𝑡 = 0.66𝑓𝑦

If the compression flange is not restrained laterally against buckling, αbc or αbt

should not exceed the values given by the above equation nor the values given

in table 6.1 A to 6.1 F and 6.2 of IS: 800.

4. Bearing stress (αp) (clause 6.3 of IS: 800):

The bearing stress in any part of a beam when calculated on the net area of

contact shall not exceed the values determined by the formula.

𝛼𝑝 = 0.75𝑓𝑦

Where, αp = maximum yield stress of steel, in MPa

5. Maximum Shear Stress (τvm) (clause 6.4.1 of IS: 800):

The maximum shear stress in a member shall not exceed the value given by

the formula

τ𝑣𝑚 = 0.45𝑓𝑦

Where,

τvm = maximum permissible shear stress

fy = minimum yield stress of steel, in MPa

Average Shear Stress (τva):

The average shear stress in a member calculated on the cross section of the

web shall not exceed the value given by the formula

τ𝑣𝑎 = 0.4𝑓𝑦

Where,

τva = average shear stress

fy = minimum yield stress of steel, in MPa

Increase in Permissible Stresses (clause 3.10.2.1 IS: 800):

When the effect of wind or earthquake load is taken into account in the design

1. The permissible stresses in structural steel may be increased by 33% and

2. Permissible stress in rivets, bolts and tension maybe increased by 25%

Load combinations:

The following combinations of loads which ever produces maximum effect

maybe assumed for general design of most of the structures.



1. Dead load alone

2. Dead load + partial or full live load which ever causes the most critical

condition in the structure

3. Dead load + wind or seismic load and

4. Dead load + part or full live load + wind or seismic load.

The partial safety factors for loads (γf) for the limit states of strength and

serviceability for different load combinations is shown in table below:

Combination

Limit state of strength Limit state of

serviceability

DL

LL

WL/E

L AL DL

LL

WL/E

L L

ead

ing

Acc

om

p

an

yin

g

Lea

din

g

Acc

om

p

an

yin

g

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DL+LL+CL 1.5 1.5 1.05 --- --- 1.0 1.0 1.0 ---

DL+LL+CL+WL/

EL 1.2 1.2 1.05 0.6 --- 1.0 0.8 0.8 0.8

DL+LL+CL+WL/

EL 1.2 1.2 0.53 1.2

DL+WL/EL 1.5

(0.9) --- --- 1.5 --- 1.0 --- --- 1.0

DL+ER 1.2

(0.9) 1.2 --- --- --- --- --- --- ---

DL+LL+AL 1.0 0.3

5 0.35 --- 1.0 --- --- --- ---

(1) When action of different live loads is simultaneously considered, the leading live

load shall be considered to be the one causing the higher load effects in the

member/section.

(2) This value is to be considered when the dead load contributes to stability against

overturning is critical or the dead load causes reduction in stress due to other

loads.

Abbreviations:

DL= Dead Load, LL=Imposed Load (live load), WL= Wind Load, CL= Crane

Load (vertical/horizontal), AL= Accidental Load, ER= Election Load, EL=

Earthquake Load.

Note: The effects of actions (load) in terms of stresses resultant may be obtained

from an appropriate method of analysis.



12. ANALYSIS OF STEEL BUILDING

Analysis of a steel structure is same as analysis of RCC structure by using

STAAD PRO v8i explained in chapter 3 of Module I.

12.1 INPUT COMMANDS IN STAAD PRO EDITOR

STAAD SPACE

START JOB INFORMATION

ENGINEER DATE 29-Feb-12

JOB NAME comparative study on multistorey R.C.C and STEEL Building

JOB CLIENT NIET

ENGINEER NAME NIET

END JOB INFORMATION

INPUT WIDTH 79

UNIT METER KN

JOINT COORDINATES

1 0 0 0; 2 3 0 0; 3 6.7 0 0; 4 10.25 0 0; 5 11.9 0 0; 6 13.8 0 0; 7 17.5 0 0; 8 20.5 0 0; 9

6.7 0 2; 10 11.9 0 2; 11 13.8 0 2; 12 0 0 3.65; 13 3 0 3.65; 14 6.7 0 3.65; 15 10.25 0

3.65; 16 13.8 0 3.65; 17 17.5 0 3.65; 18 20.5 0 3.65; 19 0 0 7.15; 20 3 0 7.15; 21 6.7 0

7.15; 22 10.25 0 7.15; 23 13.8 0 7.15; 24 17.5 0 7.15; 25 20.5 0 7.15; 26 0 0 11.3; 27

3 0 11.3; 28 6.7 0 11.3; 29 10.25 0 11.3; 30 13.8 0 11.3; 31 17.5 0 11.3; 32 20.5 0

11.3; 33 0 1.5 0; 34 3 1.5 0; 35 6.7 1.5 0; 36 10.25 1.5 0; 37 11.9 1.5 0; 38 13.8 1.5 0;

39 17.5 1.5 0; 40 20.5 1.5 0; 41 6.7 1.5 2; 42 11.9 1.5 2; 43 13.8 1.5 2; 44 0 1.5 3.65;

45 3 1.5 3.65; 46 6.7 1.5 3.65; 47 10.25 1.5 3.65; 48 13.8 1.5 3.65; 49 17.5 1.5 3.65;

50 20.5 1.5 3.65; 51 0 1.5 7.15; 52 3 1.5 7.15; 53 6.7 1.5 7.15; 54 10.25 1.5 7.15; 55

13.8 1.5 7.15; 56 17.5 1.5 7.15; 57 20.5 1.5 7.15; 58 0 1.5 11.3; 59 3 1.5 11.3; 60 6.7

1.5 11.3; 61 10.25 1.5 11.3; 62 13.8 1.5 11.3; 63 17.5 1.5 11.3; 64 20.5 1.5 11.3; 65

6.7 3.1 0; 66 6.7 3.1 2; 67 0 4.7 0; 68 3 4.7 0; 69 6.7 4.7 0; 70 10.25 4.7 0; 71 11.9 4.7

0; 72 13.8 4.7 0; 73 17.5 4.7 0; 74 20.5 4.7 0; 75 6.7 4.7 2; 76 11.9 4.7 2; 77 13.8 4.7

2; 78 0 4.7 3.65; 79 3 4.7 3.65; 80 6.7 4.7 3.65; 81 10.25 4.7 3.65; 82 13.8 4.7 3.65;

83 17.5 4.7 3.65; 84 20.5 4.7 3.65; 85 0 4.7 7.15; 86 3 4.7 7.15; 87 3.85 4.7 7.15; 88

6.7 4.7 7.15; 89 10.25 4.7 7.15; 90 13.8 4.7 7.15; 91 16.65 4.7 7.15; 92 17.5 4.7 7.15;

93 20.5 4.7 7.15; 94 0 4.7 11.3; 95 3 4.7 11.3; 96 3.85 4.7 11.3; 97 6.7 4.7 11.3; 98

10.25 4.7 11.3; 99 13.8 4.7 11.3; 100 16.65 4.7 11.3; 101 17.5 4.7 11.3; 102 20.5 4.7

11.3; 103 6.7 6.3 0; 104 6.7 6.3 2; 105 0 7.9 0; 106 3 7.9 0; 107 6.7 7.9 0; 108 10.25

7.9 0; 109 11.9 7.9 0; 110 13.8 7.9 0; 111 17.5 7.9 0;112 20.5 7.9 0; 113 6.7 7.9 2;

114 11.9 7.9 2; 115 13.8 7.9 2; 116 0 7.9 3.65; 117 3 7.9 3.65; 118 6.7 7.9 3.65; 119



10.25 7.9 3.65; 120 13.8 7.9 3.65; 121 17.5 7.9 3.65; 122 20.5 7.9 3.65; 123 0 7.9

7.15; 124 3 7.9 7.15; 125 3.85 7.9 7.15; 126 6.7 7.9 7.15; 127 10.25 7.9 7.15; 128

13.8 7.9 7.15; 129 16.65 7.9 7.15; 130 17.5 7.9 7.15; 131 20.5 7.9 7.15; 132 0 7.9

11.3; 133 3 7.9 11.3; 134 3.85 7.9 11.3; 135 6.7 7.9 11.3; 136 10.25 7.9 11.3; 137

13.8 7.9 11.3; 138 16.65 7.9 11.3; 139 17.5 7.9 11.3; 140 20.5 7.9 11.3; 141 6.7 9.5 0;

142 6.7 9.5 2; 143 0 11.1 0; 144 3 11.1 0; 145 6.7 11.1 0; 146 10.25 11.1 0; 147 11.9

11.1 0; 148 13.8 11.1 0; 149 17.5 11.1 0; 150 20.5 11.1 0; 151 6.7 11.1 2; 152 11.9

11.1 2; 153 13.8 11.1 2; 154 0 11.1 3.65; 155 3 11.1 3.65; 156 6.7 11.1 3.65; 157

10.25 11.1 3.65; 158 13.8 11.1 3.65; 159 17.5 11.1 3.65; 160 20.5 11.1 3.65; 161 0

11.1 7.15; 162 3 11.1 7.15; 163 3.85 11.1 7.15; 164 6.7 11.1 7.15; 165 10.25 11.1

7.15; 166 13.8 11.1 7.15; 167 16.65 11.1 7.15; 168 17.5 11.1 7.15; 169 20.5 11.1

7.15; 170 0 11.1 11.3; 171 3 11.1 11.3; 172 3.85 11.1 11.3; 173 6.7 11.1 11.3; 174

10.25 11.1 11.3; 175 13.8 11.1 11.3; 176 16.65 11.1 11.3; 177 17.5 11.1 11.3; 178

20.5 11.1 11.3; 179 6.7 12.7 0; 180 6.7 12.7 2; 181 0 14.3 0; 182 3 14.3 0; 183 6.7

14.3 0; 184 10.25 14.3 0; 185 11.9 14.3 0; 186 13.8 14.3 0; 187 17.5 14.3 0; 188 20.5

14.3 0; 189 6.7 14.3 2; 190 11.9 14.3 2; 191 13.8 14.3 2; 192 0 14.3 3.65; 193 3 14.3

3.65; 194 6.7 14.3 3.65; 195 10.25 14.3 3.65; 196 13.8 14.3 3.65; 197 17.5 14.3 3.65;

198 20.5 14.3 3.65; 199 0 14.3 7.15; 200 3 14.3 7.15; 201 3.85 14.3 7.15; 202 6.7 14.3

7.15; 203 10.25 14.3 7.15; 204 13.8 14.3 7.15; 205 16.65 14.3 7.15; 206 17.5 14.3

7.15; 207 20.5 14.3 7.15; 208 0 14.3 11.3; 209 3 14.3 11.3; 210 3.85 14.3 11.3; 211

6.7 14.3 11.3; 212 10.25 14.3 11.3; 213 13.8 14.3 11.3; 214 16.65 14.3 11.3; 215 17.5

14.3 11.3; 216 20.5 14.3 11.3; 217 6.7 15.9 0; 218 6.7 15.9 2; 219 0 17.5 0; 220 3

17.5 0; 221 6.7 17.5 0; 222 10.25 17.5 0; 223 11.9 17.5 0; 224 13.8 17.5 0; 225 17.5

17.5 0; 226 20.5 17.5 0; 227 6.7 17.5 2; 228 11.9 17.5 2; 229 13.8 17.5 2; 230 0 17.5

3.65; 231 3 17.5 3.65; 232 6.7 17.5 3.65; 233 10.25 17.5 3.65; 234 13.8 17.5 3.65;

235 17.5 17.5 3.65; 236 20.5 17.5 3.65; 237 0 17.5 7.15; 238 3 17.5 7.15; 239 3.85

17.5 7.15;240 6.7 17.5 7.15; 241 10.25 17.5 7.15; 242 13.8 17.5 7.15; 243 16.65 17.5

7.15; 244 17.5 17.5 7.15; 245 20.5 17.5 7.15; 246 0 17.5 11.3; 247 3 17.5 11.3; 248

3.85 17.5 11.3; 249 6.7 17.5 11.3; 250 10.25 17.5 11.3; 251 13.8 17.5 11.3; 252 16.65

17.5 11.3; 253 17.5 17.5 11.3; 254 20.5 17.5 11.3; 255 6.7 20.7 0; 256 10.25 20.7 0;

257 11.9 20.7 0; 258 13.8 20.7 0; 259 11.9 20.7 2; 260 13.8 20.7 2; 261 6.7 20.7

3.65;262 10.25 20.7 3.65; 263 13.8 20.7 3.65;

MEMBER INCIDENCES

1 33 1; 2 34 2; 3 35 3; 4 36 4; 5 37 5; 6 38 6; 7 39 7; 8 40 8; 9 41 9; 10 42 10; 11 43

11; 12 44 12; 13 45 13; 14 46 14; 15 47 15; 16 48 16; 17 49 17; 18 50 18; 19 51 19;

20 52 20; 21 53 21; 22 54 22; 23 55 23; 24 56 24; 25 57 25; 26 58 26; 27 59 27; 28 60

28; 29 61 29; 30 62 30; 31 63 31; 32 64 32; 101 33 67; 102 34 68; 103 65 69; 104 35

65; 105 36 70; 106 37 71; 107 38 72; 108 39 73; 109 40 74; 110 66 75; 111 41 66;

112 42 76; 113 43 77; 114 44 78; 115 45 79; 116 46 80; 117 47 81; 118 48 82; 119 49

83; 120 50 84; 121 51 85; 122 52 86; 123 53 88; 124 54 89; 125 55 90; 126 56 92;

127 57 93; 128 58 94; 129 59 95; 130 60 97; 131 61 98; 132 62 99; 133 63 101; 134

64 102; 201 67 105; 202 68 106; 203 103 107; 204 69 103; 205 70 108; 206 71 109;



207 72 110; 208 73 111; 209 74 112; 210 104 113; 211 75 104; 212 76 114; 213 77

115; 214 78 116; 215 79 117; 216 80 118; 217 81 119; 218 82 120; 219 83 121; 220

84 122; 221 85 123; 222 86 124; 223 88 126; 224 89 127; 225 90 128; 226 92 130;

227 93 131; 228 94 132; 229 95 133; 230 97 135; 231 98 136; 232 99 137; 233 101

139; 234 102 140; 301 105 143; 302 106 144; 303 141 145; 304 107 141; 305 108

146; 306 109 147; 307 110 148; 308 111 149; 309 112 150; 310 142 151; 311 113

142; 312 114 152; 313 115 153; 314 116 154; 315 117 155; 316 118 156; 317 119

157; 318 120 158; 319 121 159; 320 122 160; 321 123 161; 322 124 162; 323 126

164; 324 127 165; 325 128 166; 326 130 168; 327 131 169; 328 132 170; 329 133

171; 330 135 173; 331 136 174; 332 137 175; 333 139 177; 334 140 178; 401 143

181; 402 144 182; 403 179 183; 404 145 179; 405 146 184; 406 147 185; 407 148

186; 408 149 187; 409 150 188; 410 180 189; 411 151 180; 412 152 190; 413 153

191; 414 154 192; 415 155 193; 416 156 194; 417 157 195; 418 158 196; 419 159

197; 420 160 198; 421 161 199; 422 162 200; 423 164 202; 424 165 203; 425 166

204; 426 168 206; 427 169 207; 428 170 208; 429 171 209; 430 173 211; 431 174

212; 432 175 213; 433 177 215; 434 178 216; 501 181 219; 502 182 220; 503 217

221; 504 183 217; 505 184 222; 506 185 223; 507 186 224; 508 187 225; 509 188

226; 510 218 227; 511 189 218; 512 190 228; 513 191 229; 514 192 230; 515 193

231; 516 194 232; 517 195 233; 518 196 234; 519 197 235; 520 198 236; 521 199

237; 522 200 238; 523 202 240; 524 203 241; 525 204 242; 526 206 244; 527 207

245; 528 208 246; 529 209 247; 530 211 249; 531 212 250; 532 213 251; 533 215

253; 534 216 254; 601 255 221; 602 256 222; 603 257 223; 604 258 224; 605 259

228; 606 260 229; 607 261 232; 608 262 233; 609 263 234; 1001 33 34; 1002 34 35;

1003 35 36; 1004 36 37; 1005 37 38; 1006 38 39; 1007 39 40; 1008 42 43; 1009 44

45; 1010 45 46; 1011 46 47; 1012 47 48; 1013 48 49; 1014 49 50; 1015 51 52; 1016

52 53; 1017 53 54; 1018 54 55; 1019 55 56; 1020 56 57; 1021 58 59; 1022 59 60;

1023 60 61; 1024 61 62; 1025 62 63; 1026 63 64; 1027 35 41; 1028 37 42; 1029 38

43; 1030 33 44; 1031 34 45; 1032 36 47; 1033 39 49; 1034 40 50; 1035 41 46; 1036

43 48; 1037 44 51; 1038 45 52; 1039 46 53; 1040 47 54; 1041 48 55; 1042 49 56;

1043 50 57; 1044 51 58; 1045 52 59; 1046 53 60; 1047 54 61; 1048 55 62; 1049 56

63; 1050 57 64; 1051 65 66; 2001 67 68; 2002 68 69; 2003 69 70; 2004 70 71; 2005

71 72; 2006 72 73; 2007 73 74; 2008 76 77; 2009 78 79; 2010 79 80; 2011 80 81;

2012 81 82; 2013 82 83; 2014 83 84; 2015 85 86; 2016 86 87; 2017 87 88; 2018 88

89; 2019 89 90; 2020 90 91; 2021 91 92; 2022 92 93; 2023 94 95; 2024 95 96; 2025

96 97; 2026 97 98; 2027 98 99; 2028 99 100; 2029 100 101; 2030 101 102; 2031 67

78; 2032 68 79; 2033 69 75; 2034 75 80; 2035 70 81; 2036 71 76; 2037 72 77; 2038

77 82; 2039 73 83; 2040 74 84; 2041 78 85; 2042 81 89; 2043 84 93; 2044 85 94;

2045 87 96; 2046 88 97; 2047 89 98; 2048 90 99; 2049 91 100; 2050 93 102; 2051

103 104; 3001 105 106; 3002 106 107; 3003 107 108; 3004 108 109; 3005 109

110;3006 110 111; 3007 111 112; 3008 114 115; 3009 116 117; 3010 117 118; 3011

118 119; 3012 119 120; 3013 120 121; 3014 121 122; 3015 123 124; 3016 124 125;

3017 125 126; 3018 126 127; 3019 127 128; 3020 128 129; 3021 129 130; 3022 130

131; 3023 132 133; 3024 133 134; 3025 134 135; 3026 135 136; 3027 136 137; 3028

137 138; 3029 138 139; 3030 139 140; 3031 105 116; 3032 106 117; 3033 107 113;



3034 113 118; 3035 108 119; 3036 109 114; 3037 110 115; 3038 115 120; 3039 111

121; 3040 112 122; 3041 116 123; 3042 119 127; 3043 122 131; 3044 123 132; 3045

125 134; 3046 126 135; 3047 127 136; 3048 128 137; 3049 129 138; 3050 131 140;

3051 141 142; 4001 143 144; 4002 144 145; 4003 145 146; 4004 146 147; 4005 147

148; 4006 148 149; 4007 149 150; 4008 152 153; 4009 154 155; 4010 155 156; 4011

156 157; 4012 157 158; 4013 158 159; 4014 159 160; 4015 161 162; 4016 162 163;

4017 163 164; 4018 164 165; 4019 165 166; 4020 166 167; 4021 167 168; 4022 168

169; 4023 170 171; 4024 171 172; 4025 172 173; 4026 173 174; 4027 174 175; 4028

175 176; 4029 176 177; 4030 177 178; 4031 143 154; 4032 144 155; 4033 145 151;

4034 151 156; 4035 146 157; 4036 147 152; 4037 148 153; 4038 153 158; 4039 149

159; 4040 150 160; 4041 154 161; 4042 157 165; 4043 160 169; 4044 161 170; 4045

163 172; 4046 164 173; 4047 165 174; 4048 166 175; 4049 167 176; 4050 169 178;

4051 179 180; 5001 181 182; 5002 182 183; 5003 183 184; 5004 184 185; 5005 185

186; 5006 186 187; 5007 187 188; 5008 190 191; 5009 192 193; 5010 193 194; 5011

194 195; 5012 195 196; 5013 196 197; 5014 197 198; 5015 199 200; 5016 200 201;

5017 201 202; 5018 202 203; 5019 203 204; 5020 204 205; 5021 205 206; 5022 206

207; 5023 208 209; 5024 209 210; 5025 210 211; 5026 211 212; 5027 212 213; 5028

213 214; 5029 214 215; 5030 215 216; 5031 181 192; 5032 182 193; 5033 183 189;

5034 189 194; 5035 184 195; 5036 185 190; 5037 186 191; 5038 191 196; 5039 187

197; 5040 188 198; 5041 192 199; 5042 195 203; 5043 198 207; 5044 199 208; 5045

201 210; 5046 202 211; 5047 203 212; 5048 204 213; 5049 205 214; 5050 207 216;

5051 217 218; 6001 219 220; 6002 220 221; 6003 221 222; 6004 222 223; 6005 223

224; 6006 224 225; 6007 225 226; 6008 228 229; 6009 230 231; 6010 231 232; 6011

232 233; 6012 233 234; 6013 234 235; 6014 235 236; 6015 237 238; 6016 238 239;

