EFFECT OF INFILL ON THE DESIGN OF COLUMNS IN A MULTISTORIED BUILDING

BY

NOORE ALAM PATWARY

ABSTRACT

The contribution of infill in the structural analysis and design is generally not considered.

The object of this thesis is to investigate the effect of infill on the design of column in a

six storied building using based on finite element analysis. The study is carried out by

three dimensional modeling of a six storied building structures with and without infill.

The infills are modeled as diagonal struts. The amount of infill in building frame was

varied from 20% to 80% of no. of panel. One corner column, one edge column and one

center column was selected for study. After analyzing and designing, it is seen that there

had no significant effect of infill on the design of corner and edge column. But in the

design of center column, it is found that the reinforcement required for infilled frame is

less than the steel needed for without infill. So it may be conclude that, from the above

discussion, the design of column without considering the infill contribution is more

conservative.

Chapter Topic Page No.

Acknowledgement

Abstract

List of symbols

CHAPTER 1: INTRODUCTION 1

1.1: General 1

1.2: Frames with infill 1

1.3: Existing background related to this thesis 3

1.4: Objective and Scope 4

CHAPTER 2: FRAME STRUCTURES WITH INFILL 6

2.1: Introduction 6

2.2: Characteristics of infilled frames 6

2.3: Analysis of infilled frames 9

2.3.1: Approximate method 10

2.3.2: Equivalent strut method 12

2.3.3: Plasticity model 15

2.3.4: Coupled boundary element method 16

2.3.5: Choice of the model 17

2.4: Equivalent strut modeling 18

2.5: Beam and Column moment capacity 19

2.6: Determination of equivalent strut stiffness (Ko) 20

CHAPTER 3: FINITE ELEMENT MODELING 27

3.1: Introduction 27

3.2: Finite element packages 27

3.3: Finite element modeling of infilled frames 28

3.3.1: Modeling of Beams and Column 29

3.3.2: Modeling of Slab 31

3.3.3: Modeling of Infill 33

3.4: Description of the model under study 36

3.5: Earthquake load calculation 37

3.6: Location of Infill and Finite element modeling 39

CHAPTER 4: RESULTS AND DISCUSSION 45

4.1: Introduction 45

4.2: Output Results 45

4.3: Discussions 45

4.3.1: For corner column 45

4.3.2: For edge column 45

4.3.3: For center column 50

CHAPTER 5: CONCLUSIONS AND RECOMMENDATION 51

5.1: Conclusions 51

5.2: Recommendation 52

REFERENCES

APPENDIX: TYPICAL ANSYS SCRIPT

LIST OF SYMBOLS

xy : Shear stress, kN/m2

y : Vertical compressive stress, kN/m2

Q : Horizontal shear load, KN

l : Length of MR in m

h' : Height of infill in m

t : Wall thickness in m

d : Diagonal tensile stress, KN/ m2

mE : Elastic modulus of Masonry, KN/ m2

tE : Flexural rigidity of column, kN- m2

: The parameter expressing the bearing stiffness of the instill relative to the flexural rigidity of the column.

'mf : Masonry compressive strength, KN/ m2

'cQ : Ultimate horizontal shear, kip

cQ : Allowable horizontal shear, kip

cV : Maximum lateral force, kip

mu : Maximum lateral displacement, m

'm : Masonry ultimate strain, m

: Inclination of the diagonal strut degree : Basic shear strength, KN/ m2

dA : Area of equivalent diagonal strut, m2

dL : Length of equivalent diagonal struts, in

ok : The initial stiffness of MR kN-m

pcM : Plastic resisting moment of column, kN-m

pbM : Plastic resisting moment of beam, kN-m

pjM : Plastic resisting moment of beam and column joint, kN-m

r : Aspect ratio of the frame

h : Centre to height of beam, m

l : Centre to center length of column, m

: A constant value 0.65 co : Normal stress in column, KN/ m

2

'cf : Effective compressive strength of masonry, KN/ m2

tF : Coefficient of friction between frame and insult interface

c : Normalized length of contact for column

b : Nonaligned length of contact for beam

o : A reduction factor 0.2 cA : Contact normal stress area in column, m

2

bA : Contact normal stress area in beam, m2

c : The real nominal contact stress in column, KN/ m2

b : The real normal contact stress in beam, KN/ m2

b : Normal contact shear stress in beam, KN/ m2

c : Nominal contact shear stress in column, KN/ m2

af : Actual compressive strength of masonry, KN/ m2

V : Base shear, KN

Z : Zone factor

I : Structural importance coefficient

C : Numerical coefficient

R : Response modification coefficient

W : Total building dead weight, KN

S : Site coefficient for soil characteristics

T : Fundamental period of vibration, see

tC : Constant

nh : Height of the building, m

tF : Concentrated lateral force considered at top of the building, KN

ACKNOWLEDGEMENT

This project was undertaken under the supervision of Dr. Khan Mahmud Amanat, Associate

Professor, Department of Civil Engineering, Bangladesh University of Engineering and

Technology (BUET).The author would like to express his sincere gratitude & profound

indebtedness to the thesis supervisor Dr. Khan Mahmud Amanat, for his inspiring guidance,

constant advice, encouragement and kind help in carrying out the project works as well as in

preparing this thesis.

The author also pays his deepest homage to his parents for their inspiration.

1

CHAPTER 1

INTRODUCTION

1.1 GENERAL

The structural effect of brick infill is generally not considered in the analysis of frame

structure. Frame structure is the most common structure in construction and design in Civil

Engineering field. All building is designed as frame structure. The lack of knowledge about

the mechanical properties of the brick masonry and the absence of well-recognized method

for infill frame design prohibits us from considering the infill as a structural element. The

brick walls have significant in plane stiffness contributing to the stiffness of the frame against

lateral load. The stiffness of framed tall building depends on the characteristics of Column

Stiffness, Beam Stiffness and the stiffness of the infill. Present code of practice does not

include provision of taking into consideration the effect of infill. It can be understood that if

the effect of infill is taken into account in the analysis of frame the resulting structures may

be significantly different .In western countries a number of researchers like Mander et al.

(1993), Holmes (1961), Stafford smith and Carter (1969), Saneinejad and Hobbs (1995) and

recently Erdem Canbay, Uger Erosy and Guney Ozcebe (2003) addressed this problem and

suggested a number of methods to take into account the effect of infill in the analysis of

frame. However all of these methods correspond to the stone masonry infill

1.2 FRAMES WITH INFILL

The infilled frame consists of a steel or reinforced concrete column-and girder frame with

infill of brick works or concrete block work shown in fig 1. 1

In addition to functioning as partitions, exterior walls, and walls around stair, elevator, and

service shafts, the infill may also serve structurally to brace the frame against horizontal

loading. The frame is designed for gravity loading only and in the absence of an accepted

design method, the infill is presumed to contribute sufficiently to the lateral strength of the

structure for it to withstand the horizontal loading. The simplicity of. Construction and highly

developed expertise in building that type of structure have made the infilled frame one of the

most rapid economical structural forms for tall buildings.

2

Fig 1.1 Structural frame infilled with masonry

In countries with stringently applied codes of practice the absence of a well recognized

method of design for infilled frames has severely restricted their use for bracing. It has been

more usual in such countries, when designing an infilled frame structure to arrange for the

frame to carry the total vertical and horizontal loading and to include the infill on the

assumptions that, with precautions taken to avoid load being transferred to them, the infills

do not participate as part of the primary structure. It is evident from the frequently observed

diagonal cracking of such infill walls that the approach is not always valid. The walls do

sometimes attract significant bracing loads and, in so doing, modify the structures mode of

behavior and the forces in the frame (axial force, bending moment, shear force etc). In such

cases it would have been better to design the walls for the lateral loads, and the frame to

allow for its modified mode of behavior.

Certain reservations arise in the use of infilled frames for bracing a structure. For example, it

is possible that as part of a renovation project, partition walls are removed with the result that

the structure becomes inadequately braced. Precautions against this, either by including a

generously excessive number of bracing walls, or by somehow permanently identifying the

vital bracing walls, should be considered as part of the design.

3

1.3 EXISTING BACKGROUND RELATED TO THIS THESIS

In order to analyze the soft floor in a framed tall building one need to know about existing

background related to this thesis. In most cases infills are assumed not to participate as part

of primary structure. The significance of infilling walls in the actual strength and stiffness of

framed building subjected to lateral load has been recognized.

Since any study should start with an analysis of the current state of art report about the

subject matter, efforts would now be made to investigate the achievements regarding sway of

RC frame structures by other researchers.

A number of researches have been on RC frame behavior subjected to lateral loads.

