Design of Clay Masonry for Compression - South...

Design of Clay Masonry forCompression

Manual 6

Think Brick AustraliaPO Box 751, Willoughby NSW 2068(1/156 Mowbray Road, Willoughby)Tel (02) 8962 9500 Fax (02) 99585941 [email protected]

Representing Australia’s claybrick and paver manufacturers

This publication updates and supersedesthe publication of the same name published February 2004.

While the contents of this publicationare believed to be accurate and complete, the information given isintended for general guidance and doesnot replace the services of professionaladvisers on specific projects. Local orstate regulations may require variation from the practices and recommendations contained in this publication. Think Brick Australia disclaims any liability whatsoeverregarding the contents of this publication.

This publication, its contents and formatare copyright 2009 of Think BrickAustralia and may not be reproduced,copied or stored in any medium withoutprior, written authorisation from ThinkBrick Australia. ABN 30 003 873 309.

Cover: Building EB at the University of Western Sydney’s Parramatta campus consolidates teaching andadministrative facilities while allowingthe flexibility required for future alternative uses. Passive design principles have been incorporatedthroughout, with bold external blades offace brickwork forming an effective thermal barrier on the long western elevation. The deep shadows thus created contribute towards a sense ofrhythm and dynamism and break up theoverall bulk into more harmonious scale.Building EB was a finalist in the 2010Horbury Hunt Awards. Designed byHASSELL, structural engineering byArup, constructed by Lipman and bricklaying by Fugen. Photo by LucRemond.

Published February 2009

Prepared by Dr Stephen Lawrence, SPL Consulting Pty Ltd and EmeritusProfessor Adrian Page, The University of Newcastle. W

oodridge

Med

ia 09/10

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9

10

Introduction 8

General principles 9

2.1 Behaviour of masonry elements in compression 10

2.2 Compressive strength of masonry 11

2.2.1 Action in compression 11

2.2.2 Masonry units 12

2.2.3 Masonry strength 14

2.2.4 Special masonry 15

2.3 Effect of engaged piers 16

General basis of design for compression 17

Basic compressive strength capacity 19

Design by simple rules 20

5.1 Procedure 20

5.2 Design charts 24

5.2.1 Walls 2.4 metres high 25

5.2.2 Walls 3.0 metres high 32

Design by refined calculation 39

6.1 Slenderness ratio 41

6.2 Assessment of eccentricity 42

6.3 Reduction factors for slenderness and eccentricity 44

Concentrated loads 46

Composite action between walls and beams 49

8.1 Wall-beam interaction 49

8.2 Composite action in walls with openings 50

Worked examples 51

9.1 Simple wall governed by panel action 51

9.2 Ground floor wall in a three-storey residential walk-up 51

9.3 Concentrated load 54

References 55

ContentsClick on any entry

Figures

1. Frame action in a loadbearing building (typical section) 10

2. Single and double curvature in compression 10

3. Effect of slenderness and eccentricity on compressive capacity 11

4. Behaviour of masonry in compression 12

5. Platen restraint effect for masonry in compression 12

6. Aspect ratio factor for masonry in compression 13

7. Compressive strength of masonry for various unit strengths 14

8. Factor to adjust for unit height/joint thickness 14

9. Thickness coefficients for engaged piers 16

10. Width and spacing of engaged piers 16

11. Equivalent eccentricity approach to combined compression and bending 17

12. Flow chart for the general basis of compression design 18

13. Basic factored compressive load capacity 19

14. Panel action in walls under compressive loading 21

15. Slenderness ratios for various length and support conditions (walls 2.4 m high and 110 mm thick) 21

16. Wall loaded by a concrete slab 22

17. Wall loaded by other than a slab 22

18. Wall loaded on one face 22

19. Slenderness reduction factors for design by simple rules 23

20. Flow chart for compression design by simple rules 23

21. Compressive load capacities for walls 2.4 m high and 90 mm thick, with four edges supported and loaded by a concrete slab 25

22. Compressive load capacities for walls 2.4 m high and 90 mm thick, with three edges supported and loaded by a concrete slab 25

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23. Compressive load capacities for walls 2.4 m high and 90 mm thick, with four edges supported and loaded by a roof or floor other than a slab 26

24. Compressive load capacities for walls 2.4 m high and 90 mm thick, with three edges supported and loaded by a roof or floor other than a slab 26









