LOAD BEARING MASONRY - A REVIEW

A W PAGE Senior Lecturer, Department of Civil Engineering and Surveying, University of Newcastle, N.S.L~ . Australia D S BROOKS Specialist Consultant, Kinhill Stearns Pty Ltd, Consulting Engineers, Adelaide, S.A. Australia

,ll.8 STRACT This paper reviews the current state of the art of the design of load bearing masonry \<Jalls voJith particular reference to Australian codes and recent Australian research.

The factors affecting the compressive strength of brickwork are discussed and recent research into the influence of brick size and shape on brickwork strength described. The strength of brickwork subjected to complex stress states is also reviewed with particular reference to a material model derived from an extensive series of biaxial tests recently performed at the University of Newcastle.

The behaviour of storey height walls subjected to vertical loads is then reviewed, and recent research at the University of Adelaide described. An analytical model which is capable of reproducing wall behaviour up to and including failure is briefly described and the results from the model compared with existing code provisions. The relevance of recent research to the new unified SAA Masonry Code is discussed and the code provisions briefly outlined.

1. I NTRODUCTI ON

Masonry has been used as a load bearing material for centuries. In the early gravity structures, levels of stress were low and factors of safety against compression failure were high, so that detailed knowledge of compressive behaviour was not essential. However in recent years, with the use of shear walls to resist lateral loads, walls have become very thin and consequently often highly stressed under vertical loads. The need for better knowledge of the behaviour of vertically loaded walls has led to substantial research in this area in recent years. Signi­ficant advances in the understanding of the behaviour of masonry structures has resulted, with code provisions reflecting these developments.

The purpose of this paper is to review the current state of knowledge in this area with particular reference to Australian codes and research. This is timely, since masonry codes in this country are currently undergoing substantial change and review. The existing brickwork and blockwork codes are to be replaced by a unified code which will have common provisions for all types of masonry. The new codewill reflect recent research developments and will be in ultimate strength format as a first step towards later limit states conversion. The new code is due for publication in mid 1985.

The first half of this paper discusses the factors which influence the compressive strength of masonry and the methods used to estimate masonry compressive strength for design purposes. The behaviour of masonry under complex stresses, (relevant to the design of shear walls, walls in infilled frames, etc), is also discussed and appropriate material models described.

The second half of the paper is devoted to the behaviour of storey height walls subjected to vertical loads. Recent research in this area is reviewed with particular refe rence to Australian work which has been used to develop the new SAA code provisions. The background to the new code provisions is also outlined and the provisions themselves briefly discussed.

81

2. MASONRY PROPERTIES

This section deals with the material characteristics which affect the strength of small specimens of masonry. Other factors which influence the strength of full sized walls (such as lateral instability) are discussed in Section 3.

2.1 Compressive Strength

Since the principal function of most masonry structures is to carry compressive loads, the compressive strength of the material is of prime importance. Many factors affect the compressive strength of brick masonry. These include the strength and geometry of the brick unit, the strength of the mortar, the joint thickness, the suction of the units and the water retention of the mortar, and the brickwork bonding pattern. Extensive research into the significance of these various factors has been carried out in many parts of the world, and several comprehensive reviews of this work have been published (1 - 8). For purposes of design, the influence of these various factors must be included in co de rules. The following sections discuss these factors, with particular reference to the existing SAA Brickwork Code (9) and the draft SAA Masonry Code (10).

2.1.1 Code Methods for Estimating Compressive Strength. use two methods to estimate the compressive strength of brickwork. Most overseas codes have provisions similar methods.

Australian masonry codes a particular sample of to either or both of these

The first method is based on the correlation between the compressive strength of the brick unit, the mortar type and the resulting brickwork strength. This relation­ship does not reflect the influence of workmanship and other factors (such as brick extrusion pattern) which can significantly influence masonry compressive strength. The values quoted in the SAA Brickwork Code, AS1640 (Table 4.4) are approximate lower bounds to widely scattered test results. In many cases, therefore, higher design strengths could be used if confirmatory prism tests were carried out. A similar approach has been adopted in the draft SAA Masonry Code, except the number of mortar types has been truncated from 6 to 3" (again reflecting the approximate nature of this relationship).