Alameddine and ehsani (1991) have done extensive investigation on high- strength RC

connections subjected to inelastic cyclic loading. The primary variable for this test specimens

were concrete compressive strength, joint shear stress and joint transverse reinforcement.

Their study ultimately revealed that in spite of the brittle nature of plain high-strength

concrete, properly detailed frames constructed with high-strength concrete exhibit ductile

hysteric response similar to those for ordinary-strength concrete.

Zekai Akbay and Haluk M. Aktan (1991) studied the experimental research that is a method

to evaluate the vulnerability of reinforced concrete structural walls to shear failure. This

method utilizes an experimentally developed shear stiffness model for distribution of shear

stresses along reinforced concrete structural walls. Seven wall specimens tested by other

investigators are analyzed to assess their shear strength supply and critical M/V ratios. The

results of the study presented here bring up two important points: 1) the design shear strength

of the wall is a function of the moment capacity, and 2) the wall under compression while

subjected to yielding moment is a key indicator of shear capacity.

Daniel P.Abrams and Thomas J. Paulson (1992) performed a thesis which includes modeling

considerations used in an experimental investigation of the earth quake response of

reinforced concrete masonry buildings. Intended response of reduced-scale structures has

4

been correlated with measured response to demonstrate the acceptability of engineering

principles for estimating peak dynamic response of masonry structures and the precision of

physical models.

Reduced-scale test structures can play important role for investigating inelastic response of

masonry building systems. Behavior of the two test structures showed that modeling can

provide unique information for confirming the accuracy of numerical models , verifying

design procedures, probing new questions regarding internal resistance mechanisms, and

providing demonstrations of nonlinear dynamic response.

Mehrabi et al. (1997) performed a comprehensive research; they studied the influence of

masonry infill panels on the seismic performance of reinforced concrete frame. Two types of

frame were considered. One was designed for wind load and the other for strong earthquake

forces. Twelve 1/2 scale, single-story, single-span frame specimens were tested. The

parameters investigated included the strength of infill panels with respect to that of bounding

frame, the panel aspect ratio, the distribution of vertical loads and the lateral load history.

The experimental results indicated that the infill panels could significantly improved the

performance of RC frames. However, specimens with strong frames and strong panels

exhibited a better performance than those with weak frames and weak panels in terms of the

load resistance and energy dissipation capability. The lateral loads developed by the infilled

frame specimens were always higher than that of bare frame.

Erdem Canbay, Uger Erosy, and Guney Ozcebe (2003) performed a thesis on contribution of

reinforced concrete Infills to seismic behavior of structural systems.

1.4 OBJECTIVE AND SCOPE In the context of Bangladesh moderately tall building may be considered to have storied

ranges from six through fourteen. Each high-rise building has a parking facility in the ground

floor without infill. The main objective of this thesis is to design the selected column of a

four by four span six storied building with infill and without infill for five different load

combinations including lateral load such as earthquake load. Infill will be provided in

5

building as a percentage such as 20%, 40%, 40% and 60% of panel nos. in a building. For

investigation the effect of infill a four by four bay six storied building will be considered and

Infills will be replaced by an Equivalent Diagonal Strut proposed by Saneinejad and Hobbs

(1995). For modeling and analysis finite element based computer software will be used. The

difference in steel requirements to sustain design load for some representative columns

including infill and without infill is the final objective of this thesis.

6

CHAPTER 2

FRAME STRUCTURES WITH INFILL

2.1 INTRODUCTION A large number of buildings are constructed with masonry infills for architectural needs or

aesthetic reasons. In non-earthquake regions where the wind forces are not severe, the

masonry infilled frame is one of the most common structural forms high-rise constructions.

The significance of infilling walls in determining the actual strength and stiffness of framed

buildings subjected to lateral force has long been recognized. Despite rather intensive

investigations during the last four decades, the inclusion of infilling walls as structural

elements is not common, because of the design complexity and lack of suitable theory.

However because of the complexity of the problem and absence of a realistic, yet simple

analytical model, the combination of masonry infill panels is often neglected in the nonlinear

analysis of building structures. During the same period the analysis and design of

multi-storey frames have developed rapidly. According to the latest development, the P-

effect in a fully restrained multistory frame is a major design factor. The more flexible the

frames, the greater the secondary bending moments become. Therefore the influence of

infilling walls is much more significant today than in the past, they provide lateral stiffness

and minimize the P- effect.

2.2 CHARACTERISTICS OF INFILLED FRAMES The behavior of masonry infilled frames has been extensively studied in the last four decades

in attempts to develop a rational approach for design of such frames. The use of a masonry

infill to brace a frame combines some of the desirable structural characteristics of each, while

overcoming some of their deficiencies. The high in-plane rigidity of the masonry wall

significantly stiffens the otherwise relatively flexible frame, while the ductile frame contains

the brittle masonry, after cracking, up to loads and displacements much larger than it could

achieve without the frame. The result is, therefore a relatively stiff and tough bracing system.

7

The wall braces the frame partly by its inplane shear resistance and partly by its behavior as

a diagonal bracing strut in the frame Figure 2.1 shows such modes of behavior. When the

frame is subjected to horizontal loading, it deforms with double-curvature bending of the

columns and beams.

Fig 2.1 Interactive behavior of frame and infill

The translation of the upper part of the column in each story and the shortening of the leading

diagonal of the frame cause the column to lean against the wall as well as to compress the

wall along its diagonal. It is roughly analogous to a diagonally braced frame, shown in fig 2.2

The potential modes of failure, of the wall arise as results of its interaction with the frame are given below:

1. Tension failure of the tension column due to overturning moments.

2. Flexure or shear failure of the columns.

3. Compression failure of the diagonal strut.

4. Diagonal tension cracking of the panel and

5. Sliding shear failure of the masonry along horizontal mortar beds.

The above failure modes shown in figure 2.3 and 2.4,

8

Fig 2.2 Analogous braced frame

Fig 2.3 Modes of infill failure

9

Fig 2.4 Modes of frame failure

The "perpendicular" tensile stresses are caused by the divergence of the compressive stress

trajectories on opposite sides of the leading diagonal as they approach the middle region of

the infill. The diagonal cracking is initiated at and spreads from the middle of the infill,

where the tensile stresses are a maximum, tending to stop near the compression corners,

where the tension is suppressed.

The nature of the forces in the frame can be understood by referring to the analogous braced

frame shown in fig. 2.2. The windward column or the column facing earthquake load first, is

in tension and the leeward column or the other side of the building facing earthquake load

last, and is in compression. Since the infill bears on the frame not as a concentrated force

exactly at the comers, but over short lengths of the beam and column adjacent to each

compression comer, the frame members are subjected also to transverse shear and a small

amount of bending. Consequently, the frame members or their connections are liable to fail

by axial force or shear, and especially by tension at the base of the windward column shown

in fig 2.4

2.3 ANALYSIS OF INFILLED FRAMES An extensive review of research on infilled frames through the mid 1980's has been reported

by Moghaddam and Dowling (1987). Holmes (1961) proposed replacing the infill by an

equivalent pin-jointed diagonal strut of the same material with a width one-third of the in

fill's diagonal length. Stafford Smith and carter (1969) proposed a theoretical relation for the

10

width of the diagonal strut linked to infill-frame stiffness parameter h . The theory of plasticity, is adopted to describe the inelastic behavior, utilizing modem algorithmic

concepts, including an implicit Euler backward return mapping scheme, a local

Newton-Raphson method and a consistent tangential stiffness matrix. The stiffness of the

structural system is determined with variations in geometrical and mechanical characteristics.

The analysis is carried out by utilizing the Boundary Element Method (BEM). In this method

the frame is divided into finite elements, so as to transform the mutual interactions of the two

subsystems into stresses distributed along the boundary for the infill and into nodal actions

for the frame.

2.3.1 Approximate Method The method presented here is developed by Smith and Coull (1985) which draws from a

combination of test observations and the results of analyses. It may be classified as an elastic

approach except for the criterion used to predict the infill crushing, for which a plastic type

of failure of the masonry infill is assumed.

Stresses in the infill Relating to shear failure:

Shear failure of the infill is related to the combination of shear and normal stresses induced at

points in the infill when the frame bears on it as the structure is subjected to the external

lateral shear. An extensive series of plane stress membrane finite-element analysis has shown

that the critical value of this combination of stresses occur at the center of the infill and that

they can be expressed empirically by,

Shear stress, 1.43xyQ

Lt = (2.1)

Vertical compressive stress, (0.8 / 0.2)xyh l Q

Lt

= (2.2)

Where Q is the horizontal shear load applied by the frame to the infill of length L, height h,

and thickness t.