33. Compressive load capacities for walls 2.4 m high and 150 mm thick, with four edges supported and loaded by a floor attached to the face 31

34. Compressive load capacities for walls 2.4 m high and 150 mm thick, with three edges supported and loaded by a floor attached to the face 31


FiguresClick on any entry

Figures












47. Compressive load capacities for walls 3.0 m high and 150 mm thick, with four edges supported and loaded by a floor attached to the face 38

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48. Compressive load capacities for walls 3.0 m high and 150 mm thick, with three edges supported and loaded by a floor attached to the face 38

49. Flow chart for compression design by refined calculation 40

50. Slenderness ratios for walls 2.4 m high and 110 mm thick, with three edges supported 41

51. Slenderness ratios for walls 2.4 m high and 110 mm thick, with four edges supported 42

52. Simplified assessment of eccentricity 43

53. Slenderness and eccentricity reduction factors for walls with edge supports (single curvature) 44

54. Slenderness and eccentricity reduction factors for e1/tw = 0.2 showing the effect of end restraints and double curvature 45

55. Concentrated bearing factor for solid, cored or grouted masonry 47

56. Dispersion zones for concentrated loads acting on a wall 47

57. Flow chart for concentrated load design 48

58. Simple model of composite action behaviour 49

59. Composite action behaviour 49

60. Composite action with a central opening 50

61. Composite action with an offset opening 50

FiguresClick on any entry

Masonry walls in a structure canresist loads by compression, shearor flexure, depending on the typeof structure and the location of thewalls within it. These actions canoccur in combination, but there isusually one action that governs thebehaviour of each particular wall.This manual deals with design forcompression loading, while designfor shear and flexure are dealt within the CBPI Manual 4, Design of ClayMasonry for Wind & Earthquake

1.

As well as design for compression,shear and flexure forces, all wallsshould be checked for robustnessto ensure that they are serviceablein the absence of specific appliedloading. Design for robustness isdealt with in Think Brick AustraliaManual 7, Design of Clay Masonry forServiceability

2.

This manual follows the procedures set out in MasonryStructures (AS 3700)

3for the

design of unreinforced clay masonry to resist compressiveforces. For any aspects not coveredhere, reference should be made toAS 3700. Useful guidance on theinterpretation of AS 3700 can alsobe found in its commentary

4.

This manual covers the generalarrangement of loadbearingmasonry structures, material properties for clay masonry, specific design procedures for vertical loading, both simple andrefined, design for concentratedloads, and composite actionbetween walls and beams. It covers walls and piers subjectedto predominantly vertical loading.Design charts for vertical loadingand worked examples for typicalcases are included.

1. Introduction

8 / Design of Clay Masonry for Compression

Unreinforced loadbearing masonrystructures greater than fourstoreys in height are common inother parts of the world (for example in Europe) and have beenbuilt in Australia in the past.Modern Australian codes and standards permit the use of unreinforced loadbearing masonryin structures up to 15m in height,provided earthquake loading isproperly considered. Multiple-occupancy domestic units of loadbearing masonry up to fourstoreys in height are common inAustralia and two-storey semi-detached townhouses are becoming increasingly popular. Inthese buildings, the masonry wallsand piers usually support concretefloor slabs and the roof structure,without any separate buildingframe. The masonry walls mustalso provide the resistance to lateral in-plane (shear) forces, with the floor and roof acting asdiaphragms to distribute forces tothe walls, and this requires a cellular form of structure. Wallsizes in these structures are usuallydetermined by their capacity toresist vertical load.

Loadbearing walls are defined asthose that carry significant verticalload in addition to their ownweight. In other words, they rely ontheir compressive load resistance tosupport other parts of the structure. Buckling and crushingeffects, which depend on the wallslenderness and interaction withthe elements supported by thewall, determine the compressivecapacity of each individual wall. The shape of the units, particularlythe presence and size of hollowcores, influences the compressivestrength of the masonry. Externalloadbearing walls will usually be ofcavity construction to ensure adequate water penetration resistance.

Masonry piers can either be isolated(supporting a slab) or engaged (providing enhanced load resistanceto a wall). Isolated piers aredesigned for compressive loadcapacity in the same way as loadbearing walls. The effect ofengaged piers in stiffening a wall istaken into account by the use of aneffective thickness for the wall/piercombination.

