dhan shekar

Proc. Instn Cio. Engrs, Part 2,1986,81, Dec., 593-605 PAPER 9061 STRUCTURAL ENGINEERING GROUP

The influence of brick masonry infill properties on the behaviour of infilled frames

M. DHANASEKAR, BE, MTech*

A. W. PAGE, ASTC, BE, PhD, MIE(Aust)*

The influence of brick masonry infill properties on the behaviour of infilled frames is studied, using a finite element model to simulate the behaviour of infilled frames subjected to racking loads. The finite element program incorporates a material model for the infill brick masonry which includes appropriate elastic properties, inelastic stress-strain relations and a failure surface. The program is capable of simulating progressive cracking and final failure of the infill. The model is verified by comparison with racking tests on infilled frames. It is then used to carry out a more extensive study of the influence of infill properties on the failure loads and failure modes of the panels. It is shown that the behaviour of the composite frame not only depends on the relative stiffness of the frame and the infill and the frame geometry, but is also critically influenced by the strength properties of the masonry (in particular the magni- tude of the shear and tensile bond strengths relative to the compressive strength).

Young's modulus of elasticity of brick masonry normal stresses perpendicular and parallel to the bed joint shear stress on the bed joint stress levels at which the inelastic strains attain a significant value dimensionless constants normal strains perpendicular and parallel to the bed joint shear strain along the bed joint Poisson's ratio of brick masonry relative stiffness parameter height of infill thickness of infill angle between the infill diagonal and horizontal elastic modulus of surrounding frame second moment of area of the frame member

Introduction Brick masonry is commonly used as infill in framed structures. Although the masonry significantly enhances both the stiffness and strength of the frame, its contribution is often not considered on account of the lack of knowledge of the composite behaviour of the frame and the infill. One of the difficulties in predicting the behaviour of the composite frame is the realistic stress analysis of the masonry infill which is in a state of biaxial stress. The in-plane deformation and failure of masonry is influenced by the properties of its components, the bricks and the

Written discussion closes 16 February 1987; for further details see p. ii. * Department of Civil Engineering and Surveying, The University of Newcastle, New South Wales, Australia.

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D H A N A S E K A R A N D P A G E

mortar. The influence of the mortar joints is particularly significant as these joints act as planes of weakness.

2. This Paper describes the use of finite element techniques to assess the contribution of the infill to the behaviour of infilled frames. A previously reported material model-3 (which includes the influence of the mortar joints) is incor- porated into an incremental, iterative finite element program capable of simulating racking tests on infilled frames. With increasing racking load, the finite element model can reproduce the progressive separation of the wall and its surrounding frame, the non-linear deformation characteristics of the infill masonry and the progressive failure of the infill. This progressive failure typically takes place as either a shearing type of failure down the panel diagonal, or a crushing failure near the loaded or reaction corners.

3. The influence of the properties of the masonry infill on the behaviour of infilled frames is assessed by means of a parametric study. It is shown that the behaviour of the composite frame not only depends on the relative stiffness of the frame and the infill and the frame geometry, but is also critically influenced by the magnitudes of the shear and tensile bond strengths relative to the compressive strength of the masonry.

The behaviour of frames with brick masonry infill 4 . When a racking load (with or without vertical loading) is applied to an

infilled frame, the frame usually separates from the infill at a low load level at the unloaded corners, and the load is transferred by diagonal strut action within the masonry (see Fig. 1). This diagonal strut action results in zones of high compressive stress near the loaded and reaction corners, and shear and normal stresses on the jointing planes in the interior of the panel. As the racking load is increased, further separation of the frame and infill occurs, with contact finally being restricted to regions adjacent to the loaded corners. At higher loads, a local shear failure usually occurs near the centre of the panel, with the failure then progressing towards the loaded and reaction corners. The final failure mode of the masonry depends on the relative stiffness of the frame and the infill. When the frame is flexible, a corner crushing failure is observed. For stiffer frames, failure occurs as a continuous path of sliding and cracking of the infill down the loaded diagonal.

5 . A number of experiments have been carried out on model and full-scale infilled frames over the past three decades4-I6 in an attempt to assess the contribution of the brick masonry infill to the behaviour of composite frames. The contribution was found to be substantial and to depend on the relative stiffness of the frame and the infill. To allow for the effects of varying frame stiffness, Stafford- Smith has suggested the use of a relative stiffness parameter ( I h ) defined as

= ( 4 E , I h ) E, t sin 28 in which E , , t and h are the Youngs modulus, thickness and height of the brick masonry infill, E , and I are the Youngs modulus and moment of inertia of the frame member, and 8 is the angle between the infill diagonal and the horizontal. It has been shown that the strength of the infill decreases as I h increases (that is, as the frame becomes more flexible).