11

Relating to diagonal tensile failure: Similarly, diagonal cracking of the infill is related to the maximum value

of diagonal tensile stress in the infill. This also occurs at the center of the infill and based on

the results of the analyses, may be expressed empirically as,

Diagonal tensile stress, 0.58dQ

Lt = (2.3)

These stresses are governed mainly by the proportions of the infill .They are little influenced

by the stiffness properties of the frame because they occur at the center of the infill, away

from the region of contact with the frame.

Relating to compressive failure of the corners:

Tests on model infilled frames have shown that the length of bearing of

each story-height column against its adjacent infill is governed by the flexural stiffness of the

column relative to the in plane bearing stiffness of the infill The stiffer the column, the longer

the length of hearing and the lower the compressive stresses at the interface. Tests to failure

have borne out the deduction that stiffer the column, the higher the strength of the infill

against compressive failure. They have also shown that crushing failure of the infill occurs

over a length approximately equal to the length of bearing of the column against the infill

shown in fig: 2.3

As a crude approximation, an analogy may be drawn with the theory for a beam on an elastic

foundation, from which it has been proposed that the length of column bearing a may be

estimated by,

2r

= (2.4)

Where, 44

mE tEIh

= (2.5)

in which mE is the elastic modulus of the masonry and El is the flexural rigidity of the

column. The parameter expresses the bearing stiffness of the infill relative to the flexural

12

rigidity of the column: the stiffer the column, the smaller the value of and the longer the length of bearing.

If it is assumed that when the comer of the infill crushes, the masonry bearing against the

column within the length a is at the masonry ultimate compressive stress for then the

corresponding ultimate horizontal shear 'cQ on the infill is given by-

' 'c mQ f t= (2.6)

4 4' '2c m m

EIhQ f tE t

= (2.7)

Considering now the allowable horizontal shear cQ on the infill, and assuming a value for

E/ mE of 30 in the case of a steel frame and 3 in the case of a reinforced concrete frame, the

allowable horizontal shear on a steel framed infill corresponding to a compressive failure is

given by,

345.2c mQ f Iht= (2.8)

and for a reinforced concrete framed infill

342.9c mQ f Iht= (2.9)

in which mf is the masonry allowable compressive stress.

These semi empirical formulas indicate the significant parameters that influence the

horizontal shear strength of an infill when it is governed by a compressive failure of one of

its comers. The masonry compressive strength and the wall thickness have the most direct

influence on the infill strength. While the column inertia and infill height exert control in

proportion to their fourth roots. The infill strengths indicated by Equation (2.8) and (2.9) are

very approximate. Experimental evidence has shown them to overestimate the real values;

therefore, they will be modified before being used in the design procedure.

2.3.2 Equivalent Strut Method Saneinejad and Hobbs (1995) developed a method based on the equivalent diagonal strut

approach for the analysis and design of steel and concrete frames with concrete or masonry

13

infill walls subjected to in-plane forces. The proposed analytical development assumes that

the contribution of the masonry infill panel shown in fig 2.5 to the response of the infilled

frame can be modeled by "replacing the panel by a system of two diagonal masonry

compression struts shown in fig 2.6. The stress-strain relationship for masonry in

compression shown in fig 2.7 is used to determine the strength envelope of the equivalent

strut, can be idealized by a polynomial function. Since the tensile e strength of masonry is

negligible, the individual masonry struts are considered to be ineffective in tension.

However, the combination of both diagonal struts provides a lateral load resisting mechanism

for the opposite lateral directions of loading

The lateral force-deformation relationship for the structural masonry infill panel is assumed

to be a smooth curve bounded by a bilinear strength envelope with an. initial elastic stiffness

until the yield force yV there on a post yield degraded stillness until the maximum force mV is

reached shown in fig 2.8 The corresponding lateral displacement values are as yu and mu

respectively. The analytical formulations for the strength envelope parameters were

developed on the basis of the available equivalent strut model for infilled frames.

Fig 2.5 Masonry infill frame sub assemblage in masonry infill panel frame structures.

14

Fig 2.6 Masonry infill panel in frame structures.

Fig 2.7 Constitutive model for infill panel.

Fig 2.8 Strength envelope for masonry infill panel.

15

2.3.3 Plasticity Model

The theory of plasticity, which is adopted by Lourenco et a. (1997) to describe the inelastic

behavior, utilizes modem algorithmic concepts, including an implicit Euler backward return

mapping scheme, a local Newton-Raphson and a consistent tangential stiffness matrix. The

model is capable of predicting independent responses along the material axes. It features a

tensile fracture energy and a compressive fracture energy, which are different for each

material axis.

A large number of anisotropic materials exist in engineering such, as masonry, plastics, and

wood and most composites. The framework of plasticity theory is general enough to apply to

both isotropic and anisotropic behavior. Indeed, the past decade has witnessed numerous

publications on sound numerical implementations of isotropic plasticity models.

Nevertheless, it appears that, while some anisotropic plasticity models have been proposed

from purely theoretical and experimental standpoints, only a few numerical implementations

and calculations have actually been carried out examples include the work of Borst and

Feenstra and Schellekens and de Borst who fully treated the implementation of

elastic-perfectly-plastic Hill and Hofftnan criteria, respectively. More recently, linear

tensorial hardening has been incorporated in the Hill criterion. It is not surprising that only a

few anisotropic models have been implemented and tested successfully. An accurate analysis

of anisotropic materials requires a description for all stress states. The yield criterion

combines the advantages of modem plasticity concepts with a powerful representation of

anisotropic material behavior, which includes different hardening or softening behavior along

each material axis. In order to model orthotropic material behavior, we purpose a hill-type

criterion for compression and Rankine-type criterion for tension, the internal damage due to

these failure mechanisms is represented with two internal parameters, one for damage in

tension and one for damage in compression. The fig2.9 shows the proposed composite yield

criterion with iso-shear lines.

16

Fig 2.9 Proposed composite yield criterion with iso-shear stress lines

2.3.4 Coupled Boundary Element Method

The behavior of infilled frames subjected to horizontal loads is analyzed by an iterative

numerical procedure by Papia (1998). The stiffness contribution by brickwork or concrete

panels in reinforced concrete. or steel frames can prove to be decisive in relation to structure

safety. Neglecting the presence of such systems in the calculation of structures subjected to

horizontal loads leads to an evaluation of stresses in the frames which is often far from the

real situation and may compromise safety. In fact, on account of the high degree of stiffness,

panels not placed symmetrically in the plan produce very dangerous in foreseen torsional

effects.

The analysis is carried out utilizing the boundary element method (BEM) for the infill and

opportunely dividing the frame into finite elements, so as to transform the mutual interactions

of the two subsystems into stresses distributed along the boundary for the infill and into

nodal actions for the frame. This makes it possible to take into account the separation arising

between the two substructures when mutual tensile stresses are involved.

At first, infill without openings are considered, using BEM with constant elements for

two-dimensional problems in elasticity. Then the results are compared with those obtained

17

using the simplified equivalent pin-jointed strut model, which is very common in the

literature.

Subsequently, using an analogous procedure panels with openings or doors and windows are

considered, which cause a loss of stiffness. The behavior of brickwork or concrete panels in

infilled frames subjected to horizontal actions has been analyzed by several researchers,

mostly experimentally working in the following main fields:

1. Evaluation of stiffness and analysis of modes of failure,

2. Dissipation capacity of the structural system under monotonic and cyclic loads.

2.3.5 Choice of the Model

In the previous articles several computational models are described which can be used to

model and analyze infills. Of the models first one is described in section 2.3.1 is an

approximate method primarily intended for preliminary design purpose through manual

calculation. The last two models are based on continuum plasticity approach in which infill is

modeled as an assemblage of several plane stress elements interacting with frame elements

via special interface element. The material, properties for the plane stress elements are

plasticity or damage model approach. Such modeling is suitable for a detailed and micro

level study of the infill panels where stress, strain, damage, cracks and failure etc at various

locations of the infill are of primary importance. Such model requires a considerable amount

of computational effort due to their highly nonlinear iterative solution procedure. Such

modeling is not suitable for investigating overall structural behavior of Building where infill

is only a structural component. In such a situation the equivalent strut model proposed by

SaneineJad and Hobbs (1995) is a relatively recent model capable of representing the

behavior of infill satisfactorily. The model is based on an equivalent diagonal strut and uses a

time-rate dependent constitutive model which can be used for a static nonlinear analysis as

well as time-history analysis. The Same model will hysteretic formulation has been

successfully used by Manders et al.(1997) for static monotonic analysis, qusi-static cyclic

analysis. They have successfully verified the model by simulating experimental behavior of

tested masonry infill frame subassemblage. The equivalent diagonal strut model considers

18

entire infill panel as a single unit and takes in to account only the equivalent global behavior.

