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STUDY OF MACRO MODELS UNDER SEISMIC PERFORMANCE OF
MASONRY INFILLED RC FRAMES
Manoj, S.B, Post-Graduate Scholar, S.J.C.E., Mysore, E-mail: [email protected]
Raghavendra Prasad, Research Scholar, S.J.C.E., Mysore, Email :[email protected]
Chandradhara, G.P, Professor, S.J.C.E., Mysore, E-mail:[email protected]
ABSTRACT
Reinforce concrete frames are infilled by brick or concrete-block masonry walls. For decades
now, these infill walls were not taken into account when designing the bearing structures.
However, extensive experimental and analytical investigations have shown that there is a strong
interaction between the infill masonry wall and the surrounding frame, leading to considerable
increase of the overall stiffness. It is well known that the presence of infill walls in reinforced
concrete structures can decisively influence the structural behavior to seismic loads. The
influence of infill on frame members is studied by several authors and developed various models
to understand the behavior and they are grouped in to two main categories: macro-models, based
on the equivalent strut method, and micro-models, based on the finite element method.
The primary objective of this paper is to present a general review of the different macro models
used for the analysis of infilled frames and based on the results a simplified model shall be
proposed from the Indian perspective. Also, the present study aims at providing a contribution
for the simplified analysis and design procedure for the infilled frames, based on the numerical
parametric study. For this purpose, ETABS, a finite element software has been used and the
comparison between the performances of masonry infill frames is made using different macro
models. Axial force in column and beam, the roof displacement are obtained to identify the
seismic performances of infilled frames. The study also focuses on the effects of number of
storeys on the overall performance of masonry infill frames against earthquake force. It was
inferred that the effect of provision of infill is to strengthen the frames against lateral dynamic
load and the effects are more pronounced in taller structures.
Key words: Infilled frames; Masonry; Macro models; ETABS; 2D RC frame; seismic strengthening
1.0 INTRODUCTION
A large number of Reinforced concrete buildings containing unreinforced masonry infill walls
are commonly used in structural system around the world. Masonry infills are often used to fill
the void between the vertical and horizontal resisting elements of the building frames with the
assumption that these infills will not take part in resisting any kind of load either axial or lateral
load, hence its significance in the analysis of frame is generally neglected. Many buildings of
this type have performed poorly during earthquakes.
The presence of infill changes the lateral load transfer mechanism of the framed
structure from predominant frame action to predominant truss actions as shown in fig.1. This
presence of infill changes the behavior of the frame and is responsible for huge reduction in
bending moments and slight increase in axial forces in the frame members. The presence of infill
also increases damping of the structures due to the propagation of cracks with increasing lateral
drift. However, behavior of masonry infill is difficult to predict because of significant variations
in material properties and failure modes that are brittle in nature. If not judiciously placed, during
seismic excitation, the infills also have some adverse effects. This is due to absence of infill wall
in a particular storey. The absence of infill in some portion of an irregularly planned building
will induce torsion moment. Also, the partially infilled wall, if not properly placed may induce
short column effect or captive column effect creating localized stress concentration.
Fig 1 Change in lateral-load transfer mechanism due to masonry infills (Murty and Jain - 2000)
Moreover in seismic areas, ignoring the frame-infill panel interaction is not always safe, because
under lateral loads the infill walls dramatically increase the stiffness by acting as a diagonal strut,
resulting in a possible change of the seismic demand because of significant reduction in the
natural period of the composite structural system. Non availability of realistic and simple
analytical models of infill becomes another hurdle for its consideration in analysis. In fact it has
been recognized that frames with infill have more strength and rigidity in comparison to the
bared frames and their ignorance has become the cause of failure of many the multi storied
buildings. The recent example in this category is report that RC frames with unreinforced
masonry infill are currently being built in India in violation of the building codes, and that they
performed poorly during the 2001 January, 26 Bhuj earthquake. The main reason of the failure
is the stiffening effect of infilled frame that changes the basic behavior of buildings during
earthquake and creates new failure mechanism. The 2008 earthquake in Wenchuan, China,
provides numerous examples of frame wall interaction (Li et al. 2008); see Figs. 1.1.
