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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.
593
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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 contri- bution 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 compres- sive 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 contribu- tion of the brick masonry infill to
the behaviour of composite frames. The contri- bution 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
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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
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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
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B R I C K M A S O N R Y I N F I L L
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 struc- tures 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
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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
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B R I C K M A S O N R Y I N F I L L
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 experimen- tal 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 progres- sive 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
599
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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
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B R I C K M A S O N R Y I N F I L L
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
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D H A N A S E K A R A N D P A G E
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
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B R I C K M A S O N R Y I N F I L L
* 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 proper- ties 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
603
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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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