analyses and ddesign of a two storied rc building

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Civil & Environmental Engineering Department

First semester -Term (131)

CE 315 – Reinforced Concrete

Term project

Analyses and Design of a Two-Storied RC Building

Instructors: Dr.Mohammed Baluch

Dr.Mohammed Al-Osta

Prepped by: Mohammed Jamal Sandougah

ID# 200816060

Email: [email protected]

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Table of Contents 1. Introduction ........................................................................................................................................... 4

2. Project Objectives and scope of work ................................................................................................... 4

2.1. Description of Structure ................................................................................................................ 5

2.2. Loads Calculation ......................................................................................................................... 7

2.2.1. Slab Loads ............................................................................................................................. 7

2.3. Building Geometry ...................................................................................................................... 11

2.3.1. Modeling Stages .................................................................................................................. 11

2.3.2. Normal Structure ................................................................................................................. 11

2.3.3. Full Structure Modeling ...................................................................................................... 14

2.4. Loads Assigned ........................................................................................................................... 15

2.5. Ribbed Slab Design ..................................................................................................................... 17

2.6. Beam Design ............................................................................................................................... 20

2.7. Column Design ........................................................................................................................... 25

2.8. Foundation Design ...................................................................................................................... 28

2.8.1. Procedure ............................................................................................................................ 28

2.8.2. Results ................................................................................................................................. 30

Conclusion .................................................................................................................................................. 67

References ................................................................................................................................................... 68

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List of Figures

Figure 2-1: Side View of the Building .......................................................................................................... 5

Figure 2-2: Top View of the Building .......................................................................................................... 6

Figure 2-3: Top View of the Building with Direction of Load ..................................................................... 7

Figure 2-4: Minimum Thickness for One-Way Solid and Ribbed Slabs ...................................................... 8

Figure 2-5: Block Dimensions ...................................................................................................................... 9

Figure 2-6: Ribbed Slab Dimensions ...................................................................................................... 10

Figure 2-7-1: Normal Structure (Front view) ............................................................................................. 11

Figure 2-7-2: Normal Structure (Side view) ............................................................................................... 12

Figure 2-8: Normal Structure (Top view) ................................................................................................... 13

Figure 2-9: Full Structure (3D Model) ....................................................................................................... 12

Figure 2-10: Load on Grade Beams ............................................................................................................ 13

Figure 2-11: Load on Parapet...................................................................................................................... 16

Figure 2-12: ACI Coefficients Conditions .................................................................................................. 17

Figure 2-13 : ACI Moment Coefficients (1) ............................................................................................... 18

Figure 2-14: ACI Moment Coefficients (2) ................................................................................................ 19

Figure 2-16: Critical Beam ......................................................................................................................... 20

Figure 2-17: Moment diagrom of beam#200 .............................................................................................. 21

Figure 2-18: Steel arrangement of beam#200 (1) ....................................................................................... 21

Figure 2-19: Steel arrangement of beam#200 (2) ....................................................................................... 22

Figure 2-20: Shear Diagram for beam #200 ............................................................................................... 23

Figure 2-21: Specifications of shear reinforcement of beam #200 ............................................................. 24

Figure 2-22: Critical Column #127 ............................................................................................................. 25

Figure 2-23: Output of column#127 ........................................................................................................... 26

Figure 2-24: Footings distribution of Solid Slab Structure ......................................................................... 28

Figure 2-25: Concrete and Rebar Parameters ............................................................................................. 28

Figure 2-26: Cover and soil parameters ...................................................................................................... 29

Figure 2-27: Footing geometry parameters ................................................................................................. 29

Figure 2-28: Typical elevation section of footing ....................................................................................... 30

Figure 2-29: Typical plan section of footing .............................................................................................. 30

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1. Introduction

The design of the Two-story reinforced concrete structure entailed a number of steps

and calculations. Each section listed below describes one step in the process of the design.

Attached to the end of this report are sample hand calculations for each step in the design

process.

2. Project Objectives and scope of work

The main objectives revolved around the application of the theoretical background in

reinforced concrete design courses to design a full structure instead of elements (beam,

column, foundation and slab). Another objective of this project is to learn how to utilize the

AutoCAD drawing software and the (STAAD.Pro) software tools in the best manner which

would be time saving and practical in modeling, analyzing and designing the structure.

Moreover, the project would help the group in interpreting the architectural drawings of the

building which would be useful in future careers.

On the managerial side, the group will conduct cost estimations and comparisons study for all

alternatives which would help to improve the decision-making process and the quantity

surveying skills. In addition, the project will help the group in improving time-management

skills.

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2.1. Description of Structure

Building comprises of two story reinforced concrete structure. Basic building dimensions

are as follows:

Building footprint: 13.5 m x 13.5 m.

Building height: Building height: 9.6 m.

STADD side and top view drawings of the Building are shown in Figure and Figure 2-2.

Figure 2-1: Said View

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Figure 2-2: Top View

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2.2. Loads Calculation

2.2.1. Slab Loads

a) Slab self weight

Since the ratio of long edge to the short edge of slab =𝟓

𝟓= 𝟏 𝐚𝐥𝐬𝐨

𝟑.𝟓

𝟓= 0.7 the load will

transfer in the short direction as shown in Figure 2-3 and the design will assumed as one way

solid slab and the hidden square as flour slab.

Figure 2-3: Top View of the Building with Direction of Load

UP

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Minimum slab depth:

Following ACI-318-08 the minimum thickness for one-way solid slabs as shown in Figure 2-4

is 𝑙

24 for one end continuous and

𝑙

28 for both ends continuous.

Figure 2-4: Minimum Thickness for One-Way Solid and Ribbed Slabs

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One end continuous 𝑙

24=

5000

24= 208.33 𝑚𝑚

Both ends continuous 𝑙

28=

5000

28= 178.57 𝑚𝑚

Weight of Block:

No. of rib/m =1

0.5= 2 ribs

No. of blocks/𝑚2 = 2 × 5 = 10

The weight of blocks in one meter square of ribbed slab =

(Number of blocks) × (weight of one block) × (9.81)

Weight of blocks/𝑚2 = 10 × 12 ×9.81

1000= 1.2

kN

𝑚2

Weight of ribs:

Each one meter of ribbed slab has two ribs as shown in Figure 2-6.