The second method for estimating the compressive strength is by the use of uniaxial compression tests on brickwork prisms. These are constructed on site as a stack bonded wallette which is then separated into a series of prisms. Since similar mortar and laying techniques are used for both walls and prisms, tests on these prisms should therefore more realistically reflect the influence of workmanship. The influence of other factors (such as brick extrusion pattern and shape) will also be reflected in the tests, since the failure mode of the units in the prism test will be similar to that in the wall.

2.1.2 Aspect Ratio Effects. The observed strength of a specimen tested in uniaxial compression will depend upon its size and shape. For specimens with low aspect ratios (heightjleast width) a significant artificial strengthening is produced by the restraining effects of the platens of the testing machine. Lateral expansion of the specimen is prevented by the friction between the ends of the specimen and the platens, with a resulting increase in the failure load. As the specimen aspect ratio increases, this effect diminishes, and the apparent strength reduces.

The influence of the aspect ratio has important implications in both the standard test methods described in the previous section. The brickwork compressive strength obtained using the first method is based on the compressive strength of a brick unit obtained from a standard compression testo Since the aspect ratio of a typical brick unit is low (approximately 0.7), significant platen restraint occurs with a high apparent strength resulting (almost double the true compressive strength).

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The empirical relationship in Table 4.4, AS1640 has been determined from tests on brickwork prisms constructed from standard sized units (230 mm long x 110 mm thick x 76 mm high). The results do not reflect the variation in compressive strength with changing aspect ratio for both the bricks themselves and the resulting prisms (whose aspect will also be influenced by brick size). The table will therefore be sa ti s factory for bri ckwork cons tructed from s tandard si zed bri cks , but will underestimate brickwork strength when bricks with aspect ratio greater than 0.7 are used (and conversely, overestimate brickwork strength for bricks with aspect ratio less than 0.7).

The influence of aspect ratio can be eliminated by the use of a correction factor which converts the apparent (confined) strength of a specimen to an equivalent unconfined value (corresponding to the strength of a specimen with an aspect ratio in excess of say 5 or 6). A relationship to correct for aspect ratio has been recently developed at the University of Newcastle and is shown in Figure 1.

1·0 u ~

L-o

0-8 u o u..

c o u 0-6 11> L-L-o

U

~ O-L. o

o::

u Q.> o- 0·2 til ~

o

x x •

)(

Relationship . : Bricks

x: Br i ckwo r k Pri sms

2 3 5

ASPECT RATIO

Fig Aspect ratio correction factor for bricks and prisms

This relationship has been derived from a series of confined and unconfined compression tests on bricks and prisms of various sizes and shapes. The unconfined tests were carried out using brush platens which minimized the effects of platen restraint. Details of this investigation are reported at this Conference (11) and elsewhere (12). This correction factor can be applied to both bricks and prisms to obtain a true estimate of compressive strength.

2.1.3 Relationship between Prism Strength and Wal1 Strength. For purposes of design, the compressive strength of the wal1 is the prime consideration. Prism strength will give a reasonable indication of wall strength, but will not completely reflect all the factors which influence the strength of the wall (such as perpend joints and differences in workmanship). The aspect ratio of the prism wil1 also

83

have an influence. The SAA Brickwork Code, AS1640 (9) recognises this difference and applies a factor of 0.75 to the prism strength to obtain the wall strength. This has been empirically derived from comparisons of the strength of four high prisms and walls constructed from the same brickwork (13,14,15).

2.1.4 Provisions of Draft SAA Masonry Code. The draft SAA Masonry Code provisions for determining compressive strengths has some significant changes when compared to the existing SAA Brickwork Code. To be consistent with the partial conversion to a limit states format, all strengths are now expressed as 95% characteristic values (compared to 85% characteristic values in AS1640). To allow for brick units of different size, all unit compressive strengths determined from the standard test are converted to an equivalent unconfined value using the correction factor described in Section 2.1.2. A similar correction factor is also applied to any prism tests.

For calculated masonry (when no confirmatory prism testing is required) the com­pressive strength is estimated from a table relating unconfined compressive unit strength and mortar type to masonry strength. As mentioned previously, the number of mortar types has been truncated from 6 to 3, with the table applying to all types of masonry (clay, concrete and calcium silicate brick and concrete block).