Strength properties of masonry canbe difficult to predict from knownproperties of the mortar andmasonry units, because of the relatively complex interaction of thetwo component materials. For thisreason, values given in AS 3700 formasonry strengths based on theseproperties are conservative.Whenever practical, it is better tomeasure the strength of masonryby testing small specimens (stack-bonded prisms) than to usethe conservative AS 3700 figures.

Tests will always give a more accurate measure of propertiesthan can be obtained from typicalvalues. This can be worthwhile onlarger projects, and classifies themasonry as Special Masonry (seeSection 2.2.4).

Masonry as a material has inherently variable properties. This variability arises because ofnatural variations in the materials,the manufacturing processes and the site conditions, and workmanship. Partial safety factors used for design makeallowance for this variability andensure that the resulting structures are safe and serviceable,provided that the workmanship isadequate. Masonry is sometimesconsidered to be an architecturalrather than a structural materialand this can mean that supervisionis not as thorough as it is for structural elements. The importance of supervision of construction cannot be overestimated for loadbearingmasonry, especially when it isclassed as Special Masonry. The potential economic benefits inthe use of structural materials aregreat when the full strength of thematerial is utilized in design andensured by adequate supervision.

Design of Clay Masonry for Compression / 9

2. General principles


Figure 1. Frame action in a loadbearing building (typical section)

Figure 2. Single and double curvature in compression

Depending on the relative signs ofthe eccentricity at opposite ends ofthe wall, the combined loading willgive rise to either single or doublecurvature (see Figure 2). A wall subjected to double curvature hasa much higher resistance to buckling than a wall in single curvature, because of the reducedsecond-order (P-δ) effect and thiscan be taken account of in design.

2.1 Behaviour of masonryelements in compression

In loadbearing masonry buildings,the masonry is basically designedto act in compression, with theloadbearing walls transmitting vertical loads from storey to storeydown to the foundation. Lateralloads caused by wind and earthquake are transmitted to thefoundation by shear wall action and also produce bending moments in the walls that are normal to the direction of the loads.Further bending moments arise inthe walls from the floor loading,

which is transmitted to the wallsbecause of partial joint fixity wherethe floors rest on the walls. Full orpartial frame action in the structureis therefore mobilised, with thedegree of joint fixity depending onthe level of pre-compression (seeFigure 1). The masonry walls aretherefore subjected to combinedcompressive and bending actions.These combined compressive forcesand bending moments acting simultaneously can be expressed asa compressive force acting at anequivalent eccentricity, as detailedin Section 3.

Floorslab

Bearing walls

A

B

A

B

Combined bendingand compressionactions on wall A-B

Dead +Live Load

Positiveeccentricity


Negativeeccentricity

SingleCurvature

DoubleCurvature


Dead Load


In general, the compressive loadcapacity of a masonry wall or pierdepends on four factors:

• The characteristic compressivestrength of the masonry.

• The cross-sectional area resistingthe load.

• The slenderness.

• The effective eccentricity of loading at each end and theresulting deflected shape (single or double curvature).

2.2 Compressive strengthof masonry

2.2.1 Action in compressionWhen slenderness effects are eliminated, the compressivestrength of masonry is a functionof the masonry units and the mortar. The compressive strengthof masonry is usually less than thatof the units alone, because of theinfluence of the mortar joints.When considering the action ofmasonry in compression, a distinction must be made betweensolid and hollow masonry units.These terms are used in AS 3700 asfollows:

• Solid masonry units, whichmight have frogs or cores, arelaid in a bed of mortar coveringthe full bed face area (called fullbedding).

• Hollow masonry units, whichusually have a large proportionof hollow cores, are laid withstrips of bedding mortar on theface shells and no mortar on thewebs (called face-shell bedding).

There are two possible modes offailure for masonry membersunder eccentric compression.These mechanisms are quite different and would rarely occur intheir pure form; most walls andpiers, if overloaded in a building,would fail by a combination ofboth effects. The first mechanismis crushing, which would only beobserved in short stocky mem-bers, and the second mechanismis buckling, which would occur inlong slender members. The transition between these twoextremes is shown schematicallyin Figure 3, with the various curvesshowing the effect of increasingeccentricity of loading. The calculation of member capacitytherefore requires both the compressive strength of themasonry and the effects of buckling to be taken into account.