6. In contrast with the experimental investigations, only limited theoretical studies have been performed on the behaviour of frames with brick masonry

594

B R I C K M A S O N R Y I N F I L L

Racklng - load

failure Dlagonal tension

- Separation of frame and Dane1

- Compression diagonal

Fig . 1. Behaviour of injilled frames subjected to racking loads

infill.17-22 In almost all these studies, the infill was assumed to be elastic and isotropic. The influence of the directional properties of masonry as well as its non-linear deformation characteristics have therefore not been considered.

7. This Paper describes the application to this problem of a realistic finite element model for masonry. The material model used in the finite element analysis is comprehensive and accounts for non-linear deformation characteristics as well as the influence of the mortar joints on the behaviour of the infill.

Material model 8. A comprehensive, macroscopic material model for brick masonry has been

derived from a large number of biaxial tests on half-scale, solid clay brick masonry panels.23* 24 A total of 186 panels, each 360 mm square, was tested with the prime aim of establishing a failure criterion for brick masonry under biaxial stress. The panels were tested under biaxial compression

D H A N A S E K A R A N D PAGE

consideration was found to be isotropic on average.' Average values of 5700 MPa for Young's modulus and 0.19 for Poisson's ratio were found to be reasonably representative of the behaviour.

10. In the inelastic range, however, the behaviour was found to be significantly influenced by the orientation of the mortar joints to the applied stresses.' From the non-linear segments of the stress-strain curves of the biaxial compression- compression tests, relatively simple inelastic stress-strain relations were derived

in which the superscript p denotes plastic and the subscripts n and p refer to directions normal and parallel to the bed jointing planes. The constants B,, Bp and B, have been taken as 7.3 MPa, 8.0 MPa and 2.0 MPa respectively, and indicate the stress levels at which the plastic strains become significant. The average values of the constants nn , np and n, are 3.3, 3.3 and 4.0 respectively. The variability in the data does not warrant more complex relations.

Failure surface 11. The mode of failure of solid brick masonry under biaxial stress depends on

both the state of stress and the orientation of the stresses to the jointing planes. If one or both of the principal stresses at a particular location is tensile, failure occurs

l

Fig. 2. Failure surface for brick masonry in on, op, T space

596


in a plane (or planes) normal to the surface of the wall with the joints playing a significant role. If both principal stresses are compressive, the influence of the joints is less significant and failure usually occurs by spalling or splitting of the panel in a plane parallel to the surface of the wall. In general, therefore, failure must be expressed in terms of the principal stresses at a point and their orientation to the bed joints. An alternative formulation is to define the failure surface in terms of stresses normal and parallel to the bed jointing planes (normal stress U " , parallel stress np, and shear stress T). A failure surface in this form has been derived from the biaxial tests3 The surface, consisting of three intersecting elliptic cones, is shown in Fig. 2. The three elliptic cones do not exactly correspond to the various modes of failure. However, the two end cones correspond approximately to tensile bond and compression failures, and the bulk of the intermediate cone corresponds to a combined shear and compression failure.

Finite element model 12. An iterative non-linear finite element model incorporating the material

model described above has been developed with a view to analysing framed structures with brick masonry infiILz5 As the emphasis in the study is on the failure of the infill, the surrounding frame is assumed to remain elastic. The mortar joint between the infill and the frame is modelled using one-dimensional joint elements. These elements can simulate the progressive separation of the frame and the infill, as well as shear failure in the joint, as the load is progressively increased. If failure occurs under combined shear and compression, the element is assigned a limited residual shear stiffness to simulate frictional forces.

13. In the finite element model, the loads are applied incrementally. At each increment of load, two sets of iterations are performed: one allows for material non-linearity; the other accounts for progressive local failure. At a given load level, iteration continues until the unbalanced nodal forces associated with material non-linearity are less than a prescribed tolerance limit. The stresses are then checked for violation of the failure criterion. If failure is indicated, the stiffness coefficients are reduced to a value appropriate to the mode of failure and the problem re-solved. Once convergence has been achieved, a further increment of load is applied and the process repeated. Loading continues until the solution fails to converge, indicating failure of the infill.