For special masonry, the specified strength has to be confirmed using prism tests similar to that required by the existing code (except 7 day rather than 28 day strengths are used). When aspect ratio effects, the change from a 28 day to a 7 day strength, and conversion from 85% to 95% characteristic strength values are taken into account, the factor relating prism strength to wall strength conveniently increases from 0.75 to 1.0 . The 7 day, 95% characteristic unconfined prism strength therefore also represents the long term wall strength.

2.2 Strength of ~1asonry Subjected to Complex Stresses

Many masonry elements in a structure are subjected to a complex state of stress produced by in-plane loading (for example shear walls, walls in infilled frames, walls subjected to concentrated loads etc.) Most existing design recommendations for these situations are semi-empirical and have been derived from experimental studies of the overall behaviour of complete structural elements. With the advent of computer based numerical techniques such as the finite element method, it is now possible to study the behaviour of masonry structures by examining the behaviour in localised regions rather than looking at the average overall behaviour. In this way, stress redistribution, local cracking and progressive failure can be simulated and the final collapse of the complete structural element predicted. This type of analysis can only be carried out if realistic material models for masonry are available (these must include definitionof its elastic and inelastic properties as well as a failure criterion). The formulation of these characteristics is further complicated by the directional properties of masonry caused by the mortar joints acting as planes of weakness. ~1asonry properties therefore must be formulated not only in terms of the principal stresses at a point, but also in terms of the inclination of these stresses to the jointing planes.

2.2.1 Previous Research. Researchers have long been aware of the directional properties of masonry. Various types of uni axial tests have been performed to study this effect. These include diametral compression tests on masonry discs and uniaxial compression tests on samples with sloping bed joints to obtain varying ratios of shear stress to normal stress on the bed joints. A review of this work has been previously published (8).

There have been few attempts to obtain a general failure criterion for masonry

84

subjected to in-plane forces due to the difficulty in developing a representative biaxial test as well as the large number of tests involved. Samarasinghe and Hendry (6) obtained a partial ( 01, O 2 , 8) failure surface for one-sixth scale brick masonry for biaxial tension-compression (where 8 and 900 + 8 are the inclin­atio n of the principal stresses oj and 02 to the bed joint). Biaxial tests have also been carried out in North America by Hegemier et al (17) on grouted concrete masonry and in Europe by Ganz and Thürlimann (18) and Hofmann and Stükl (19) on highly perforated clay brickwork. Some of these testing programmes are still in progresso

2.2.2 Australian Research. An extensive series of biaxial tests has been performed on half scale solid clay brickwork at the University of Newcastle over the past five years. These tests have been aimed at establishing a representative material model for masonry for incorporation into a finite element analysis.

A total of 180 panels were tested under biaxial loading with various combinations of principal stresses 01 and 02 incl ined at varying angles to the bed joint. To minimize the effects of platen restraint on the panels, flexible steel brush platens were used on the four bearing surfaces of the specimen. In each test, three sets of strains were measured on each side of the panel over a gauge length which encompassed several bricks and joints. The general arrangement of the tests is shown in Figure 2 and a summary of the tests performed is contained in Table 1.

(a) Loading Frame

_ - _ Strain measured

Pump

\ ...-/

To jack B

(b) Load Oistribution Oevice

To jack A

Movable jack

Fig 2 Bia xial Testing Rig

85

TABLE 1 SUMMARY OF BIAXIAL TESTS

STRESS STATE Bedjoint angle a Jioz ratio No . Df Remarks (e) panels

I

BIAXIAL 00

, 22.50

, 45° 10, 4 , 2 , 1 75 a J /0 z ratios COHPRESSIOl,- 67.5° and 90° Df 0.5 , 0.25

COHPRESSIOH and 0 . 1 were obtained by symmetry

I I

I !

BIAXIAL

I - 0.5, -0.2, 66

I oJ stress

TENSION- As above - 0.1 a.'1d tensile

COMPRESSIOli - 0 . 03 I

UNIAXIAL COHPRESSIOii

As above O 21 : -

I

:

e = 22.50

UNIAXIAL As above ~ 18 i ?e..nel "'as TENSION

I rectangulé.'

From the tests, a complete material model has been formulated. Various aspects of the model have been previously reported (20 - 24), so that only a brief summary will be given here.