Figure 3. Effect of slenderness and eccentricity on compressive capacity

Crushing Transition Buckling

Increasing eccentricity


Figure 4. Behaviour of masonry in compression

Solid masonry unitsWhen masonry constructed withsolid units is subjected to directcompression and loaded to its fullcapacity, failure will be initiated bythe lateral expansion of the mortarjoints (the Poisson’s Ratio effect),which causes vertical tensile cracksto form in the masonry units. Whileboth materials expand laterally, themortar joints are weaker and therefore more flexible than theunits are, and expand to a greaterextent. This induces tensile stressesin the units and corresponding lateral compressive stresses in themortar (see Figure 4).

The measured compressive strength is therefore affected by the following:

• Tensile strength of the masonryunit. For clay units, the materialitself, the degree of firing, and thecoring pattern all affect this property.

• Mortar joint thickness. In highlystressed loadbearing walls, thicker mortar joints wouldincrease the splitting force on theunits. An appropriate correctionfactor can be applied, but the jointthickness is best limited to 10 mmin these structures.

• Mortar strength. Because mortarwith a low strength generally hasa lower elastic modulus, it has agreater lateral expansion underload and therefore a higher tendency to split the units. It istherefore important to use a mortar with adequate strength in loadbearing masonry construction. If the mortarstrength is very low, then crushingof the mortar itself might occureven before tensile failure isinduced in the units.

2.2.2 Masonry unitsWhen a prism of any material istested in compression, the rigidplatens of the testing machine,through friction, confine the upperand lower faces and resist the tendency of the material to spreadunder load (see Figure 5). This phenomenon has the effect ofenhancing the apparent strengthof the material. The platenrestraint effect varies with the relative height to width of themasonry unit. Because masonryunits are available in a wide rangeof sizes and shapes, the effect isnot the same for all units and mustbe corrected so that all unit shapesare treated equally for design.

Hollow masonry unitsFor hollow units, the compressivestrength of masonry is based uponface-shell bedding and when prismtests are carried out with hollowunits they use this form of loading.In this case, the mode of failure differs from that applying for solidand cored units. Load appliedthrough the face shells is transferred into the webs, causingtransverse tensile stresses. Thiscauses web splitting followed bycrushing of the mortar joints andspalling of the face shells as aresult of the subsequent stressredistribution. Because of this different mode of behaviour, thestrength of hollow unit masonry isless affected by mortar strengththan is the strength of solid andcored unit masonry.

Grouted hollow masonryWhere hollow units are filled withgrout, the compressive strengthsof the blocks and the grout cannotbe simply added. The grout, whichis usually less stiff than the units,has a greater lateral expansionunder compressive load and tendsto burst the units. AS 3700 allowsfor this when determining thebasic compressive capacity.

Figure 5. Behaviour ofmasonry in compression

Tendency of mortarto expand laterallyto a greater extentthan the units

Induced tensilestresses in the units

PlatenFriction

Load

Splitting Force


For hollow units, the aspect ratiofactor is based on the height-to-thickness ratio of the face shell,which is usually greater than 5. The factor is therefore usually 1.0.

The compressive strength for units used in design is called anunconfined strength, which meansthat the effects of platen restrainthave been eliminated. An adjustment factor based on theheight-to-width ratio of the unit isused. There is no international standard method of adjusting forthis effect, and this makes comparisons between variousnational standards difficult. AS 3700 adopts the strength corresponding to a prism of material with height equal to fivetimes its width as a standard basisfor this adjustment. This assumesthat the platen restraint effect isnegligible at these proportions andthat the effects of load eccentricityhave not yet become significant.The correction factor is called theaspect ratio factor and is tabulatedin AS 3700 Appendix C (see Figure 6).

Figure 6. Aspect ratio factor for masonry in compression

The dimensions used for finding theaspect ratio factor are the work sizedimensions of the unit, that is, thenominal dimensions specified by themanufacturer. This is particularlyimportant for hollow units, wherethe face shells might vary in thickness (taper from top to bottom) but the manufacturer nominates a single work size dimension. This ensures that anycompressive strength calculationsare made on the same basis as thatused by the manufacturer to ratethe strength of the units.

The standards require compressivestrength for hollow units to bedetermined by testing under loadapplied to the face shells only, tosimulate the way in which they willbe laid. This ensures that the failuremechanisms in compression for thetest and the units in the structurewould be the same.

The symbol used for the characteristic unconfined compressive strength of units is f ‘uc. As for other structural designproperties, the compressivestrength used in design is the 95%characteristic value. This strength isexpected to be exceeded by 95% ofthe material, ensuring a very lowrisk of structural failure.