6017 239 240; 6018 240 241; 6019 241 242; 6020 242 243; 6021 243 244; 6022 244

245; 6023 246 247; 6024 247 248; 6025 248 249; 6026 249 250; 6027 250 251; 6028

251 252; 6029 252 253; 6030 253 254; 6031 219 230; 6032 220 231; 6033 221 227;

6034 227 232; 6035 222 233; 6036 223 228; 6037 224 229; 6038 229 234; 6039 225

235; 6040 226 236; 6041 230 237; 6042 233 241; 6043 236 245; 6044 237 246; 6045

239 248; 6046 240 249; 6047 241 250; 6048 242 251; 6049 243 252; 6050 245 254;

7001 255 256; 7002 256 257; 7003 257 258; 7004 259 260; 7005 261 262; 7006 262

263; 7007 255 261; 7008 256 262; 7009 257 259; 7010 260 258; 7011 260 263;

DEFINE MATERIAL START

ISOTROPIC STEEL

E 2.05e+008

POISSON 0.3

DENSITY 76.8195

ALPHA 1.2e-005

DAMP 0.03



END DEFINE MATERIAL

MEMBER PROPERTY INDIAN

1044 1045 1047 1049 TO 1051 2009 TO 2022 2024 2029 2031 TO 2035 2037 TO

2040 2044 2050 2051 3009 TO 3022 3024 3031 TO 3035 3037 TO 3040 3051 4009

TO 4022 4024 4031 TO 4035 4037 TO 4040 4046 TO 4048 4051 5009 TO 5022

5024 5031 TO 5035 5037 TO 5040 5044 5046 TO 5048 5050 5051 6045 6049

TABLE ST ISHB250

1001 TO 1030 1032 1034 TO 1043 2001 TO 2008 2023 2025 TO 2028 2030 2036

2041 2042 TO 2043 3001 TO 3008 3023 3025 TO 3028 3030 3036 3041 TO 3043

4001 TO 4008 4023 4025 TO 4028 4030 4036 4041 TO 4043 5001 TO 5008 5023

5025 5026 TO 5028 5030 5036 5041 TO 5043 6001 6002 6004 TO 6010 6012 TO

6044 6046 6047 TO 6048 6050 7001 TO 7011 TABLE ST ISHB200

1 TO 32 101 TO 134 201 TO 234 301 TO 334 401 TO 434 501 TO 534 601 TO 608

609 TABLE ST ISWB600A

2045 2049 3045 3049 4045 4049 5045 5049 TABLE ST ISHB300

1031 1033 1046 1048 2046 TO 2048 3029 3044 3046 TO 3048 3050 4029 4044 4050

5029 6003 6011 TABLE ST ISHB400

CONSTANTS

MATERIAL STEEL ALL

SUPPORTS

1 TO 32 PINNED

DEFINE 1893 LOAD

ZONE 0.1 RF 5 I 1 SS 1 ST 1 DM 5 PX 0 DT 1.5

SELFWEIGHT 1

MEMBER WEIGHT

1001 TO 1050 2001 2002 2005 TO 2008 2011 2012 2023 2024 2026 TO 2028 2030

2031 2036 TO 2038 2040 2042 2044 2047 2050 3001 3002 3005 TO 3008 3011 3012

3023 3024 3026 TO 3028 3030 3031 3036 TO 3038 3040 3042 3044 3047 3050 4001

4002 4005 TO 4008 4011 4012 4023 4024 4026 TO 4028 4030 4031 4036 TO 4038

4040 4042 4044 4047 4050 5001 5002 5005 TO 5008 5011 5012 5023 5024 5026

5027 TO 5028 5030 5031 5036 TO 5038 5040 5042 5044 5047 5050 6003 TO 6005

6008 6011 6012 6033 6034 6036 TO 6038 UNI 16

2009 2010 2013 TO 2022 2032 TO 2035 2039 2045 2046 2048 2049 3009 3010 3013

3014 TO 3022 3032 TO 3035 3039 3045 3046 3048 3049 4009 4010 4013 TO 4022



4032 TO 4035 4039 4045 4046 4048 4049 5009 5010 5013 TO 5022 5032 TO 5035

5039 5045 5046 5048 5049 UNI 8

6001 6002 6006 6007 6023 TO 6031 6040 6041 6043 6044 6050 7001 TO 7003 7005

7006 TO 7007 7010 7011 UNI 2

1051 2051 3051 4051 5051 UNI 20

ONEWAY LOAD

YRANGE 4.7 20.7 ONE -3.6 XRANGE 0 20.5 ZRANGE 0 3.65 TOWARDS 7007


ONEWAY LOAD


CHECK SOFT STOREY

DEFINE WIND LOAD

TYPE 1

INT 0.67 HEIG 19.2

EXP 1 JOINT 33 TO 263

LOAD 1 LOADTYPE None TITLE EQ XP

1893 LOAD X 1

LOAD 2 LOADTYPE None TITLE EQ XN

1893 LOAD X -1

LOAD 3 LOADTYPE None TITLE EQ ZP

1893 LOAD Z 1

LOAD 4 LOADTYPE None TITLE EQ ZN

1893 LOAD Z -1

LOAD 5 LOADTYPE None TITLE WL XP

WIND LOAD X 1 TYPE 1

LOAD 6 LOADTYPE None TITLE WL XN

WIND LOAD X -1 TYPE 1

LOAD 7 LOADTYPE None TITLE WL ZP

WIND LOAD Z 1 TYPE 1

LOAD 8 LOADTYPE None TITLE WL ZN



WIND LOAD Z -1 TYPE 1

LOAD 9 LOADTYPE None TITLE DEAD LOAD

SELFWEIGHT Y -1 LIST 1 TO 32 101 TO 134 201 TO 234 301 TO 334 401 TO 434

501 502 TO 534 601 TO 609 1001 TO 1037 1040 1043 TO 1051 2001 TO 2051 3001

TO 3051 4001 TO 4051 5001 TO 5051 6001 TO 6050 7001 TO 7011

MEMBER LOAD

1001 TO 1026 1028 TO 1034 1036 TO 1050 2001 2002 2005 TO 2008 2011 2012

2023 2024 2026 TO 2028 2030 2031 2036 TO 2038 2040 2042 2044 2047 2050 3001

3002 3005 TO 3008 3011 3012 3023 3024 3026 TO 3028 3030 3031 3036 TO 3038

3040 3042 3044 3047 3050 4001 4002 4005 TO 4008 4011 4012 4023 4024 4026 TO

4028 4030 4031 4036 TO 4038 4040 4042 4044 4047 4050 5001 5002 5005 TO 5008

5011 5012 5023 5024 5026 TO 5028 5030 5031 5036 TO 5038 5040 5042 5044 5047

5050 6003 TO 6005 6008 6011 6012 6036 TO 6038 UNI GY -16

1027 1035 2009 2010 2013 TO 2022 2032 TO 2035 2039 2045 2046 2048 2049 3009

3010 3013 TO 3022 3032 TO 3035 3039 3045 3046 3048 3049 4009 4010 4013 TO

4022 4032 TO 4035 4039 4045 4046 4048 4049 5009 5010 5013 TO 5022 5032 TO

5035 5039 5045 5046 5048 5049 6033 6034 UNI GY -8

6001 6002 6006 6007 6023 TO 6031 6040 6041 6043 6044 6050 7001 TO 7003 7005

7006 TO 7007 7010 7011 UNI GY -2

1051 2051 3051 4051 5051 UNI GY -20

ONEWAY LOAD

YRANGE 4.7 20.7 ONE -3.6 XRANGE 0 20.5 ZRANGE 0 3.65 GY TOWARDS

7007


ONEWAY LOAD


LOAD 10 LOADTYPE None TITLE LIVE LOAD

ONEWAY LOAD

YRANGE 4.7 20.7 ONE -2 XRANGE 0 20.5 ZRANGE 0 3.65 GY TOWARDS 7007


ONEWAY LOAD


LOAD COMB 11 SERVICE (DL+LL)



9 1.0 10 1.0

LOAD COMB 12 ULTIMATE 1.5 (DL+LL)

9 1.5 10 1.5

LOAD COMB 13 1.2 (DL+LL+WL XP)

9 1.2 10 1.2 5 1.2

LOAD COMB 14 1.2 (DL+LL+WL XN)

6 1.2 9 1.2 10 1.2

LOAD COMB 15 1.2 (DL+LL+WL ZP)

9 1.2 10 1.2 7 1.2

LOAD COMB 16 1.2 (DL+LL+WL ZN)

9 1.2 10 1.2 8 1.2

LOAD COMB 17 1.2 (DL+LL+EQ XP)

1 1.2 9 1.2 10 1.2

LOAD COMB 18 1.2 (DL+LL+EQ XN)

9 1.2 10 1.2 2 1.2

LOAD COMB 19 1.2 (DL+LL+EQ ZP)

3 1.2 9 1.2 10 1.2

LOAD COMB 20 1.2 (DL+LL+EQ ZN)

4 1.2 9 1.2 10 1.2

LOAD COMB 21 1.5(DL+EQ XP)

9 1.5 1 1.5

LOAD COMB 22 1.5(DL+EQ XN)

2 1.5 9 1.5

LOAD COMB 23 1.5(DL+EQ ZP)

3 1.5 9 1.5

LOAD COMB 24 1.5(DL+EQ ZN)

4 1.5 9 1.5

LOAD COMB 25 1.5(DL+WL XP)

5 1.5 9 1.5



LOAD COMB 26 1.5(DL+WL XN)

6 1.5 9 1.5

LOAD COMB 27 1.5(DL+WL ZP)

7 1.5 9 1.5

LOAD COMB 28 1.5(DL+WL ZN)

9 1.5 8 1.5

LOAD COMB 29 0.9DL+1.5 EQ XP

9 0.9 1 1.5

LOAD COMB 30 0.9DL+1.5 EQ XN

9 0.9 2 1.5

LOAD COMB 31 0.9DL+1.5 EQ ZP

3 1.5 9 0.9

LOAD COMB 32 0.9DL+1.5 EQ ZN

4 1.5 9 0.9

LOAD COMB 33 0.9DL+1.5 WL XP

9 0.9 5 1.5

LOAD COMB 34 0.9DL+1.5 WL XN

9 0.9 6 1.5

LOAD COMB 35 0.9DL+1.5 WL ZP

9 0.9 7 1.5

LOAD COMB 36 0.9DL+1.5 WL ZN

8 1.5 9 0.9

PERFORM ANALYSIS

LOAD LIST 11 TO 36

PARAMETER 1

CODE INDIAN

STEEL TAKE OFF ALL

FINISH



12.2 ANALYSIS OF STEEL BUILDING FOR GRAVITY LOADS

The structure is a residential building which comes under the category of

residential cum commercial building. Hence it has taken care of different types of

dead loads. The dead loads could be of its own self weight, furniture’s, some

equipment, machineries, computers, store keeps, etc. Hence the building has to be

designed in such a way that it has to take care of all the loads imposed on it. The

easiest way to withstand these loads is by providing proper beams and columns. The

live load of the building could be taken from the standards.

FIG.12.1 DEFORMED SHAPE OF THE BUILDING UNDER GRAVITY

LOADS



FIG 12.2 MAXIMUM BENDIG MOMENT DIAGRAM FOR GRAVITY

LOADS



12.3 MAX BM ON BEAM NO 3029 DUE GRAVITY LOADS

12.4 SUMMARY OF BEAM END FORCES DUE TO GRAVITY LOADS



12.3 ANALYSIS OF STEEL BUILDING FOR WIND LOADS.

WIND LOADS:

Building and their components are to be designed to withstand the

code-specified wind loads. Calculating wind loads is important in design of the wind

force-resisting system, including structural members, components, and cladding

against shear, sliding, overturning, and uplift actions.

FIG 12.5 WIND LOAD ACTING FROM X-VE DIRECTION



FIG 12.6 MAXIMUM BENDING MOMENT DIAGRAM FOR COLUMN NO

125 WIND LOAD ACTING FROM Z -VE DIRECTION

FIG 12.7 SUMMARY OF BEAM END FORCES DUE TO WIND LOAD



12.4 ANALYSIS OF STEEL BUILDING FOR SIESMIC LOADS:

FIG 12.8 DISPLACEMENT OF BUILDING UNDER SIESMIC LOAD FROM

Z+VE DIRECTION



FIG 12.9 MAX BM ON COLUMN NO 21 DUE TO SEISMIC LOAD

FROM Z -VE DIRECTION

FIG 12.10 SUMMARY OF BEAM END FORCES DUE TO SEISMIC LOADS



13. DESIGN OF DECK SLAB

13.1 Introduction

The principal merit of steel-concrete composite construction lies in the

utilization of the compressive strength of concrete in conjunction with steel sheets 0r

beams, in order to enhance the strength and stiffness.

Composite floors with profiled decking consist of the following structural

elements in addition to in-situ concrete and steel beams:

Profiled decking

Shear connection

Reinforcement for shrinkage and temperature stresses

Composite floors using profiled sheet decking have are particularly

competitive where the concrete floor has to be completed quickly and where medium

level of fire protection to steel work is sufficient. However, composite slabs with

profiled decking are unsuitable when there is heavy concentrated loading or dynamic

loading in structures such as bridges. The alternative composite floor in such cases

consists of reinforced or pre-stressed slab over steel beams connected together using

shear connectors to act monolithically.

There is presently no Indian standard covering the design of composite floor

systems using profiled sheeting. The structural behaviour of Composite floors using

profiled decks is similar to a reinforced concrete slab, with the steel sheeting acting as

the tension reinforcement. The main structural and other benefits of using composite

floors with profiled steel decking are:

Savings in steel weight are typically 30% to 50% over non-composite

Construction

Greater stiffness of composite beams results in shallower depths for the same

span. Hence lower storey heights are adequate resulting in savings in cladding

costs, reduction in wind loading and savings in foundation costs.

Faster rate of construction

The steel deck is normally rolled into the desired profile from 0.9 mm to 1.5

mm galvanised sheets. It is profiled such that the profile heights are usually in the

range of 38-75 mm and the pitch of corrugations is between 150 mm and 350 mm.

Generally, spans of the order of 2.5 m to 3.5 m between the beams are chosen and the

beams are designed to span between 6 m to 12 m. Trapezoidal profile with web

indentations is commonly used.

The steel decking performs a number of roles, such as:

It supports loads during construction and acts as a working platform

It develops adequate composite action with concrete to resist the imposed



Loading

It transfers in-plane loading by diaphragm action to vertical bracing or shear

walls

It stabilizes the compression flanges of the beams against lateral buckling,

until concrete hardens.

It reduces the volume of concrete in tension zone

It distributes shrinkage strains, thus preventing serious cracking of concrete.

FIG 13.1: Steel beam bounded to concrete slab with shear

FIG 13.2: Composite floor system using profiled sheets

Profiled sheet decking as permanent form work

Construction stage: During construction, the profiled steel deck acts alone to

carry the weight of wet concrete, self weight, workmen and equipments. It must be

strong enough to carry this load and stiff enough to be serviceable under the weight of

wet concrete only. In addition to structural adequacy, the finished slab must be

capable of satisfying the requirements of fire resistance.

Design should make appropriate allowances for construction loads, which

include the weight of operatives, concreting plant and any impact or vibration that

may occur during construction. These loads should be arranged in such a way that

they cause maximum bending moment and shear. In any area of 3 m by 3 m (or the

span length, if less), in addition to weight of wet concrete, construction loads and

weight of surplus concrete should be provided for by assuming a load of 1.5 kN/m2.

Over the remaining area a load of 0.75 kN/m2 should be added to the weight of wet

concrete.

Composite Beam Stage: The composite beam formed by employing the

profiled steel sheeting is different from the one with a normal solid slab, as the

profiling would influence its strength and stiffness. This is termed ‘composite beam

stage’. In this case, the profiled deck, which is fixed transverse to the beam, results in

voids within the depth of the associated slab. Thus, the area of concrete used in

calculating the section properties can only be that depth of slab above the top flange



of the profile. In addition, any stud connector welded through the sheeting must lie

within the area of concrete in the trough of the profiling. Consequently, if the trough

is narrow, a reduction in strength must be made because of the reduction in area of

constraining concrete. In current design methods, the steel sheeting is ignored when

calculating shear resistance; this is probably too conservative.

Composite Slab Stage: The structural behaviour of the composite slab is

similar to that of a reinforced concrete beam with no shear reinforcement. The steel

sheeting provides adequate tensile capacity in order to act with the concrete in

bending. However, the shear between the steel and concrete must be carried by

friction and bond between the two materials. The mechanical keying action of the

indents is important. This is especially so in open trapezoidal profiles, where the

indents must also provide resistance to vertical separation. The predominant failure

mode is one of shear bond rupture that results in slip between the concrete and steel.

13.2 Design method As there is no Indian standard covering profiled decking, we refer to Euro

code 4 (EC4) for guidance. The design method defined in EC4 requires that the slab

be checked first for bending capacity, assuming full bond between concrete and steel,

then for shear bond capacity and, finally, for vertical shear. The analysis of the

bending capacity of the slab may be carried out as though the slab was of reinforced

concrete with the steel deck acting as reinforcement. However, no satisfactory

analytical method has been developed so far for estimating the value of shear bond

capacity. The loads at the construction stage often govern the allowable span rather

than at the composite slab stage.

The width of the slab ‘b’ shown in Figure is one typical wavelength of profiled

sheeting. But, for calculation purpose the width considered is 1.0 m. The overall

thickness is ht and the depth of concrete above main flat surface hc. Normally, ht is not

less than 80 mm and hc is not less than 40 mm from sound and fire insulation

considerations.

The neutral axis normally lies in the concrete in case of full shear connection.

For sheeting in tension, the width of indents should be neglected. Therefore, the

effective area 'Ap' per meter and height of centre of area above bottom 'e' are usually

based on tests. The plastic neutral axis ep is generally larger than e.

The simple plastic theory of flexure is used for analysis of these floors for

checking the design at Limit State of collapse load. IS 456:2000 assumes the

equivalent ultimate stress of concrete in compression as 0.36 (fck) where (fck) is

characteristic cube strength of concrete.



FIG 13.3: Resistance of composite slab to sagging bending moment

Full shear connection is assumed. Hence, compressive force Ncf in concrete is

equal to steel yield force Npa.

𝑁𝑐𝑓 = 𝑁𝑝𝑎 =𝐴𝑝𝑓𝑝𝛾𝑎𝑝

𝑁𝑐𝑓 = 0.36 𝑓𝑐𝑘. 𝑏. 𝑥

Where

Ap = Effective area per meter length

Fy = yield strength of steel

ϒap = partial safety factor (1.15)

The natural axis depth is given by

𝑥 =𝑁𝑐𝑓

𝑏(0.36𝑓𝑐𝑘)

This is valid when x ≤ hc, i.e natural axis lies above steel decking.

Mp.Rd is the design resistance to sagging bending moment and is given by:

𝑝. 𝑅𝑑 = 𝑁𝑐𝑓 (𝑑𝑝 − 0.42𝑥)

The shear resistance of composite slab largely depends on connection

between profiled deck and concrete. The following three types of mechanisms

are mobilised:

(i) Natural bond between concrete and steel due to adhesion.

(ii) Mechanical interlock provided by dimples on sheet and shear connectors.

(iii) Provision of end anchorage by shot fired pins or by welding studs when

sheeting is made to rest on steel beams.

Natural bond is difficult to quantify and unreliable, unless separation at the

interface between the sheeting and concrete is prevented. Dimples or ribs are

incorporated in the sheets to ensure satisfactory mechanical interlock. These are



effective only if the embossments are sufficiently deep. Very strict control during

manufacture is needed to ensure that the depths of embossments are consistently

maintained at an acceptable level. End anchorage is provided by means of shot-fired

pins, when the ends of a sheet rest on a steel beam, or by welding studs through the

sheeting to the steel flange.

Quite obviously the longitudinal shear resistance is provided by the combined

effect of frictional interlock, mechanical interlock and end anchorage. No

mathematical model could be employed to evaluate these and the effectiveness of

the shear connection is studied by means of load tests on simply supported composite

slabs as described in the next section.

Serviceability criteria: The composite slab is checked for the following

serviceability criteria:

Cracking, Deflection and Fire endurance. The crack width is calculated

for the top surface in the negative moment region using standard methods prescribed

for reinforced concrete. Normally crack width should not exceed 3 mm. IS 456: 2000

gives a formula to calculate the width of crack. Provision of 0.4 % steel will normally

avoid cracking problems in propped construction and provision 0.2 % of steel is

normally sufficient in unpropped construction. If environment is corrosive it is

advisable to design the slab as continuous and take advantage of steel provided for

negative bending moment for resisting cracking during service loads.

The IS 456: 2000 gives a stringent deflection limitation of l/350 which may

be un- realistic for un-propped construction. The Euro code gives limitations of l/180

or 20 mm whichever is less. It may be worthwhile to limit span to depth ratio in the

range of 25 to 35 for the composite condition, the former being adopted for simply

supported slabs and the later for continuous slabs. The deflection of the composite

slabs is influenced by the slip-taking place between sheeting and concrete. Tests seem

to be the best method to estimate the actual deflection for the conditions adopted.