It was found more appropriate to transform the stresses from the (01' 02 ' e) system to direct stresses normal (on) and parallel (op) to the bed joint and shear stress (T) along the bed joint. When tensile stresses were present on the bed joint, the material behaviour was found to be elastic - brittle (in th i s case, isotropic elastic assumptions were found to be appropriate). For other cases, (corresponding to bia xial compression), the deformation characteristics were distinctly non-linear . In this case the "pl as tic" strains, (i.e. the proportion of total strains remaining after the subtraction of the elastic strains), were found to be dependent only upon their corresponding stresses. The plastic strains could therefore be modelled as a function of a power of t heir corres ponding stresses.

The failure mode for each (01' 02 , e) combination varied markedly with the stress state. For uniaxial compression and all tension-compress i on cases, failure occurred in a plane normal to the free surface of the panel with the joints usually having a preddominant influence on the mode of fai l ure. For biaxial compression, a splitting failure occurred in a plane parallel to the free surface of the specimen at mid-thickness. A three dimensional failure surface exp ressed in terms of 01 ' 02 and e was not regular and was found to be difficult to express analytically. An alternative formulation in terms of 0n' 0p , T yielded a closed surface which could be idealized as three intersecting elliptic cones (see Figure 3).

86

Fig 3 Failure Surface for Brickwork in 0n' 0p, T Space

The material characteristics have been incorporated into an iterative, plane stress finite element program which is capable of reproducing non-linear material characteristics, progressive local failure and final collapse of brickwork panels subjected to in-plane loads. Local failure can take the form of tensile cracking, shear failure (usually joint sliding) and crushing. One of the advantages of the model is that average properties which include the influence of both brick and joint have been derived. This means that a relatively coarse finite element mesh can be used with any element typically encompassing several bricks and joints. Considerable computational advantages result when analysing large panels. The application of the model to the analysis of infilled frames is described in a paper presented elsewhere at this conference (25). Good agreement has been obtained between theory and experimento

In the near future it is intended to carry out parametric studies of the behaviour of shear walls and infilled frames with the aim of formulating usable design methods.

3. AUSTRALIAN RESEARCH ON THE VERTICAL LOAD CARRYING CAPACITY OF MASONRY WALLS

3.1 A Review of Previous Research

The behaviour of brick walls and columns subjected to vertical loads which produce axial compression and one way flexure is generally well known and has been extensively documented. The characteristic feature of this type of masonry is the bed joint cracking that occurs when the eccentricity of the load moves outside the kern points of the section. This cracking generally occurs only at the bed joints because the tensile strength of the bricks is considerably greater than the flexural bond strength of the brick-mortar interface.

Previous studies by Angervo (26), Chapman and Slatford (27), Sahlin (28), Risager (29), Yokel (30) and Chen (31) have been based on closed form methods of analysis for the behaviour of brick walls in which bed joint cracking may occur over the height of the wall. In most cases these analyses have been based on the assumptions that the ma sonry units themselves cannot sustain any tension stresses so that all the material outside the zones carrying compression stresses may be disregarded in calculating the stiffness and the strength properties of the walls. The work of Sahlin contains extensive results for walls with various end support conditions and load combinations. These analytical methods however are generally difficult

87

to apply to real brick walls, where imperfect end support conditions, initial lack of straightness, and material non-linearity may all signifi cant ly i nfl uence the behaviour of the wall up to the point of collapse .

More recently, Contaldo, Faella and Mazzolani (32) and Sawko and Towler (33) have presented numerical methods employing finite difference techniques to account for various end conditions and initial eccentricities. The results obtained by computer calculations with these methods have been found to agree well with a numerical method of analysis developed at the University of Adelaide (34) which was confirmed by a series of tests on slender walls loaded to failure under vertical eccentric compression.

3.2 Finite Element - Finite Difference Analyses

In this latter method, a combination of finite element and finite difference techniques has been used to incorporate the effects of initial imperfections, tension field stiffening within the masonry units, or bricks, and the range of end support conditions that could be expected in actual construction. The method can be used to allow for either linear or non-linear material behaviour. As an initial step, the stress distribution in the brick carrying an eccentric load which acts outside the kern is determined by a finite element method, and a flexural stiffness coefficient for the brick is established. This coefficient depends on the load eccentricity and the aspect ratio of the brick, and is subsequently used to estimate the global stiffness of the cracked brickwork, which is considered as a series of modules. Each module is chosen to contain one brick with one of its adjacent bed joints. Once the effective flexural stiffness of each module has been evaluated, a finite difference calculation is carried out to determine wall displacements. When the material is non-linear, the effective stiffness depends on the stress levels in the modules. Typical results obtained by using the method are shown in Figure 4, in which the load-deformation characteristics are plotted for two walls, A and B, each of which has a fixed base and is pinned against lateral deflections at the topo The height to thickness ratio in each case is 32 and the load eccentricity to thickness ratio at the top of the wall is 1/12 for wall A and 1/4 for wall B.