Verification of the finite element model 14. Several half-scale infilled frames were tested to check the validity of the

finite element model described in the previous section. A range of frame stiffness and panel geometries was chosen to produce the various modes of failure typical for infilled frames. The results have been reported previously.26. 27 In all cases, good agreement was obtained between theory and experiment. In the following, only the results of two of the infilled frame tests relevant to the ensuing discussion are presented. The two frames exhibited the two typical modes of failure (one failed by diagonal splitting, the other by corner crushing), and are thus ideally suited as a basis for the parametric studies which follow.

Frame tests 15. Of the two frames, one was square and the other rectangular. In both

infilled frames, the frame members consisted of light gauge channel sections welded back to back to form an I section 51 mm deep with a flange width of

597


50 mm. The square infilled frame (frame # l), with brickwork panel'dimensions of 1030 mm long X 995 mm high, was tested with the brick masonry still moist and at an age of 28 days. The rectangular frame (frame #2), with brickwork panel dimensions of 1495 mm long X 995 mm high, was tested with the brick masonry dry at an age of 105 days. (Previous tests on moist and dry specimens of the brick masonry had revealed that the shear and tensile bond strengths of the dry, older, masonry were approximately 75% greater than the moist, younger, specimens. In contrast, the compressive strength remained unchanged). Both infilled frames were tested under a monotonically increasing racking load until failure of the masonry infill occurred. Frame # 1 failed along the loaded diagonal in a series of steps along the bed and header joints. Failure originated near the centre of the panel

60-

z

2 40- X 0

-.- Flnlle element model o Experimental

v' o/'

P' d

Q' ,d

Deflexlon: mm

( 4

100- o Experimental

-0- Finite element model

80 - d" T o

P/ Z 1 60- o/* U

O .' m "f - O/*

0

C .- 5 40- LT m

0 .l o./ d

cm/ 20-

4 oY/ f

OO 1 .o 2.0 3 .O Deflexion- mm

( W

Fig. 3. Observed and predicted load-deflexion curves for infilled frames: (a) frame # 1 ; (b)yrume # 2

598


and then progressed towards the loaded and reaction corners. Frame # 2 (with infill possessing higher bond strength), failed by local crushing of the masonry near the loaded corner.

Comparison ofpredicted and observed performance 16. Both tests were simulated using the previously described finite element

model with 5 kN loading increments. For frame # 1, the original material model was used. For frame # 2, the failure characteristics were modified to allow for the increased shear and tensile bond strengths.

17. The observed and predicted load-deflexion curves for the two infilled frames are compared in Fig. 3. It can be seen that the finite element model satisfactorily reproduces the loadcleflexion behaviour of the infilled frames. For frame # 1, the behaviour is markedly non-linear, with the slope of the curve being similar to that of the bare frame once substantial cracking of the infill has occurred. (For purposes of these analyses, the ultimate load is taken as the load at which the infill has failed.) It is also significant to note from the curve that appre- ciable shear stresses are still being transmitted across the failure planes even when cracking has progressed completely down the panel diagonal. Frame # 2 did not exhibit significant non-linear behaviour as failure occurred suddenly by corner crushing. Frame # 1 failed in a stepped manner from the loaded to the reaction corner. Good agreement was obtained between the observed and predicted failure pattern. For frame # 2, failure was confined to a local area near the loaded corner of the infill (under the action of biaxial compressive stresses). The location and extent of the failure zone was again in good agreement with those predicted by the analysis.

18. The predicted and observed failure loads also agreed well. The experimental ultimate loads for panels # 1 and # 2 were 45 kN and 85.5 kN respectively; the corresponding ultimate loads predicted by the finite element analysis were 43 kN and 85 kN. Satisfactory agreement was also obtained between the observed and predicted brick masonry infill strains and frame bending moments. Detailed results of these comparisons have been reported elsewhere.26.

Parametric study of brick masonry properties 19. As a result of the good agreement between predicted and observed per-

formance, the finite element model was used to carry out a more extensive study of the relative importance of the parameters used to define the material model. The study also helps to establish the masonry properties which have a significant influence on the behaviour of practical infilled frames. The parametric study involved the analysis of the two previously described infilled frames, with progressive variations in the parameters defining the material model for the masonry infill.

20. The following parameters were varied: the elastic properties (Eb and v ) ; the constants of the inelastic stress-strain equations (B , , B , , B , , n, , n, and n J ; and the compressive strength and the shear and tensile bond strengths (that is, varying the size and shape of the failure surface). Only one parameter was modified at a time.