Fig-1.1 Damages of masonry infilled RC frames after the Wenchuan earthquake (Bixiong, Li et al.(2008)
2.0 MODELING OF INFILL FRAME
Model development of any structures is crucial to achieve accurate output results. However, it is
difficult to model the as-built structures due to numerous constraints with as it is difficult to
incorporate all physical parameters associated with the behavior of an infilled frame structure.
Even if all the physical parameters, such as contact coefficient between the frame and infill,
separation and slipping between the two components and the orthotropic of material properties
are considered, there is no guarantee that the real structure behaves similar to the model as they
also the structural behavior could also depend on the quality of material and construction
techniques. However, to simulate the structural behavior of infilled frames, two methods have
been developed such as Micro model and Macro model.
The Micro model method is a Finite Element Method (FEM) where the frames elements,
masonry work, contact surface, slipping and separation are modeled to achieve the results.
This method has seems to be generating the better results but it has not gained popularity due to
its cumbersome nature of analysis and computation cost.
The Macro models which is also called a Simplified model or Equivalent diagonal strut method
was developed to study the global response of the infilled frames. This method uses one or more
struts to represent the infill wall. The drawback of it is to the lack of its capability to consider the
opening precisely as found in the infill wall.
2.1 MICRO –MODELS
Micro models are represented by using Finite Element Method (FEM). The finite element
method is the most popular analysis tool for complex structural engineering problems. Since the
pioneer work of Mallick and Severn (1967), several difficulties were evident from the
simulations, namely the issues of modeling the separation between frame and panel, of the bond
strength and friction of the connection between frame and panel, and of the mechanical
constitutive behavior of masonry itself. Riddington and Stafford-Smith (1977) found that the
critical stresses for the masonry panel are located in the centre and are mostly associated with
tensile and shear failure. In this case, the frame-panel interaction was modeled by using double
nodes and normal springs at the interfaces, with contact/separation modeled in a simplified way.
King and Pandey (1978) further extended the numerical representation by adding interface
elements capable of taking into account contact and friction for the frame-panel interaction. This
work was further extended with non-linear behavior of the panel and frame, by Liauw and Kwan
(1982) and Dhanasekar and Page (1986) in the framework of continuum modeling, and by
Mehrabi and Shing (1997) in the framework of discontinuous modeling. The benefit of using
finite element approach is to study in detail all possible modes of failure but its use is limited due
to the greater computational effort and time required in analysis & modelling.
2.2 MACRO-MODELS
In order to overcome the complexity and computational requirement using micro-models,
research has been done to simplify the modelling of infill panel with a single element. The main
idea has been to study the global effects of infill panel on structures under lateral loads. Since
first attempts from Polyakov (1956), analytical and experimental tests have shown that a
diagonal strut with appropriate mechanical properties can provide a solution to the problem.
Several authors have modified the characteristics of single strut model with multi strut
configuration to better understand the effect of micro-cracking in the corner of the infill panel
due to tensile stresses and higher shear strength of the infill panel relative to the frame. A brief
review of few models has been presented.
Based on elastic studies Polyakov (1956) conducted one of the first analytical studies on infilled
frames. He considered the effect of infill in each panel as equivalent to diagonal bracing. Holmes
(1961) took the idea and suggested that infill panel can be replaced by an equivalent pin-jointed
diagonal strut. He proposed that the diagonal strut to have the same material and thickness as the
infill panel. The width of strut(b¿¿w)¿ was taken equal to one third of the strut length(dw ).
bw=dw
3 (2.1)
Stafford (1966) performed a series of test on square steel infilled frames. He observed that
contact length between the wall and frame is related to the width of the strut. From the
experimental result he proposed the following relation for finding the contact length between the
wall and infill frame.
λ h=4√ Emtm hm
3
4 Ec I c
(2.2)
α= π2 λ
(2.3)
Where λ h is the non dimensional parameter known as relative stiffness between the reinforced
concrete frame and the infill wall. Em and tm are the elastic modulus and thickness of the
masonry wall and Ec and I care the elastic modulus and moment of inertia of the bounding
concrete frame members. Height of the masonry infill is represented byhm and α represents the
contact length.