[_p ] " \! -[~1 '~6;91 ~p 1< Pc r 1' t 1, ' 1'~1 419 i -+<-"

,: -I - -; 0~rA+J----i-----j 1-···· 1 0-- - - - ------1 ---~:' I -~,- -t-----t----,----,

O,B90 ........ . ~ O. 37

o,sl--- I-- - -- - - -l -------I --- - -- --- - ,;: -~~-'UC7 6--

I : 7//'"

06 --- - - - - - - J------~~' ••• ..• I 1

: i 04 \ - ---- I ~

I WA L 'A' -e------e- l i n ear Mor l .:!'

i I I 01,

0. 2

- ---- - --- -j

- - -- No- t ens;on Mdleri a l

T- ' - --+ No n - I lnea r (01\ \11' 1.),

o , o,

Fig 4 Load-Deformation Curves from Analytical Method (34)

88

3.3 Experi menta l Investigations on Wa11s

A series of full scale tests on relatively slender brick walls was carried out to compare the theoretical load-deformation performance predictions with the behaviour of real brickwork. The walls had height to thickness ratios of either 19 or 36 and were eccentrically loaded at the top support with the base being perfectly fixed against rotations and displacements. The load eccentricities at the top of the wall were either 1/6 or 1/3 of the wall thickness. The tests were thus designed to represent the behaviour of walls supported on a rigid footing. The non linear material behaviour was determined experimentally from tests on short control specimens of brickwork. Typical deflection profiles for the walls taken from the experimental results are compared with the predicted profile in Figure 5, and load-deformation characteristics obtained from the tests together with the predictions are typified in Figure 6.

27'4~, ~" J

I " I " I " ~

i 00 I

I !

I I I I

f

I I I ".~ 2242 f----'-----i-""*~_T__---'--------j

! ''\1 -----, i --i-------j --'-'1

I I I I

QJ Vl

'" '" QJ

> o

.D

'" +-> ..::

'" QJ

I

\~ I\L

1770 f------ ---i---6----;ff+-e--- +-------J

W

I J298 f------'-----'-~----.<;'r-I.//"--:----i-----1

j;,/ , ~!J I I

826 1-----11 -l'/-i?7. /.,-- _+_1,-, - --T1-'--;-/1 ---j

1/ I 11 + Wa l l No . 1

A Wall No. 3

I! ! lS4 f-j\<H---- -+---l

e Wall No . 5

[J Vo'a 11 No . 7

I -e---e- PR OC, RAM PIERI

I' Mean of Wal rs 3 . ~- 4t-S an d 7

f fi

O-O _ L--i: ----', .0----C.1---::-::-2

.1-----, Latera l Di sp lacement (mm)

Fig 5 Initial Displacement Profiles for 2714 mm Wa lls with Fi xed Base; Top Load Eccentricity d/3

"O

'" O -'

cc u

+-> '­QJ

;>

I I , I r. dure .,! 29fN ~

00 ! I !.-- ""'_. -_rt_- j ~,;Sk ,...- ,.f!r ' -<t"" 'y6"" /. ..- ' . I .' F a il ure olt

~r ,

~kN 1 , ,

I I I I

l/ ! o

~ I I I I 7/ I ~.