As a result the approach does not permit study of local effects such as frame-in fill

interaction within the individual infilled frame subassemblage. More detailed micro

modeling approaches such as tile plasticity approach and the boundary element approach

discussed earlier need to be used to capture the spatial and temporal variations of local

conditions within tile infill. However the equivalent strut model allows for adequate

evaluation of the nonlinear force deformation response of the Structure and individual

components under lateral load. The computed force-deformation response may be used to

asses the overall structure damage and its distribution to a sufficient degree of accuracy.

Thus, the proposed macro model is better suited for representing the behavior of infills in

nonlinear time-history analysis of large or complex structures with multiple components

particularly in cases where the focus is on evaluating the inelastic structural response. In

thesis, the equivalent strut modeling, therefore, is chosen for modeling and studying the

behavior of plane frames

2.4 EQUIVALENT STRUT MODELLING.

Considering the infilled masonry frame shown in fig. 2.5 the maximum lateral force mV and corresponding displacement mu in the infill masonry panel proposed by Saneinejad (1995) are

' 0.83 '( ) 'cos(1 0.45 tan )cos cosm m d m

vtl tlV V A f

+

(2.10)

'( )cos

m dm m

Lu u

+ = (2.11)

Here,

t = thickness of the infill panel;

l= lateral dimension of the infill panel

mf = masonry compressive strength;

'm = masonry compressive strain;

=inclination of the diagonal strut; v= basic shear strength of masonry;

19

dA =area of equivalent diagonal strut

dL =length of equivalent diagonal strut

SaneineJad and Hobbs (1995) proposed that area and length of equivalent diagonal strut can

be calculated by the following formula:

(1 ) '

0.5cos cos

c b ac c b

c c cd

fth tl thf f fA

+

= (2.12)

2 2 2(1 ) ' 'd cL h l= + (2.13)

Where, the quantities c , b , c , b , af and cf depending on the geometric and material

properties of the frame and infill panel, can be estimated using formulations of the

"equivalent strut model" proposed by Saneinejad and Hobbs (1995). The monotonic lateral

force-displacement curve is completely defined by the maximum force mV corresponding

displacement mu , the initial stiffness Ko and the ratio a of the post yield to initial stiffness.

The initial stiffness Ko of the infill panel may he estimated using the following proposed

formula,

02 m

m

VKu

= (2.14)

2.5 BEAM AND COLUMN MOMENT CAPACITY

To find out the stiffness of equivalent strut (Ko) it requires to determine the following

properties of beam and column, therefore,

pcM = Plastic resisting moment of column

pbM = Plastic resisting moment of beam

pjM = Plastic resisting moment of beam and column joint

pjM is the minimum value of pbM and pcM . To determine the value of pbM and pcM it

requires to provide reinforcement in beam and column. We provide 3 percent reinforcement

20

for column and 2 percent reinforcement for beam in this analysis. As the column size for Six-

storey frame is 375 mm X 375 mm, so it requires 1800 mm2 .The size of beam is 250 mm X

300 mm, so it requires 3000 mm2.

2.6 DETERMINATION OF EQUIVALENT STRUT STIFFNESS Ko

The equivalent strut model proposed by Saneinejad (1995) and later modified by Madan et

al. (1997) is discussed in details here.The mathematical derivation of the equivalent strut

model begins with an idealized free body diagram of an Infill panel and the surrounding

frame as shown in Fig 2.10

Fig 2.10 Frame forces equilibrium

From fig 2.5 and fig 2.10,

/ 1r h l= < (2.15)

Where,

r = aspect ratio of the frame

21

h = center to center height of beam

l = center to center length of beam

' '/ 'r h l= (2.16)

Where,

h= height of infill

l = length of infill

1tan hl

= (2.17)

1 '' tan'

hl

= (2.18)

Where,

= inclination of the diagonal strut.

The effective compressive strength of infill, cf can be calculated by ,

0.6 'c mf f= (2.19)

Where,

is a constant value and its value is 0.65

'mf = compressive strength of masonry

The nominal values of the contact normal stresses in the rectangular stress blocks shown in

fig.2.12 can be written in terms of co and bo .

The contact normal stresses in column can be determined by the following formula ,

2 41 3

cco

fr

=

+ (2.20)

Where, cf = effective compressive strength of infill.

= coefficient of friction of the frame or infill interface. r = aspect ratio of the frame.

22

The contact normal stresses in beam bo can be determined by,

21 3c

bof

=

+ (2.21)

The length of proposed rectangular stress block fig. 2.12 may not exceed 0.4 times the

corresponding infill dimensions, i.e.

0.4 'ch h and 0.4 'bl l (2.22)

where,

= normalized length of contract and subscripts c and h designate column and beam

respectively.

The normalized length of contract for column c can be determined by the following

formula,

(2.23)

The normalized length of contract for beam b can be determined by the following ,

2 2pj pbb

bo

M Ml

t

+= (2.24)

Where,

pjM = the beam, the column, and their connection plastic resisting moment or joint plastic

resisting moment.

pcM = plastic resisting moment for column.

pbM = plastic resisting moment for beam.

o = nominal or rather upper-bound value of the reduction factor, = 0.2

2 2pj pcc

co

M Mh

t

+=

23

t= thickness of the masonry infill.

co = the contact normal stress in column

bo = the contact normal stress in beam.

The failure of infill in the loaded corners do not necessarily occur at the beam and column

interfaces simultaneously. It depends upon the contact normal stress area in beam and

-column. The contact normal stress area in beam and column can be determined by the

following formula,

2 (1 )c co c cA r r = (2.25)

(1 )b bo b bA r = (2.26)

where,

cA = The contact normal stress area in column

bA = The contact normal stress area in beam

r = aspect ratio of the frame

The real normal contact stress generated from the nominal contact stresses following the

condition given below:

If c bA A>

cc cob

AA

= and b = bo (2.27)

If c bA A<

cb bob

AA

= and c = co (2.28)

24

Where,

c = the real normal contact stress in column

b = the real normal contact stress in beam.

The nominal contact shear stresses in beam and column can be calculated as follows:

2c cr = and b b = (2.29)

Where,

c = nominal contact shear stresses in column

b = nominal contact shear stresses in beam

The effective length of equivalent diagonal strut, dL can be determined as follows,

2 2 2(1 ) ' 'd cL h l= + (2.30)

The actual compressive strength of masonry depends on the direction of stresses and it can be

calculated as follows: 2

140

da c

Lf ft

=

(2.31)

Where,

dL = not greater than 40t and cf is the effective compressive strength of infill.

The cross-section area of the diagonal strut for the effective compressive strength of infill, cf

are as follows,

(1 ) '0.5

cos cos

c b ac c b

c c cd

fth tl thf f fA

+

= (2.32)

The maximum lateral force mV and corresponding maximum lateral force mu in the infill

masonry panel are as follows,

' 0.83 '( ) 'cos(1 0.45 tan )cos cosm m d m

vtl tlV V A f

+

(2.33)

25

'( )cos

m dm m

Lu u

+ = (2.34)

The initial stiffness Ko of the infill panel may he estimated using the following proposed

formula:

02 m

m

VKu

= (2.35)

Example of determining Ko (6-storey):

Equations 2.15 to 2.35 are used to determine Ko

h = 3000 mm , l = 4500 mm , h = 3000-600 =2400 mm, l = 4500-600=3900 mm ,

= 0.65 , 'mf = 12 MPa , = 0.6 , o = 0.2 , m = 0.002 , v = 6 MPa

Table 2.1 Calculation of determining stiffness (Ko)

T h h l L 150 mm 3000 mm 2400 mm 4500 mm 3900 mm 0.65

250 mm 3000 mm 2400 mm 4500 mm 3900 mm 0.65

T 'mf o pjM pcM pbM 150 mm 0.65 12 MPa 0.2 2.42E7 N-mm 3.37E8 N-mm 2.42E7N-mm

250 mm 0.65 12MPa 0.2 2.42E7 N-mm 3.37E8 N-mm 2.42E7N-mm

26

T r R ' cf co

150 mm 0.667 0.6154 0.588 0.5517 4.68 MPa 4.2487 N/mm

250 mm 0.667 0.6154 0.588 0.5517 4.68 MPa 4.2487 N/mm

T co c b cA bA c

150 mm 3.245 MPa 0.1787 0.076 0.1422 0.13 3.67

250 mm 3.245 MPa 0.1787 0.076 0.1422 0.13 3.67

T b b c dL af dA

150 mm 3.245MPa 1.947MPa 1.04

Mpa

4369.84 mm 2.1976 MPa 75303.7mm2

250 mm 3.245MPa 1.947MPa 1.04

MPa

4369.84 mm 2.1976 MPa 75303.7mm2

t mu mV oK

150 mm 10.504 mm 583558.5 N 111114 N/mm

250 mm 10.610 mm 963291.2 N 181571 N/ mm

27

CHAPTER 3

FINITE ELEMENT MODELING

3.1 INTRODUCTION

The computational modeling of infilled frames has been described briefly in this chapter. The

finite clement modeling of infilled frames including plan and location of infill of the

proposed building, modeling of beams, columns and slabs, modeling of infill, consideration

of different types of dead, live loads as well as lateral load (earthquake) according to BNBC,

developing of finite element mesh with or without infill has also been described in this

chapter. Selection of element type of modeling frames including beam, column, slab and

linear spring also described. The linear spring element is used to represent the diagonal strut

of infill.