The fire endurance is assumed based on the following two criteria:

Thermal insulation criterion concerned with limiting the transmission of heat

by conduction

Integrity criterion concerned with preventing the flames and hot gases to

nearby compartments.

It is met by specifying adequate thickness of insulation to protect combustible

materials. R (time in minutes) denotes the fire resistance class of a member or

component. For instance, R60 means that failure time is more than 60 minutes. It is

generally assumed that fire rating is R60 for normal buildings.



13.3 Metal Decking:

Metal decking are corrugated steel panels used as a working platform during

construction and eventually as formwork for site cast concrete slab. The decking

panels are secured with puddle-welds or shear welded through the decking to the

supporting steel joist or beams. The panels are fastened to each other along their sides

with screws, weld, or button punching standing seams. If the deck is to serve as a

structural diaphragm and transfer lateral loads to shear walls. Its entire perimeter is

welded to steel supports. In addition, more stringent requirements to support and side

lap fastening may apply. There are three major types of metal

FIG 13.4: Metal Decking

1. Form Decking:

Serves as a permanent formwork for a reinforced concrete slab until

the slab can support itself and its live load.

FIG 13.4: Form Decking



2. Composite Decking:

Serves as a tensile reinforcement for the concrete slab to which it is bonded

with embossed rib pattern. Composite action between the concrete slab and

the floor beams or joists can be achieve by welding shear studs through the

decking to the supporting beam below.

FIG 13.4: Composite Decking

3. Cellular Decking:

Is manufactured by welding a corrugated sheet to a flat steel sheet, forming a

series of spaces or raceways for electrical and communications wring; special

cutouts are available for floor outlets. The decking may serve as an acoustic

ceiling when the perforated cells are filled with glass fiber.

FIG 13.5: Cellular Decking

13.4 Design of deck slab

From KIRBY TECHNICAL HANDBOOK kirby decking (KD) section

properties and load tables page no 5.9

Assuming 0.7 mm thick Kirby Decking sheet

Weight of sheet = 6.99 kg/m2

= 0.06857 kN/ m2

Dead load on Deck slab

Self weight of deck slab= 0.1x25 = 2.5 kN/m2

Self weight of decking sheet =

Floor finish = 1 kN/m2

Live load on deck slab = 2 kN/m2

Total load on deck slab = 5.568kN/m2

Width of deck slab = 1.2 m



Allowable load on kirby decking = 6.82 kN/m2

Properties of decking sheet

For Panel nominal thickness of 0.7 mm,

Girth = 11.45 mm



Weight = 6.99 𝑘𝑔/𝑚2

Shear and web crippling

𝑉𝑎 𝐾𝑁 = 26.19 kN

𝑃𝑎 𝐾𝑁 = 17.54 kN

Top flat in compression:

Deflection 𝑙𝑥 in 𝑐𝑚4 = 12.55

Sx (top) in 𝑐𝑚3 = 10.01

Sx (bot) in 𝑐𝑚3: = 4.03

Ma (kN-m) = 0.83

Bottom flat in compression

Deflection 𝑙𝑥 in 𝑐𝑚4 = 12.58

Sx (top) in 𝑐𝑚3 = 11.28

Sx (bot) in 𝑐𝑚3 = 3.95

Ma (kN-m) = 0.81

Provide 0.7 mm thick Kirby decking sheet and 100 mm thick slab

Reinforcement in slab

Provide nominal reinforcement 8 mm dia @ 250 mm C/C in both directions

GIRTH CONNECTIONS

The decking sheet is connected to beams and columns with suitable nuts and

bolts. The typical drawing of connection of girth to column and beam is shown below.



14.DESIGN OF BEAMS

14.1 INTRODUCTION:

A member subjected to bending moment and shear force due to transverse

loads is called a ‘Beam’ (or) the member carrying loads perpendicular to its axis is

called a Beam.

Classification of Beams:

The steel beams are generally classified as follows:

1. Simple Beams

2. Compound beam/ Built-up beam/ Plated beam.

3. Plate girders

1. Simple beam

When a single rolled section is provided to support the lateral load is called a

simple beam.

2. Compound Beam (or) Built up Beam:

When two or more rolled sections (or) rolled sections with plates are used as

flexural member is called a compound beam (or) built up beam. A rolled

section with one (or) more crown plates on its flange, when used as a beam is

called plated beam.

3. Plate griders:

When heavy loads are to be carried on large span, it may not be possible to

provide simple (or) compound beams. In such cases plate griders made up of

plates either riveted (or) welded together are used.

Laterally Restrained Beams:

A beam is said to be laterally restrained, when its compression flange is

supported laterally and it is not allowed to have moments in the lateral direction.

Because, the tendency of the compression flange to buckle under axial compressive

stresses is prevented, the safe allowable bending stress in compression may be taken

the same as that for tension.

Permissible Bending Stress:

If the compression flange of the beam is restrained laterally (or) ‘(flat)’ for

laterally restrained beam the bending stress in the compression may be taken same as

that of bending stress in tension.

i.e., 𝜎𝑏𝑡 = 0.66𝑓𝑦

where fy= minimum yield stress of steel in Mpa.



if fy= 250 Mpa,

𝜎𝑏𝑡 = 0.66x250 = 165 𝑀𝑃𝑎.

Effective Span:

Effective span of beam shall be taken as the length of the beam between the

centres of the support (or) the length between assumed points of applications of

reactions. It is denoted by ‘l’.

14.2 Design Procedure:

A beam section is usually chosen which can resist maximum bending moment

occurring over its span. The shear stress and deflection for the chosen sections are

then checked to be with in the permissible limits. Check for web crippling and web

buckling are the secondary design requirements to be checked in some cases of beams

with heavy concentrated loads (or) reaction of supports.

(i) Design for Bending:

The bending stress 𝜎bc (or) bt at any point on a cross-section of a beam due

to bending moment ‘M’ is given by.

M

IxY = 𝜎𝑏𝑐 (or)𝜎𝑏𝑡

Where,

𝜎𝑏𝑐 (cal)(or)𝜎𝑏𝑡 (cal)= bending stress (compressive or tensile) calculated

at a point at a distance ‘y’ from the neutral axis.

M = bending moment

I = moment of inertia of the cross-section of beam.

The point of maximum bending stress occurs at the extreme fibre and the

corresponding I

Y ratio is called the sectional modulus designated by Z.

M

Z= 𝜎𝑏𝑐 (cal)(or)𝜎𝑏𝑡 (cal)

Since the calculated bending stress 𝜎𝑏𝑐 (cal)(or)𝜎𝑏𝑡 (cal) is lesser than the

permissible bending𝜎𝑏𝑐 (or)𝜎𝑏𝑡 .

M

Z ≤ 𝜎𝑏𝑐 or 𝜎𝑏𝑡

Z ≥ M

𝜎𝑏𝑐

Z ≥ M

𝜎𝑏𝑡

A suitable beam section is chosen which have the sectional modulus

slightly more than Z calculated from the equations.



14.3Moment of Resistance:

It is the bending moment which a beam can resist.

Moment of resistance = Z x 𝜎𝑏𝑐 or 𝜎𝑏𝑡

The external loads should not cause a bending moment more than the moment of

resistance of the beam.

Load Carrying Capacity of the Beam:

1. From the strength consideration, the load carrying capacity of the beam

is calculated by the equation.

Moment of resistance = Zxx x 𝜎𝑏𝑐 or 𝜎𝑏𝑡

2. Calculate the max. Bending moment in the beam depending upon the

type of the beam and loading.

i. Simply supported carrying u.d.l max. Bending Moment = 𝑤𝑙2

8

ii. Simply supported carrying point load Max. B.M.= 𝑤𝑙

8

iii. Cantilever carrying u.d.l, Max. B.M. =𝑤𝑙2

2

iv. Cantilever carrying point load Max. B.M. = 𝑤. 𝑙

14.4 Shear:

1. Calculate maximum shear force in the beam depending upon the type of

loading .

i. Simply supported carrying u.d.l max. Shear force (𝑣) = 𝑤𝑙

2

ii. Simply supported carrying point load Max. S.F. 𝑣 = 𝑤

2

iii. Cantilever carrying u.d.l, Max. S.F. 𝑣 = 𝑤𝑙

iv. Cantilever carrying point load Max. S.F. 𝑣 = 𝑤

2. Calculate average shear stress 𝜏𝑣𝑎 ,𝑐𝑎𝑙

𝜏𝑣𝑎 ,𝑐𝑎𝑙 =V

𝑕x𝑡𝑤

3. 𝜏𝑣𝑎 ,𝑐𝑎𝑙 should be less than permissible avg. Shear stress.

𝜏𝑣𝑎 = 0.4𝑓𝑦

14.5 Maximum Deflection:

i. Simply supported carrying u.d.l over span 𝜕𝑚𝑎𝑥 =5

384 𝑤𝑙4

EI

ii. Simply supported carrying point load 𝜕𝑚𝑎𝑥 =1

48 𝑤𝑙3

EI

iii. Cantilever carrying u.d.l, 𝜕𝑚𝑎𝑥 = 𝑤𝑙4

8EI

iv. Cantilever carrying point load. 𝜕𝑚𝑎𝑥 = 𝑤𝑙3

3EI



Permissible Deflection (Allowable Deflection):

𝜕𝑚𝑎𝑥 = span

325

To satisfy the strength and stiffness requirements of the beam 𝜕𝑚𝑎𝑥 should not

be greater than 𝜕𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 of the beam.

Web Crippling and Web Buckling:

A beam may fail under a concentrated load or at end reaction due to crippling

of web or by buckling of web.

14.6 Web Crippling:

The depression of load is assumed to be at 300

The bearing stress in the web at the root of the fillet will be equal to

𝑤

𝑡𝑤 (𝑎+2𝑕2 3) ≯ 𝜎𝑝 for inter mediate loads.

𝑅

𝑡𝑤 (𝑎+2𝑕2 3) ≯ 𝜎𝑝 for end supports.

Where, w= concentrated loads on the beam (N)

R= end reaction at supports (N)

tw= thickness of web (mm)

a= bearing length (mm)

h2= depth of the root of the fillet from the top of the flange (mm).

𝜎p= maximum permissible bearing stress = 0.75𝑓𝑦

fy= yield stress of steel.

14.7 Web Buckling:

Load bearing stiffeners at all points of concentrated loads (including points of

support) should be provided where,

W or R > 𝜎𝑎𝑐 x 𝑡𝑤x B

Where W or R= concentrated load or reaction at support respectively.

𝜎ac= maximum permissible axial stress for columns in Table 5.1 of IS: 800 for

slenderness ratio = 𝑕1

𝑡𝑤 3



B= the length of the stiff portion of the bearing + additional length + thickness

of seating angle

h1= clear depth of the web between root fillets normally check for web

crippling and web buckling is not required for rolled steel sections under normal

loading.

14.8 Design of Tension Members:

Tension members subjected to axial forces may fail by rupture at a critical

section or it may become non-functional due to excessive elongation. Plates and other

rolled sections in tension may also fail by block shear of end bolted regions.

The factored design tension ’T’ in the member should comply with the

following criteria:

𝑇 < 𝑇𝑑

Where 𝑇𝑑= lowest design strength of the member due to yielding of gross section

under axial tension.

Design strength due to yielding of gross section: As per is 800-2007 the

design strength of the member under axial tension Tdg, as governed by yielding of

gross section, is expressed as

𝑇𝑑𝑔=

𝐴𝑔 𝑓𝑦𝛾𝑚𝑜

Where 𝑓𝑦 = yield stress of material

𝐴𝑔 = gross area of cross-section

Ὑ𝑚𝑜 = partial safety factor for failure in tension by yielding as compiled in the

following table.

Table 14.1: Partial safety factor for materials (γm)

Sl

No. Definitions Partial factor of safety

1 Resistance, governed by yielding 𝛾Ὑ𝑚𝑜 1.10

2 Resistance of member to buckling, Ὑ𝛾𝑚𝑜 1.10

3 Resistance, governed by ultimate stress,

γml 1.25

4 Resistance of connection Type of fabrications

Shop Field

a. Bolts: friction type, γmf 1.25 1.25

b. Bolts: bearing type, γmb 1.25 1.25

c. Rivets, γmr 1.25 1.25



d. Welds, γmw 1.25 1.50

Design strength due to rupture of critical section:

a. Plates: the design strength of a plate Tdn, as governed by rupture of the net

cross- sectional area. An at the hole is given by

𝑇𝑑𝑛=

0.9 𝐴𝑔 𝑓𝑦

𝛾𝑚 1

Where Ὑm1= partial safety factor for failure at ultimate stress as compile in the table

above

Fu= ultimate stress of the material

An= 𝑏 − 𝑛𝑑𝑕 + 𝑃𝑠𝑖

2

4𝑔𝑖 1

𝑖

Where b, t = width and thickness of the plate, respectively

dh = diameter of the bolt hole (2mm in addition to the diameter of the hole in

case of directly punched hole).

g = gauge length between the bolt holes as shown in the figure below

ps = staggered pitch length between line of the bolt holes as shown in the

figure below

n = number of bolt holes as shown in the figure below

I = subscript for summation of all the inclined legs.

b. Threaded rods : the design strength of threaded rods in tension, Tdn, as

governed by rupture is expressed as



𝑇𝑑𝑛=

0.9 𝐴𝑔 𝑓𝑦

Ὑ𝑚 1

Where An= net root area at the threaded section

c. Single Angles: the rupture strength of an angle connected through one leg is

affected by shear lag. The design strength Tdn as governed by the rupture at

net section is given by the relation

𝑇𝑑𝑛

0.9 𝐴𝑛𝑐 𝑓𝑢Ὑ𝑚 1

+ 𝛽 𝐴𝑔𝑜 𝑓𝑦

Ὑ𝑚 0

Where

Β= 1.4-0.076 𝑤

𝑡

𝑓𝑦

𝑓𝑢

𝑏𝑠

𝐿𝑐 ≤

𝑓𝑢Ὑ𝑚𝑜

𝑓𝑦Ὑ𝑚 1≥ 0.7

Where w= outstand leg width

bs = shear lag width, as shown in figure below

Lc = length of end connection, that is, the distance between the outermost bolts

in the end joint measured along with the load direction or length of the weld along the

load direction.

For preliminary sizing, the rupture strength of net section may be approximately taken

as :

𝑇𝑑𝑛 =𝛼𝐴𝑛𝑓𝑢Ὑ𝑚1

Where α = 0.6 for one or two bolts, 0.7 for three bolts and 0.8for four or more bolts

along the length in the end connection or equivalent weld length



An= net area of the total cross-section

Anc= net area of the connected leg

Ago= gross area of the outstanding leg

t= thickness of the leg

in the case of double angles, channels, I-sections and other rolled steel sections,

connected by one or more elements to an end gusset, the rupture strength is also

governed by tearing of net section may also be calculated using the above- mentioned

equation. However the value of β is calculated based on the shear leg distance bs taken

from the farthest edge of the outstanding leg to the nearest bolt/weld line in the

connected leg of the cross- section.

Design strength due to block shear: The design strength controlled by block shear

end connection of plates and angles is computed using the following equations:

a) Bolted connections : the block shear strength, Tdb of connection is taken as

the smaller value of

𝑇𝑑𝑏

𝐴𝑣𝑔𝑓𝑦

3Ὑ𝑚0

+0.9 𝐴𝑡𝑛𝑓𝑢

Ὑ𝑚0

Where, Avg= minimum gross and net area in shear along bolt line parallel to

external force respectively (1-2 and 3-4 as shown in the figure a. and 1-2 as

shown in the fig b)

Atn= minimum gross and net area in tension from the bolt hole to the

toe of the angle, end bolt line, perpendicular to the line of force, respectively

(2-3 as shown in the figure b.)

fu= ultimate and yield stress of the material, respectively



b) Welded connections: the block shear strength, Tdb shall be checked for

welded end connections by taking an approximate section in the member

around the end weld which can shear off as a block.

Design of flexural members:

1. General aspects

Flexural members such as beams should have adequate design strength to

resist the bending moments and shear forces resulting from imposed loads. In

addition, they should satisfy the serviceability criteria comprising the

deflection limits specified in table. given below for different types of

structural members. The maximum deflection under service loads should not

exceed the limits expressed as a function of the span given in the code. The

effective span of a beam is generally taken as the distance between the centre

of the supports.

Type of

building

(1)

Deflecti

on

(2)

Design

load

(3)

Member

(4)

Supporting

(5)

Maximu

m

deflection

(6)

Industrial

building Vertical

Live

load/

wind

load

Purlins and

girts

Elastic

cladding Span/150

Brittle

cladding Span/180

Live

load Simple span

Elastic

cladding Span/240

Brittle

cladding Span/300

Live

load

Cantilever

span

Elastic

cladding Span/120

Brittle

cladding Span/150

Live

load

Rafter

supporting

Profiled metal

sheeting Span/180

Plastered

sheeting Span/240

Crane

load

(manual

operatio

n up to

50 t)

Gantry Crane Span/500

Crane

load

(electric

operatio

n up to

50 t)

Gantry Crane Span/750

Crane Gantry Crane Span/100



load

(electric

operatio

n over

50 t)

Lateral

No

crane Column

Elastic

cladding

Height/15

0

Masonry/brittl

e cladding

Height/24

0

Crane +

wind

Gantry

(lateral)

Relative

displacement

between rails

supporting

crane

10 mm

Crane

(absolute) Span/400

Crane +

wind

Column/fram

e

Gantry (elastic

cladding;

pendent

operated)

Height/20

0

Gantry (brittle

cladding; cab

operated)

Height/40

0

Other

building

Vertical

Live

load

Floor and

roof

Elements not

susceptible to

cracking

Span/300

Elements

susceptible to

cracking

Span/360

Live

load Cantilever

Elements not

susceptible to

cracking

Span/150

Elements

susceptible to

cracking

Span/180

Lateral

Wind Building

Elastic

cladding

Height/30

0

Brittle

cladding

Height/50

0

Wind Inter storey

drift ----

Storey

height/300

2. Design strength in flexure

The following specifications govern the design of flexural members. Flexural

members adequately supported against lateral torsional buckling(laterally

supported beams) is governed by the yield stress. The factored design

moment, M at any section, in a beam due to external loads should satisfy the

relation



M ≤ Md

Where Md = design bending strength of the section

a) The design bending strength of a section which is not susceptible to web

buckling under shear before yielding and factored design shear force does

not exceed 0.6 Vd, where Vd is the design shear strength of the cross-

section, the bending strength Md is calculated by the relation

M𝑑 =𝛽𝑏𝑍𝑝𝑓𝑦𝛾𝑚0

Where 𝛽𝑏 = 1.0 for plastic and compact sections

= 𝑍𝑒

𝑍𝑝 for semi- compact sections

zp, ze = plastic and elastic section moduli of the cross-section,

respectively

𝑓𝑦 = yield stress of the material

𝛾𝑚0 = partial safety factor

To avoid irreversible deformation under serviceability loads, Md

should be less than [ 1.2𝑧𝑒 𝑓𝑦

𝛾𝑚0 ]in case of simply supported and

[1.5𝑧𝑒 𝑓𝑦

𝛾𝑚0 ] in cantilever beams.

b) In the case of laterally unsupported beams, the resistance to lateral

torsional buckling need not be checked separately in the following cases:

1) Bending is about the minor axis of the section,

2) Section is hollow (rectangular/tubular) or solid bars,

3) In case of bending about the major axis, the non-dimensional

slenderness ratio (λLT) is less than 0.4

The design bending strength of laterally unsupported beams as

governed by lateral torsional buckling is calculated by the relation

M𝑑 = 𝛽𝑏 𝑍𝑝 𝑓𝑏𝑑

Where 𝑓𝑏𝑑 = design bending compressive stress, computed as

= 𝑋𝐿𝑇 𝑓𝑦

𝛾𝑚 0

𝑋𝐿𝑇 = bending stress reduction factor to account for lateral

torsional buckling, given by the relation:

𝑋𝐿𝑇 = 1

∅𝐿𝑇 +[∅𝐿𝑇2 +𝜆𝐿𝑇

2 ]0.5 ≤ 1.0

∅𝐿𝑇 = 0.5[1 +∝𝐿𝑇 𝜆𝐿𝑇 − 0.2 + 𝜆𝐿𝑇2 ]



The imperfection parameter ∝𝐿𝑇 is given by

∝𝐿𝑇 = 0.21 for rolled steel section

∝𝐿𝑇 = 0.49 for welded steel section

The non-dimensional slenderness ratio, 𝜆𝐿𝑇 is given by the relation

𝜆𝐿𝑇 = 𝛽

𝑏𝑍𝑝𝑓𝑦

𝑀𝑐𝑟

≤ 1.2𝑍𝑝𝑓𝑦

𝑀𝑐𝑟

= 𝑓

𝑦

𝑓𝑐𝑟,𝑏

Where fcr,b = extreme fibre bending compressive stress

Mcr = elastic critical moment calculated by the expression,

𝑀𝑐𝑟 = { 𝜋2 𝐸𝐼𝑦 𝐿𝐿𝑇

2 𝐺𝐼𝑡 +

𝜋2 𝐸𝐼𝑤 𝐿𝐿𝑇

2 } = 𝛽𝑏𝑍𝑝𝑓𝑐𝑟 ,𝑏

The extreme fibre bending compressive stress fcr,b of non-slender rolled steel

sections in the above equation may be approximately calculated from the values

compiled in table in IS: 800 which has been prepared using the following equation:

𝑓𝑐𝑟 ,𝑏 =1.1𝜋2 𝐸

(𝐿𝐿𝑇𝑟𝑦

)2 [1 +

1

20

𝐿𝐿𝑇𝑟𝑦𝑕𝑓

𝑡𝑓

2

]0.5

A simplified equation has been suggested by the Indian standard code IS: 800-

2007 for computing the elastic lateral buckling moment of prismatic members made

of standard rolled I-sections and welded doubly symmetric I-sections given as

𝑀𝑐𝑟 =𝜋2 𝐸𝐼𝑦𝑕𝑓

2𝐿𝐿𝑇2 [1 +

1

20

𝐿𝐿𝑇𝑟𝑦𝑕𝑓

𝑡𝑓

2

]0.5

Where Iy = moment of inertia about the weaker axis

ry = radius of gyration about the weaker axis

It = torsional constant = 𝑏𝑖𝑡𝑖3/3 for open section

Iw = warping constant

LLT = effective length for lateral torsional buckling

hf = centre to centre distance between flange



tf = thickness of the flange

The Indian Standard Code IS: 800-2007 also recommends the use of a more

accurate method given in Annexure E of the code for computing the elastic critical

moment considering loading, support conditions and non-symmetric sections of the

member.