Weigh of 𝑟𝑖𝑏 = (width(b) × depth(d) × number of ribs) × (density of concrete) ×

(length)

Weight of ribs/𝑚2 = 2 × 0.1 × 0.2 × 25 = 1kN

𝑚2

Figure 2-5: Block Dimensions

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Weight of top slab (t):

Top slab weight = (minimum thickness – depth of rib (d)) × (density of concrete) × (length)

Weight of toping slab/m2 = 0.07 × 25 = 1.75kN

𝑚2

Self weight of the ribbed slab:

Self weight = (Weight of Block) + ( weight of rips) + ( Top mat weight)

Self Weight of ribbed slab = 1 + 1.2 + 1.75 = 3.95kN

𝑚2

Figure 2-6: Ribbed Slab Dimensions

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2.3. Building Geometry

According to the Architectural drawings, the building is mainly composed of a 13.5 m X

13.5 m rooms with main beams spanning over 5, 3.5 and 3 meters with a center-to-center of

column spacing of 5 and 3.5 meters. In addition, the building includes a rectangular bathroom

with a thickness of 0.15 meters and with area of10.5 𝑚2.

2.3.1. Modeling Stages

1. Draw the normal structure using STAAD.Pro software

2. Define section properties of the structure (columns, beams and slab)

2.3.2. Normal Structure

Front view dimensions of the two structures are shown in Figure 2-7-1.

Figure 2-7-1: Normal Structure (Front view)

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Side view dimensions of the two structures are shown in Figure 2-7-2.

Figure 2-7-2: Normal Structure (Side view)

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Top view dimensions are shown in Figure 2-8 .

Figure 2-8: Normal Structure (Top view)

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2.3.3. Full Structure Modeling

3D of the structure is shown in Figure 2-9.

Figure 2-9: Full Structure (3D Model)

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2.4. Loads Assigned

Dead load on grade beam is 17.375 𝐾𝑁

𝑚 as shown in Figure 2-10.

Figure 2-10: Load on Grade Beams

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Dead load on parapet is 12.2𝐾𝑁

𝑚 as shown in Figure 2-11.

Figure 2-11: Load on Parapet

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2.5. Ribbed Slab Design

Using ACI-318-08 chapter 8.3.3, Check the ACI limits which is shown in Figure 2-12.

Figure 2-12: ACI Coefficients Conditions

All conditions are satisfied.

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Figure 2-13: ACI Moment Coefficients (1)

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−𝑊𝑢𝑙𝑛2

24 +

𝑊𝑢𝑙𝑛2

14 −

𝑊𝑢𝑙𝑛2

10 −

𝑊𝑢𝑙𝑛2

11 +

𝑊𝑢𝑙𝑛2

16 −

𝑊𝑢𝑙𝑛2

11

Figure 2-15: ACI Moment Coefficients (2)

𝑊𝑢 = 1.2(𝐷𝐿) + 1.6(𝐿𝐿)

𝑊𝑢 = 1.2(6.95) + 1.6(2.5) = 12.34 𝐾𝑁

𝑚

Apply moment coefficients which are shown in Figure 2-15:

Equations used for calculations [1]:

1) 𝑀𝑢 = 𝑚𝑜𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 × 𝑊𝑢 × 𝑙𝑛2

2) 𝑅𝑛 =𝑀𝑢

∅𝑏𝑑2

3) 𝑚 =𝑓𝑦

0.85𝑓′𝑐

4) 𝜌 =1

𝑚(1 − √1 −

2𝑚𝑅𝑛

𝑓𝑦 )

5) 𝜌min = 3 ×√𝑓𝑐′

𝑓𝑦 but not less than

200

𝑓𝑦

6) 𝐴𝑠 = 𝜌𝑏𝑑

𝑊𝑛 12.34 KN/m 𝑏 0.3048 m

𝑙𝑛 5,3.5 m 𝑑 0.27 m

𝑓′𝑐 40 MPa

𝑓𝑦 420 MPa

𝑀𝑢 -12.85 22.035 -30.85 -13.75 9.45 KN-m

𝑅𝑛 -642.567 1101.864 -1542.65982 -687.571 472.5489 KN/m2

𝑚 12.35294 12.35294 12.35294 12.35294 12.35294 -

𝜌 0.001546 0.002667 0.003760 0.0016539 0.001133 -

𝜌𝑚𝑖𝑛 0.00142857 0.00142857 0.00142857 0.00142857 0.00142857 -

𝐴𝑠 127.229616 219.5190 309.4606 136.1094 117.5656 𝑚𝑚2

Bar #4 1 2 3 2 1

5.0 m 3.5 m

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2.6. Beam Design

Critical beam found to be beam # 200 as shown in Figure 2-16.

Figure 2-16: Critical Beam

Checking the design of beam # 200

For main re-bars

Take cover = 0.04 𝑚 , ℎ = 0.5 𝑚 , 𝑏 = 0.2 𝑚 , 𝑑 = 0.46 𝑚

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From STAAD.pro analysis, max (-ve) moment

𝑀𝑢 = −33.6𝐾𝑁. 𝑚 , 𝐴𝑠 = 3 ×𝜋

4× 122 = 339.3 𝑚𝑚2

Max (+ve) moment

𝑀𝑢 = 10.6 𝐾𝑁. 𝑚 , 𝐴𝑠 = 3 ×𝜋

4× 122 = 339.3 𝑚𝑚2

As Shown in Figure .

Figure 2-17: Moment diagram of beam #200

Moment diagram of beam #200

Figure 2-18: Steel arrangement of beam#200 (1)

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Figure 2-19: Steel arrangement of beam#200 (2)

Calculating moment capacity of the beam in compression and tension, then check it

with the applied moments.