Influence of masonry elastic properties 21. The elastic properties of the masonry would be expected t o have a signifi-

cant influence on the behaviour of infilled frames, as they directly affect the relative stiffness of the infill and its surrounding frame. In addition to the load-deflexion

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DHANASEKAR AND PAGE

Table 1. Influence of the elastic properties of brick masonry on the ultimate strength of the infill

Elastic properties ~~

E , , MPa I "

5700 0.10 57007 5700

Frame # l

load, kN Ratio* Ultimate Ratio* Ultimate

Frame #2

load, kN

46

0.76 65 0.93 40 1 .oo 85 1 43 1.12 95 1.07

43 1 .00 85 1 .Oo 43

0.94 80 l .00 43 1.00 85 1 .00

* Ratio = ultimate load/ultimate load for original material model. t Original material model.

characteristics, the ultimate load and failure mode of the infill could also be affected. This can be seen with reference to equation (l), where the relative stiffness parameter Ih is proportional to A summary of the results of the analyses is contained in Table 1. In all cases, failure occurred by diagonal cracking for frame # 1 and corner crushing for frame # 2. It can be seen that variations in E , do have some influence on the racking strength, but the influence is not strong for most cases. The infill stiffness has a greater influence on the failure load when failure occurs by corner crushing. In this case, a 100% increase in E , resulted in a 24% decrease in the ultimate load. The influence of Poisson's ratio was not significant.

22. The loaddeflexion curves obtained from the analysis of frames # 1 and # 2 with varying E , values are given in Fig. 4. The curves are given only up to the ultimate load of the masonry infill. The curve for the bare frame is also shown for each case. Curves for changes in Poisson's ratios are not shown, as variations in this parameter were found to be insignificant. The curves show the expected influence of masonry stiffness. Comparisons with the curve for the bare frame in each case highlights the contribution of the infill to the overall frame stiffness, with even a very flexible infill making a significant contribution. Comparisons of the lateral frame deflexion at a load corresponding to approximately half the ultimate load for each frame are shown in Table 2. At this load level, all load-deflexion curves are still linear. It can be seen that the influence of infill stiffness on lateral deflexion is significant. For example, halving the value of E , resulted in a 64% increase in deflexion for frame # 2.

Table 2. Lateral frame deflexions at a racking load approximately halj the ultimate load for varying E ,

Elastic modulus 7 Frame # 1 ~~~ I Frame #2 1 Deflexion, mm I Ratio* I Deflexion, mm I Ratio*

0,5E,

0.69 0.68 0.56 0.29 2.0Eb 1 .00 0.99 1 .00 0.52 1.64 1.62 1.38 0.72

* Ratio = lateral deflexion/lateral deflexion for E , = 5700 MPa. 600


2 I 40- Q m

./. -0 m

0- E, 2850 MPa v- E, 5 7 0 0 MPa 0- E,. 11400 MPa

Bare frame

0 1 0 2 .o 3.0 Deflexlon: mm

(a) 1 O O r

Deflexion: mm (b)

Fig. 4. Load-deflexion curves for infilled frames with varying stiffness: (a)frame # 1 ; (b)frame # 2

brick masonry

Influence of the constants of the inelastic stress-strain equations 23. The influence of the constants B,, B,, B,, nn, np and n, of equations (2), (3)

and (4) was studied by varying the value of the constants one at a time. In each case, a value double and half the original value was adopted. Racking tests for both frames # 1 and # 2 were simulated. For completeness, an analysis assuming elastic-brittle behaviour was also performed. The values used in the analyses are summarized in Table 3. For the infilled frames considered, variations in the inelastic constants were found to have no influence on either the load-deflexion behaviour or the ultimate load of the infill, with all the non-linear behaviour being caused by progressive cracking. This was confirmed by the elastic-brittle analysis which gave identical results. The insensitivity of these parameters could be partly attributable to the nature of the test, as the bulk of the infill panel is in a state of biaxial tension+ompression (for this stress state, elastic-brittle behaviour is

60 1


Table 3. Constants of the inelastic stress-strain equations used in the parametric study

(elastic-brittle behaviour: E , = 5700 MPa; v = 0.19)

Factor n, np n, B, , MPa B, , MPa B , , MPa

0.5 1.0*

2.00 1.65 1.65 1 .00 4.00 3.65

8.00 6.60 6.60 4.00 16.00 14.60 2.0 4.00 3.30 3.30 2.00 8.00 7.30

* Original constants.

assumed in the material model). This insensitivity of the inelastic constants may not be as apparent for cases in which larger areas of the wall are in a state of biaxial compression.

