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: manojsbsit@gmail.com

Raghavendra Prasad, Research Scholar, S.J.C.E., Mysore, Email :rpvconsultants@yahoo.co.in

Chandradhara, G.P, Professor, S.J.C.E., Mysore, E-mail:chandu_gpc@yahoo.com

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