Equations used [1]:

1) 𝑀𝑛 = 𝐴𝑠𝑓𝑦 (𝑑 −𝑎

2)

2) 𝑎 =𝐴𝑠𝑓𝑦

0.85𝑓𝑐𝑏

𝑀𝑛− = 𝐴𝑠𝑓𝑦 (𝑑 −𝑎

2) , 𝑎 =

𝐴𝑠𝑓𝑦

0.85𝑓𝑐𝑏=

339.3×420

0.85×40×200= 20.96 𝑚𝑚

𝑀𝑛− = 339.3 × 420 (460 −20.96

2) ×

1

1000 𝑚𝑚×

1

1000 𝑁= 64.059 𝐾𝑁. 𝑚

𝑀𝑛+ = 𝐴𝑠𝑓𝑦 (𝑑 −𝑎

2) , 𝑎 =

𝐴𝑠𝑓𝑦

0.85𝑓𝑐𝑏=

339.3×420

0.85×40×200= 20.96 𝑚𝑚

𝑀𝑛+ = 339.3 × 420 (460 −20.96

2) ×

1

1000 𝑚𝑚×

1

1000 𝑁= 64.059 𝐾𝑁. 𝑚

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Check (-ve) moment:

∅𝑀𝑛− = 0.9(64.059 ) = 57.65 > 33.6 𝐾𝑁. 𝑚 OK

Check (+ve) moment:

∅𝑀𝑛+ = 0.9(64.059 ) = 57.65 > 10.6 𝐾𝑁. 𝑚 OK

For Stirrups:

From STAAD.pro analysis and design the values of Vu, Vc and Vs as well as specifications of

shear reinforcement is shown below in Figure and Figure .

Figure 2-20: Shear Diagram for beam #200

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Figure 2-21: Specifications of shear reinforcement of beam #200

Check:

∅𝑉𝑛 = 𝑉𝑠 + 𝑉𝑐 = 0 + 98.7 = (0.75) × 98.7 = 74.03 𝐾𝑁

∅𝑉𝑛 ≥ 𝑉𝑢 → 74.03 ≥ 27.62 OK

∅𝑉𝑐

2> 𝑉𝑢 → 37.01 > 27.62 OK

So, no need for stirrups.

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2.7. Column Design

Critical Column found to be beam # 127 as shown in Figure .

Figure 2-22: Critical Column #127

The column output given by STAAD.pro for column # 127 is shown in the

following table and Figure .

SI Unit English Unit

𝑃𝑢 18.03 𝐾𝑁 4.1 𝐾𝑖𝑝

𝑀𝑧 125.14 𝐾𝑁. 𝑚 1107.6 𝐾𝑖𝑝. 𝑖𝑛

𝑀𝑦 11.96 𝐾𝑁. 𝑚 105.9 𝐾𝑖𝑝. 𝑖𝑛 𝑏 13.78 𝑖𝑛

𝐴𝑔 0.263 𝑚2 407.7 𝑖𝑛2 𝑑 29.5 𝑖𝑛

𝐴𝑠 3176 𝑚𝑚2 4.923 𝑖𝑛2

𝑓′𝑐 40 𝑀𝑝𝑎 5.8 𝐾𝑠𝑖

𝑓𝑦 420 𝑀𝑝𝑎 60.9 𝐾𝑠𝑖

𝑐𝑜𝑣𝑒𝑟 0.04 𝑚 1.57 𝑖𝑛

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Figure 2-23: Output of column#127

To check the column reinforcement, checking whether the column is short or long should be

done first. If the column is long the effect of slenderness should be taken in consideration, if

not, no need to consider the effects of slenderness.

Slendernen ratio→𝑘𝑙𝑢

𝑟

Check:

Since the structure is braced frame if 𝑘𝑙𝑢

𝑟≤ 34 − 12

𝑀1

𝑀2 it is short column, otherwise it is

long column.

34 − 12𝑀1

𝑀2= 34 − 12

11.96

125.14= 32.85

Since the column both fixed ends 𝑘 = 1

𝑙𝑢 = 3.5 𝑚

𝑟 = √𝐼

𝐴= √

𝑏ℎ3

12𝑏ℎ= √

0.750 × 0.3503

12(0.750)(0.350)= 0.101 𝑚𝑚

𝑘𝑙𝑢

𝑟=

1(3.5)

0.101= 34.7 > 33.73, so it is long column.

𝛾 =ℎ − 2 × 𝑐𝑜𝑣.

ℎ=

13.78 − 2 × 1.57

13.78= 0.77

Since that the column has biaxial moments acting on it, the equivalent eccentricity method

will be applied.

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Equations used:

𝑥𝑏 =87000

𝑓𝑦+87000× 𝑑 → 𝑥𝑏 =

87000

60.9+87000× 29.5 = 29.48 𝑖𝑛

𝑎 = 𝛽 × 𝑥𝑏 → 𝑎 = 0.85 × 29.48 = 25.1 𝑖𝑛

𝑐𝑐 = 0.85𝑓𝑐𝑏𝑎 → 𝑐𝑐 = 0.85 × 5.8 × 13.78 × 25.1 = 1705 𝐾𝑖𝑝𝑠

𝑇 = 𝐴𝑠 × 𝑓𝑦

→ 𝑇 = 4.9 × 60.9 = 298.4 𝐾𝑖𝑝𝑠

𝜀𝑠 =29.5−1.57

29.5× 0.003 = 0.0028 >

𝑓𝑦

𝐸𝑠 → 𝑠𝑡𝑒𝑒𝑙 𝑦𝑖𝑒𝑙𝑑𝑒𝑑

𝑐𝑠 = 𝐴𝑠 × (𝑓𝑦

− 0.85𝑓𝑐 ) → 𝑐𝑠 = 4.9 × (60.9 − 0.85 × 5.8) = 274.3 𝐾𝑖𝑝𝑠

𝑃𝑛 = 𝑐𝑐 + 𝑐𝑠 − 𝑇 → 𝑃𝑛 = 1705 + 274.3 − 298.4 = 1680.9 𝐾𝑖𝑝𝑠

𝑀𝑛 = 1705 (10.64 −25.1

2) + 274.3(10.64 − 2.4) + 298.4(10.64 − 2.4) = 1462.49 𝐾𝑖𝑝 − 𝑓𝑡

𝑒 =𝑀𝑛

𝑝𝑛

→1462.49

1680.9= 10.4

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2.8. Foundation Design

Foundations design was done using STAAD.foundation software.