3. Effective length for lateral torsional buckling

In the case of simply supported beams and griders of span length, L,

where no lateral restraint to the compression flanges is provided, but where

each end of the beam is restrained against torsion, the effective length LLT to

be used for different types of restraint at supports and loading conditions are

compiled in table given below.

In the case of cantilever beams of projecting length L, the effective

length LLT to be used in table—for different support conditions.

4. Shear

The factored shear force V, in a beam due to external actions should

satisfy the relation,

V ≤ Vd

Where Vd = design strength = 𝑉𝑛𝛾𝑚0

The nominal shear strength of a cross-section, Vn may be governed by

plastic shear resistance or strength of the web influenced by shear buckling

outlined below;

Table on effective length for simply supported beams, LLT

SI

NO.

Conditions of restraint at

support Loading condition

(1)

Torsional

restraint

(2)

Warping

restraint

(3)

Normal

(4)

Destabilizing

(5)

(i) Fully

restrained

Both flanges

fully

restrained

0.70L 0.85L

(ii) Fully

restrained

Compression

flange fully

restrained

0.75L 0.90L

(iii) Fully

restrained

Both flanges

fully

restrained

0.80L 0.95L

(iv) Fully

restrained

Compression

flange

partially

restrained

0.85L 1.00L

(v) Fully

restrained

Warping not

restrained in

both flanges

0.00L 1.20L



(vi)

Partially

restrained by

bottom flange

support

connection

Warping not

restrained in

both flanges

1.0L+2D 1.2L+2D

(vii)

Partially

restrained by

bottom flange

bearing

support

Warping not

restrained in

both flanges

1.2L+2D 1.4L+2D

Notes:

1. Torsional restraint prevents rotation about the longitudinal axis

2. Warping restraint prevents rotation of the flange in its plane.

3. D is overall depth of the beam



1) Plastic shear resistance

The nominal plastic shear resistance under pure shear is expressed by the

relation,

Vn = Vp

Where 𝑉𝑛 = 𝐴𝑣𝑓𝑦𝑤

3

Av = shear area

fyw = yield strength of the web

the shear area for various sections

is computed using the following relations:

a) I and channel sections

Major axis bending. Minor axis bending

Hot-rolled: h.tw Hot-rolled or welded: 2b tf



b) Rectangular hollow sections of uniform thickness

Loaded parallel to depth (h): [Ah/(b+h)]

Loaded parallel to width (b): [Ab/(b+h)]

c) Circular hollow tubes of uniform thickness: [ 2 A/π]

d) Plates and solid bars: A

Where

A = cross-section of area

b= overall depth of tubular section, breadth of I-section flanges

d= clear depth of web between flanges

h= overall depth of the section

tf= thickness of the flange

tw= thickness of the web

2) Resistance to shear buckling

The resistance to shear buckling should be verified when

𝑑

𝑡𝑤 > 67𝜀 for a web without stiffeners

> 67𝜀 𝐾𝑣

5.35 for a web with stiffeners

Where Kv = shear buckling coefficient defined in the following paragraphs

𝜀 = 250

𝑓𝑦

The computations for shear buckling design are detailed as below:

The nominal shear strength, Vn of webs with or without intermediate

stiffeners as governed by buckling may be evaluated using one of the

following methods:

(a) Simple post-critical method

The simple post-critical method, based on shear buckling strength can

be used for webs of I-sections griders, with or without intermediate

transverse stiffeners, provided that the web has transverse stiffeners at

the supports.

The nominal shear strength is given by:

Vn = Vcr

Where

Vcr = shear force corresponding to web buckling

= (AvTb)

Tb = shear stress corresponding to web buckling determined as follows:

1) When λw ≤ 0.8

𝑇𝑏 = 𝑓𝑦𝑤

3

2) When 0.8 < λw < 1.2

𝑇𝑏 = [1 − 0.8 𝜆𝑤 − 0.8 ] 𝑓𝑦𝑤

3

3) When λw≥ 1.2



𝑇𝑏 = 𝑓𝑦𝑤

3𝜆𝑤2

Where λw = non-dimensional web slenderness ratio for shear

buckling stress, given by

𝜆𝑤 = 𝑓𝑦𝑤

3𝑇𝑐𝑟 ,𝑒

Tcr,e= the elastic shear stress of the web

= 𝐾𝑣𝜋

2𝐸

12(1−𝜇2) 𝑑

𝑡𝑤

2

Where

μ = Poisson’s ratio

Kw= 5.35 when transverse stiffeners are provided only at supports

= 4+ 5.35/ (c/d)2 for (c/d) < 1.0

= 5.35 +4.0 / (c/d)2 for (c/d) ≥ 1.0

Where c, d are the spacing of transverse stiffeners and depth of

web, respectively.

(b) Tension field method

This method is based on the post-shear buckling strength. It is

normally used for webs with intermediate transverse stiffeners. In the

tension field method, the nominal shear resistance, Vn, is given by

Vn= Vtf

Where

𝑉𝑡𝑓 = 𝐴𝑣𝑇𝑏 + 0.9𝑤𝑡𝑓 𝑡𝑤𝑓𝑣 sin ∅ ≤ 𝑉𝑝

Where Tb = buckling strength as computed from the simple post-

critical method.

fv = yield strength of the tension field computed as

= 𝑓𝑦𝑤2 − 3𝑇𝑏

2 + ∅2 0.5

− ∅

∅ = 1.5𝑇𝑏 sin 2∅

∅ = inclination of the tension field

= tan−1 𝑑

𝑐

wtf = width of the tension field given as

= 𝑑 cos ∅ + 𝑐 − 𝑠𝑐 − 𝑠𝑡 sin ∅

fyw = yield stress of the web

c = spacing of stiffeners in the web

Tb= shear stress corresponding

sc, st = anchorage lengths of the tension flange respectively, obtained

from the relation:

𝑠 = 2

sin ∅

𝑀𝑓𝑟

𝑓𝑦𝑤 𝑡𝑤

0.5

≤ 𝑐



Where Mfr = reduced plastic moment capacity of the respective flange

plate ( disregarding any edge stiffener) after accounting for the axial

force in the cross-section, and is calculated as:

𝑀𝑓𝑟 = 0.25𝑏𝑓𝑡𝑓2𝑓𝑦𝑓 1 −

𝑁𝑓

𝑏𝑓𝑡𝑓𝑓𝑦𝑓 /𝛾𝑚0

2

Where bf, tf = width and thickness of the relevant flange respectively

fyf = yield stress of the flange

CALCULATIONS:

Design:

The unit weight of reinforced concrete deck slab = 25 kN/m3

Live load on the floor = 2 kN/m2

3.00m

3.60m

(1) DESIGN OF SECONDARY BEAMS:

Each secondary beams supports load from strip 1.2 m wide. Uniformly

distributed load per meter length of the beam:

(a) Load Support:

Weight of reinforced concrete slab = 1.2 x 1x100

1000x25 = 3 kN

Live load on the floor = 1.2x1x2 = 2.4 kN

Assume self-weight of the beam = 0.50 kN

1.2 m 1.2 m 1.2 m



Total uniformly distributed load = 3 + 2.4 + 0.50 = 5.9 kN ≅ 6 kN

(b) Bending Moment and Shear Force:

The effective span of the beam is 3m the maximum bending moment, M

occurs at the centre.

M = 𝑤𝑙2

8 =

6x32

8 = 6.75 kN − m

The maximum shear force, F occurs at the support,

F = 𝑤𝑙

2 =

6x3

2 = 9 kN

(c) Permissible Bending Stress:

It is assumed that the value of yield stress fy for the structural steel is 250

N/mm2 (Mpa). The ratios’s

T

𝑡𝑤 &

𝑑1

𝑡𝑤 are less than 2.0 and 85

respectively. The maximum permissible stress in compression (or) tension

may be assumed below.

𝜎𝑏𝑐 = 𝜎𝑏𝑡 = 0.66x250 = 165 kN/mm2

(d) Section Modulus Required:

z = M

𝜎𝑏𝑐 =

6.75x1000x1000

165= 40909.09 mm3

The steel beam section shall have D

T &

𝑙

𝑟𝑦 ratios should be not more

than 8 and 40, respectively. The trial section of beam selected may have

more of section, Z x 1.5 times more than that needed.

The trial section modulus

= 1.5 x 40909.09 = 61363.635 mm3

(e) Check for Section Modulus:

D

T=

200

5.0 = 40



T

𝑡𝑤=

5.0

3.4 = 1.47 < 2.00

Also

𝑑1

𝑡𝑤=

179.5

3.4 = 52.79 < 85

The effective length of compression flange of beam may be assumed equal

to effective span,

𝑙

𝑟𝑦 =

0.7x3x1000

11.7 = 179.4

From Table 6.1(b), IS: 800-1984 maximum permissible bending stress.

𝑙

𝑟𝑦 = 170, 𝜎𝑏𝑐 = 75

𝑙

𝑟𝑦 = 180, 𝜎𝑏𝑐 = 71

𝑙

𝑟𝑦 = 179.4, 𝜎𝑏𝑐 =?

𝜎𝑏𝑐 = 75 − 75 − 71

180 − 170 179.4 − 170 = 71.24 N/𝑚𝑚2

Section Modulus required

z = 6.75x1000x1000

71.24 = 94.75 cm3

Provide sectional area 36.71 cm3 due to economical and architectural

purposes.

(f) Properties of Trial Sections:

From steel sections tables, ISJB 200 @ 0.99 kN/m

Section Modulus provided Zxx = 78.1 x 10 3 mm

3

Moment of Inertia, Ixx = 780.7 x 104 mm

4

Thickness of web tw = 3.4 mm



Depth of Section h= 300 mm

Mean Thickness of Flange, tf = 9.4 mm

(g) Check for Shear Force:

Average shear stress = F

h𝑡𝑤 =

9

200x3.4 = 13.23 N/𝑚𝑚2

Allowable shear stress

= 0.4x𝑓𝑦 = 0.4 x 250 = 100 > 𝐴𝑣𝑔. 𝑠𝑕𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 13.23

(h) Check for Deflection:

𝑦𝑚𝑎𝑥 = 5

342 𝑤𝑙4

EI

= 5x6x34x(1000)4

342x2.047x105x780.7x104= 3.959 mm

Allowable deflection

= 𝑙

325=

3000

325= 9.23 mm

The maximum deflection is less than allowable deflection.

Hence, design is satisfactory.

(2) DESIGN OF MAIN BEAM:

(a) Load Supported:

The effective span is taken as distance c/c of bearings

Effective span = 3.60 m

Load transferred from each secondary beam = 6 x 1.2 = 7.2 kN

Assume self-weight of beam = 2 kN/m

(b) Bending moment:

The maximum bending moment occurs at centre due to UDL

𝑤1 = 16 + 2 = 18



M1 = 𝑤1𝑙

2

8 =

18x3.62

8 = 29.16 kN − m

End reaction due to concentrated load = 𝑤𝑙

2=

7.2 x 1.2

2= 4.32 kN

Total load w2 = 2x4.32 = 8.64 kN

M2 = moment due to secondary beam

No. of secondary beams = 2

M2 = 𝑤2𝑙

2

8 = 13.99 kN − m

M = M1 + M2 = 29.16 + 13.99 = 43.15 kN − m

The secondary beams are connected to the web at 1.2 m c/c. The

compression flange is assumed to the fully supported against lateral

deflection.

(c) Permissible Bending Stress:

It is assumed that the value of yield stress, fy for the structural steel is 250

N/mm2(Mpa). The ratios’s

T

𝑡𝑤 &

𝑑1

𝑡𝑤 are less than 2.0 and 85

respectively. The maximum permissible stress in compression or tension

may be assumed as under (for laterally supported beam)

𝜎𝑏𝑐 = 𝜎𝑏𝑡 = 0.66x250 = 165 kN/mm2

(d) Section Modulus Required:

z = M

𝜎𝑏𝑐 =

43.15x1000x1000

165= 261515.1515 mm3

From steel section tables try ISHB 250 @ 51.0 kN/m

Section modulus provided

𝑧𝑥𝑥 = 618.9 x 103 mm3

Moment of Inertia I𝑥𝑥 = 7736.5 x 104 mm4



Thickness of web, 𝑡𝑤 = 6.9 𝑚𝑚

Depth of section, h = 250 mm

Total load on griders inclusive of its own weight

= 6.75x1.2x1.2 + 0.51x3.60 = 11.556 kN

Maximum Shear Force

=11.556

2= 5.778 kN

(e) Check for Average Shear Stress:

Avg. shear stress

𝜏𝑣𝑎 ,𝑐𝑎𝑙 = 5.778x1000

250x6.9 = 3.349 N/mm2

Allowable shear stress

= 0.4x𝑓𝑦 = 0.4 x 250 = 100 > 𝐴𝑣𝑔. 𝑠𝑕𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 3.349

Hence, safe.

(f) Check for Moment:

z = M

𝜎𝑏𝑐

M = 𝑧. 𝜎𝑏𝑐 = 165x618.9x1000

1000x1000 = 102.1185 > 43.15 kN − m Hence, safe.



15. DESIGN OF COLUMN

15.1 INTRODUCTION:

An element or a member subjected to primary compression is called a

compression member.

There are two main types of such members

1. Column and

2. Struts

1. Column: The vertical compression member in a building is called column

or stanchion.

2. Strut: The structural member carrying compressive load in a truss is

called strut.

15.2STEEL COLUMNS:

Steel columns are of the following types:

a. Struts of one or two angles:

These are used for compression members in roof trusses, light towers, and

lattice griders. The two angles of double struts are riveted together by

rivets driven through washers placed between the two angles at intervals of

4 to 6ft.

b. Starred angles:

Starred angles of two or four connected by batten plate spaced at intervals

of 3 to 4ft. these are used to support the light loads.

c. Latticed columns:

These are made up of channels or angles connected by lattice bars are

often used where light loads are to be supported on long columns.

d. Rolled H-columns:

These are obtainable with depths ranging from 6’’ to 16’’ and are now

commonly used instead of built-up columns in steel skeleton construction.

e. Built-up columns:

These are usually H-shaped section formed by a combination of plates and

angles although box-columns with two or more webs are not uncommonly

used in heavy building frames.

f. Top chord sections:

These are made up of heavy trusses are usually unsymmetrical and are

made of two rolled or built-up channel sections and cover plate. The

open(bottom) side of the section is latticed.

g. Columns for bents:

These are sometimes made up of a pair of channels and a I-beam with

batten plates at intervals of 3 to 4ft. connecting the flanges of the channels.



Columns made of four angles and a web-plate are commonly used in mill

buildings bents.

h. Battened columns:

Battened columns are those in which two component parts of the column

are connected only by battened plates. They are decidedly inferior to

latticed columns and should be avoided if a continuous plate or latticing

can be used instead.

15.3 Effective Length:

Effective length is defined as that length of column for which it acts as if both

the ends are hinged. At these points, the flexure changes its sign or in other words it is

the distance between two points of zero moments.

Effective length for different end conditions are enlisted in Table-5.2 of IS: 800-

1984

Radius of Gyration:

Radius of gyration of a section is given by

𝑟 = I

𝐴

Where I= moment of inertia

A= area of cross-section

Slenderness Ratio:

Slenderness ratio is the ratio of effective length to the least radius of gyration.

It is denoted by λ

𝜆 = 𝑙

𝑟𝑚𝑖𝑛

The maximum slenderness ratio of a strut should not exceed the values given in table-

3.1 of IS: 800-1984.

Table 15.1: Maximum slenderness ratio

S.No. Member Maximum slenderness

1. A member carrying

compressive loads

resulting from dead and

imposed loads

180



2. A member subjected to

compressive forces

resulting from wind/

earthquake forces provided

the deformation of such

member does not

adversely affect the stress

in any part of the structure

250

3. A member normally

carrying tension but

subjected to reversal of

stresses due to wind or

earthquake forces

350

15.4 Permissible Stress in axial Compression (𝜎ac):

The direct stress in compression on the cross-sectional area of axially loaded

compression members shall not exceed 0.6fy nor calculated using the formula.

𝜎𝑎𝑐 =𝑓𝑐𝑐𝑓𝑦

𝑓𝑐𝑐 𝑛 + 𝑓𝑦

𝑛

1𝑛

Where 𝜎ac= permissible stress in axial compression

fy= yield stress of steel, in Mpa.

fcc= elastic critical stress in compression =𝜋2E

𝜆2

n = a factor assumed as 1.4 the values of 𝜎ac for steel with various yield stress

are given in Table-4.3 of IS: 800-1984

15.5 Strength of Axially Loaded Compression Member (column &

strut):

The maximum axial compressive load ‘P’ which can be permitted on a

compression member is given by

P = 𝜎𝑎𝑐 x A

Where P= axial compressive load (N)

𝜎ac= permissible stress in axial compression (Mpa)

A= effective cross-sectional area of the member (mm2)

Note: The axial compressive load (or) load carrying capacity of a column (or)

compression member depends on the following parameters



(i) Slenderness rtatio, 𝜆 = 𝑙

𝑟𝑚𝑖𝑛

(ii) Yield stress of steel (fy)

(iii) Permissible stress in axial compression (𝜎ac)

(iv) Effective cross-sectional area of the member (A)

15.6 Design of Compression Members

In design of steel columns the following should be taken into consideration:

No part of steel column should be less than ¼’’ thick

No material whether in a body of the column or used as a lattice bar or

stay plate, shall be of less thickness than 1/32 of its unsupported width,

measured between centers of rivets transversely, or 1/6 of the distance

between center of rivets in the direction of stress.

Tie-plates are to have not less than 4 rivets and are to be spaced so that

the ratio of length to the least radius of gyration of the parts connected

does not exceed 40, the distance between nearest rivets of two stay

plates in this case being considered as length

In built-up columns the thickness of any outstanding member (for

example, the outstanding legs of angles) shall not be less than 1/12 of

the width of the outstanding portion.

Base plates for steel column are usually made of steel plates and

shapes.

Cast-iron bases are sometimes used for very heavy columns. Ribbed

cases may also be used instead of plates and when bolted to the

columns, add greatly to the stability of the supporting members

because of their greater width.

Lally columns:

These are columns made up of a cylindrical steel pipe shell filled with

1: 11

2: 3 portland cement concrete. The standard type of lally column is

reinforced with only the steel pipe shell. Special types of columns are

obtainable with additional reinforcement consisting of steel pipe,

reinforcing bars or structural steel shapes. The light weight column of

0.134”, while the heavy- weight columns are from 31

2 to 12

3

4 inches in

outside diameter with shell thickness of 0.216 to 0.375 inches.

Composite columns:

These are columns in which a concrete core is further reinforced with a

steel or cast-iron core designed to support a part of the load. Steel cores

may be structural H-sections or four angles, latticed or battened; cast-iron

cores are usually either solid shafts or hollow pipe sections. The column



may be further reinforced by vertical rods or bars placed at the

circumference and enclosed by spirals.

1. Design strength: steel structural members carrying usually fail by flexural

buckling. The buckling strength is affected by the residual stresses, initial

curvature and accidental eccentricities if the load. These factors are considered

while computing the strength of structural steel members subjected to axial

compression by introducing an imperfection factor α and categorizing the

columns under buckling class a, b, c or d as shown in the table no.1

Table 1:

Buckling class a b C D

Α 0.21 0.34 0.49 0.76

The design compressive strength Pd of a compression member is given by the relation:

𝑃 < 𝑃𝑑

Where

𝑃𝑑 = 𝐴𝑒𝑓𝑐𝑑

Where 𝐴𝑐 = effective cross-sectional area of the member

𝑓 𝑐𝑑=design compressive stress computed by using the following equation:

𝑓𝑐𝑑 =

𝑓𝑦𝛾𝑚0

𝛷2 − 𝜆2 0.5=

𝑓𝑦𝜒

𝛾𝑚0≤

𝑓𝑦

𝛾𝑚0

Where ф = 0.5 1 + 𝛼 𝜆 − 0 + 𝜆2

𝜆 = non- dimensional effective slenderness ratio

= 𝑓𝑦

𝑓𝑐𝑐=

𝑓𝑦 𝐾𝐿

𝑟

2

𝜋2𝐸

𝑓𝑐𝑐= Euler buckling stress = 𝜋2𝐸

𝐾𝐿

𝑟

2

Where 𝐾𝐿

𝑟 = effective slenderness ratio or ratio of effective length, KL to

approximate radius of gyration, r



Table 15.2

α = imperfection factor compiled in table

χ = stress reduction factor as shown in the table for different buckling classes,

slenderness ratios and yield stresses.