3.2 THE FINITE ELEMENT PACKAGES

A number of good finite element analysis computer packages are available in the civil

engineering field. They vary in degree of complexity, usability and versatility. The names of

such packages are

a) Micro Feap b) ABAQUA c) STAAD d) SAP 90 e) MARC

f) FEMSKI g) ADINA h) ANSYS i) DIANA j) STRAND

Some of these programs are intended for a special type of structure. For example Micro Feap

PI is developed for the analysis of plane frames and truss while Micro Feap P2 is for the

analysis of slab and roof system. Of these, here the package ANSYS has been for its relative

ease of use, detailed documentation, flexibility and vastness of its capabilities. The version of

ANSYS has been used was the special Student's Edition Version ANSYS 5.6

ANSYS is one of the most powerful and versatile packages available for finite element

structural analysis. The term structural implies not only civil engineering structures such as

bridges and buildings, but also naval, aeronautical and mechanical structures such as ship

28

hulls, aircraft bodies, and machine housings as well as mechanical components such as

pistons, machine parts and tools. The seven types of structural analysis available in the

ANSYS family of products

1) Static analysis

2) Modal analysis

3) Harmonic analysis

4) Transient dynamic analysis

5) Spectrum analysis

6) Buckling analysis

7) Explicit dynamic analysis

The primary unknowns (nodal degrees of freedom) calculated in a structural analysis are

displacements. Other quantities such as strains, stresses, and reaction forces, are then derived

from the nodal displacements. Especially its graphical representations are very distinct.

Finally the ANSYS program is user friendly. It has a comprehensive graphical user interface

(GUI) that gives user easy, interactive access to program functions, commands,

documentations and reference material. An intuitive menu system helps user to navigate

through the ANSYS program. User can input data using a mouse, a keyboard or a

combination of both.

Moreover, the assumptions and restrictions in ANSYS are enumerated below:

1. Valid for structural and fluid degrees of freedom

2. The structure has constant stiffness and mass effects

3. There is no damping unless the damped eigensolver is selected

4. The structure has no time varying forces, displacements, pressures, or temperature

applied (that is , free vibration)

3.3 FINITE ELEMENT MODELING OF INFILLED FRAMES

Reinforced concrete frame is a composite type of structure. Reinforced cement concrete,

speaking in very common sense, is a mass of hardened concrete with steel reinforcement

29

embedded within it. In usual practice reinforced cement concrete frames is assumed as a

homogeneous and isotropic material. For simplicity in analysis 3-13 elastic beam of ANSYS

has been selected to model the RC frame. Tile concrete properties are used for 3-13 elastic

beam. Several past studies on RC frames and ACI recommend that if only concrete

properties are used for 3-D elastic beam element, the analysis will give sufficiently accurate

result.

Infill is provided in RC frame for increasing stability and reducing displacement against

lateral load. The infill acts as a diagonal strut against load according to equivalent strut

method. This method is described in Art. 2.3.2. Since the tensile strength of masonry is

negligible, so only compressive diagonal strut is liable to resist the lateral load. In this

analysis we select nonlinear spring element to represent the equivalent diagonal strut. The

values u versus V of nonlinear u-V curve is used as real constants.

3.3.1 Modeling of Beams and Columns

The beams and columns of the frame were represented by the same element Beam4 3-D

elastic beam. It is basically a two nodded frame element having three displacements and

three rotational degrees of freedom at each node. All the beams and columns elements of the

frame are modeled by the base element Beam4 3-13 elastic beam owing to simplicity. All

beams and columns element are rectangular in shape. Here the base elements of ANSYS

package are discussed in details.

Beam4 3-D elastic beam

Beam4 is a uniaxial element with tension, compression, torsion and bending capabilities. The

element has six degrees of freedom at each node, translation in the nodal x, y and z directions

and rotations about the nodal x, y and z axes. Fig 3.1 shows a typical shape of beam4 3-D

elastic beam.

30

Input data

The geometry, node locations, and co-ordinate systems for this element are shown in fig 3.1.

The element is defined by two or three nodes, the cross sectional area, two area moment of

inertia ( zzI and yyI ), two thickness ( yTK and zTK ) and the material properties.

A summary of the element input is given below in table 3.5.1

Table 3.1 Beam4 Input Summary

Element name BEAM4

Nodes 1, J, K ( K orientation node is optional)

Degrees of Freedom Ux, Uy, Uz, ROTx, ROTy and ROTz

Real Constants AREA, Izz,Iyy,Tky, TKz

Material Properties Ex, Density and Poisson's Ratio

Fig 3.1: BEAM4 3-D Elastic Beam

31

Output data: The solution output associated with the element is in two forms:

1) nodal displacements included in the overall nodal solutions

2) the element solutions

By plotting result from general postprocessor we can see the deformed shape of nodes and

elements. From list result of general post processor we can get nodal translation in the X, Y

and Z directions and rotation about X, Y and Z directions. As our applied force lateral in X

direction, so the displacement of node in Z and rotation in the X and Y axis are zero. From

the list result element solutions we can get moments, force in X, Y and Z directions for

various elements. The main purpose of this analysis is to calculate translations of nodes in the

X direction for lateral load.

Assumptions and restrictions

The beam must not have a zero length or area. The moments of inertia, however, may be zero

if large deflections are not used. But in this analysis the moment of inertia is not zero. The

beam can have any cross sectional shape for which the moments of inertia can be computed.

3.3.2 Modeling of slab

SHELL63 Elastic shell

SHELL 63 has bending and membrane capabilities both in-plane and normal loads are

permitted. The element has six degrees of freedom at each node, translations in the nodal X,

Y and Z directions and rotations about the nodal x, y and z axes. Stress stiffening and large

deflection capabilities are included a consistent tangent matrix option is available for use in

large deflection (finite rotation) analyses.

32

Fig 3.2: A typical SHELL63 Elastic Shell

Input Data

The thickness of the four comer nodes is given in the input data

Table 3.2 SHELL 63 Input Summary

Element Name

SHELL63

Nodes 1, J, K J-

Degrees of Freedom

Ux, Uy, Uz, ROTx, ROTy and ROTz

Real Constants

TK(l), TK(J), TK(K), TK(L),EFS etc

Material Properties

EX,EY,DENS etc

33

Output Data

The solution output associated with the element is in two forms:

1) Nodal displacements included in the overall nodal solution.

2) Additional element output solution.

The moment about X face (MX), the moment about Y face (MY) and twisting moments

(MXY).the moments are calculated per unit length in the element coordinate system. The

element stress directions are parallel to the element co-ordinate system.

Assumptions and restriction

The Assumptions and restrictions are -

I) zero area elements are not allowed this occurs most often whenever the elements are

not-numbered properly.

2) Zero thickness elements or elements tapering down to a zero thickness at any comer are

not allowed.

3) The applied transverse thermal gradient is assumed to vary linearly through the thickness

and vary billinearly over the shell surface.

4) An assemblage of flat shell elements can produce a good approximation to a curved shell

surface provided that each flat element does not extend over more than a 15 degree arc.

5) If elastic foundation stiffness is input, one-fourth of the total is applied at each node.

6) Shear deflection is not included in this thin-shell element.

3.3.3 Modeling of infill

One of the most remarkable features of our FE (Finite Element) modeling is modeling the

infill. ANSYS element COMBIN 14 is used to model the infill as diagonal strut. It is

basically a pin ended truss element with linear capabilities. We will first describe the element

that is used to simulate the infill characteristics in the finite element model.