2.8.1. Procedure

1) Analyze the structure using STAAD.pro.

2) Import STAAD.pro file into STAAD.foundation. Figure shows the distribution

of isolated footings.

Figure 2-24: Footings distribution of Solid Slab Structure

3) Define concrete and rebar parameters as shown in Figure :

Figure 2-25: Concrete and Rebar Parameters

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4) Define cover and soil parameters as shown in Figure 2-26:

Figure 2-26: Cover and soil parameters

5) Define footing geometry parameters as shown in Figure :

Figure 2-27: Footing geometry parameters

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2.8.2. Results

Below are two tables of footings sizes and reinforcement. Typical steel arrangement

and footing sizes are shown in Figure 2-28 and Figure 2-29.

Figure 2-28: Typical elevation section of footing

Figure 2-29: Typical plan section of footing

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Foundation geometry for shear wall

Isolated Footing 21

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Input Values

Footing Geomtery

Footing Thickness (Ft) : 500.00 mm

Footing Length - X (Fl) : 1000.00 mm

Footing Width - Z (Fw) : 1000.00 mm

Eccentricity along X (Oxd) : 0.00 mm

Eccentricity along Z (Ozd) : 0.00 mm

Column Dimensions

Column Shape :

Rectangular

Column Length - X

(Pl) :

0.75 m

Column Width - Z

(Pw) :

0.35 m

Pedestal

Include Pedestal?

No

Pedestal Shape :

N/A

Pedestal Height (Ph) :

N/A

Pedestal Length - X

(Pl) :

N/A

Pedestal Width - Z

(Pw) :

N/A

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Design Parameters

Concrete and Rebar Properties

Unit Weight of Concrete : 25.000 kN/m3

Strength of Concrete : 25.000 N/mm2

Yield Strength of Steel : 415.000 N/mm2

Minimum Bar Size : # 6

Maximum Bar Size : # 40

Minimum Bar Spacing : 50.00 mm

Maximum Bar Spacing : 500.00 mm

Pedestal Clear Cover (P, CL) : 50.00 mm

Footing Clear Cover (F, CL) : 50.00 mm

Soil Properties

Soil Type : UnDrained

Unit Weight : 22.00 kN/m3

Soil Bearing Capacity : 200.00 kN/m2

Soil Surcharge : 0.00 kN/m2

Depth of Soil above Footing : 0.00 mm

Undrained Shear Strength : 0.00 N/mm2

Sliding and Overturning

Coefficient of Friction : 0.50

Factor of Safety Against Sliding : 1.50

Factor of Safety Against Overturning : 1.50

------------------------------------------------------

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Design Calculations

Footing Size

Initial Length (Lo) = 1.00 m

Initial Width (Wo) = 1.00 m

Applied Loads - Allowable Stress Level

LC Axial

(kN)

Shear X

(kN)

Shear Z

(kN)

Moment X

(kNm)

Moment Z

(kNm)

5 74.877 99.102 5.015 1.482 -348.409

6 -279.122 -0.531 137.333 17.802 0.941

7 -67.530 -185.540 -5.085 -1.439 488.882

8 281.613 0.436 -82.371 -13.372 -0.766

9 203.757 -6.409 -1.239 2.688 6.289

10 16.648 -2.920 -0.046 0.267 2.133

11 285.260 -8.973 -1.735 3.763 8.804

12 271.146 -12.363 -1.561 3.654 10.959

13 261.157 -10.611 -1.533 3.493 9.679

14 304.410 71.590 2.525 4.412 -271.181

15 21.211 -8.116 108.379 17.467 8.299

16 190.484 -156.123 -5.555 2.075 398.652

17 469.799 -7.343 -67.384 -7.472 6.934

18 380.960 147.952 6.491 5.865 -547.775

19 -185.438 -11.461 218.200 31.977 11.185

20 153.108 -307.475 -9.669 1.191 791.890

21 711.737 -9.914 -133.327 -17.902 8.455

22 261.157 -10.611 -1.533 3.493 9.679

23 261.157 -10.611 -1.533 3.493 9.679

24 261.157 -10.611 -1.533 3.493 9.679

25 261.157 -10.611 -1.533 3.493 9.679

26 303.185 152.795 6.909 4.791 -551.795

27 -263.213 -6.618 218.618 30.903 7.166

28 75.333 -302.632 -9.251 0.117 787.871

29 633.962 -5.072 -132.909 -18.976 4.435

30 183.381 -5.768 -1.115 2.419 5.660

31 183.381 -5.768 -1.115 2.419 5.660

32 183.381 -5.768 -1.115 2.419 5.660

33 183.381 -5.768 -1.115 2.419 5.660

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Applied Loads - Strength Level

LC Axial

(kN)

Shear X

(kN)

Shear Z

(kN)

Moment X

(kNm)

Moment Z

(kNm)