1

ф + Φ2 − λ2 0.5



𝜆 𝑚0= partial factor of safety for material strength.

The calculated values of the design compressive stress, fcd for different

buckling classes a, b, c or d are compiled in table no.2 for different types rolled steel

cross-section such as I, channel, angle, tee, solid and built –up sections. The stress

reduction factor χ and design compressive stress fcd for different buckling classes,

yield stresses and effective slenderness ratios is compiled in the code book and these

are useful in design computations. In addition, the curves corresponding to different

buckling classes are shown in non- dimensional form in the figure below.

2. Effective length of compression members: the effective length of

compression members depends upon the end support conditions influencing

the rotation and translation of the member. The end conditions are either

restrained or free depending upon the type construction at supports. The actual

length is generally taken from centre to centre of its intersections with a free

end, the free end standing length from the centre of the intersecting member at

the supported end is considered as the actual length.

If L is the actual length of the compression member, the effective length varies

from 0.65L to 2L depending upon the type of support and boundary conditions.

The effective length KL can be calculated using table no.3 for different types of

boundary conditions encountered in practice.

In case of bolted, riveted or welded trusses and braces frames, the effective

length, KL of the compression members should be taken as 0.7 to 1.0 times the

distance between centre's of connections, depending on the degree of end restraint

provided by the connection. In the case of members of trusses, effective length,

KL is taken as the distance between the centre's of intersection.

3. Column bases:column bases should be designed to have sufficient strength

and stiffness to transmit the axial force, bending moments and shear forces

developed at the base of the columns without exceeding the load carrying

capacity of the supports. Suitable anchor bolts and shear keys are designed

whenever necessary.

The nominal bearing pressure between the base plate and the support may be

determined on the basis of linearly varying distribution of pressure. The maximum

bearing pressure should not exceed the bearing strength should exceed the bearing

strength which is limited to 0.6fck, where

fck = smaller of the characteristic cube strength of concrete or bedding material

In case where the base plate is larger than the required to limit the bearing

pressure, an equal projection c of the base plate beyond the face of the column and

gusset may be taken as effective in transferring the column load as shown in the



table no.2, such that the bearing pressure on the effective area does not exceed the

bearing capacity of the concrete base.

When a column is provided with a slab base, the minimum thickness, ts of the

rectangular slab base supporting the column under axial compression is calculated

by the relation

𝑡𝑠 = (2.5𝑤(𝑎^2 − 0.3𝑏^2 ) 𝛾𝑚0 )

𝑓𝑦 > 𝑡𝑓

Table 15.3



FIG : Effective area of base plate

Where w = uniform pressure from below, on th slab base under the factored load axial

compression.

𝑎, 𝑏 = larger and smaller projection, respectively of the slab base beyond the

rectangle circumscribing the column

𝑡𝑓 = flange thickness of compression member.

When only the effective area of the base plate is used, 𝑐2 may be used in the above

equation instead of 𝑎2 − 0.3𝑏2 .

4. Design of lacings: columns comprising two main components are generally

Tied together by lacings and battens for composite action. Typical examples of

different types of lacings used in columns are shown in the figure given below

The following specifications are applicable for design of laced columns:

a) The lacing is proportioned to resist a total transverse shear Vt at at any

point in the member equal to at least 2.5 percent of the axial force in the

member and shall be divided equality among all transverse lacing systems

in parallel planes.

b) The slenderness ratio (KL/r) of the lacing bars should not exceed 145. The

effective length of the lacing bars should be taken as he length between the

inner end fasteners of the bars for single lacing and 0.7 times the distance



between the inner ends of welds connecting the lacing bars to the member.

The effective slenderness ratio (KL/r)e, of laced columns should be taken

as 1.05 times the (KL/r)0 , the actual maximum slenderness ratio, in order

to account for shear deformation effects.

c) The minimum width of lacing bars in bolted/riveted connections should be

three times the nominal diameter of the end bolt or rivet.

d) The thickness of the lacing bars should be less not than one-fortieth of its

effective length for double lacings. The inclination of the lacings and one-

sixtieth of the effective length for double lacings. The inclination of the

lacing bars should lie in the range of 40 to 70 degrees to the axis of the

member.

The maximum spacing of lacing bars should be such that maximum

slenderness ratio of the components of the main member between consecutive

lacing connections is not greater than 50 to 0.7 times the most unfavorable

slenderness ratio of the member as a whole, whichever is less.

5. Design of battens: compression members built up of two components

connected by battens should preferably have the same cross-section

symmetrically arranged about their major axis.

The code also recommends that the compression member should have

a radius of gyration about the axis perpendicular to the plane of the batten not

less than the radius of gyration about the axis parallel to the plane of the batten

as shown in the figure

The following specifications are applicable for the design of battens:

(a.) Battens are designed to resist the bending moment and transverse shear

force Vt equal to 2.5 per cent of the total axial force on the whole

compression member. They are also designed to resist simultaneously a

shear force and a moment computed by the equations

𝑉𝑏 = 𝑉𝑡 𝑐

𝑁𝑆 And 𝑀 =

𝑉𝑡 𝐶

2𝑁

Where Vt = transverse shear force as defined above

C = distance between centre- to-centre of battens in the longitudinal

direction

N = number of parallel planes of battens

S = minimum transverse distance between the centroid of the rivet/bolt

group/ welding connecting the batten to the main member.



(b.) The thickness of the plates used as battens should be not less than one-

fortieth of the distance between the inner-most connecting line of rivets,

bolts or welds, the end battens should have an effective depth,

longitudinally not less than the perpendicular distance between the

centroids of the main members.

The intermediate battens should have an effective depth of not more

than three quarters of this distance, but in no case should the effective depth of

any batten be less than twice the width of one member, in the plane of the

battens. The effective depth of the batten is taken as the longitudinal distance

between the outer-most bolts, rivets or welds at the ends.

(c.) The spacing of the battens, centre-to-centre of its end fastenings, should be

such that the slenderness ratio (KL/r) of any component over that distance

should not exceed a value of 50, nor be greater than 0.7 times the

slenderness ratio of the member as a whole about its axis parallel to the

battens (z – z).

(d.) Tie plates, members provided at the ends of battened or laced members,

should also be designed in the same method as battens.

Design of flexural member:

General aspects: flexural members such as beams should have adequate design

strength to resist the bending moments and shear forces resulting from impose loads.

In addition, they should satisfy the serviceability criteria comprising the deflection

limits specified in the table no.4 for different types of structural members. The

maximum deflection under service loads should not exceed the limits expressed as a

function of the span given in the code. The effective span of the beam is generally

taken as the distance the centre of the supports.

Design strength in flexure: the following specifications govern the design of flexural

members. Flexural members adequately supported against lateral torsion buckling

(laterally supported beams) are governed by the yield stress. The factored design

moment, M at any section, in a beam due to external loads should satisfy the relation

𝑀 ≤ 𝑀𝑑

Where 𝑀𝑑= design bending strength of the section

a.) The design bending strength of a section which is not susceptible to web

buckling under shear before yielding and factored design shear force does

not exceed 0.6 Vd, where Vd is the design shear strength of the cross-

section, bending strength Md is calculated by the relation

𝑀𝑑 =𝛽𝑏𝑍𝑝𝑓𝑦

𝛾𝑚0



Where 𝛽𝑏 = 1.0 for plastic and compact sections

= 𝑍𝑒

𝑍𝑝 for semi-compact sections

𝑍𝑝 = plastic and elastic section modulii of the cross- section,

respectively

𝑓𝑦 = yield stress of the material

𝛾𝑚0= partial safety factor

To avoid irreversible deformation under serviceability loads Md should b less

than [1.2𝑍_𝑒 𝑓_𝑦 ]

𝛾𝑚 0 in case of simply supported and

[1.5𝑍_𝑒 𝑓_𝑦 ]

𝛾𝑚 0 in cantilever beams.

b.) In the case of laterally supported beams, the resistance to lateral torsional

buckling need not be checked separately in the following cases:

1) Bending is about the minor axis of the section

2) Section is hollow (rectangular/tubular) or solid bars,

3) In case of bending about the axis, the non-dimensional slenderness

ratio (γLT) is less than 0.4.

The design loading strength of laterally unsupported bemas as governed by

lateral torsional buckling is calculated by the relation

𝑀𝑑 = 𝛽𝑝 𝑍𝑝 𝑓𝑏𝑑

Where 𝑓𝑏𝑑 = design bending compressive stress, computed as

= 𝜒𝐿𝑇 𝑓𝑦

𝛾𝑚 0

𝜒𝐿𝑇= bending stress reduction factor to account for lateral torsional

buckling, given by the relation:

𝜒𝐿𝑇 = 1

ф𝐿𝑇 + ф𝐿𝑇2 − 𝜆𝐿𝑇

2 0.5 ≤ 1.0

ф𝐿𝑇 = 0.5 1 + 𝛼𝐿𝑇 𝜆𝐿𝑇 − 0.2 + 𝜆𝐿𝑇2

The imperfection parameter 𝛼𝐿𝑇 is given by

𝛼𝐿𝑇 = 0.21 for rolled steel section

𝛼𝐿𝑇 = 0.49 for welded steel section



The non-dimensional slenderness ratio, 𝜆𝐿𝑇 is given by the relation

𝜆𝐿𝑇 = 𝛽𝑏 𝑍𝑝 𝑓𝑦

𝑀𝑐𝑟≤

1.2𝑍𝑒𝑓𝑦

𝑀𝑐𝑟=

𝑓𝑦

𝑓𝑐𝑟 ,𝑏

Where 𝑓𝑐𝑟 ,𝑏 = extreme fiber bending compressive stress

𝑀𝑐𝑟 = elastic critical moment calculated by the expression

𝑀𝑐𝑟 = 𝜋2𝐸𝐼𝑤

𝐿𝐿𝑇 2 𝐺𝐼𝑡 + 𝜋2𝐸𝐼𝑤

𝐿𝐿𝑇 2 = 𝛽𝑏 𝑍𝑟 𝑓𝑐𝑟 ,𝑏

The extreme fiber bending compressive stress 𝑓𝑐𝑟 ,𝑏 of non-slender rolled steel

sections in the above equation may be approximately calculated from the

values from steel tables which have been prepared using the following

equation:

𝑓𝑐𝑟 ,𝑏 = 1.1𝜋2𝐸

𝐿𝐿𝑇𝑇𝑦

2

1 +1

20

𝐿𝐿𝑇𝑇𝑦ℎℎ𝑡𝑓

2

0.5

CALCULATIONS:

1. Selection of Trial Section:

Length of the column = 3.2 m

Effective length of column

Load = 574.253 kN

𝒍 = 𝟎. 𝟖𝟓𝐋 = 𝟎. 𝟖𝟓𝐱𝟑. 𝟐𝐱𝟏𝟎𝟎𝟎 = 𝟐𝟕𝟐𝟎 𝐦𝐦

In order to support load, the slenderness ratio of the rolled steel column

and the value of yield stress for the steel may be taken 60 and 250 N/mm2

respectively.

Allowable working stress from IS: 800-1984

𝜎𝑎𝑐 = 122 N/mm2

Effective sectional area required = 574.253x100

122= 4706.99 mm2



2. Properties of Trial Section:

From steel table try ISWB600A @ 1.451 kN/m section.

Sectional area A = 18486 mm2

Radius of gyration 𝑟𝑥𝑥 = 250.1 𝑚𝑚

𝑟𝑦𝑦 = 53.5 𝑚𝑚

3. Slenderness Ratio:

𝑟𝑚𝑖𝑛 = 53.5 𝑚𝑚

Slenderness ratio 𝑙

𝑟𝑚𝑖𝑛=

2720

53.5= 50.84

4. Check for Safe Load:

From IS: 800-1984, allowable axial stress in compression for having yield stress

250 N/mm2

𝑓𝑦 = 250 N/mm2

𝜆 = 50 𝜎𝑎𝑐 = 132

𝜆 = 60 𝜎𝑎𝑐 = 122

𝜆 = 50.84 𝜎𝑎𝑐 = ?

𝜎𝑎𝑐 = 122 − 132 − 122

60 − 50 60 − 50.84 = 112.84 N/mm2

Safe load carrying capacity

p = 112.84x18486

1000 = 2085.96 kN

Hence, safe.



16. DESIGN OF STRUCTURAL CONNECTIONS

Design of connections and splices is a critical aspect of the design process.

Because each fabricator has unique equipment and methods, the detailed

configuration of connections plays an important part in determining the cost of the

fabricated product. Consequently, the detailed design of these elements is a part of the

work performed by the fabricator. In the industry, this work is known as detailing.

Usually, the structural engineer indicates the type of connections and type and

size of fasteners required; for example, “framed connections with 7/8 inches in A325

bolts in bearing-type joints,” or the type of connection with reference to IS:800

requirements. For beams, the design drawings should specify the reactions. If, how –

ever, the reactions are not noted, the detailer will determine the reactions from the

uniform load capacity (tabulated in IS steel manual), giving due considerations to the

effect of large concentrated loads near the connection. For connections resisting

lateral loads, live, wind, or seismic, the design drawing should stipulate the forces and

moments to be carried. Generally, the design should also include a sketch showing the

type of moment connection desired.

The various types of connections used for connecting the structural members

are given below:

1. Riveted connections.

2. Bolted connections.

3. Welded connections.

These connections are named after the type of fastening (viz., rivets, bolts and

nuts, pins and welds) used for connecting the structural members.

1. Rivets :

A piece of round steel forged in place to connect two or more than two steel members

together is known as rivet. The rivet for structural purposes are manufactured from

mild steel and high tensile rivet bars. A rivet consists of a head and a body. The body

of rivet is termed as shank. The rivets are manufactured in different lengths to suit

different purposes. The sizes of rivets is expressed by the diameter of the shank.

For driving the rivets, they are heated till they become red hot and are then

placed in the hole. Keeping the rivets pressed from one side, a number of blows are

applied and a head at other end is formed. The hot-driven rivets are divided into

following three types, according to the method of rivet-driving.

1. Power driven rivets.

2. Hand driven rivets.

3. Field rivets.



i) Rivet heads:

The proportions of various shapes of rivet heads have been expressed in terms

of diameter „D‟ of shank of rivet. The snap head is also termed as round head and

button head. The snap heads are used for rivets connecting structural members. The

countersunk heads are used to provide a flush surface.

ii) Rivet holes:

The rivet holes are made in the plates or structural members by one of the following

methods:

1. Punching

2. Drilling.

When the rivet holes are made by punching , the holes are not perfect, but

taper. A punch damages the material around the hole. The operation known as

reaming is done in the hole made by punching.

When the rivet holes are made by drilling, the holes are perfect and provide

good alignment for driving the rivets.

The diameter of a rivet hole is made larger than the nominal diameter of the

rivet by 1.5 mm of rivets less than or equal to 25 mm diameter and by 2 mm for

diameters exceeding 25 mm.

Riveted joint:

The riveted joints are of two types:

1. Lap joint

a. Single riveted lap joint

i. Chain riveted lap joint

b. Double riveted lap joint

i. Zigzag riveted lap joint

2. Butt joint

a. Single cover butt joint

b. Double cover butt joint

16.1 Transmission of load in riveted joint:

There are two modes of transmission of load in riveted joints. When the load is

transmitted by bearing between plates and shanks of rivets, the rivets are subjected to

shear. When the shear of rivets is only across one cross section of the rivet, it is

known as single shear. When the shear of rivet is across two cross-section of the

rivet, it is known as double shear.



16.2 Failure of Riveted Joint:

The failure of a riveted joint may take place in any of the following ways:

1. Shear failure of rivets

2. Shear failure of plates

3. Tearing failure of plates

4. Bearing failure of plates

5. Splitting failure of plates at the edges.

6. Bearing failure of rivets

16.3 Arrangements of Rivets

The rivets in a riveted joint are arranged into two forms:

1. Chain riveting

2. Diamond riveting

16.4 Specifications for design of riveted joints:

1. Members meeting at joint.

The centroidal axes of the members meeting at a joint should intersect at one

point, and if there is any eccentricity. Adequate resistance should be provided in the

connection.

2. The centre of gravity of group of rivets should be on the line of action of load

whenever practicable.

3. Pitch:

Minimum pitch: The distance between centres of adjacent rivets should not be

less than 2.5 times the gross diameter of the rivet.

Maximum pitch

(i) The maximum pitch should not exceed 12t or 200 mm whichever is less in

compression member, and 16t or 200 mm whichever is less in case of tension

member, when the line of rivets lies in the direction of stress. In the case of

compression members in which the forces are transferred through the butting faces,

this distance shall not exceed 4.5 times the diameter of the rivets for a distance from

the abutting faces equal to 1.5 times the width of the member.

(ii) The distance between centers of any two consecutive rivets in a line adjacent and

parallel to an edge of an outside plate shall not exceed (100mm + 4t) or 200 mm,

whichever is less in compression or tension members.

(iii)When the rivets are staggered at equal intervals and the gauges does not exceed 75

mm, the distances specified in Para i and ii between centres of rivets may be

increased by 50 percent.



(iv) If the line of rivets (including tacking rivets) does lie in the direction of stress,

the maximum pitch should not exceed 32 t or 300 mm whichever is less where t is the

thickness of the thinner outside plate.

4. Edge distance:

A minimum edge distance of approximately 1.5 times the gross diameter of

the rivet measured from the centre of the rivet hole is provided in the riveted joint

Table 16.1

Edge distance of holes

Gross diameter of rivet

mm

Edge Distance of Hole

distance to sheared or

hand flame cut edge

mm

Distance to rolled

machine flame cut or

planed edge

Mm

13.5 & below 19 17

15.5 25 22

17.5 29 25

19.5 32 29

21.5 32 29

23.5 38 32

25.5 44 38

29.0 51 44

32.0 57 51

35.0 57 51

5. Rivets through packing’s:

The rivets carrying calculated shear stress through a packing greater than 6

mm thick shall be increased above number required by normal calculations by 2.5

percent for each 2 mm thickness of packing. For double shear connections packed

on both sides, the number of additional rivets required shall be determined from the

thickness of the thicker packing. The additional rivets should preferably be placed in

an extension of the packing. When the properly fitted packing are subjected to direct

compression, then, the above mentioned specifications shall not apply.

6. Long grip rivets

When the grip of rivets carrying calculated loads exceeds 6 times the diameter

of the holes, then, the rivets are subjected to bending in addition to shear and bearing.

The number of rivets required by normal calculations shall be increased by not less

than one percent for each additional 1.6 mm of grip, but the grip shall not exceed 8

times the diameter of the holes.

7. Rivet line distance



When two or more parts are connected together, a line of rivet shall be

provided at a distance of not more than 37 mm + 4t from the nearest edge where t is

the thickness in mm of thinner outside plate. In case steel work is not exposed to

weather, this may be increased to 12t

8. Tacking rivets:

When the maximum distance between centres of two adjacent rivets

connecting the members subjected to either compression or tension exceeds the

maximum pitch, then, the tacking rivets not subjected to calculated stresses shall be

used

The tacking rivets shall have a pitch in line not exceeding 32 times the

thickness of the outside plate or 300 mm whichever is less. Wherever the plates are

exposed to the weather, the pitch in line not exceed 16 times the thickness of the

outside plate or 200 mm , whichever is less. In both cases, the lines of rivets shall not

be apart at a distance greater than these pitches.

For the design and construction composed of two flats, angles, channels or tees in

contact back or separated back to back by a distance not exceeding the aggregate

thickness of the connected parts, tacking rivets with solid distance pieces where the

parts are separated, shall be provided at a pitch in line not exceeding 1000 mm.

16.5 Design procedure for riveted joint:

For the design of a lap joint or butt joint the thickness of plates to be joined are

known and the joint is designed for the full strength of the plate. For the design of a

structural steel work, force (pull or push) to be transmitted by the joint is known and

riveted joint can be designed. Following are the usual steps for the design of a riveted

joint:

Step1: The size of the rivet is determined for the unwin‟s formula i.e.,

𝑑 = 6.04 (𝑡)1

2

Where t = thickness of plate in mm

d = nominal diameter of rivet

The diameter of the rivet computed is rounded off to available size of rivets.

The rivets are manufactured in nominal diameters of 12, 14, 16 .18, 20, 22, 24, 30, 33,

36, 39, 42 and 48mm.

In structural steel work, rivets of nominal diameter of 16, 18, 20 and 22 mm are used.

The nominal diameter of rivets to be used in a joint is assumed.

Step 2: The strength of rivets in shearing and bearing are computed. The working

stress in rivets and plates are adopted as per BIS. The rivet value R is found. For

designing lap joint or butt joint tearing strength of plate is determined as under:



𝑃𝑡 = 𝑔 − 𝑑 . 𝑡. 𝜎𝑡𝑓

Where g = gauge of rivets to be adopted

t = thickness of plate

𝜎𝑡𝑓 = working stress in direct tension for plate

The tearing strength of plate should not exceed the rivet value R( Ps or Pb which ever

is less) or

𝑔 − 𝑑 . 𝑡. 𝜎𝑡𝑓 ≤ 𝑅

From this relation gauge of the rivets is determined.