Influence of masonry compressive strength 24. The influence of masonry compressive strength on the behaviour of infilled

frames was studied by increasing and decreasing the original compressive strength by 20%. This was achieved by modifying the cone of the failure surface (Fig. 2) corresponding to compression failure and reanalysing the two infilled frames. Changes in the compressive strength of the masonry did not influence the load- deflexion behaviour of either of the infilled frames. The failure of the infill of frame # 1 was also unaffected, as its mode of failure was one of diagonal cracking. However, for frame #2 (when failure occurred by corner crushing), variations in compressive strength has a direct influence. A reduction of 20% in masonry strength resulted in a corresponding reduction of 18% in the capacity of the infill. An increase of 20% in masonry strength produced an increase in ultimate load of 12%. Strengthening of the infill can also influence the mode of failure. For frame # 2, with the increased compressive strength, corner crushing failure was accom- panied by some shear failure at the centre of the panel. This suggests that a further increase in compressive strength (without a corresponding increase in bond stress) would inhibit corner crushing and cause failure to occur by diagonal cracking at only marginally increased loads.

Table 4. Influence of bond strength on the failure of brick masonry injill

Analysis

I t

Tensile bond strength,

MPa

0.40 0.00 0.80 0.40 0-40 0.80 0.20

Shear bond Ultimate load, strength, kN

MPa

0.30 0.30

43

12 0.15 75 0.60 15 0.60 16 0.15 63 0.30 10

* l . Diagonal cracking; 2. Corner crushing. t Original material model.

602

Mode of failure, MPa*

1 1 1 1 1 2 1


* O r

z 1 ,q

a !i 401

Deflexlon: mm

Fig. 5. Load-deflexion curves for injilledframes with brick masonry of varying bond strength

Influence of the shear and tensile bond strength of the masonry 25. For frame # 1, the tensile and shear bond strengths of the masonry were

varied both independently and together, while holding all the other material properties constant. The cases considered, the ultimate load and the mode of failure for each analysis are summarized in Table 4. The load-deflexion curves for the analyses are shown in Fig. 5. It can be seen that the load-deflexion curves are coincident until cracking of the masonry infill commences. The level at which this reduction in stiffness occurs varied markedly, and is directly related to the bond strengths. The ultimate load of the infill is also significantly affected in all cases. The mode of failure remained the same except for analysis # 6 . In this case, the increased shear and tensile bond strength was sufficient to prevent a diagonal shear failure and thus to precipitate corner crushing failure.

26. It can be concluded, therefore, that accurate definition of the bond properties of the infill is required if realistic predictions of infilled frame behaviour are to be made, as variations in bond strengths can affect both the stiffness and the strength of the composite frame. It is significant to note that most of the previous studies of infilled frame behaviour have not considered the influence of the tensile and shear bond strength on the behaviour of the composite frame.

Summary and conclusions 27. The results from a large number of biaxial tests on half-scale brick

masonry panels have been used to establish representative stress-strain relations and failure criteria for solid brick masonry. These properties have been expressed in terms of stress and strain components related to the jointing directions, and have been used to formulate an iterative finite element model for the analysis of

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DHANASEKAR AND PAGE

brick masonry. The incremental finite element model is able to reproduce the non-linear behaviour caused by material non-linearity and progressive failure. The adequacy of the finite element model has been verified by comparison with the results of racking tests on steel frames with brick masonry infill.

28. A detailed parametric study of the influence of brick masonry properties on the behaviour of infilled frames subjected to racking loads using the finite element model has revealed the following.

(a) The modulus of elasticity of the infill masonry significantly influences the load4eflexion characteristics of the composite frame, and to a lesser extent can influence its ultimate strength. The influence of variations in Poissons ratio is insignificant.

(b) For a racking test (where the bulk of the masonry is in a stress state of biaxial tension-compression), the influence of the inelastic deformation characteristics of the masonry is insignificant. Elastic-brittle material characteristics were found satisfactorily to reproduce the behaviour in this case.

(c) Variations in masonry compressive strength do not influence the racking capacity of infilled frames when failure occurs by shearing down the panel diagonal. If failure occurs by corner crushing, the ultimate strength is influenced by changes in compressive strength. A progressive increase in masonry compressive strength for panels which fail by corner crushing will eventually cause the mode of failure to change to one of diagonal shearing.

(6) The tensile and shear bond strengths of the masonry critically influence the load-deflexion behaviour, the ultimate load and, in extreme cases, the mode of failure of the infilled frame. Realistic methods of analysis of infilled frames must therefore consider these parameters as well as the relative frame-wall stiffness and frame geometry.

Acknowledgements 29. The contribution of Mr P. W. Kleeman, Senior Lecturer, Department of

Civil Engineering and Surveying, University of Newcastle to this research work is gratefully acknowledged. Part of the research was funded by the Australian Research Grants Scheme.

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