5 74.877 99.102 5.015 1.482 -348.409

6 -279.122 -0.531 137.333 17.802 0.941

7 -67.530 -185.540 -5.085 -1.439 488.882

8 281.613 0.436 -82.371 -13.372 -0.766

9 203.757 -6.409 -1.239 2.688 6.289

10 16.648 -2.920 -0.046 0.267 2.133

11 285.260 -8.973 -1.735 3.763 8.804

12 271.146 -12.363 -1.561 3.654 10.959

13 261.157 -10.611 -1.533 3.493 9.679

14 304.410 71.590 2.525 4.412 -271.181

15 21.211 -8.116 108.379 17.467 8.299

16 190.484 -156.123 -5.555 2.075 398.652

17 469.799 -7.343 -67.384 -7.472 6.934

18 380.960 147.952 6.491 5.865 -547.775

19 -185.438 -11.461 218.200 31.977 11.185

20 153.108 -307.475 -9.669 1.191 791.890

21 711.737 -9.914 -133.327 -17.902 8.455

22 261.157 -10.611 -1.533 3.493 9.679

23 261.157 -10.611 -1.533 3.493 9.679

24 261.157 -10.611 -1.533 3.493 9.679

25 261.157 -10.611 -1.533 3.493 9.679

26 303.185 152.795 6.909 4.791 -551.795

27 -263.213 -6.618 218.618 30.903 7.166

28 75.333 -302.632 -9.251 0.117 787.871

29 633.962 -5.072 -132.909 -18.976 4.435

30 183.381 -5.768 -1.115 2.419 5.660

31 183.381 -5.768 -1.115 2.419 5.660

32 183.381 -5.768 -1.115 2.419 5.660

33 183.381 -5.768 -1.115 2.419 5.660

Reduction of force due to buoyancy = -0.00 kN

Effect due to adhesion = 0.00 kN

Min. area required from bearing pressure, Amin = P / qmax = 3.621 m2

Area from initial length and width, Ao = Lo * Wo = 1.00 m2

36 | P a g e

Final Footing Size

Length (L2) = 8.60 m Governing Load Case : # 28

Width (W2) = 8.60 m Governing Load Case : # 28

Depth (D2) = 0.50 m Governing Load Case : # 28

Area (A2) = 73.96 m2

Pressures at Four Corners

Load Case

Pressure at corner 1

(q1) (kN/m^2)


(q2) (kN/m^2)


(q3) (kN/m^2)


(q4) (kN/m^2)

Area of footing in uplift (Au)

(m2)

20 23.4557 5.6150 5.6837 23.5244 -0.0000

21 21.4516 21.1986 22.7940 23.0471 -0.0000

21 21.4516 21.1986 22.7940 23.0471 -0.0000

18 23.4297 11.6994 11.8712 23.6015 -0.0000

If Au is zero, there is no uplift and no pressure adjustment is necessary. Otherwise, to account for uplift, areas of negative pressure will be set to zero and the pressure will be redistributed to remaining corners.

Summary of Adjusted Pressures at 4 corners Four Corners

Load Case

Pressure at corner 1 (q1)

(kN/m^2)


(kN/m^2)


(kN/m^2)


(kN/m^2)

37 | P a g e

20 23.4557 5.6150 5.6837 23.5244

21 21.4516 21.1986 22.7940 23.0471

21 21.4516 21.1986 22.7940 23.0471

18 23.4297 11.6994 11.8712 23.6015

Adjust footing size if necessary.

Check for stability against overturning and sliding

- Factor of safety against sliding Factor of safety against overturning

Load Case

No.

Along X-

Direction

Along Z-

Direction

About X-

Direction

About Z-

Direction

5 5.042 99.634 1077.012 10.798

6 607.904 2.350 32.092 2299.745

7 2.309 84.264 925.514 6.335

8 1384.520 7.321 95.058 5274.047

9 88.014 455.234 2345.246 511.025

10 161.146 10206.828 16563.146 1126.246

11 67.409 348.657 1796.190 391.387

12 48.353 383.021 1789.319 299.929

38 | P a g e

13 55.866 386.674 1869.768 340.213

14 8.583 243.336 931.256 17.213

15 58.261 4.363 56.748 329.068

16 3.571 100.358 6821.752 10.057

17 94.942 10.346 145.646 565.310

18 4.412 100.556 616.140 9.028

19 32.242 1.693 22.525 187.861

20 1.752 55.724 1271.710 4.900

21 82.517 6.136 83.198 524.584

22 55.866 386.674 1869.768 340.213

23 55.866 386.674 1869.768 340.213

24 55.866 386.674 1869.768 340.213

25 55.866 386.674 1869.768 340.213

26 4.017 88.846 640.209 8.403

27 49.961 1.512 20.279 271.454

28 1.652 54.037 953.567 4.577

29 153.646 5.863 78.441 961.341

30 96.027 496.681 2558.767 557.551

31 96.027 496.681 2558.767 557.551

32 96.027 496.681 2558.767 557.551

33 96.027 496.681 2558.767 557.551

Critical Load Case And The Governing Factor Of Safety For Overturning And Sliding - X Direction

Critical Load Case for Sliding along X-Direction : 28

Governing Disturbing Force : -302.632 kN

Governing Restoring Force : 499.900 kN

Minimum Sliding Ratio for the Critical Load Case : 1.652

Critical Load Case for Overturning about X-Direction : 27

Governing Overturning Moment : 140.210 kNm

Governing Resisting Moment : 2843.342 kNm

Minimum Overturning Ratio for the Critical Load Case : 20.279

39 | P a g e

Critical Load Case And The Governing Factor Of Safety For Overturning And Sliding - Z Direction

Critical Load Case for Sliding along Z-Direction : 27

Governing Disturbing Force : 218.618 kN



Critical Load Case for Overturning about Z-Direction : 28




Shear Calculation

Punching Shear Check

Total Footing Depth, D = 0.50m

Calculated Effective Depth, deff = D - Ccover - 1.0 = 0.42 m

40 | P a g e

For rectangular column, = Bcol / Dcol = 2.14

Effective depth, deff, increased until 0.75*Vc Punching Shear Force

Punching Shear Force, Vu = 702.98 kN, Load Case # 21

From ACI Cl.11.12.2.1, bo for column=

3.90 m

Equation 11-33, Vc1 =

2657.25 kN


4368.42 kN


2748.88 kN

Punching shear strength, Vc = 0.75 * minimum of (Vc1, Vc2, Vc3) = 1992.94 kN

0.75 * Vc > Vu hence, OK

One-Way Shear Check

Along X Direction

From ACI Cl.11.3.1.1, Vc =

3032.06 kN

Distance along Z to design for shear, Dz =

4.90 m

41 | P a g e

Check that 0.75 * Vc > Vux where Vux is the shear force for the critical load cases at a distance deff from the face of the column caused by bending about the X axis.