In structural steel work, force to be transmitted by the riveted joint and the

rivet value are known. Hence number of rivets requested to be provided in the joint

can be computed, as follows:

No. of rivets required in the joint = force

rivet value

The number of rivets thus obtained is provided on one side of the joint and an

equal number of rivets is provided on the other side of joint also.

For the design of joint in a tie member consisting of a flat, width/thickness of

the flat is known. The section is assumed to be reduced by rivet holes, depending

upon the arrangement of rivets to be provided. The strength of flat at weakest section

is equated to the pull transmitted at the joint.

𝑏 − 𝑑 . 𝑡. 𝜎𝑡𝑓 = P

16.6 Bolted Connections:

Introduction

Structural steel members are usually assembled using different types of

elements such as plates, angles, channels, tee and I-sections. Connections are made

using rivets or bolts to transfer the forces and moments from one member to another.

They are also required to extend the length of the members. The connections should

be designed to avoid the failure of the fasteners before the failure of the principal

member.

Design principals of connections

16.6.1 Design strength

The evaluation of design strength of connection should be evaluated using the

partial safety factors compiled in table of load combinations. In general, connection

failure may be avoided by adopting a higher safety for the joints than the members.



16.6.2 Spacing of fasteners

The minimum spacing between the centre of a fastener should be not less than

2.5 times the diameter of the fastener. The maximum spacing between the centre of

any two adjacent fasteners should not exceed 32 t or 300 mm, whichever is less,

where f is the thickness of the thinner plate.

Also the distance between the centres of two adjacent fasteners (pitch ) in a

line lying in the direction of stress, should not exceed 16t or 200 mm, whichever less,

in tension members; and 12t or 200mm , whichever is less in compression members,

where f is the thickness of the thinner plate.

16.6.3 Edge and end distance

The minimum and end distances from the centre of any hole to the nearest

edge of a plate should be not less than 1.7 times the hole diameter in case of sheared

or hand-flame cut edge; 1.5 times the hole diameter in case of rolled, machine-flame

cut, sawn and plane edges.

The maximum edge distance to the nearest line of fasteners from an edge of

any un-stiffened part should not exceed 12tε, where ε=(250/fy)0.5

and t is the

thickness of the thinner outer plate. This clause is not applicable to fasteners

interconnecting the components of back-to-back tension members. Where the

members are exposed to corrosive influences, the maximum edge distance should not

exceed 40 mm plus 4t, where t is the thickness of the thinner connected plate.

The bolt diameter, pitch edge distances as per IS: 800-2007 are compiled in

table given below.

Table :16.2 Bolt diameter, pitch and edge distances

Nominal diameter of bolt(mm) 12 14 16 18 20 22 24 27 30 Above

36

Diameter of hole(mm)

13

15

18

20

22

24

26

30

33

Bolt dia.

+ 3 mm

Minimum edge distance(mm)

For sheared or rough edge 20 26 30 34 37 40 44 51 56 1.7 x

hole

diameter

For rolled, sawn, or planed edge 19 23 27 30 33 36 39 45 50 1.5 x

hole

diameter

Maximum edge distance = 12tε, where ε=(250/fy)0.5

Maximum pitch = 2.5 x nominal diameter of bolt



Maximum pitch = 32 t or 300 mm

(a) Parts in tension = 16 t or 200 mm whichever is less

(b) Parts in compression = 12 t or 200 mm whichever is less

16.6.4 Bearing type bolts in shear

The design strength of the bolt Vdsb based on shear strength is given by the relation:

𝑉𝑑𝑠𝑏 = 𝑉𝑛𝑠𝑏

𝛾𝑚𝑏

Where Vnsb = nominal shear capacity of a bolt, computed as

𝑉𝑛𝑠𝑏 = 𝑓𝑢

3 𝑛𝑛𝐴𝑛𝑏 + 𝑛𝑠𝐴𝑠𝑏 𝛽𝑖𝑗 𝛽𝑙𝑔𝛽𝑝𝑘

Where fu = ultimate tensile strength of bolt

nn = number of shear planes with threads intercepting the shear plane

ns = number of shear planes without threads intercepting the shear plane

Asb = nominal plain shank area of the bolt

Anb = net shear area of the bolt at threads, may be taken as the area corresponding to

root diameter at the thread

βij = reduction factor for the overloading of end bolts

βlg = reduction factor for the effect of large grip length

βpk = reduction factor for packing plates in excess of 6mm

The reduction factors are computed using the following relations:

𝛽𝑖𝑗 = 1.075 − 𝑙𝑗

(200𝑑) but 0.75 ≤ βij ≤ 1.0

= 1.075 − 0.005 𝑙

𝑑

Where d = nominal diameter of the fastener.

When the grip length, lg (equal to the total thickness of the connected plates) exceeds

5 times the diameter, d of the bolts, the design shear capacity should be reduced by a

factor βlg, given by

𝛽𝑙𝑔 = 8𝑑

3𝑑 + 𝑙𝑔=

8

(3 + 𝑙𝑔 𝑑)

Also 𝛽𝑙𝑔 should not exceed 𝛽𝑖𝑗 and the grip length, lg should in no case be greater

than 8d. the design shear capacity of bolts carrying shear through a packing plate in

excess of 6 mm should be decreased by a factor of 𝛽𝑝𝑘 given by a relation,

𝛽𝑝𝑘 = (1 − 0.0125𝑡𝑝𝑘 )

Where tpk = thickness of the thicker packing expressed in mm.



16.6.5 Bolts in Tension

The nominal strength capacity of bolt Tnb depends on the ultimate tensile strength of

the bolt and the net tensile stress area. The factored tensile force, Tb should satisfy the

relation:

𝑇𝑏 ≤ 𝑇𝑑𝑏

Where

𝑇𝑑𝑏 = 𝑇𝑛𝑏

𝛾𝑚𝑏

Tnb = nominal tensile capacity of the bolt, calculated as:

(0.90𝑓𝑢𝑏𝐴𝑛) < 𝑓𝑢𝑏𝐴𝑛 𝛾𝑚𝑏

𝛾𝑚0

Where fub = ultimate tensile stress of the bolt

fyb = yield stress of the bolt

An = net tensile stress area at the bottom of the thread of the bolt

Asb = shank area of the bolt

γmb = partial safety factor for ultimate stress = 1.25

γm0 = partial safety factor yield stress = 1.10

The design capacity of ordinary bolts (Grade 4.6) based on the net cross-sectional

area in tension and single shear are compiled in Table

Table : 16.3 design capacity of ordinary bolts ( Grade 4.6)

Bolt size

diameter

d(mm)

Tensile

stress area

(Anb)(mm2)

Tension

capacity Tb

(KN) tnb =

272 Mpa

Single

shear

capacity,

Vsb(kN)

vnsb = 185

Mpa

Minimum

thickness of

ply for bolt

bearing vnpb

= 800 Mpa

tbb = tc, mm

(12) 84.3 22.9 15.6 1.6

16 157.0 42.7 29.0 2.3

20 245.0 66.6 45.3 2.8

(22) 303.0 82.4 56.0 3.2

24 353.0 96.0 65.3 3.4

(27) 469.0 124.8 84.9 3.9

30 561.0 152.5 103.8 4.3

36 817.0 222.2 151.1 5.2

𝑻𝒃

= 𝑨𝒏𝒃𝒕𝒏𝒃

𝑽𝒔𝒃

= 𝑨𝒏𝒃𝒗𝒏𝒔𝒃 𝒕𝒃𝒃 = 𝑽𝒏𝒑𝒃

𝒅𝒗𝒏𝒑𝒃

Sizes in

brackets not

preferred



16.7 Welded Connections:

General features

Welded connections result in considerable savings in material. It has the added

advantage of rapidity of construction of complicated steel structures involving the

assembly of several individual steel components into an integrated steel structure.

Welding obviates the formation of holes in the member and permit design based on

continuity at supports resulting in economy of material. Welding offers airtight and

watertight jointing of structural elements and hence is employed in the construction of

water/oil storage tanks, ships etc. Welded connections are usually aesthetic in

appearance and appear less clustered in comparison with bolted connections.

In addition, welded connections improve the rigidity of the complete structure

resulting in superior structural behavior at various limit states. Proper workmanship is

essential to produce structurally sound and effective welds connecting structural, steel

components. In the case of normal steel structures arc welding is adopted and the

design of welds should conform to the Indian Standard Codes IS: 816 and IS: 9595.

16.7.1 Types of welds

The most common types of welds used in steel structures are

(a) Fillet welds

(b) Butt welds

(c) Plug welds

(d) Slot welds

Fillet welds are the most commonly used type to connect structural

components meeting at an angle (generally between 60 and 120 degrees), while butt

or groove welds are used to connect horizontal members.

(a) Fillet weld

The size of fillet weld should be not less than 3 mm. The size of the fillet

weld is generally taken as the minimum leg length and is related to the thickness of

the connected member as detailed in Table given below:

Table :16.4 minimum size of the fillet weld (Table 21 of IS: 800-2007)

SI

No.

Thickness of

thicker part

(mm)

Minimum size

of weld

(mm)

Over Up to and

including

(1) (2) (3) (4)

i) - 10 3

ii) 10 20 5

iii) 20 32 6

iv) 32 50 10



For purposes of stress calculation in fillet welds joining faces inclined to each other,

the effective throat thickness should be taken as K times the fillet size, where K is a

constant, depending upon the angle between the fusion faces. As compiled in Table

given below.

Table:16.4 values of K for different angles between fusion faces.

Angle

between

Fusion

Faces

600

910 101

0 107

0 114

0

to to to to to

910

1000

1060

1130

1200

Constant

K

0.70 0.65 0.60 0.55 0.50

The effective length of fillet weld is taken as the length of specified size and

required throat thickness, with minimum length not less than four times the size of the

weld.

Design strength of a fillet weld, fwd is based on the throat area and is compute

as

𝐹𝑤𝑑 = 𝑓𝑤𝑛

𝛾𝑚𝑤

Where 𝑓𝑤𝑛 = 𝑓𝑢

3

fu = smaller of the ultimate stress of the weld or of the parent metal

𝛾𝑚𝑤 = partial safety factor

(b) Butt welds

When the joining plates are of equal thickness, the butt weld size is defined by

the throat thickness, taken as the thickness of the plate. If the joining plates are of

unequal thickness, the size of the weld corresponds to the thickness of the thinner

plate. The design strength of butt welds depends upon the throat thickness and the

stresses are limited to those permitted in the parent metal. However for site welds, the

partial safety factor 𝛾𝑚𝑤 = 1.5.

(c) Plug and Slot welds

Plug and slot weld s are not used exclusively in steel construction. When it is

not possible to use fillet welds or when the length of the fillet weld is limited, plug

and slot welds are used to supplement fillet welds. Plug welds are occasionally used

to fill up holes in construction, such as beam-to-column seat angles where temporary

erection bolts have been placed to align members prior to welding. The penetration of

these welds into base metal is difficult to ascertain. Moreover the inspection of these

welds is difficult. Hence, they are normally not used to connect members subjected to

tensile forces. Slot and plug welds are useful in preventing overlapping parts from

buckling.



16.8 Design of beam column connection

Beam ISHB 200

D=250 mm; b=250 mm;

tf =9.7 mm; tw =6.9 mm;

Column ISWB 600A

D=600 mm; b=250 mm;

tf =23.6 mm; tw =11.8 mm;

yield stress = 245 N/mm2

Moment M = 52 kN-m

Axial A = 71.80 kN

Shear R = 4 kN

Bolt Design

Flange force = M

D−tw -

R

2

= 52x1000

250−6.9 -

4

2

= 237.4 kN

Assuming 4 No's 16 mm diameter bolts

Tension on each bolts = 237.4/4

= 59.35 kN

From AISC Manual 89

Allowable tension in SI units

= 44 x πxd 2

4 x 25.42 x 4.448

= 61 kN

Allowable tension is greater than actual tension

Hence safe



Flange to end plate weld

= force on flange

(1.024 𝑥 2𝑥 𝑤𝑖𝑑𝑡 𝑕 𝑜𝑓 𝑓𝑙𝑎𝑛𝑔𝑒 )

= 237.4 x10

(1.024 𝑥 2𝑥 250)

= 4.64 mm weld

Effective end plate width (pb) = bf+50

= 250+50

= 300 mm

Centre of bolt to centre of

Flange distance (pf) = 40 mm

Effective bolt distance (Pe) = (𝑝𝑓 −𝑡𝑓

2) -(

𝑑𝑖𝑎

4)-0.707x thickness of

weld

= (40-9.7/2)-16/4-0.707x4.64

= 27.8719 mm

Thickness of plate required

Partial safety factor (Ca) = 1.13

Ratio of area of flange to area of web

(Af/Aw) = (250x9.7)/(250x6.9) = 1.41

Ratio of effective bolt distance to diameter of bolt

(Pe)/(d) = 27.8719/16 = 1.74

Ratio of width of flange to width of base plate

(Cb) = 250/300 = 0.83

∝ = 𝐶𝑎. 𝐶𝑏 𝐴𝑓

𝐴𝑤

13

(𝑝𝑒

𝑑𝑖𝑎)1/4

∝ = 1.212

Moment in plate Mp= ∝ x flange force x eff bolt distance/4



= 2002686.87 Nmm

Required plate thickness = 6Mp

o.75fypb

= 6x2004686 .87

o.75x365x300

=12.45 mm

Beam to end plate weld size

Min weld size = 5 mm

Required weld to develop max web tension stress (0.6fy) in web near flanges

= 0.6fy .tw

2x10.24

= 0.6x245

2x10.24x10

= 4.952 mm

Provide 5 mm weld

Provide 300 mm wide and 12.45 mm connection plate.

Use 4 No's 16 mm dia bolts each side

Welds

Flange to end plate = 4.64 mm

Web to end plate = 5.00 mm

16.9 Design of Main beam-Joist connection

Secondary beam ISJB [email protected] kN/m

Main Beam ISHB [email protected] kN/m

Shear force on Main beam from joist = 17 kN

Assuming 8.8 Grade 12 mm diameter bolts and

No of bolts on main beam (Nm) = 3

No of bolts on secondary beam (Ns) = 3

Yield strength of bolts fy = 345 N/mm2



Allowable shear = 0.25πd2Nm x0.4fy

1000

= 0.25πd1223 x0.4x345

1000

= 46.80 kN

Allowable shear > Actual shear, hence safe

Using ISA 90x90x6 as cleat angle

Shear stress in cleat angle = 1.5 x F

2xdxt

= 1.5 x 17 𝑥103

2𝑥90𝑥8

= 17.7 N/mm2

Max shear stress = 0.45fy = 0.45x250

= 112.5 N/mm2 safe



17. COLUMN BASES

Beams transfer the load to the column and the column transfer their loads to

the soil through column bases resting over concrete or masonry blocks. A column

base distributes the load over a greater area so that the pressure on the concrete block

does not exceed the permissible bearing stress

Column base should be designed to have sufficient strength and stiffness to

transmit the axial force, bending moments and shear forces developed at the base of

the columns without exceeding the load carrying capacity of the supports. Suitable

anchor bolts and shear keys are designed wherever necessary.

The nominal bearing pressure between the base plate and the support may be

determined on the basis of linearly varying distribution of pressure. The maximum

bearing pressure should not exceed the bearing strength which is limited to 0.6fck,

where.

fck= smaller of the characteristic cube strength of concrete

In cases where the base plate is larger than that required to limit the bearing

pressure, an equal projection c of the base plate beyond the face of the column and

gusset may be taken as effective in transferring the column load given in fig. below

such that the bearing pressure on the effective area does not exceed the bearing

capacity of the concrete base.

When a column is provided with a slab base, the minimum thickness, ts of the

rectangular slab base supporting the column under axial compression is calculated by

the relation

𝑡𝑠 = 2.5𝑤(𝑎2 − 0.3𝑏2)𝛾𝑚0

𝑓𝑦 > 𝑡𝑓

There are three types of column bases which are generally used

1. Slab base

2. Gusseted base

3. Grillage foundation

17.1 Slab Base:

The consists of a base plate underneath a column end which is machined so as

to have a complete bearing on the plate. The column is properly secured to the base

plate by means of fastenings as shown.



Fastenings are simply used to secure it with the base plate and secondly to

resist all moments and forces due to transit, unloading and erection. Those are not

designed to resist the direct compression in the column.\

Design of a Slab Base and Concrete block:

The following steps are to be followed when axial load to which the column is

subjected is known

1. Calculating the bearing area (A) of the base plate

Bearing Area = Axial load in the column

permissible compressive stress in concrete ,𝐴 =

P

𝜎𝑐

2. Assuming the shape of base plate to be square calculating the size of one side.

If it is rectangular calculate the length and breadth of the base plate. Arrange

the section of the column centrally on the base plate

3. Calculate the thickness of base plate as per

IS: 800-1984 (5.4.3).

𝑡 = 3𝑤

𝜎𝑏𝑠 𝑎2 −

𝑏2

4

Where t = slab thickness, (mm)

w= the pressure or loading on the underside of base (Mpa)

a= the greater projection of the plate beyond column

b= the lesser projection of the plate beyond column

𝜎bs= the permissible bending stress in slab bases = 185 Mpa for all

steels.

If a square base plate is used for solid round steel column, the

thickness of the plate will be taken as.

𝑡 = 10 90𝑤

16𝜎𝑏𝑠x

B

B − d0

Where, t= thickness of plate (mm)

w= the total axial load, (kN)

B= the length of side of cape or base (mm)

𝜎bs = permissible bending stress in slab base = 185 Mpa for all

steels

d0= diameter of the reduced end (if any) of the column (mm)

The cap or base plate should not be less than 1.5 (d0 + 75) mm in

length or diameter.



17.2cGusseted Base:

A gusseted base consists of base plate connected to the column through gusset

plates. The thickness of base plate in this case will be less than the thickness of the

slab base for the same axial load as the bearing area of the column on the base plate

increases by the gusset plate.

As per IS: 800-1984 for the columns with gusseted base; gusset plates, angle

cleats, stiffeners, fastening, etc. In combination with the bearing area of the shaft

should be sufficient to take the loads, bending moment and reaction to the base plate

without exceeding the specified stresses. All bearing surfaces are machined to ensure

perfect contact. Where the ends of the column shaft and the gusset plate are not faced

for complete bearing, the fastening shall be sufficient to transmit all the forces to

which the base is subjected.

Design of Gusseted Base and Concrete Block:

Following design steps are to be followed:

1. Calculate the area (A) of base plate

𝐀 = 𝐀𝐱𝐢𝐚𝐥 𝐥𝐨𝐚𝐝 𝐨𝐧 𝐜𝐨𝐥𝐮𝐦𝐧

𝐩𝐞𝐫𝐦𝐢𝐬𝐬𝐢𝐛𝐥𝐞 𝐜𝐨𝐦𝐩𝐫𝐞𝐬𝐬𝐢𝐯𝐞 𝐬𝐭𝐫𝐞𝐬𝐬 𝐢𝐧 𝐜𝐨𝐧𝐜𝐫𝐞𝐭𝐞

2. Assume the materials used in gusseted base. Generally the thickness of

gusseted plate is assumed as 12 to 16 mm. The size of angle used generally is

ISA 150x115x12 mm or ISA 150x100x12 mm in rivet design and no gusset

angle is used in welds. The depth of column section, thickness of gusset plate

and length of leg of angle being known the width of gusset plate for these

distances can be calculated. Then calculate the length of gusset plate by

dividing area by width of gusset plate.

3. Provide suitable rounded size of gusset plate and calculate actual upward

concrete pressure.

4. See fig. let ‘w’ be the upward reaction of concrete and ‘l’ be the projection of

base plate beyond column face xx. Calculate the hogging bending moment at

column face as per mm width plate.

Mxx = 𝑤𝑙2

2

Calculate the moment of resistance per mm width of section xx.

Mxx = 𝑧.𝜎𝑏𝑐

Equating B.M to M.R., find the thickness ‘t’.

5. Consider another section yy of base plate at the centre of column as shown in

fig.

Calculate Hogging B.M= 𝑤𝑙2

2 and sagging B.M=

𝑤𝑑2

8

Net B.M at the center of base plate



Myy =𝑤𝑑2

8−

𝑤𝑙2

2

Calculate the moment of resistance per mm width at section yy

M𝑟𝑦 = 𝑧.𝜎𝑏𝑐 =1

6x𝑡2x1𝜎𝑏𝑐

Equating max. B.M. (Myy), find‘t’. Providing thickness‘t’ whichever is

maximum (considering Mxx and Myy).

6. Calculate the thickness of concrete block and size of block as in case of slab

base.