I I W/ I /(/ I I

20

1'1 I I 1

I

o I I 'O

I ( I

{~ .. " -, ~ E)(p~rlmel"'lla I ~W<l ll No 7

'i I {*- -x- LInea r prER l

~l Theo l el rt:dl -& __ -&- Non- Ir near

p I E ~ ;

I I I i O

'O 20 l O

Rotation at Top (x l O- 3 radians )

Fig 6 2714 mm Walls Loaded at an Eccentricity of d/3

89

The agreement between calculated and experimental failure 10ads was generally within 10 per cent for those walls that failed by buckling, but the scatter was larger for the walls where failure was associated with splitting of the brickwork. The maximum difference in the latter cases was less than 30 per cento

3.4 Behaviour of Wall Panels Supported on Four Sides

A second stage of the investigation carried out at the University of Adelaide was to examine the behaviour of masonry panels supported on four sides but carrying a vertical eccentric line 10ad along the top edge . These panels would thus deflect under the action of two-way flexure together with torsion or twisting of the panel under the action of the moments arising from the eccentric load at the top edge. This plate type action may lead to cracking in both the horizontal bed jOints and the vertical perpend joints if the tension stresses across the brick-mortar interfaces exceed the bond strength or the tension strength of the mortar. Additional cracking may also occur because of the torsional effects. It will be apparent that cracking may develop progressively as the lateral deflections increase with load, and thus give rise to reductions in the flexural and torsional stiffnesses as in the case of walls subjected to one way bending only.

To model this behaviour mathematically, finite element techniques were again used, and the flexural and torsional stiffnesses of the brickwork were estimated for the various cracked states, and expressed as functions of the applied stress resultants acting on the brickwork module units. This analysis entailed represent­ing the cracking process as a progressive uncoupling of the element nodes as tension stresses developed at the brick-mortar interfaces. Typical combinations of perpend cracking patterns are shown in Figure 7 and the panel modules in Figure 8.

Fig 7

, .-

p

(a)

Perpend Crack

Bedjoint

Crack

-x

NOTE: ~

Bedjoint C,.ack

is resultant vertical load

P

~

Perpend Crack

)(

Possible Combinations of Perpend and Bed joint Cracking

90

Fig 8 Subdivision of Brickwork into Panel Modules (showing twisting moments )

The analysis of the complete wall panel was based on a finite difference formulation of the equilibrium equation for a plate of variable thickness. This thickness was taken as the thickness of the uncracked portion at any point, and the results of the finite element analysis were used to obtain the effective stiffness values. The analysis was carried out by iterative techniques fora series of load increments up to the point of failure which could occur by either buc kling or excessive compression. At each load stage the deflected shape of the panel was determined such that the finite difference expressions for equilibrium of the plate were satisfied to within a pre-set error tolerance . Typical results for a panel having a height of 2400 mm with eccentricity-thickness ratios of either 1/12 or 1/4 are given for a series of panel lengths in Figure 9.

91

1 I' I ! 2500 -t i

~TI--+-I ~-+I~ --i-----

2000

1500

Fig 9 E E

---z:

-O

'" O -' (1) 1000 S-

~

'" '-'-

500

I j 2.0 •. 0 6.0 8.0 10.0 12.0

Panel As pect Rat i o (~/h)

3.5 Tests on Wall Panel with Supports on Four Sides

Buckling Failure Loads of Cracked Brickwork Panels

A full scale experiment on a wall panel approximately 3600 mm long by 2400 mm high was conducted by applying eccentric loads at the top and bottom horizontal edges. The wall thickness was 65 mm and the load eccentricity was 20 mm. The load-deflection behaviour observed in the tests was in close agreement with the predictions and the failure load was within 7 per cent of that predicted in the calculations.

4. PROVISIONS OF THE DRAFT SAA MASONRY CODE FOR THE DESIGN OF WALLS CARRYING VERTI CAL LOADS

4.1 General

Despite the considerable amount of research carried out on the behaviour of masonry walls subjected to axial loads, the state of the art is such that design rules based on a rigorous analysis are still very difficult to formulate.

The strength of a masonry wall will be influenced by the eccentricity of loading andthe slenderness ratio. The slenderness ratio is in turn dependent upon the wall geometry, the relative stiffnesses of the walls and floors, and the degree of fixity at the joints. The calculation of masonry strength is further compli­cated by the low tensile strength of the material. Cracking may occur when the axial load is applied at high eccentricities, leading to variations in effective sectional properties.

Code provisions are currently based on the results of wall and pier tests with various slenderness ratios and load eccentricities with idealized end conditions.

92

This idealized behaviour has been adapted to real conditions by approximating assumptions with regard to end restraint and eccentricity of loading. Covered by large safety factors, these rather crude methods have given satisfactory results, but more rational design methods are clearly desirable. Hendry (7) has reviewed this difficult problem and summarised most of the recent research.