Paulay & Priestley (1992) took a conservatively high value for the width of equivalent strut.
According to them, a high value of bw will result in a stiffer structure. The relation given by them
is as follows:
bw=dw
4 (2.4)
Mainstone (1971) relates the width w of equivalent strut to parameter λh, given by equation (2.2)
and diagonal length d as shown in the equation (2.5).
wd
=0.175 ( λ h )−0.4 (2.5)
The proposed macro models and respective equivalent diagonal strut width equations for
masonry infill by various researchers is tabulated in table 2.1
Table.2.1 Equations for strut width value for full infill by various researchers
Researchers Strut width(w) Remark
Holmes[4] 0.333 dm dm is the length of diagonal
Mainstone[6 0.175 D (λ1 H)- 0.4
λ1 H = H[EmtSin2θ/4 Ec Ic
hm]1/4
Liauw and Kwan[7] 0.95 hm Cos θ/√(λhm)
λ = Em t Sin 2 θ/ 4 Ec Ic
hm]1/4
Paulay and Priestley[8] 0.25 dm dm is the length of diagonal
Hendry[9] 0.5[αh + αL]1/2
αh = π/2[EcIchm/2
Emtsin2θ]1/4 and αL = π[EcIbL/
2 Emtsin2θ]1/4
Decanini & Fantin
(1986)
λ = Emt Sin 2 θ/ 4 EcIchm]1/4
d z is the length of diagonal
Durrani & Luo (1994) γ √L '2+H '2 xsin2θ
3.0 METHODOLOGY
In the present study reinforced concrete members and masonry infill members are modelled
using ETABS 9.6 software. It is powerful finite element software developed by Computers
& Structures Inc., which can greatly enhance a designer’s analysis & design capabilities for
structures.
4.0 MODEL DESCRIPTION
Three models have been selected and compare the results with different proposed macro models.
Experiments are very important to observe the behavior of complex structures. Many a times,
analytical models have been developed on the basis of experimental results, and sometimes,
experimental studies have been carried out to verify the analytically developed model.
The proposed analytical model is initially compared with the experimental results of Chiou, Y.
J., et al., (1999). They have conducted a full scale test to study the behavior of one bay one
storey framed masonry walls. The infill panel size of the specimen tested is 2.4m x 2.3m. The
cross sections of the beam and column elements are 0.35m x 0.40m and 0.3m x 0.35m
respectively. The thickness of the masonry wall is 0.2m and the elastic modulus of concrete &
masonry are 2.4247 x 107 kN/m2 and 2.087 x 106 kN/m2 respectively. The monotonic loading is
adopted in this study (Fig.4.1).
The main output of the experimental investigation was a load versus displacement curve for solid
frame. The results from the experimental investigation are used to compare the results of finite
element model. Fig.4.2 presents lateral force and the corresponding lateral displacement at the
top of the leeward column for the proposed macro models. A good agreement is observed
especially at lower loads. Considering this fact, a finite element method is chosen for the present
work in order to understand the behavior of infilled frames.
Fig 4.1 Analytical model Fig 4.2 Macro model using ETABS
The proposed analytical model is initially compared with the analytical results of P. G.
Asteris, M.ASCE1.They have conducted a analytical model (fig 4.3) to study the behavior of
one bay one storey framed masonry walls. The infill panel size of the specimen tested is
3.6m x 3.8m. The cross sections of the beam and column elements are 0.40m x 0.40m and
0.3m x 0.40m respectively. The thickness of the masonry wall is 0.1m and the elastic
modulus of concrete & masonry are 2.9 x 107 kN/m2 and 4.5 x 106 kN/m2 respectively. The
proposed macro models at 1,2 nd 3 stories are represented in fig(4.4,4.5,4.6).
Fig 4.3 Analytical model Fig 4.4 Macro model at one story using ETABS
Fig 4.5 Macro model at Two story using ETABS Fig 4.6 Macro model at Three story using ETABS
The proposed analytical model is initially compared with the analytical results of P. G. Asteris,
M.ASCE1.They have conducted a analytical model to study the behavior of one bay one storey framed masonry walls. The infill panel size of the specimen tested is 4.0 x 4.0m. The cross sections of the beam and column elements are 0.30m x 0.30m and 0.3m x 0.30m respectively.