7. Design the fastners.

17.3 CALCULATION:

Column section IM 350 𝑋 225 𝑋 12

Properties of column:

𝐴𝑥 = 124 𝑐𝑚2 ; 𝐷 = 368 𝑚𝑚 ; 𝐵𝑓 = 140 𝑚𝑚

𝑇𝑓 = 14 𝑚𝑚 ; 𝑇𝑤 = 8𝑚𝑚 ; 𝐼𝑧 = 29902 𝑋 104 𝑚𝑚4

Axial load = 1340 𝐾𝑁

Bearing strength of concrete = 4 𝑁 𝑚𝑚2

Bending stress for steel base plate 𝜎𝑏𝑠 = 185 𝑁 𝑚𝑚2

Safe bearing capacity of the soil = 200 𝐾𝑁 𝑚𝑚2

Area of the base plate required = 1340 𝑋 103

4

Let 12 𝑚𝑚 thick gusset plate and ISA 90 𝑋 90 𝑋 12

Minimum width of the base plate = 368 + 2 𝑋 12 + 2 𝑋 90

= 572 ≅ 575 𝑚𝑚

Length of the base plate = 335 𝑋 103

575

= 585 mm

Provide 575 𝑋 585 base plate

Actual bearing pressure intensity on the base plate = 1340 𝑋 103

575 𝑋 585



= 3.983 𝑁 𝑚𝑚2

Cantilever projection = 90 − 12 = 78 𝑚𝑚

Consider a cantilever strip of the base plate of 1mm wide and 78 mm long

Maximum cantilever moment = 30983 𝑋 782

2

= 12107.16 𝑁 𝑚

Equating the moment of resistance to cantilever moment = 1

6𝜎𝑏𝑠𝑏𝑡

2

1

6 𝑋 185 𝑋 1 𝑋 𝑡2 = 12107.16

𝑡 = 12107.16 𝑋 6

185

𝑡 = 19.81 𝑚𝑚 ≅ 20 𝑚𝑚

Bending moment at critical section XX = 368 + 2 𝑋 12

= 392 𝑚𝑚

= 3.98 𝑋 3922

8− 3.98 𝑋

902

2

= 60374.3 𝑁 𝑚𝑚

Equating the moment of resistance to the bending moment

= 1

6 𝑋 185 𝑋 1 𝑋 𝑡2 = 60374.3

𝑡 = 60374.3 𝑋 6

185

𝑡 = 44.25 ≅ 45 𝑚𝑚

Hence provide = 575 𝑋 585 𝑋 45 𝑚𝑚

Design of concrete block:

Axial load = 1340𝐾𝑁

Self-weight of the foundation 10 % = 134 𝑘𝑁



Total load on soil = 1474 𝐾𝑁

Area of concrete block = 𝑙𝑜𝑎𝑑

𝑠𝑎𝑓𝑒 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡𝑕𝑒 𝑠𝑜𝑖𝑙

= 1474

200= 7.37 𝑚𝑚2

Side length of the bed block = 7.37

= 2.71 𝑚

∴ Adopt 2.75 m X 2.75 m square concrete block

Assuming 450 load dispersion

Depth of concrete block = 0.5 2750 − 5851

= 1082.5 ≅ 1090 𝑚𝑚

= 1.09 𝑚

∴ Provide the size of concrete pedestal as 2.75 X 2.75 X 1.09 m

Connections:

Outstand on each side = 585−360

2

= 108.5 𝑚𝑚

Load on end connection =108.5 𝑋 585 𝑋 3.983

1000

= 252.81 𝐾𝑁

Single shear strength = 2 𝐾𝑁

No. of bolts = 252.81

29

= 8.71 ≅ 10

∴ Adopt 10 bolts connecting gusset angles with gusset plates and same number of

anchor bolts to connect the gusset plate with column.

COMPARTIVE STUDY ON MULTI-STOREY R.C.C AND STEEL BUILDING


18. DESIGN OF STAIR CASE

Floor to floor height (H) = 3.2 m

Width of stair case = 1.0 m

No of flights in a stair case = 2

Assuming width of landing = 0.80 m

Live load on stairs = 3 kN/m2

Assuming Riser (R) = 160 mm

Tread = 250 mm

Angle of inclination = 2502 + 1602

secϕ = 1.187

No of riser = 3200/160

= 20 no's

Risers in each flight = 10

Treads in each flight = 10-1

= 9

Going = 250x 9=2250 mm

Using Indian standard channel section as a stair(step)

From structural steel tables

Try ISMC 250

D = 250 mm bf = 80 mm wt = 0.351 kN/m

Wt of cement concrete in the channel = 24 x 0.25 x 0.16 = 0.96 kN/m

Live load on stairs /meter length = 3.0 kN/m

Total load = 3.96 kN/m

Factored load = 1.5 x 3.96 = 5.96 kN/m

Bending Moment (M) = 𝑤𝑙 2

8 =

5.96 𝑥 12

8 = 0.74 kN-m

Permissible bending stress in steel (𝜎𝑏𝑐 )= 0.66 fy

COMPARTIVE STUDY ON MULTI-STOREY R.C.C AND STEEL BUILDING


= 0.66x 250 = 165 N/mm2

Section modulus about y direction Zyy = 𝑀

𝜎𝑏𝑐

Zyy = 4500 mm3

Allowable section modulus is 38.4 x103 mm

3

Allowable section modulus is greater than required section modulus

Reaction of loads on stringer beam

Self weight of ISMC 250 = 0.298 kN/m

Load on stairs = 5.96 kN/m

Shear force on stringer beam = ( 0.298 + 5.96 x 1 )/2

= 3.129 kN = 3.2 kN

No of treads in each flight = 10 x

Uniformly distributed load on stringer beam

= (10 x3.2)/2.76

= 11.59 = 11.6 kN/m

Length of stringer beam = 𝐺𝑜𝑖𝑛𝑔2 + (𝐻/2)2

= 2.252 + (1.6/2)2

= 2.76 m

Bending Moment of stringer = 𝑤𝑙 2

8

= 11.6 x2.762

8 = 11.04 kN-m

Section modulus about x is Zxx = 𝑀

𝜎𝑏𝑐 = 66909.09 mm

3

From steel tables try ISLC 300

Allowable section modulus about x is Zxx = 403.2 x 103

Hence safe

MODULE III



20. ESTIMATING AND COSTING

20.1ESTIMATING:

Before undertaking a construction of a project it is necessary to know it’s

probable cost which is worked out by estimating, an estimate is computation or

calculation of the quantities required and expenditure likely to be incurred in the

construction of the work. Estimation can be done by various methods but accurate

estimate is prepared by detailed estimate method.

There are two methods of estimation:

Detailed estimate

Actual cost.

DETAILED ESTIMATE AND ACTUAL COST:

Detailed of the measurements form.

Abstract of the estimate cost

20.2 Main items of the work:

1. EARTHWORK

2. CONCRETE IN FOUNDATION

3. SOILING

4. DAMP PROOF COURSE

5. MASONARY

6. ARCH MASONARY WORK

7. LINTELS OVER OPENINGS

8. R.C.C AND R.B WORKS

9. FLOORING AND ROOFING

10. PLASTERING AND POINTING

11. CORNICE

12. PILLARS

13. DOORS AND WINDOWS

14. WOOD WORK

15. IRON WORK



20.2.1 EARTHWORK

It is usually taken out in earthwork excavation and earth work filling

separately upon different items.

Earthwork in excavation in foundation is calculated by taking the

dimension of each trench(𝒍𝒆𝒏𝒈𝒕𝒉 ∗ 𝒃𝒓𝒆𝒂𝒅𝒕𝒉 ∗ 𝒅𝒆𝒑𝒕𝒉).

Earthwork in plinth filling is calculated by taking the internal dimensions

in between plinth wall which is usually less than internal dimension of

room.

Its units are cu-m.

20.2.2 CONCRETE IN FOUNDATION

The concrete is take out in cu-m by length*breadth*thickness.

The thickness of the concrete varies from 20 cm to 45 cm. But usually it

taken as 30 cm.

The proportion of the cement concrete in foundation may be 1:4:8 or

1:5:10.

20.2.3 SOILING

When the soil is soft or bad on layer of dry thick or stone soiling is

applied below foundation concrete

The soil layer is computed in sq-mts.

20.2.4 DAMP PROOF COURSE

D.P.C is usually of 2.5 cm thick rich cement concrete 𝟏 ∶ 𝟏 ½ ∶ 𝟑.

Plinth levels are computed in sq-mts.

20.2.5 MASONARY

Masonry is measured in (𝑳𝒆𝒏𝒈𝒕𝒉 ∗ 𝒃𝒓𝒆𝒂𝒅𝒕𝒉 ∗ 𝒉𝒆𝒊𝒈𝒉𝒕)

In taking out the quantities the walls are measured solid and deduction are

made for openings as doors and windows etc.

Masonry is computed in cu-m.

20.2.6 ARCH MASONARY WORK

By product of the mean length of the arch by thickness of the arch and

width of the wall



Quantity of arch masonry = lm * t * thickness of the wall

Masonry work in arches is calculated in cu-m

20.2.7 LINTELS OVER OPENINGS

Lintels are either R.C.C or R.B. work

Length of lintel = clear span + two bearings.

If dimension the bearing is not given the bearing may be taken as

thickness of lintel with the minimum of 12 cm.

L = s + 2t

Quantity of lintel = ( 𝒍𝒎 ∗ 𝒕 ∗ 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔 𝒐𝒇 𝒕𝒉𝒆 𝒘𝒂𝒍𝒍 ).

It is measured in cu-m.

20.2.8 R.C.C AND R.B WORKS

R.C.C and R.B work may be in roof or floor slab, in beams, lintels,

columns, foundations, etc.

Bearings are added with clear span to get the dimension.

It is measured in cu-m

R.C.C and R.B work may be estimated exclusively of steel, centering and

and shuttering for complete work.

Centering and shuttering are mainly used in R.B and R.C.C.

20.2.9 FLOORING AND ROOFING

1. Ground floor :

The base line concrete and floor finishing of C.C or stone or marble or

mosaic are usually taken as one item.

It is calculated by multiplication of length and breadth

It is measured in sq-m.

2. FIRST AND SECOND FLOOR:

As R.C.C or R.B. and floor finishing is separately taken in sq-m as

2.5cms Supporting structure is taken separately in cu-m

3. ROOF

Supporting structure is taken in cu-m and line concrete terracing is computed in

sq-m with thickness specified. The compacted thickness of the lime concrete terracing is

7.5 – 12 cms.



20.2.10 PLASTERING AND POINTING

Plastering usually 12 mm thick

Its calculated in sq-mts

For walls Measurement are taken for the whole of the wall or both sides as a solid

and deductions for the openings are in following manner

No deduction is made for Beams, rafters and posts

For small openings up to 0.5 sq-mts no deduction is made

For openings more than 0.5 sq-mts deductions are made

For openings more than 3 deductions are made both sides of the faces.

20.2.11 CORNICE

Ornamental or large cornice is measured in running meters for the complete work

which includes masonry, plastering, mouldings, etc. are paid in running meter.

Similarly, string course, drip course, cor-belling, coping, etc. are measured and

paid in running meter for the complete work.

20.2.12 PILLARS

Pillars are taken separately in cu-m for their net volume and quantities are calculated by

correct geometrical measurements.

Quantity = (𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 ∗ 𝑕𝑒𝑖𝑔𝑕𝑡 ) = (𝜋𝑑2

4) ∗ 𝑕𝑒𝑖𝑔𝑕𝑡 𝑐𝑢 − 𝑚 𝑓𝑜𝑟 𝑟𝑜𝑢𝑛𝑑 𝑝𝑖𝑙𝑙𝑎𝑟𝑠,

d is dia.

= ( 𝑎2 ∗ 𝑕𝑒𝑖𝑔𝑕𝑡 𝑐𝑢 − 𝑚 𝑓𝑜𝑟 𝑠𝑞𝑢𝑎𝑟𝑒 𝑝𝑖𝑙𝑙𝑎𝑟𝑠 ),

a is the side.

Plastering in pillars are calculated in sq.m multiplying the circumference of perimeter by

the height.

20.2.13 DOORS AND WINDOWS

a. Chowkhat or frame – It is measured in cu-m. Vertical members should be

inserted into the floor about (2.5 to 4 )cm. Length is obtained by adding the length

of all members of the frame, top and two verticals. Also by adding bottom and

this length is multiplied by the two dimensions of the cross-section of the

member.



b. Door or Window Leaves or shutters – It is measured in sq-m. It can be

calculated by multiplying the (breadth * height) of the structures

20.2.14 WOOD WORK

Wooden beams, burgahs, posts, wooden roof trusses come under this item.

It is measured in cu-m.

20.2.15 IRON WORK

This is measured in kilo grams. The quantities are calculated out correctly

by multiplying the weights per running meter by the length. For steel joint the length

is equal to clear span plus two bearings. The bearings may be taken as ¼ thickness of

the wall.

20.3 DEGREE OF ACCURACY IN ESTIMATING

Accuracy to be observed in preparing an estimate depends upon the rate of item

and the unit of payment. The rate the greater should be accuracy with which

quantities are calculated.

PRINCIPLE OF UNITS FOR VARIOUS ITEMS OF WORKS:

Units of different works depend upon their nature, size and shape

Mass, voluminous and thick works shall be taken in cubic unit or volume.

The measurements of length, breadth, and height or depth shall be taken to

compute the volume.

Shallow, thin and surface works shall be taken in square unit. This can be

measured by length and breadth or height shall be taken to compute area.

Long and thin work shall be taken in linear

Piece work, job work etc.

Area of 6 mm bar = 2.827 x 10-5

m2 = 28.27 mm

2

Area of 8 mm bar = 5.026 x 10-5

m2 = 50.26 mm

2

Area of 10 mm bar = 7.853 x 10-5

m2 = 78.53 mm

2

Area of 12 mm bar = 1.130 x 10-4

m2 = 113.08 mm

2

Area of 16 mm bar = 2.010 x 10-4

m2 = 201.0 mm

2

Area of 18 mm bar = 2.544 x 10-4

m2 = 254.4 mm

2



20.4 ESTIMATATION OF QUANTITY OF CONCRETE

Item

no

Particular and

items of work No

Len

gth

m

Bre

ad

th

m

Dep

th

m Quantity

m3

Remarks

I SLABS

S1

S2

S3

S4

S5

S6

S7

10

10

12

10

10

10

10

3.8

3.65

3.65

3.65

4.3

4.15

4.15

3.15

3.85

3.7

10.25

3.15

3.85

3.7

0.12

0.12

0.12

0.14

0.12

0.12

0.12

14.364

16.863.

19.4472

52.3775

16.254

19.173

18.426

3.65+0.15=3.8

3+3.15=3.15

3.7+3.15=3.85

3.55+0.15=3.7

3.5+0.15=3.65

4.15+0.15=4.30

3.00+0.15=3.15

3.7 +0.15=3.85

3.55 +0.15=3.7

156.904 M3

II PLINTH

BEAMS

1001, 1007, 1009,

1014,1015, 1020,

1021, 1026.

1002,1006, 1010,

1013, 1016, 1017,

1022, 1025

1003, 1011, 1012,

1017, 1018, 1023,

1024

1004, 1030, 1034

8

8

7

3

3.00

3.70

3.55

1.65

0.3

0.3

0.3

0.3

0.4

0.4

0.4

0.4

2.88

3.552

2.982

0.594



1005,1008

1027, 1028,

1031, 1035, 1036

1044, 1045, 1046,

1047, 1048, 1049,

1050

1029, 1032, 1051

2

5

7

3

1.9

3.65

4.15

2.00

0.3

0.3

0.3

0.3

0.4

0.4

0.4

0.4

0.456

2.19

3.486

0.72

16.86 m

3

III

TYPICAL

BEAMS

2001, 2007, 2009,

2014, 2015, 2022,

2023, 2030, 3001,

3007, 3009, 3014,

3015, 3022, 3023,

3030, 4001, 4007,

4009, 4014, 4015,

4022, 4023, 4030,

5001 5007, 5009,

5014, 5015, 5022,

5023, 5030

2002, 2006, 2010,

2013, 3002, 3006,

3010, 3013, 4002,

4006, 4010, 4012,

5002, 5006, 5010,

5013

2003, 2011, 2012,

2018, 2019, 2026,

2027, 3003, 3011,

3012, 3018, 3019,

3026, 3027, 4003,

4011, 4012, 4018,

4019, 4026, 4027,

5003, 5011, 5012,

32

16

28

3.00

3.70

3.55

0.3

0.3

0.3

0.4

0.4

0.4

11.52

7.104

11.92



5018, 5019, 5026,

5027

2004, 2034,

2038,3004, 3034,

3038,4004, 4034,

4038, 5004, 5034,

5038

2005, 2008, 3005,

3008, 4005, 4008,

5005, 5008

2016, 2021, 2024,

2029, 3016, 3021,

3024, 3029, 4016,

4021, 4024, 4029,

5016, 5021, 5024,

5029

2017, 2020, 2025,

2028, 3017, 3020,

3025, 3028, 4017,

4020, 4025, 4028,

5017, 5020, 5025,

5028

2031, 2032, 2035,

2039, 2040, 3031,

3032, 3035, 3039,

3040, 4031, 4032,

4035, 4039, 4040,

5031, 5032, 5035,

5039, 5040

2033, 2036, 2037,

2051, 3033, 3036,

3037, 3051, 4033,

4036, 4037, 4051,

5033, 5036, 5037,

5051

2041, 2042, 2043,

12

8

16

16

20

16

1.65

1.90

0.85

2.85

3.65

2.00

0.3

0.3

0.3

0.3

0.3

0.3

0.4

0.4

0.4

0.4

0.4

0.4

2.376

1.824

1.632

5.472

8.76

3.84



IV

3041, 3042, 3043,

4041. 4042, 4043,

5041, 5042, 5043

2044,2045, 2046,

2047, 2048, 2049,

2050,3044, 3045,

3046, 3047, 3048,

3049, 3050, 4044,

4045, 4046, 4046,

4047, 4048, 4049,

4050, 5044, 5045,

5046, 5047, 5048,

5049, 5050

ROOF BEAMS

6001, 6007, 6009,

6014, 6015, 6023,

6030

6002, 6006, 6010,

6013

6003, 6011, 6012,

6018, 6019, 6026,

6027, 7001, 7005,

7006

6004, 6034, 6038,

7002, 7011

6005, 6008, 7003,

7004

6016, 6021, 6024,

6029

6017, 6020, 6025,

6028

6031, 6032, 6035,

6039, 6040

12

29

7

4

10

5

4

4

4

5

3.50

4.15

3.00

3.70

3.55

1.65

1.9

0.85

2.85

3.65

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.4

0.4

0.4

0.4

0.4

0.4

0.4

0.4

0.4

0.4

5.04

14.442

73.93 m3

2.52

1.776

4.26

0.99

0.912

0.408

1.368

2.19



6033, 6036, 6037,

7009, 7010

6041, 6042, 6043

6044, 6045, 6046,

6047, 6048, 6049,

6050

5

3

7

2.00

3.5

4.15

0.3

0.3

0.3

0.4

0.4

0.4

1.2

1.26

3.486

20.36 m3

V

COLUMNS

GROUP

1A

1B

2A

2B

3

10

3

14

1

4

17.5

17.5

17.5

17.5

17.5

0.3

0.3

0.3

0.3

0.3

0.5

0.4

0.5

0.4

0.5

26.25

6.21

36.75

2.1

10.5

81.81 m3

VI

STAIR CASE

No of stair

cases= 6

24

3.56

1.0

0.15

12.81 m3

12.81 m3

VII FOOTING

GROUP

I

II

III

IV

4

14

10

4

1.80

2.30

2.50

1.80

1.60

2.10

2.30

1.70

0.4

0.52

0.52

0.41

4.608

35.162

29.90

5.018

74.688 m3



20.5 ESTIMATION OF QUANTITY OF STEEL

SLABS

Slab

panel

(1)

No. of

slabs

(2)

Dia

mm

(3)

No. of

bars

(4)

Length of

bar

m

(5)

Total

length of

bars

m

(6)=4 x 5

Quantity

m3

(7) =

Area of (3) x

(6)

Total

quantity

m3

(8) = (2)x(7)

S1 10

8 15 3.184 47.76 2.40x10-3

0.024

8 19

3.834 72.846 3.67x10-3

0.0367

S2 10

8 19 3.884 73.796 3.708 x10-3

0.03708

8 15 3.834 57.51 2.89 x10-3

0.0289

S3 12 8 15 3.734 56.01 2.81 x10

-3 0.03372

8 19 3.834 72.846 3.67 x10-3

0.04404

S4 10 8 74 10.434 772.116 0.0388 0.388

8 13 3.604 46.852 2.36 x10-3

0.0236

S5 10 8 20 4.034 80.68 4.06 x10

-3 0.0406

8 21 4.334 91.014 4.58 x10-3

0.0458

S6 10 8 12 3.034 36.408 1.83 x10

-3 0.0183

8 17 4.334 73.678 3.703 x10-3

0.03703

S7 10 8 15 3.734 56.01 2.815 x10

-3 0.0281

8 17 4.334 73.678 3.703 x10-3

0.03703



BEAMS

Main Reinforcement in Plinth Beams B

eam

Ty

pe

No

of

Bea

ms

Len

gth

Bea

m

(m)

Dia

Mm

No. of

bars

Length of bar

m

To

tal

len

gth

of

ba

rs

m Quantity

m3

Total quantity

m3

(1) (2) (3) (4) (5) (6) (7)=5x6 (8) =

Area of (4) x (7) (9) = (2)x(8)