From above calculations, 0.75 * Vc = 2274.05 kN

Critical load case for Vux is # 21

320.71 kN

0.75 * Vc > Vux hence, OK

Along Z Direction


3032.06 kN

Distance along X to design for shear, Dx =

3.50 m

Check that 0.75 * Vc > Vuz where Vuz is the shear force for the critical load cases at a distance deff from the face of the column caused by bending about the Z axis.


42 | P a g e

Critical load case for Vuz is # 21

291.95 kN

0.75 * Vc > Vuz hence, OK

Design for Flexure about Z axis

Calculate the flexural reinforcement along the X direction of the footing. Find the area of steel required, A, as per Section 3.8 of Reinforced Concrete Design (5th ed.) by Salmon and Wang (Ref. 1)

Critical Load Case # 21

The strength values of steel and concrete used in the formulae are in ksi

Factor from ACI Cl.10.2.7.3 for Fc' 4 ksi, 0.85

From ACI Cl. 10.3.2, =

0.02573


0.01929

From ACI Cl. 7.12.2, = 0.00180

From Ref. 1, Eq. 3.8.4a, constant m =

19.53

43 | P a g e

Calculate reinforcement ratio for critical load case

Design for flexure about Z axis is performed at the face of the column at

a distance, Dx =

3.93 m

Ultimate moment,

643.30 kNm

Nominal moment capacity, Mn =

714.78 kNm

Required =

0.00180

Since

OK

Area of Steel Required, As =

10.19 in2

Find suitable bar arrangement between minimum and maximum rebar sizes

Available development length for bars, DL =

3875.00 mm

Try bar size # 8 Area of one bar = 0.08 in2

Number of bars required, Nbar =

131

Because the number of bars is rounded up, make sure new reinforcement ratio < max

Total reinforcement area, As_total = Nbar * (Area of one bar) = 10.21 in2

deff = D - Ccover - 0.5 * (dia. of one bar) = 0.45 m

Reinforcement ratio, =

0.00172

From ACI Cl.7.6.1, minimum req'd clear distance between bars, Cd =

max (Diameter of one bar, 1.0, Min. User Spacing) =

65.32 mm

Check to see if width is sufficient to accomodate bars

44 | P a g e

Design for Flexure about X axis

Calculate the flexural reinforcement along the Z direction of the footing. Find the area of steel required, A, as per Section 3.8 of Reinforced Concrete Design (5th ed.) by Salmon and Wang (Ref. 1)





0.02573


0.01929

From ACI Cl.7.12.2, = 0.00180


19.53


Design for flexure about X axis is performed at the face of the column at

a distance, Dz =

4.47 m

Ultimate moment,

743.82 kNm

45 | P a g e


826.46 kNm

Required =

0.00180

Since

OK


10.00 in2



4075.00 mm



129





0.00179



58.34 mm


Bending moment for uplift cases will be calculated based solely on selfweight, soil depth and surcharge loading.

As the footing size has already been determined based on all servicebility load cases, and design moment calculation is based on selfweight, soil depth and surcharge only, top reinforcement value for all pure uplift load cases will be the same.

46 | P a g e

Design For Top Reinforcement About Z Axis

Calculate the flexural reinforcement along the X direction of the footing. Find the area of steel required




0.02573


0.01929

From ACI Cl. 7.12.2, = 0.00180


19.53


Design for flexure about A axis is performed at the face of the column at

a distance, Dx =

4.13 m

Ultimate moment,

0.00 kNm


0.00 kNm

Required =

0.00180

Since

OK


10.00 in2


47 | P a g e

Design For Top Reinforcement About X Axis

First load case to be in pure uplift # 0

Calculate the flexural reinforcement along the Z direction of the footing. Find the area of steel required




0.02573


0.01929

From ACI Cl.7.12.2, = 0.00180


19.53



a distance, Dx =

3.93 m

Ultimate moment,

0.00 kNm


0.00 kNm

Required =

0.00180

Since

OK


10.19 in2


48 | P a g e

Foundation geometry

Isolated Footing 22

49 | P a g e

Input Values

Footing Geomtery

Footing Thickness (Ft) : 500.00 mm

Footing Length - X (Fl) : 1000.00 mm

Footing Width - Z (Fw) : 1000.00 mm

Eccentricity along X (Oxd) : 0.00 mm

Eccentricity along Z (Ozd) : 0.00 mm

Column Dimensions

Column Shape :

Rectangular

Column Length - X

(Pl) :

0.35 m

Column Width - Z

(Pw) :

0.75 m

Pedestal

Include Pedestal?

No

Pedestal Shape :

N/A

Pedestal Height (Ph) :

N/A

Pedestal Length - X

(Pl) :

N/A

Pedestal Width - Z

(Pw) :

N/A

Design Parameters

Concrete and Rebar Properties

50 | P a g e

Unit Weight of Concrete : 25.000 kN/m3

Strength of Concrete : 25.000 N/mm2

Yield Strength of Steel : 415.000 N/mm2

Minimum Bar Size : # 6

Maximum Bar Size : # 40

Minimum Bar Spacing : 50.00 mm

Maximum Bar Spacing : 500.00 mm

Pedestal Clear Cover (P, CL) : 50.00 mm

Footing Clear Cover (F, CL) : 50.00 mm

Soil Properties

Soil Type : UnDrained

Unit Weight : 22.00 kN/m3

Soil Bearing Capacity : 200.00 kN/m2

Soil Surcharge : 0.00 kN/m2

Depth of Soil above Footing : 0.00 mm

Undrained Shear Strength : 0.00 N/mm2

Sliding and Overturning

Coefficient of Friction : 0.50

Factor of Safety Against Sliding : 1.50

Factor of Safety Against Overturning : 1.50

------------------------------------------------------

51 | P a g e

Design Calculations

Footing Size

Initial Length (Lo) = 1.00 m

Initial Width (Wo) = 1.00 m

Applied Loads - Allowable Stress Level

LC Axial

(kN)

Shear X

(kN)

Shear Z

(kN)

Moment X

(kNm)

Moment Z

(kNm)