The thickness of the masonry wall is 0.1m and the elastic modulus of concrete & masonry are 2.2 x 107 kN/m2 and 7.5 x 106 kN/m2 respectively. The proposed macro model is shown in fig 4.7.
Fig 4.7 Macro model using ETABS
5.0 RESULTS AND DISCUSSION
Comparison of lateral displacement of various macro models with the experimental and analytical
micro models is shown in table 5.1
Table 5.1: Comparision of Lateral displacement
Technical
papers
Load
kN
EXPT
Micro
model
Analytical
Micro
model
Lateral displacement of Macro Models
(mm)
M1 M2 M3 M4 M5 M6 M7
ASTERIES
(1990) 85 - 0.7
1.71
(0.78)
0.828
(1.88)
2.24
(0.56)
1.04
(1.41)
1.22
(1.16)
0.496
(3.815)
1.262
(1.12)
YAW-JENG
CHOW
(1999)
100 1.8 -
1.137
(1.03)
1.08
(1.08)
1.915
(0.39)
1.3
(0.83)
1.40
(0.73)
0.624
(2.44)
0.769
(1.83)
ASTERIES
(2003) (1.21) (1.74) (0.55) (1.31) (1.29) (4.84) (1.28)
At one story
30 - 0.5 0.481 0.364 0.835 0.453 0.164 0.164 0.46
At Two story
30 - 1.28 1.16 0.91 1.97 1.10 1.11 0.494 1.12
At Three story
30 - 2.3 2.127 1.736 3.4 2.03 2.05 1.099 2.059
NOTE:-The equivalent width of the diagonal strut for various macro models is shown in the bracket (-).
The proposed macro models by various researchers and load Vs displacement curves is
shown below-
Hendry[9] M1
Holmes[4] M2
Mainstone[6] M3
Paulay and Priestley[8] M4
Liauw and Kwan[7] M5
Decanini & Fantin (1986) M6
Durrani & Luo (1994) M7
Fig.5.1:comparision of lateral deflection of macro models and analytical model for solid infill
Fig.5.2:comparision of lateral deflection of macro models and experimental model for solid infill
Fig.5.3:comparision of lateral deflection of macro models and analytical model at various stories
6.0. CONCLUSIONS
The primary objective of this paper is to present a general review of the different macro models
used for the analysis of infilled frames. The macro models that can be used in everyday
engineering are of practical importance. The simpler ones are the equivalent-strut models, which
represent infills with a diagonal strut element. The basic parameter of these struts is their
equivalent width, which affects their stiffness and strength. Several formulas have been proposed
by researchers to calculate this equivalent width. In all the cases, there are considerable
differences among the values obtained.
The comparative study of different expressions for calculating the diagonal strut width reveals
the Paulay and Priestley equation as the most suitable choice, due to its simplicity and because it
gives an approximate average value (among those studied). In the analysis involving analytical
models for masonry infills in a single-storey, single-bay reinforced concrete frame, the single-
strut model was found to be predicting the global behavior of the system with reasonable
accuracy.
7.0 REFERENCES
1. Asteris P.G., (2003), “Lateral stiffness of brick masonry infilled plane frames”, Journal
of the Structural Engineering, ASCE, pp. 1071-1079
2. Chiou, Y. J., Tzeng, J. C., and Liou, Y. W., (1999), “Experimental and analytical study
of masonry infilled frames”, Journal of Structural Engineering, Vol. 125, No. 10, pp.
1109–1117
3. Asteris P.G., (1996), “Analytical investigation of infill wall influence on the aseismic
behaviour of plane frame”, diploma thesis(Supervisor C.A Syrmakezis)”, National
Technical University of Athens,(in greek)
4. Diana M. Samoilă*1., “Analytical Modelling of Masonry Infills”1 Technical University
of Cluj-Napoca, Faculty of Civil Engineering. 15 C Daicoviciu Str., 400020, Cluj-
Napoca, Romania
5. Prachand Man Pradhan., “Equivalent Strut Width for Partial Infilled Frames”,
Department of Civil and Geomatics Engineering, Kathmandu University, Dhulikhel,
Nepal