Pli

nth

Bea

ms

8 3.00 12 5 3.56 17.8 2.01 x 10-3 16.08 x 10-3

1+1=2 1.314+0.9=2.214 4.428 5.00 x 10-4 4 x 10-3

8 3.70 12 5 3.70 18.5 2.09 x 10-3 16.73 x 10-3

1+1=2 1.075+1.075=2.15 4.3 4.85 x 10-4 3.88 x 10-3

7 3.55 12 5 3.55 17.75 2.00 x 10-3 14 x 10-3

1+1=2 1.04+1.04=2.08 4.16 4.70 x 10-4 3.29 x 10-3

3 1.65 12 5 1.65 8.25 9.32 x 10-4 2.79 x 10-3

1+1=2 0.42+0.42=0.84 1.68 1.89 x 10-4 5.6 x 10-4

2 1.90 12 5 1.95 9.75 1.10 x 10-3 2.2 x 10-3

1+1=2 0.63+0.63=1.26 2.52 2.84 x 10-4 5.68 x 10-4

5 3.65 12 5 3.65 18.25 2.06 x 10-3 10.3 x 10-3

1+1=2 1.48+1.063=2.55 5.1 5.76 x 10-4 2.88 x 10-3

7 4.15 12 5 4.71 23.55 2.66 x 10-3 18.62 x 10-3

5+4=9 1.60+1.18=2.78 25.02 2.82 x 10-3 19.74 x 10-3

3 2.00 12

5 3.56 17.8 2.01 x 10-3 6.03 x 10-3

2+2=4 1.06+0.65=1.71 6.84 7.72 x 10-4 2.31 x 10-3



Main Reinforcement in Typical Floor Beams

Bea

m

Ty

pe

No

of

Bea

ms

Len

gth

Bea

m

(m)

Dia

Mm

No

. o

f

ba

rs

Length of bar

m

Total

length

of bars

m

Quantity

m3

Total quantity

m3

(1) (2) (3) (4) (5) (6) (7) =

(5) x (6)

(8) =

Area of (4) x (7) (9) = (2)x(8)

Typ

ical

Flo

or

Bea

ms

32 3.00

12 3 3.56 10.68 1.20 x 10-3 38.4 x 10-3

16 1+1=2 1.50+0.9=2.4 4.8 9.64 x 10-4 30.84 x 10-3

16 2 3.75 7.5 1.50 x 10-3 48 x 10-3

12 3.70

12 3 3.70 11.1 1.25 x 10-3 15 x 10-3

16 1+1=2 1.075+1.075=2.15 4.3 8.64 x 10-4 10.36 x 10-3

16 2 3.70 7.4 1.48 x 10-3 17.76 x 10-3

28 3.55

12 3 3.55 10.65 1.20 x 10-3 33.6 x 10-3

16 2+2=4 1.04+1.04=2.08 8.32 1.67 x 10-3 46.76 x 10-3

16 2 3.55 7.1 1.42 x 10-3 39.76 x 10-3

12 1.65

12 4 1.65 6.6 7.45 x 10-4 86.94 x 10-3

16 1+1=2 0.42+0.42=0.84 1.68 3.37 x 10-4 4.04 x 10-3

16 2 1.65 3.3 6.63 x 10-4 7.95 x 10-3

8 1.90 12

3 1.90 5.7 6.44 x 10-4 5.15 x 10-3

2+2=4 0.63+0.63=1.26 5.04 5.69 x 10-4 4.55 x 10-3

2 1.90 3.8 4.29 x 10-4 3.43 x 10-3

12 0.85

12 3 0.85 2.55 2.88 x 10-4 3.45 x 10-3

16 2+2=4 0.37+0.37=0.74 2.96 5.94 x 10-4 7.12 x 10-3

16 2 0.85 1.7 3.41 x 10-4 4.09 x 10-3

12 2.85

12 3 2.85 8.55 9.66 x 10-4 11.59 x 10-3

16 1+1=2 0.87+0.87=1.74 3.48 6.99 x 10-4 8.38 x 10-3

16 2 2.85 5.7 1.14 x 10-3 13.68 x 10-3

12 3.65

12 3 4.40 13.2 1.49 x 10-3 17.88 x 10-3

16 2+1=3 1.7+1.06=2.76 8.28 1.66 x 10-3 19.92 x 10-3

16 2 4.40 8.8 1.76 x 10-3 21.12 x 10-3



12

3.50

12 3 3.50 10.5 11.86 x 10-3 142.32 x 10-3

16 2+1=3 1.03+1.03=2.06 6.18 1.242 x 10-3 14.90 x 10-3

16 2 3.50 7 1.40 x 10-3 `16.8 x 10-3

28 4.15 16 5 4.90 24.5 4.92 x 10-3 137.76 x 10-3

2+1=3 1.79+1.19=2.98 8.94 1.79 x 10-3 50.12 x 10-3

16 2.00 12 5 2.75 13.75 1.55 x 10-3 24.8 x 10-3

2+2=4 1.064+0.65=1.71 6.84 7.72 x 10-4 11.55 x 10-4

Main Reinforcement in Roof Beams

Bea

m

Ty

pe

No

of

Bea

ms

Len

gth

of

Bea

m

( m

)

Dia

mm

No. of

bars

Length of bar

m

Total

length

of bars

m

Quantity

m3

Total quantity

m3

(1) (2) (3) (4) (5) (6) (7)=5x6 (8) =

Area of (4) x (7) (9) = (2)x(8)

Roof

Bea

ms

7 3.00 12 5 3.56 17.8 2.01 x 10-3 14.07 x 10-3

1+1=2 1.314+0.9=2.21 4.42 4.99 x 10-4 3.49 x 10-3

4 3.70 12 5 3.70 18.5 2.09 x 10-3 8.36 x 10-3

1+1=2 1.075+1.075=2.15 4.3 4.85 x 10-4 1.94 x 10-3

10 3.55 12 5 3.55 17.75 2.0 x 10-3 20 x 10-3

1+1=2 1.04+1.04=2.08 4.16 4.7 x 10-4 4.7 x 10-3

5 1.65 12 5 1.65 8.25 9.32 x 10-4 4.66 x 10-3

1+1=2 0.42+0.42=0.84 1.68 1.89 x 10-4 9.45 x 10-4

4 1.90 12 5 1.95 9.75 1.10 x 10-3 4.4 x 10-3

1+1=2 0.63+0.63=1.26 2.52 2.84 x 10-4 1.13 x 10-3

4 0.85 12 5 0.85 4.25 4.80 x 10-4 1.92 x 10-3

1+1=2 0.36+0.36=0.72 1.44 1.62 x 10-4 6.48 x 10-4

4 2.85 12 5 2.85 14.25 1.61 x 10-3 6.44 x 10-3

1+1=2 0.86+0.86=1.72 3.44 3.88 x 10-4 1.55 x 10-3

5 3.65 12 5 3.65 18.25 2.06 x 10-3 10.3 x 10-3

1+1=2 1.48+1.063=2.55 5.1 5.76 x 10-4 2.88 x 10-3

3 3.50 12 5 3.5 17.5 1.97 x 10-3 5.91 x 10-3

1+1=2 1.025+1.025=2.05 4.1 4.63 x 10-4 1.38 x 10-3

7 4.15 12 5 4.71 23.55 2.66 x 10-3 18.62 x 10-3

1+1=2 1.60+1.18=2.78 5.56 6.28 x 10-4 4.39 x 10-3

5 2.00 12 5 3.56 17.8 2.01 x 10-4 1.0 x 10-3

1+1=2 1.06+0.65=1.71 3.42 3.86 x 10-4 1.9 x 10-3



Shear Reinforcement in Beams (stirrups)

S.NO

(1) TYPE (2)

Dia

mm

(3)

No. of

stirrups

(4)

Length of

stirrups

m

(5)

Total

length of

stirrups

m

(6)=4 x 5

Quantity

m3

(7) =

Area of (3) x (6)

1 Plinth

Beams 6 107 1.328 142.096 4.013x 10

-3

2

Typical

Floor

Beam

6 127 1.328 168.656 4.767x 10-3

3 Roof

Beams 6 107 1.328 142.096 4.013x 10

-3

COLUMNS

Longitudinal Reinforcement of column

Group

(1)

No of

columns

(2)

Dia

mm

(3)

No. of

bars

(4)

Length of

bar

m

(5)

Total

length of

bars

m

(6)=4 x 5

Quantity

m3

(7) =

Area of (3) x (6)

Total

quantity

m3

(8) = (2)x(7)

1. 10 16 10 19.00 190.00 0.038 0.38

3 12 10 19.00 190.00 0.021 0.063

2. 14 16 8 19.00 152.00 0.030 0.42

1 12 8 19.00 152.00 0.017 0.017

3 4 16 8 19.00 152.00 0.030 0.122

Transverse Reinforcement (Lateral Ties)

Group

(1)

No of

columns

(2)

Dia

mm

(3)

No. of

stirrups

(4)

Length of

stirrups

m

(5)

Total

length of

stirrups

m

(6)=4 x 5

Quantity

m3

(7) =

Area of (3) x (6)

Total quantity

m3

(8) = (2)x(7)

1. 10 6 70 1.338 93.66 2.648 x 10

-3 0.0264

3 6 70 1.188 83.16 2.35 x 10-3

7.05 x 10-3

2. 14 6 70 1.338 93.66 2.648 x 10

-3 0.0370

1 6 70 1.188 83.16 2.35 x 10-3

2.35 x 10-3

3 4 6 70 1.338 93.66 2.648 x 10-3

0.0105



FOOTINGS

Group

(1)

No of

footings

(2)

Dia

mm

(3)

No. of

bars

(4)

Length of

bar

m

(5)

Total

length of

bars

m

(6)=4 x 5

Quantity

m3

(7) =

Area of (3) x (6)

Total quantity

m3

(8) = (2)x(7)

1. 4

12 9 1.892 17.028 1.925 x 10-3

7.7 x 10-3

12 10

1.692 16.92 1.913 x 10-3

7.65 x 10-3

2. 14

12 12 2.392 28.704 3.246 x 10-3

0.0454

12 13 2.192 28.496 3.222 x10-3

0.0451

3 10 16 13 2.592 33.696 6.774 x 10

-3 0.0677

16 14 2.392 33.488 6.733 x10-3

0.0673

4 4 12 9 1.892 17.028 1.925 x 10

-3 7.7 x 10

-3

12 10 1.792 17.92 2.026 x 10-3

8.107 x 10-3

STAIR CASE

Type

(1)

No of

flights

(2)

Dia

mm

(3)

No. of

bars

(4)

Length

of bar

m

(5)

Total

length of

bars

m

(6)=4 x 5

Quantity

m3

(7) =

Area of (3) x

(6)

Total

quantity

m3

(8) = (2)x(7)

Main

Rein 12

10 6 3.75 22.5 1.76 x 10-3

0.0212

10 6

1.74 10.44 8.198 x 10-4

9.838 x 10-3

Dist

Rein 12 8 13 0.95 12.35 6.207 x 10

-4 7.449 x 10

-3



SUMMARY OF REINFORCEMENT S

.no

Dia

of

bar Quantity

Total

quantity

(cu-m)

Density

(kg/m3)

Weight

kgs S

lab

Bea

m

Colu

mn

Footi

ng

Sta

ir

case

1 6 -------- 12.8x

10-3

0.084

-------

- ------ 0.0968 7850 759.88

2 8 0.8229

5 ------- ------- ------ 7.449 x 10

-3 0.8304 7850 6518.64

3 10 -------- ------- ------- ------ 0.031038 0.031038

7850 243.65

4 12 ------- 0.622 0.08 0.130

3 ------ 0.8323 7850 6533.55

5 16 ------- 0.500 0.922 0.135 ----- 1.557 7850 12222.45

Schedule of Rate (As per APSSR 2011-2012)

s.no Description of item unit Rate

1 R.C.C M20 design mix using 20 mm graded HBG metal

from approved quarry including cost of conveyance of all

materials to the site(including labour charges, batching

machinery, vibrators, centering and water )

Foundations

Plinth beams

Beams

Columns

Slabs

1 cu.m

1 cu.m

1 cu.m

1 cu.m

1 cu.m

6086.74

7550.84

8103.56

6601.02

8236.21

2 TMT Bars (HYSD Fe 415)

Supplying, fitting and placing TMT bars reinforcement as

per drawings and technical specifications for Bars below

36 mm dia including binding wire, over laps and wastage,

where they are not welded.

1 kg

65.042

3 Mild steel bars

Supplying, fitting and placing mild steel bars

reinforcement as per drawings and technical

specifications including binding wire, over laps and

wastage, where they are not welded.

6 mm diameter

1 kg 52.080



Abstract of Estimate

Item

no Particulars

Quantit

y Unit Rate Per Cost

1 slabs 156.904 Cu.m 8236.21 Cu.m 1292294.29

2 Roof beams 20.36 Cu.m 8103.56 Cu.m 164988.48

3 Typical floor beams 73.93 Cu.m 8103.56 Cu.m 599096.19

4 Plinth beams 16.86 Cu.m 7550.84 Cu.m 127307.16

5 Columns 81.81 Cu.m 6601.02 Cu.m 540029.44

6 Footings 74.688 Cu.m 6086.74 Cu.m 454606.43

7 Stair case 12.81 Cu.m 8103.56 Cu.m 103806.60

8 TMT 8mm dia 6518.64 Kg 65.042 Kg 423985.38

9 TMT 10 mm dia 243.65 Kg 65.042 Kg 15847.48

10 TMT 12 mm dia 6533.55 Kg 65.042 Kg 424955.15

11 TMT 16 mm dia 12222.45 Kg 65.042 Kg 794972.59

12 Mild steel 6mm dia 759.88 Kg 52.080 Kg 39574.55

Lump sum cost = Rs 49,81,463.74

Add 5% extra = Rs 2,49,073.18

Total cost Rs 52,30,537.00

Approximately Rs 52,30,537.00 is required to construct the G+4 residential and

commercial RCC building.



21. ESTIMATION OF STRUCTURAL STEEL MEMBERS

Structural steel members may be of single I section or double I sections,

channel sections, angles, tee sections, flat plates and other fastening accessories. The

cost estimates for steel structures are significantly different from calculation of the

estimated cost of RCC structures, as they need special designs. The most important

part of the design and construction of steel structure are the connections. It is well

known that connections costs are about 12% of major structural elements such as

stanchions (columns), beams in a building.

The connections , either through the use of welds or high-stress bolts, have the

largest share in the process of preparing detailed drawings, where the most important

and most critical phase is the accuracy of the details of the connection.

21.1 STEEL TAKE-OFF FROM STAAD PRO OUT PUT

PROFILE LENGTH(M) WEIGHT( kN)

ST ISWB600A 588.80 836.327

ST ISHB200 508.10 185.402

ST ISHB400 66.75 50.610

ST ISHB250 351.00 175.264

ST ISHB300 33.20 19.077

TOTAL = 1266.680 kN



21.2 Estimation of Quantity of structural steel members

S.

no Particulars No

Length

m

Breadth

m

Qty

Wt.

per

unit

Total

weight

(kN)

I Rolled steel

I sections

ISWB600A

ISHB200

ISHB400

ISHB250

ISHB300

1

1

1

1

1

588.80

508.10

66.75

351.00

33.20

-----

----

-----

-----

-----

------

----

-----

-----

-----

1.42

kN/m

0.364

0.758

0.499

0.574

836.33

185.41

50.61

175.30

19.1

II Mild steel plates

@ column bases

575 x 585 x 45 mm

thick base plate

Wt of 45 mm thick

plate =

0.045x7850=3.46

kN/m2

32

0.575

0.585

10.76 m2

3.46kn/

m2

37.23

III Connections (cleat

angles, stiffeners,

gusset plates anchor

bolts, welds)

Beam to columns,

Beam to Beam and

column to columns are

approximately 12 %

of the total weight of

beams and columns

12 x (836.33 +185.41+ 50.61+

175.30+ 19.1)/100

= 152. 01 kN

152. 01

IV Kirby Deck slab

Thickness of sheet 0.7

mm

Wt = 0.069 kN/m2

Total area = 5xarea of

each slab-5xarea of

staircase- 5 x area of

lift + cap slab

5 x 231-5 x 7.1-5 x 3.8 + 25.914 =

1126.414 m2

0.069

kN/m2

77.73

V Steel Stair case

Stairs

ISMC250@

0.298kN/m

12 flights & 10 treads

120

1.0

-----

-----

0.298

35.76



in each flight

Stringer beams

ISLC 300 @

0.324 kN/m

2 stringer beams per

flight

Length of stringer

beam + width of

landing (2.76+0.8)

Connections

12% of total steel

quantity of stair case.

(12 x

(35.76+27.68))/100

24

-----

3.56

-----

------

------

-----

-----

0.324

-----

27.68

7.612

Total weight 1604.77

19.3 ABSTRACT OF ESTIMATE

From Standard schedule of rates 2011-2012 the cost of M.S

I section, Angles, channels etc., = Rs 48.00 per kg.

Fabrication charges = Rs 14.00 per kg

Erection charges = Rs 12.00 per kg

Total = Rs 74.00 per kg

Total weight of steel members = 1604.77 kN = 163585.11 kgs

Cost of the steel structural members = 163585.11 x48

= Rs 78,52,085.28

Add 5% for contingencies and

Work charged establishment = Rs 3,92,604.264

Total cost of steel structure = Rs 82,44,689.54

= Rs 82,44,690.00

Approximately Rs 82,44,690.00 is required to construct the G+4 residential and

commercial STEEL Building

COMPARITIVE STUDY ON MULTI-STOREY R.C.C AND STEEL BUILDING

297

22. CONCLUSION

S.

NO PARTICULARS R.C.C BUILDING STEEL BUILDING

1 Grade/ Materials

M20

Fe250 & Fe415

Mild steel

2 Max sizes of

sections

Beams

Columns

Min sizes of

sections

Beams

Columns

Secondary beams

300 x 400 mm

300 x 500 mm

300 x 400 mm

300 x 500 mm

------------

ISHB 300

ISWB600A

ISHB 200

ISWB 600 A

ISJB 200

3 Reactions

Maximum

Gravity

Wind

Seismic

1637.006 kN (Node 15)

92.625 kN (Node 3)

152.811 kN (Node 3)

776.237 kN (Node 15)

104.611 kN (Node 3)

72.905 kN (Node 3)

4

Max Bending

moments

Gravity loads

Wind loads

Seismic loads

42.816 kN-m (Beam 5021)

19.87 kN-m (Beam 1051)

26.559 kN-m (Beam 105)

56.277 kN-m (Beam 3029)

37.618 kN-m (Beam 2048)

14.951 kN-m (Beam 1046)

5

Max shear force

130.305 kN (Beam 5021)

124.553 kN (Beam 4016)

6

Max deflection

Gravity loads

About X

About Y

About Z

0.416 mm (Node 259)

2.866 mm (Node 262)

0.757 mm (Node 263)

0.678 mm (Node 258)

2.006 mm (Node 243)

0.395 mm (Node 95)

COMPARITIVE STUDY ON MULTI-STOREY R.C.C AND STEEL BUILDING

298

Wind loads

About X

About Y

About Z

Seismic loads

About X

About Y

About Z

2.134 mm (Node 261)

0.179 mm (Node 217)

5.195 mm (Node 258)

7.342 mm (Node 263)

0.360 mm (Node 255)

9.552 mm (Node 258)

5.065 mm (Node265)

0.246 mm (Node255)

16.478 mm (Node 258)

5.651mm (Node 259)

0.198mm (Node 138)

9.967mm(Node 243)

Envelope load

case

Max BM

Max shear force

Max Reactions

97.419 kN-m(Beam 3047 )

1.5(DL+EQ ZP)

130.305 kN (Beam 5021)

1.5(DL+LL)

1637.006 kN (Node3)

1.5(DL+EQ XN)

99.318 kN-m (Beam 3029)

1.5(DL+LL)

124.553 kN (Beam 4016)

1.5(DL+LL)

1361.171 kN (Node 22)

1.5(DL+LL)

7

Quantity of

material

Concrete = 437.362 cu.m

Steel = 26,178.17 kgs

Structural Steel = 1604.77kN

8

Approximate cost

( only structure )

Rs 52,30,537.00

Rs 82,44,690.00

BIBLOGRAPHY

Reinforced concrete design by S.Unnikrishna pillai and Devdas menon.

Limit state design by B.C.Punmia, Ashok.K.Jain and Arun.K.Jain.

Illustrated design of reinforced concrete buildings by Dr. V.L.Shah and

Dr.S.R.Karve

Standard method of detailing structural concrete by B.H.G.Cresswell

Riol.

Limit state design of R.C.C structures by Ramachandra.

Design for RCC slabs by K.C Jain.

Building Design and Construction by Fredrick S.Merritt and Jonathan

T.Ricketts

Design of R.C.C Structural Elements by S.S.Bhavikatti

Design of Reinforced Concrete Structures by M.R.Dheerendra Babu

Structural Design and Drawing Reinforced Concrete and Steel by

N.Krishna Raju.

Steel Structures by K.Naga Sreenivasa Rao.

Design of Steel Structures by S.Ramamrutham and R.Narayanan.

Design of Steel Structures by Ram Chandra

comparative study on rcc & steel building

Documents

design of reinforced

design of slabs

design of beams

design of columns

design of staircase

design of steel beams

design of steel columns

design of footings