The investigations at the University of Adelaide were extended to include a parametric study of a wide range of wall types and loading conditions, and the results confirmed that the existing provisions of the Australian Brickwork Code AS1640 (9) are reasonable if minor modifications are made in some areas, but the provisions of AS1475, the Co de for blockwork (35) appeared to be unconserv­ative, particularly for walls of high slenderness bent in single curvature. The proposed new draft Unified Masonry Code which covers both brickwork and blockwork is aimed at rectifying these anomalies.

4.2 Factors Affecting Axial Load Capacity

The following factors must be considered:

(i) The cross-sectional properties of the wall based on its bedded area Ab.

For solid units, and cored units whose area of perforations is less than 25% of the total area, the gross area can be used with an appropriate reduction for any raking out of bed joints.

For hollow units, the net area based on the mortar contact area must be used.

(ii) The characteristic compressive strength of the masonry, F'm' (iii) The wall slenderness ratio, design height/design thickness.

(iv) Bending effects, such as:

(a) The effective eccentricities of load at each end of the wall (e] and e2; e] being the higher absolute magnitude).

(b) The deflected shape of the wall due to the applied bending moments and the axial load. This is a function of the end eccentricity ratio e2/e]. If e2/e] is negative, the wall is in double curvature; if e2/e] is positive, the wall is in single curvature.

(c) The extreme fibre compressive stress due to the applied bending moment and axial load. That is, a possible stress related failure.

4.3 Design Provisions

The design provlslons suggested here for the axial load capacity of masonry walls are a blend of the provisions of the old Brickwork and Blockwork Codes AS1640 and AS1475, Part I respectively. In formulating the rules, the general approach has been to adapt the rules of AS1640 to both brick and block (since agreement between theory and experiment was better using these provisions) whilst incorporating some of the more desirable features of AS1475.

The rules combine the effects of factors (i) to (iv) listed above into a single equation from which the design compressive strength can be calculated:

= Pc

where:

~ K F' Ab a m

P design compressive strength c

~a = capacity reduction factor

93

FI = m

=

=

=

=

characteristic compressive strength of masonry

bedded area

a reduction factor depending on slenderness ratio, eccentricity of load, ratio of end eccentricities, and possible stress related failure. The notation for eccentricity is as follows :

the larger eccentricity at either top or bottom end, taken as positive

the smaller eccentricity, at the other end, and is negative where the eccentricities are on opposide sides of the members

To allow for two-way effects, the following procedure is permitted.

For a wall of height h and length ~ between vertical restraints acting as a two­way panel, the design height (H) is taken as:

For ~/h < 0.67, H=0.75 ~

For 0.67 < ~/h < 2.83, H = 0.32 h + O. 24 ~

(These provisions are a linearisation of a more exact elastic analysis.)

The value of the reduction factor K combines the effects of slenderness ratio, end eccentricity ratio and the eccentricity-to-wall thickness ratio (i.e., the evaluation of Pa , Pe and Pie in the existing AS1640 Brickwork Code).

In the derivation of K, for all effective eccentricities up to 0.05 tw' a nominal eccentricity of 0.05 t has been assumed (as for Ka in AS1640). For larger eccentricities, both t~e magnitude and sense of the end eccentricities are critical, as the walls will be bent in either single or double curvature (the latter being stronger). For the case of equal end eccentricities, the factor K~ from AS1640 has been adopted. For unequal end eccentricities, the AS1640 relatlon­ship:

Pe e2 Pa e 1 e2 p l e = 2 (1 + ~) + 2 (1 - 0.6 t) (1 - e;)

w

is used in the derivation of K.

The provisions for checking a possible stress related failure are based on the assumption of a lineir stress distribution. The design compressive strength for a stress related failure can be calculated from the following:

For solid units: t

(i) For el < ....!i (uncracked section) 6

FI A m b

94

( i i )

For

t w For e l > 6 (cracked section)

ho11ow units:

t For O < e < ~

3 (uncracked section)

p = ~ l 1.25 l FI Ab c a 1 + 2.9 2 m

tw J

where e 1 = 1arger (abso1ute) va1ue of effective end eccentricity

tw = actua1 wa1l thickness

The expression for hollow units has been derived on the assumption that the shel1 thickness/total thickness ratio is 0.175. It can be shown that the relationship is not particularly sensitive to this parameter. Only one equation is given for hollow units, since for typical values of the shell thickenss/total thickness ratio, flexural tensile stresses are not present on the cross-section until the el/tw ratio exceeds 0.33.