5 143.492 39.564 0.810 2.667 -89.934

6 -51.735 -0.158 133.489 212.281 0.228

7 -161.307 -116.049 -0.540 -1.791 131.958

8 51.575 0.137 -59.207 -172.287 -0.191

9 295.056 5.351 -7.561 -5.781 -4.472

10 44.544 3.108 0.009 0.022 -2.647

11 413.078 7.491 -10.585 -8.094 -6.261

12 425.337 11.393 -9.058 -6.903 -9.602

13 398.611 9.529 -9.064 -6.916 -8.014

14 468.860 38.072 -8.425 -4.804 -77.314

15 312.678 6.294 97.718 162.887 -5.184

16 225.021 -86.419 -9.505 -8.370 100.199

17 395.327 6.530 -56.439 -144.767 -5.519

18 628.197 72.830 -7.768 -2.648 -151.908

19 315.834 9.275 204.519 332.734 -7.648

20 140.520 -176.150 -9.928 -9.781 203.118

21 481.131 9.747 -103.795 -282.574 -8.319

22 398.611 9.529 -9.064 -6.916 -8.014

23 398.611 9.529 -9.064 -6.916 -8.014

24 398.611 9.529 -9.064 -6.916 -8.014

25 398.611 9.529 -9.064 -6.916 -8.014

26 495.137 68.117 -5.509 -0.935 -147.920

27 182.774 4.562 206.778 334.446 -3.660

28 7.459 -180.863 -7.669 -8.068 207.107

29 348.070 5.034 -101.536 -280.861 -4.330

30 265.550 4.816 -6.805 -5.203 -4.025

31 265.550 4.816 -6.805 -5.203 -4.025

32 265.550 4.816 -6.805 -5.203 -4.025

33 265.550 4.816 -6.805 -5.203 -4.025

52 | P a g e

Applied Loads - Strength Level

LC Axial

(kN)

Shear X

(kN)

Shear Z

(kN)

Moment X

(kNm)

Moment Z

(kNm)

5 143.492 39.564 0.810 2.667 -89.934

6 -51.735 -0.158 133.489 212.281 0.228

7 -161.307 -116.049 -0.540 -1.791 131.958

8 51.575 0.137 -59.207 -172.287 -0.191

9 295.056 5.351 -7.561 -5.781 -4.472

10 44.544 3.108 0.009 0.022 -2.647

11 413.078 7.491 -10.585 -8.094 -6.261

12 425.337 11.393 -9.058 -6.903 -9.602

13 398.611 9.529 -9.064 -6.916 -8.014

14 468.860 38.072 -8.425 -4.804 -77.314

15 312.678 6.294 97.718 162.887 -5.184

16 225.021 -86.419 -9.505 -8.370 100.199

17 395.327 6.530 -56.439 -144.767 -5.519

18 628.197 72.830 -7.768 -2.648 -151.908

19 315.834 9.275 204.519 332.734 -7.648

20 140.520 -176.150 -9.928 -9.781 203.118

21 481.131 9.747 -103.795 -282.574 -8.319

22 398.611 9.529 -9.064 -6.916 -8.014

23 398.611 9.529 -9.064 -6.916 -8.014

24 398.611 9.529 -9.064 -6.916 -8.014

25 398.611 9.529 -9.064 -6.916 -8.014

26 495.137 68.117 -5.509 -0.935 -147.920

27 182.774 4.562 206.778 334.446 -3.660

28 7.459 -180.863 -7.669 -8.068 207.107

29 348.070 5.034 -101.536 -280.861 -4.330

30 265.550 4.816 -6.805 -5.203 -4.025

31 265.550 4.816 -6.805 -5.203 -4.025

32 265.550 4.816 -6.805 -5.203 -4.025

33 265.550 4.816 -6.805 -5.203 -4.025

53 | P a g e

Reduction of force due to buoyancy = -0.00 kN

Effect due to adhesion = 0.00 kN

Min. area required from bearing pressure, Amin = P / qmax = 3.203 m2

Area from initial length and width, Ao = Lo * Wo = 1.00 m2

Final Footing Size

Length (L2) = 6.55 m Governing Load Case : # 28

Width (W2) = 6.55 m Governing Load Case : # 28

Depth (D2) = 0.50 m Governing Load Case : # 28

Area (A2) = 42.90 m2

Pressures at Four Corners

Load Case


(q1) (kN/m^2)


(q2) (kN/m^2)


(q3) (kN/m^2)


(q4) (kN/m^2)

Area of footing in uplift (Au)

(m2)

18 31.0236 22.9815 23.2604 31.3025 -0.0000

18 31.0236 22.9815 23.2604 31.3025 -0.0000

21 16.8542 16.2908 30.5740 31.1373 -0.0000

18 31.0236 22.9815 23.2604 31.3025 -0.0000

If Au is zero, there is no uplift and no pressure adjustment is necessary. Otherwise, to account for uplift, areas of negative pressure will be set to zero and the pressure will be redistributed to remaining corners.

54 | P a g e

Summary of Adjusted Pressures at 4 corners Four Corners

Load Case


(kN/m^2)


(kN/m^2)


(kN/m^2)


(kN/m^2)

18 31.0236 22.9815 23.2604 31.3025

18 31.0236 22.9815 23.2604 31.3025

21 16.8542 16.2908 30.5740 31.1373

18 31.0236 22.9815 23.2604 31.3025

Adjust footing size if necessary.

Check for stability against overturning and sliding

- Factor of safety against sliding Factor of safety against overturning

Load Case No.