34

COMBIN14 linear spring

COMBIN 14 is a two node element and has longitudinal or torsional capability in one, two,

or three dimensional applications. The longitudinal spring damper option is a uniaxial

tension-compression element with up to three degrees of freedom at each node: translations

in the nodal X, Y and Z directions. No bending or torsion is considered. The torsional spring

damper option is a purely rotational element with three degrees of freedom at each node:

rotations about the nodal x, y and z axes. No bending or axial loads are considered. The

element has no mass and it does not need any material properties, it needs only real constants

stiffness ( oK ).

Fig 3.3 shows a typical COMBIN 14 linear spring-damper.

Fig 3.3: COMBIN14 Spring-Damper

Input Data

The geometry, node locations and the co-ordinate system for this element shown in above fig

3.2. The element is defined by two nodes, a spring constant ( oK ). The longitudinal spring

constant should have units of Force/Length.

35

Table 3.3 COMBIN14 Input Summary

Element Name COMBIN14

Nodes 1, J, K ( K orientation node is optional)

Degrees of Freedom Ux, Uy, Uz, ROTx,ROTy and ROTz

Real Constants (Ko)

Material Properties None

Figure 3.4 COMBIN14 Stress Output

Output Data

The solution output associated with the element is in two forms:

1) Nodal displacements included in the overall nodal solution.

2) Additional element output solution.

We can get nodal translation and rotation in X, Y and Z direction similarly moment in X, Y

and Z direction from list result of the general postprocessor. The only nodal translation in X

direction together with axial and moments is required for the analysis. Infill greatly reduces

36

the translation in the X direction for lateral load as well as show difference in steel

requirements in columns.

Assumptions and restriction

The longitudinal spring element stiffness acts only along its length. The element allows only

a uniform stress in the spring. The spring stiffness capability may be deleted from the

element by setting Ko equal to zero. 2-D longitudinal spring damper must lie in an X-Y

plane. The element is defined such that a positive displacement of node J relative to node I

tend to stretch the spring. If for a given set of conditions, nodes I and J are interchanged, a

positive displacement of node J relative to node I tends to compress the spring.

3.4 Description of the Model under study In this thesis we are studying 3D framed structure with or without infill of a four by four bay

six storied building. Selection of plan and beam column layout is described in article 3.23

and the location of infill in article 3.3. The plan and beam column layout is presented in fig

3.1 and fig 3.2.

The different types of load used in the design of column are described in article 3.6. All

considered loads such as dead loads, live loads, earthquake loads is calculated according to

BNBC (1993).

Therefore frame elements are used in modeling the framed structure and equivalent strut is

used for modeling of infill. These are described in article 3.5

The model is generated in ANSYS through script .The analysis is also done in that manner

using script. A representative sample of script is provided in Appendix. A representative

model is shown-in fig 3.7 and 3.8

Five combinations of load are used in the analysis. Basically there are three type of loads

those are applied in the building. The basic loads are

a) Dead load (DL)

b) Live load (LL)

c) Earthquake load ( EQ)

37

The above mentioned loads are combined in five ways to attain the most severe load

condition for the building. The analysis was done in two distinct parts. Those are

a) Building structure without Infill.

b) Building structure with Infill as 20%, 40%, 60%, and 80% of building.

The combinations of loads are the following- A) Dead load &Live load only 1) Load case_7 (that is used in modeling) = 1.4DL +1.7LL B) Earthquake Load along X-X direction 2) Load case_8 = 1.05 DL +1.27 LL+1.4 EQ (LR) 3) Load case_9 = 1.05 DL +1.27 LL+1.4 EQ (RL) C) Earthquake Load along Z-Z direction 2) Load case_10 = 1.05 DL +1.27 LL+1.4 EQ (LR) 3) Load case_11 = 1.05 DL +1.27 LL+1.4 EQ (RL) 3.5 EARTHQUAKE LOAD CALCULATION

Calculation is shown for Six-Storey building with four by four bay (x-direction bay length =

15feet and z-direction bay length = 20 feet)

Plan area of building is = 60 feet X 80 feet

Column size= 15 X 15 (375 mm X 375 mm)

Beam size= 10 X 12 (250 mm X 300 mm)

The total seismic load, W

Let, unit weight of concrete= 24 KN/m3 (150 pcf)

And unit weight of brick = 19 KN/m3

Slab thickness= 150 mm = 0.150 m (6 inch)

38

Brick wall thickness = 125 mm (5 inch)

Floor finish = 0.96 KN/ m2 (20 psf)

Slab dead load = 0.150*24= 3.6 KN/ m2 (75 psf)

Column and beam weight per floor = 730 KN per floor

Load for Infill = 2.87 KN/m2 (assume 60 psf)

Now, the total seismic dead load,W = [6*{(0.96+3.6+2.87)*18.3*24.4 +730 }

= 20636 KN

Design base shear, V

Seismic Zone coefficient (given in table 6.2.2.2), Z = 0.15

Structure importance coefficient (given in table 6.2.2.3), I = 1.0

Response modification coefficient for structural system (given in table 6.2.2.4) , R = 8

Fundamental period of vibration of the structure for the direction under consideration

(as determined by the provisions of sec.2.5.6.2) , T = = 0.073 *(19.83)3/4 = 0.686 sec

Numerical coefficient given by the relation, C = 2/ 31.25ST

= 2/31.25*1.5(0.686)

=2.41 < 2.75

C/R = 2.41/8 = 0.3 > 0.075 OK

The design base shear, V = ZICR

W = 0.15*1*2.418

x 20636 = 0.045 *20636 KN

=933 KN

Vertical distribution of lateral forces

The concentrated force, Ft = 0 ( T < 0.7 sec)

For the remaining portion, xF =

1

( )t x xn

i ii

V F w h

w h=

= (933 0)*

74.73xh =12.5 * xh KN ( xh in m)

=71.46* xh lb ( xh in inch)

39

xh (m) xF (KN)

19.825 247.81

16.775 209.69

13.725 171.56

10.675 133.44

7.625 95.31

4.575 57.09

1.53 19.13

3.6 LOCATION OF INFILL AND FINITE ELEMENT MODELING

The infill is the masonry wall in between beam and column without having any openings like

windows and doors. For the modeling of infill we consider 20%, 40%, 60% and 80% of

panel in building except ground floor. In six-storied four by four span building has 200 nos.

of panels without considering ground floor because ground floor is generally used for

parking facilities. The no. of panels infilled for 20%, 40%, 60% and 80% are 40 nos. , 80

nos. , 120 nos. and160 nos. respectively. Infills are provided uniformly throughout the height

of building. The locations of infills for various percentages are shown below with plan and

after 3D modeling:

40

Fig. 3.5 Three dimensional modeling of six storied building without infill

41

Fig. 3.6 Beam-Column layout with 20% infill

Fig. 3.7 3D modeling of six storied building with 20% infill (without showing slab

element)

42

Fig. 3.8 Beam-Column layout with 40% infill

Fig. 3.9 3D modeling of six storied building with 40% infill (without showing slab

element)

43

Fig. 3.10 Beam-Column layout with 60% infill

Fig. 3.11 3D modeling of six storied building with 60% infill (without showing slab element)

44

Fig. 3.12 Beam-column layout with 80% infill

Fig. 3.13 3D modeling of six storied building with 80% infill (without showing slab element)

45

CHAPTER 4

RESULTS AND DISCUSSION

4.1 INTRODUCTION

The essential theory of infill and finite element modeling of infill, beam and column in a six-

storied four by four bay building has been described in the previous chapters. In this chapter

an investigation has been performed based on those two chapters for designing the different

column at base level of a building that was modeled and analyzed by ANSYS 5.6. This

chapter describes the difference in steel requirements in a typical corner, edge and center

column considering infill and without infill.

4.2 OUTPUT RESULTS

After analyzing the axial force, moments has found for selected column such as one corner

column (A), one edge column (B) and one center column(C) for five load combinations and

for different percentage of infill. And corresponding steel ratio is calculated for each column

and for each load combinations. The summary of the above results are given below in tabular

form.

4.3 DICUSSIONS

4.3.1 For corner column (A)

After investigation the reinforcement required for infilled corner column is 1.07% and the

reinforcement needed for corner column without infill is 1.07%. So we can say that the effect

of infill for design of corner column is not significant.

4.3.2 For edge column (B)

In this case, the required steel ratio for edge column without infill is 1.07%. With 20% and

40% infill the required reinforcement is 1.6% and with 60% and 80% infill the required

reinforcement is same as for without infill. So we can conclude that when lateral load comes

46

Fig. Beam-Column layout without infill and location of selected column

from the other side of selected edge column, the design loads increases with increasing the

percentage of infill up to 40%. For more percentage of infill, lateral loads are distributed

throughout the infill and the design loads are almost same as design loads for without infill.

This variation may depend on the distribution of infill in building.