Stress-related fa~lures often govern for walls of low slenderness bent in doub1e curvature, particularly when the effective eccentricity is large.

Values of K which correspond to a lateral instability failure may be generated by the formula:

e e1

e H K = 0.5 (1 + e~) [(1 - 2.083 t) (0.0245 - 0.0365 -t) (f - 80) J

w w e e H + 0.5 (1 - 0.6 -t) ( 1 - 2.) [1 - 0.0225 (f - 8)J w el

4.4 Load Eccentricities

Evaluation of loading eccentricity at the top and bottom of a wall requires consideration of a number of factors. These include the relative rotation between the floor and the wa1l, local crushing in the wall-beam joint, changing wall and slab stiffness with load level, non-linear and time dependent material characteristics, two-way slab action, and the construction and loading sequence of the floor slab and walls.

Despite the significant amount of research carried out in this area, simplified design rules for this complex problem are still not available. Several semi­empirical methods have been proposed as described in detail in Reference (7). The procedure proposed by Awni and Hendry (37) appears to be the most comprehensive, but it is complex to apply in practice. A simplified technique has also been proposed by Hendry (7) whose tests have shown that approximately 80% fixity is obtained in a joint if the average masonry stress exceeds 0.3 MPa. In this

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situation, it is reasonable to assume full joint fixity, allowing the load eccentricity to be estimated by an appropriate elastic frame analysi s in wh i ch the connections between the wall under consideration and other membe rs are taken to be rigid. For the purpose of design, the far ends of the members (f loors and walls) attaching to the wall in question may be assumed to be pinned to the further parts of the structure. The use of this method is illustrated in detail in Reference (38).

It should be noted that tests by Awni and Hendry (39) indicate that the degree of fixity achieved at any joint does not depend on the magnitude of the wall compression alone, but also on the relative stiffness of the floor and the supporting wall. When the slab/wall stiffness ratio is small, (say less than unity), substantial fixity will be achieved. As the slab/wall stiffness increases, some fixity will be lost irrespective of the degree of precompression. Recent tests by Stokle (40) have also confirmed frame action but showed that the level of joint precompression required to produce frame action was also a function of the slab load and not just the wall loads from above.

Using the rigid frame approach, a conservative estimate of wall eccentricity will generally be obtained. In walls where the compression from above is high, (as in the lower floors of a multi-storey loadbearing structure), the resulting eccentricity will be small and will not usually present any problems in designo Where the precompression is lower, excessive (and unrealistic) eccentricities may be indicated by the analysis. In this case the degree of eccentricity may be controlled by the use of an insert of soft compressible material beneath the floor slab adjacent to the most heavily stressed face of the wall.

For lightly loaded walls, the assumption of rigid joint behaviour is no longer valid, since relative rotation between the floor and the wall will take place. In the absence of more precise methods, an empirical method suggested in the British code (36) could be used. It suggests that the load from a single floor or roof may be considered to act at one-third of the depth of the bearing area from the loaded face of the wall or, in the case of a continuous floor slab passing over a wall, each side of the floor may be taken as being supported on half of the total bearing area. This method should be applied with caution to slab-wall systems in which large slab deflections are expected (such as long span, heavily loaded one­way systems). In this case significant differential rotation could take place between slab and wall so the eccentricity may need to be controlled with flexible packing.

5. CONCLUSION

This paper has reviewed the factors which influence the strength of load bearing masonry both for small samples of masonry and complete wall panels. Considerable advances in the state of knowledge have occurred in recent years. Significant Australian research in some fundamental areas has been carried out and this, together with overseas research, has served as useful input to the new SAA Masonry Code which is in the final stages or preparation.

Continuing advances in numerical techniques applied to the analysis of masonry structures now enable the behaviour of masonry elements to be analytically studied, provided representative material models can be formulated. This allows parametric studies on the behaviour of structural elements to be carried out with a minimum amount of testing on full scale structural components . Recent research has illustrated the feasibility of this approach, but there is need for much more research into the fundamental behaviour of masonry to allow the formulation of representative material models for the various types of masonry in common use .

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