Along X-Direction

Along Z-Direction

About X-Direction

About Z-Direction

5 8.591 419.533 724.576 20.290

6 1528.905 1.815 5.687 5158.545

7 1.616 347.159 595.886 6.464

55 | P a g e

8 2152.745 4.964 9.536 7438.992

9 77.684 54.975 284.738 380.895

10 93.442 31772.244 72461.427 452.804

11 63.366 44.843 232.259 310.693

12 42.200 53.078 275.476 205.850

13 49.056 51.572 267.451 239.604

14 13.200 59.652 365.102 34.164

15 67.440 4.344 13.130 333.715

16 4.405 40.046 189.993 17.385

17 71.331 8.253 17.637 347.314

18 7.994 74.956 583.845 20.250

19 45.935 2.083 6.415 227.138

20 1.921 34.085 150.320 7.612

21 52.190 4.901 9.962 252.570

22 49.056 51.572 267.451 239.604

23 49.056 51.572 267.451 239.604

24 49.056 51.572 267.451 239.604

25 49.056 51.572 267.451 239.604

26 7.571 93.618 915.493 18.561

27 78.806 1.739 5.378 396.381

28 1.503 35.450 149.604 5.985

29 87.835 4.355 8.733 422.980

30 83.252 58.916 305.147 408.195

31 83.252 58.916 305.147 408.195

32 83.252 58.916 305.147 408.195

33 83.252 58.916 305.147 408.195

Critical Load Case And The Governing Factor Of Safety For Overturning And Sliding - X Direction

Critical Load Case for Sliding along X-Direction : 28

Governing Disturbing Force : -180.863 kN



56 | P a g e

Critical Load Case for Overturning about X-Direction : 27




Critical Load Case And The Governing Factor Of Safety For Overturning And Sliding - Z Direction

Critical Load Case for Sliding along Z-Direction : 27

Governing Disturbing Force : 206.778 kN



Critical Load Case for Overturning about Z-Direction : 28




57 | P a g e

Shear Calculation

Punching Shear Check

Total Footing Depth, D = 0.50m

Calculated Effective Depth, deff = D - Ccover - 1.0 = 0.42 m

For rectangular column, = Bcol / Dcol = 2.14

Effective depth, deff, increased until 0.75*Vc Punching Shear Force

Punching Shear Force, Vu = 614.87 kN, Load Case # 18

From ACI Cl.11.12.2.1, bo for column=

3.90 m


2657.25 kN


4368.42 kN


2748.88 kN

Punching shear strength, Vc = 0.75 * minimum of (Vc1, Vc2, Vc3) = 1992.94 kN

0.75 * Vc > Vu hence, OK

58 | P a g e

One-Way Shear Check

Along X Direction


2309.30 kN

Distance along Z to design for shear, Dz =

4.07 m

Check that 0.75 * Vc > Vux where Vux is the shear force for the critical load cases at a distance deff from the face of the column caused by bending about the X axis.


Critical load case for Vux is # 21

253.86 kN

0.75 * Vc > Vux hence, OK

59 | P a g e

Along Z Direction


2309.30 kN

Distance along X to design for shear, Dx =

2.68 m

Check that 0.75 * Vc > Vuz where Vuz is the shear force for the critical load cases at a distance deff from the face of the column caused by bending about the Z axis.


Critical load case for Vuz is # 18

298.27 kN

0.75 * Vc > Vuz hence, OK

60 | P a g e

Design for Flexure about Z axis

Calculate the flexural reinforcement along the X direction of the footing. Find the area of steel required, A, as per Section 3.8 of Reinforced Concrete Design (5th ed.) by Salmon and Wang (Ref. 1)





0.02573


0.01929

From ACI Cl. 7.12.2, = 0.00180


19.53


Design for flexure about Z axis is performed at the face of the column at

a distance, Dx =

3.10 m

Ultimate moment,

547.42 kNm

61 | P a g e


608.24 kNm

Required =

0.00180

Since

OK


7.76 in2



3050.00 mm



100





0.00172



65.07 mm


62 | P a g e

Design for Flexure about X axis

Calculate the flexural reinforcement along the Z direction of the footing. Find the area of steel required, A, as per Section 3.8 of Reinforced Concrete Design (5th ed.) by Salmon and Wang (Ref. 1)





0.02573


0.01929

From ACI Cl.7.12.2, = 0.00180


19.53


Design for flexure about X axis is performed at the face of the column at

a distance, Dz =

3.65 m

Ultimate moment,

447.60 kNm

63 | P a g e


497.34 kNm

Required =

0.00180

Since

OK


7.61 in2



2850.00 mm



98





0.00178



58.41 mm


Bending moment for uplift cases will be calculated based solely on selfweight, soil depth and surcharge loading.

As the footing size has already been determined based on all servicebility load cases, and design moment calculation is based on selfweight, soil depth and surcharge only, top reinforcement value for all pure uplift load cases will be the same.

Design For Top Reinforcement About Z Axis

Calculate the flexural reinforcement along the X direction of the footing. Find the area of steel required

64 | P a g e




0.02573


0.01929

From ACI Cl. 7.12.2, = 0.00180


19.53



a distance, Dx =

2.90 m

Ultimate moment,

0.00 kNm


0.00 kNm

Required =

0.00180

Since

OK


7.61 in2


65 | P a g e

Design For Top Reinforcement About X Axis

First load case to be in pure uplift # 0

Calculate the flexural reinforcement along the Z direction of the footing. Find the area of steel required




0.02573


0.01929

From ACI Cl.7.12.2, = 0.00180


19.53



a distance, Dx =

3.10 m

Ultimate moment,

0.00 kNm


0.00 kNm

Required =

0.00180

Since

OK


7.76 in2


66 | P a g e

Conclusion

I had the opportunity to learn how to use STAAD Pro software to analyze and design

two-way solid slab as well as one-way ribbed slab. Also, a hand calculation check on analysis

of the results of typical structural members gave us knowledge about checking the adequacy

of design to meet the criteria set by codes of practice. Furthermore, i was exposed to STAAD

Pro Foundation Software, which gave us new ideas about designing the foundations of a

building.

Additionally, in CE 315 project i had the chance to design a beam, column and foundation.

67 | P a g e

References

ACI Committee. Building Code Requirements for Structural Concrete (ACI 318-08)

and Commentary. Farmington Hills: American Concrete Institute, 2008.

JAMES, K WIGHT and G MACGREGOR JAMES. REINFORCED CONCRETE

Mechanics and Design. New Jersey: Pearson Education, 2012.

analyses and ddesign of a two storied rc building

Engineering

normal structure

g e list of figures

structure modeling

description of structure

ribbed slab design

beam design

column design

foundation design