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*