47

RESULTS FOR CORNER COLUMN A

Load case FY(lbs) MX(lb-in) MZ(lb-in) Steel Ratio 20% Infill: 1.4 DL+1.7 LL 1.63E+05 23362 -10067 1 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 1.19E+05 17275 7.84E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 1.72E+05 21480 -7.89E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 1.29E+05 -8.58E+05 -7131.5 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 1.63E+05 8.84E+05 -8721.7 1.07 40% Infill: 1.4 DL+1.7 LL 1.62E+05 22164 -8799.9 1 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 1.23E+05 16165 7.76E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 1.67E+05 20370 -7.78E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 1.32E+05 -8.45E+05 -6100.5 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 1.59E+05 8.68E+05 -7403.6 1.07 60% Infill 1.4 DL+1.7 LL 1.63E+05 22006 -8539.1 1 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 1.27E+05 15797 7.70E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 1.65E+05 20457 -7.72E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 1.34E+05 -8.36E+05 -5554.2 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 1.58E+05 8.59E+05 -7478.1 1.07 80% Infill: 1.4 DL+1.7 LL 1.79E+05 21838 -8120.5 1 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 1.21E+05 16720 7.69E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 2.02E+05 19235 -7.70E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 1.30E+05 -8.32E+05 -5810.4 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 1.93E+05 8.54E+05 -6446.6 1.07 Without Infill 1.4 DL+1.7 LL 1.64E+05 25322 -12008 1 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 1.12E+05 20075 8.01E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 1.83E+05 22304 -8.09E+05 1.07 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 1.22E+05 -8.88E+05 -9385.2 1.07 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 1.73E+05 9.17E+05 -10056 1.07

48

RESULTS FOR EDGE COLUMN B

Load case FY(lbs) MX(lb-in) MZ(lb-in) Steel Ratio

20% Infill: 1.4 DL+1.7 LL 3.30E+05 -2359.6 -14277 11.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 2.23E+05 -2201.1 8.28E+05 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 3.79E+05 -2165.2 -8.41E+05 1.61.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 3.01E+05 -9.30E+05 -11892 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 3.01E+05 9.26E+05 -11930 1.07 40% Infill: 1.4 DL+1.7 LL 3.28E+05 -3682.3 -12547 11.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 2.37E+05 -3447.3 8.16E+05 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 3.61E+05 -3370.1 -8.26E+05 1.61.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 3.00E+05 -9.15E+05 -10210 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 2.99E+05 9.08E+05 -10404 1.07 60% Infill 1.4 DL+1.7 LL 3.28E+05 -4060.1 -11831 11.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 2.47E+05 -3814.4 8.09E+05 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 3.51E+05 -3694 -8.17E+05 1.071.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 3.00E+05 -9.06E+05 -9559.9 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 2.98E+05 8.98E+05 -9736.3 1.07 80% Infill: 1.4 DL+1.7 LL 3.27E+05 -3944.9 -11864 11.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 2.53E+05 -3686.8 8.01E+05 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 3.44E+05 -3597.1 -8.09E+05 1.071.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 2.99E+05 -9.03E+05 -9625.9 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 2.98E+05 8.95E+05 -9761.3 1.07 Without Infill 1.4 DL+1.7 LL 3.09E+05 -6.47E-10 -16707 11.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 2.37E+05 2.99E-06 -6.02E-08 11.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 3.26E+05 -2.99E-06 -8.60E+05 1.071.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 2.82E+05 -9.63E+05 -14167 1.071.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 2.82E+05 9.63E+05 -14167 1.07

49

RESULTS FOR CENTER COLUMN C

Load case FY(lbs) MX(lb-in) MZ(lb-in) Steel Ratio 20% Infill: 1.4 DL+1.7 LL 5.76E+05 -2518.5 1847 3.52 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 5.31E+05 -2349.7 9.06E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 5.34E+05 -2310.6 -9.03E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 5.31E+05 -9.79E+05 1722.4 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 5.35E+05 9.74E+05 1693.1 3.73 40% Infill: 1.4 DL+1.7 LL 5.77E+05 -4288.2 3741.1 3.53 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 5.33E+05 -4042.9 8.94E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 5.33E+05 -3896.8 -8.87E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 5.33E+05 -9.59E+05 3520.8 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 5.33E+05 9.51E+05 3406.8 3.73 60% Infill 1.4 DL+1.7 LL 5.75E+05 -4787.3 4415.1 3.5 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 5.31E+05 -4502.5 8.85E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 5.31E+05 -4350.1 -8.77E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 5.31E+05 -9.46E+05 4142.7 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 5.31E+05 9.38E+05 4021.4 3.73 80% Infill: 1.4 DL+1.7 LL 5.75E+05 -4667.5 4395 3.5 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 5.31E+05 -4364.1 8.76E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 5.31E+05 -4233.4 -8.68E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 5.31E+05 -9.36E+05 4099.6 3.73 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 5.31E+05 9.27E+05 3995.9 3.73 Without Infill 1.4 DL+1.7 LL 5.82E+05 -7.88E-10 8.30E-11 3.6 1.05 DL+1.27 LL+1.4 EQ(L-->R) along X--X 5.38E+05 3.90E-06 -5.44E-08 2.99 1.05 DL+1.27 LL+1.4 EQ(R-->L) along X--X 5.38E+05 -3.90E-06 -9.22E+05 3.73 1.05 DL+1.27 LL+1.4 EQ(L-->R) along Z--Z 5.38E+05 -1.01E+06 -4.19E-06 4.27 1.05 DL+1.27 LL+1.4 EQ(R-->L) along Z--Z 5.38E+05 1.01E+06 4.19E-06 4.27

50

4.3.3 For center column (C)

The reinforcement required for infilled center column is 3.73% and for without infill is

4.23%. So we can say that the effect of infill for design of center column varies significantly.

51

CHAPTER 5

CONCLUTIONS AND RECOMMENDATION

5.1 CONCLUTIONS

The structural effect of brick infill is generally not considered in the analysis of frame

structure. The brick walls have significant in-plane stiffness contributing to the stiffness of

the frame against lateral load. It can be understood that if the effect of infill is taken into

account in the analysis of frame the resulting structures may be significantly different. So, the

effect of infill for the design of some representative column for a particular building has been

studied.

For analyzing and 3D modeling of four by four bay six-storied building with infill and

without infill ANSYS 5.6 finite element based software has been used. After analyzing,

design loads have been found for different load combinations and for different percentage of

infill such as 20%, 40%, 60% and 80%. From the design loads we have found corresponding

steel ratio of column for design loads. Then we have compared between the effects of with

infill and without infill. Based on the investigation in previous chapters, the following

conclusions are drawn regarding effect of infill in 3D frame structures:

For corner column, we have seen that the reinforcement required with infill is same

as reinforcement needed without infill. Therefore effect of infill for corner column

is not significant.

For edge column, steel ratio required for edge column without infill varies from

reinforcement required for with infill up to 40% infill. But for more than 40% infill

steel ratio does not vary with reinforcement required for without infill.

For center column, we have found that the reinforcement required for infilled

center column significantly varies from reinforcement needed for center column

without infill.

52

5.2 RECOMMENDATION

The analysis and design has been performed for four by four bay six storied building. But in

the context of Bangladesh multistoried building varies six to fourteen. However, much

research is needed in future to facilitate the design of column of high rise building

considering infill. The following recommendations are for future study:

We have modeled infill in building uniformly throughout the height, but infill

may be modeled randomly.

We have considered a building with regular in span and floor. Since ANSYS

scripts are made for parametric study, so one can investigate the effect of infill for

any storied building and any no. of span, span length.

To investigate the effect of infill in design of other structural components of a

building.

The analysis and design may be performed by other methods of calculation of

diagonal stiffness of infill such as approximate method, plasticity model method

and coupled boundary element method.

In this thesis frame structure is considered regular in shape. Any other structure or

frame structure of irregular shape may be studied.

REFERENCES

1. "ANSYS Elements Reference", 000853, 1997, Ninth Edition, SAS IP, inc.

2. "Bangladesh National Building Code (BNBC) ", 1993, 6.27-6.47

3. Hossam, M., "Non-Linear Finite Element Analysis of Wall-Beam Structures", PhD

Thesis, Bangladesh University of Engineering and Technology (BUET), Department of

Civil Engineering, May 1997.

4. Lourenco, P. B., Brost, R. D. and Rots, J. G. "A Plane Stress Softening Plasticity

Model For Orthotropic Materials", International Journal For Numerical Methods In

Engineering, Vol 40, 40334057 (1997).

5. Madan, A., Reinhorn, A. M., Fellow, ASCE, Mander, J. B., Member, ASCE, and

Valles, R. E. "Modeling of Masonry Infill Panels For Structural Analysis", American Soc.

Qj_ Ov. Eng. (ASCE), Journal qf Structural Engineering, Vol. 123, No. 10, October

1997, 1295-1297.

6. Papia, M. "Analysis of Infilled Frames using a Coupled Finite Element And Boundary

Element Solution Scheme", International Journal For Numerical Methods In

Engineering, Vol. 26, 731-742 (1998).

7. Saneinejad, A. and Hobbs, B. "Inelastic Design of Infilled Frames", American Soc. of

Civ. Eng. (ASCE), Journal of Structural Engineering, Vol. 12 1, No. 4. April 1995. 634-

643.

8. Smith, B. S. and Coull, A. "Infilled-Frame Structures", "Tall Building Structures

Analysis And Design", John Wiley& Sons, inc. 168-174.

9. Winter, G. and Nilson, A. H. (1987), "Design of Concrete Structures", McGraw Hill,

10th Edition.

APPENDIX I

TYPICAL ANSYS SCRIFT

! ANSYS 5.6 SCRIPT FILE!

finish

/clear

/prep7

!*************************** PARAMETERS STUDY **********************!

LX=180 ! Length of bay in X-direction (inch), LX

LZ=240 ! Length of bay in Z-direction (inch), LZ

H=120 ! Height of storey (inch), H

NBX=4 ! No of bay in X-direction, NBX (NBX must be greater or equal to one)

NBZ=4 ! No of bay in Z-direction, NBZ (NBZ must be greater or equal to one)

NF=6 ! No of storey, NF (NF must be greater or equal to one)

NDC=1 ! No. of division in column

NDB=4 ! No. of division in beam and slab

!************************** ELEMENT TYPE! ****************************!

ET, 1, BEAM4

ET, 2, SHELL63

ET, 3, COMBIN14

!*************************REAL CONSTANTS ***************************!

R, 1, 120, 1440, 1000, 10, 12 , ! Real constants for Beam!

R, 2, 225, 4218.75, 4218.75,15, 15 ! Real constants for Column!

R, 3, 6, 6, 6, 6, ! Real constants for slab!

R, 4, 130610, !Real constants for infills!

!***************** *********MATERIAL PROPERTIES *********************!

UIMP, 1, EX,,, 3600000,

UIMP, 1, NUXY,,, 0.2,

UIMP, 1, DENS,,,0.087

!**************** *****************MODEL *****************************!

K,0,0,0 ! Keypoint__01

k,0,0,H ! Keypoint__02

K,0,LX,H ! Keypoint__03

K,0,LX,0 ! Keypoint__04

L,1,2 ! Line generation between keypoint_01 and keypoint_02

L,2,3 ! Line generation between keypoint_02 and keypoint_03

L,3,4 ! Line generation between keypoint_04 and keypoint_04

ALLSEL

LGEN,2,ALL,,,,,LZ

K,,,-h/2,0

L,2,6

L,3,7

A,2,3,7,6

ALLSEL

LGEN,NBX,ALL,,,LX,,

NUMMRG,ALL

ALLSEL

LGEN,NBZ,ALL,,,,,LZ

NUMMRG,ALL

ALLSEL

AGEN,NBX,ALL,,,LX,,

NUMMRG,ALL

ALLSEL

AGEN,NBZ,ALL,,,,,LZ

NUMMRG,ALL

ALLSEL

LGEN,NF,ALL,,,,H,

NUMMRG,ALL

ALLSEL

AGEN,NF,ALL,,,,H,

NUMMRG,ALL

L,1,4

LSEL,S,LOC,Y,0,

LGEN,NBX,ALL,,,LX,,

NUMMRG,ALL

LSEL,S,LOC,Y,0,

LGEN,NBZ+1,ALL,,,,,LZ

NUMMRG,ALL

L,1,5

LSEL,S,LOC,X,0,

LGEN,NBX+1,ALL,,,LX,,

NUMMRG,ALL

LSEL,S,LOC,Z,LZ/2,

LGEN,NBZ,ALL,,,,,LZ

NUMMRG,ALL

L,1,9,

LSEL,S,LOC,Y,-H/4

LGEN,NBX+1,ALL,,,LX,

NUMMRG,ALL

LSEL,S,LOC,Y,-H/4

LGEN,NBZ+1,ALL,,,,,LZ

NUMMRG,ALL

!*********ASSIGNING ATTRIBUTES TO COLUMN AND MESHING***********!

LSEL,S,LOC,Y,-H/4

*DO,X,1,NF,1

LSEL,A,LOC,Y,(2*X-1)*H/2

*ENDDO

TYPE,1

REAL,2

MAT,1,

LESIZE,ALL,,,NDC

LMESH,ALL

!***********ASSIGNING ATTRIBUTES TO BEAMS AND MESHING **********!

LSEL,S,LOC,Y,0

*DO,P,1,NF,

LSEL,A,LOC,Y,P*H

*ENDDO

TYPE,1

REAL,1

MAT,1

LESIZE,ALL,,,NDB

LMESH,ALL

!************ASSIGNING ATTRIBUTES TO SLABS AND MESHING**********!

ALLSEL

TYPE,2

REAL,3

MAT,1

AMESH,ALL

!***********************MODELING OF INFILL**************************!

!*****************************SOLUTION ******************************!

/SOLU

!*********************** End Constraints (fixed supports) ********************!

NSEL,S,LOC,Y,-H/2

D,ALL,ALL,

!******************Dead loading (Gravity loading)************************!

ACEL,0,1,0 ! Self weight

ESEL,S,TYPE,,2

SFE,ALL,1,PRES,,0.27778*2 ! Surface dead load=80 psf (=0.27778*2 psi) for

partition wall and floor finish

lswrite,1

acel,0,0,0

sfadele,all

!***************************** Live loading *****************************!

ESEL,S,TYPE,,2

SFE,ALL,1,PRES,,0.27778 ! surface live load 40 psf=0.27778 psi

lswrite,2

sfadele,all

!**********Applying Earthquake Loading (L-R) along X-X-direction) ***********!

*DO,L,H,(NF+1)*H,H

*DO,M,0,NBZ*LZ,LZ

NSEL,S,LOC,X,0

NSEL,R,LOC,Y,L-H

NSEL,R,LOC,Z,M

F,ALL,FX,14.30*(L-H/2)

*ENDDO

*ENDDO

allsel

lswrite,3

fdele,all

!********** Applying Earthquake Loading (R-L) along X-X-direction)***********!

*DO,L,H,(NF+1)*H,H

*DO,M,0,NBZ*LZ,LZ

NSEL,S,LOC,X,NBX*LX

NSEL,R,LOC,Y,L-H

NSEL,R,LOC,Z,M

F,ALL,FX,-14.30*(L-H/2)

*ENDDO

*ENDDO

allsel

lswrite,4

fdele,all

!***********Applying Earthquake Loading (L-R) along Z-Z direction***********!

*DO,L,H,(NF+1)*H,H

*DO,M,0,NBx*Lx,Lx

NSEL,S,LOC,z,0

NSEL,R,LOC,Y,L-H

NSEL,R,LOC,x,M

F,ALL,FZ,14.30*(L-H/2)

*ENDDO

*ENDDO

allsel

lswrite,5

fdele,all

!*************Applying Earthquake Loading (R-) along Z-Z direction)**********!

*DO,L,H,(NF+1)*H,H

*DO,M,0,NBx*Lx,Lx

NSEL,S,LOC,z,NBz*Lz

NSEL,R,LOC,Y,L-H

NSEL,R,LOC,x,M

F,ALL,FZ,-14.30*(L-H/2)

*ENDDO

*ENDDO

allsel

lswrite,6

allsel

!******* ********************solution of load steps *************************!

lssolve,1,6,1

/post1

lczero

!**************************load case definition ***************************!

lcdef,1,1,1,

lcdef,2,2,1,

lcdef,3,3,1,

lcdef,4,4,1,

lcdef,5,5,1,

lcdef,6,6,1,

!************** for load combination ( 1.4*dead load+1.7*live load) *************!

lcfact,1,1.4,

lcfact,2,1.7,

lcoper,add,1

lcoper,add,2

lcwrite,7 !load case for load combination( 1.4*dead load+1.7*live load)

lczero

!***** for load combination (1.05*dead load+1.27*live load+1.4*EQ load (L->R)along X-direction)****!

lcfact,1,1.05

lcfact,2,1.27

lcfact,3,1.4

lcoper,add,1

lcoper,add,2

lcoper,add,3

lcwrite,8 ! load case for load combination (1.05*dead load+1.27*live load+1.4*