Typical characteristic strengths (f ‘uc) for clay masonry units rangefrom 12 MPa to 40 MPa or more.

1

5


2.2.3 Masonry strengthMasonry strength depends on theinteraction between the units andthe mortar. Mortar strength (andtherefore masonry strength) is usually lower than the unit strength.

As for the case of masonry units, an unconfined characteristic compressive strength of the masonry based on a height-to-thickness ratio of five is used fordesign. This compensates for platen restraint effects in testingand brings all masonry types to a common basis for comparison.

Consistent with the behaviourmechanism described in Section2.2.1, strength tests on masonryprisms have shown a strong correlation with the strength of the masonry units and the mortarcomposition. AS 3700 gives characteristic compressive strengthsfor masonry with various unitstrengths and mortar compositionsin Table 3.1 and these are showngraphically in Figure 7. The AS 3700table is based on the characteristicunconfined compressive strength of the unit, the material of manufacture, and the classificationof the mortar. The values have beenestablished from a lower bound fit toa wide range of tests carried out inAustralia and will be adequate formost cases without confirmation by testing. While it will usually bepossible to obtain a higher value ofdesign strength by carrying outtests, this would require preciseknowledge at the design stage ofthe type of unit to be used on thejob. It would also require the masonry to be classified as SpecialMasonry for compressive strengthand site control tests would then berequired during construction (seeSection 2.2.4). This is difficult, butthe potential benefit from the higherstrength will sometimes justifyaccepting these restrictions.

Figure 7. Compressive strength of masonry for various unit strengths

Figure 8. Factor to adjust for unit height/joint thickness

The compressive strength of themasonry is further adjusted in AS 3700 (Clause 3.3.2) by a factorthat allows for the effect of themortar joint thickness by relating itto masonry unit height (see Figure8). This factor is 1.0 for traditionalbrick-sized units of 76 mm heightwith mortar joints of 10 mm thickness, because the values in AS 3700 (shown in Figure 7) havebeen based on these dimensions.

For taller units, where a smallernumber of joints will be used in agiven wall height (or where thejoint is thinner in relative terms)the strength is enhanced.Conversely, for less-tall units thestrength will be reduced because of the higher number of joints. The resulting characteristic compressive strength of themasonry is referred to by the symbol f ‘m.


2.2.4 Special masonryWhenever a designer uses higherdesign strength than the defaultvalue given in AS 3700, the corresponding masonry is classifiedas Special Masonry. This means thatsite testing for quality controlbecomes mandatory for thatmasonry.

For determination of designstrength, tests must be carried outat the design stage, using the samematerials (units and mortar) andthe same workmanship as thatintended for the actual construction. These pre-construction tests are conducted asspecified in AS 3700 Appendix C andthe results are used to determine a characteristic strength in accordance with AS 3700 AppendixB. By following this procedure, thefull strength of the material in compression can be utilized and thiscan often be significantly more thanthe minimum compressive strengthguaranteed by the manufacturer.

During construction of masonryclassed as Special Masonry, testsmust be carried out for quality control and to assess compliance.The test regime is specified in AS 3700 Clause 11.7. The standardspecifies the rate of sampling as onesample per storey height or onesample per 400 m2 of walling,whichever gives the greater numberof samples, with at least two samples for any job. The number ofspecimens in a sample is at leastthree for determination of compressive strength. This qualitycontrol testing is in accordance withAS 3700 Appendix C, as for tests todetermine the design strength, butin this case, the assessment of testresults is based on the averagestrength of the test sample.

For quality control purposes, theaverage test result is compared withthe target strength. If the strengthfalls below the target then reasonsshould be sought and remedialaction taken. This is purely for thepurpose of control on site and isquite distinct from the assessmentof compliance, although the sametest samples can be used for bothpurposes. The target strength specified by AS 3700 is 1.4 f ‘m forcompression, where f 'm is thedesign characteristic strength.

For assessment of compliance ofSpecial Masonry, each individual testsample represents a segment of masonry on the job and this relationship should be tracked andrecorded on site. Then if the result ofany sample falls below a specifiedstrength level the whole of themasonry represented by that sample is deemed not to complywith AS 3700.

The use of testing to control construction of Special Masonry isdescribed in Think Brick AustraliaManual 10, Construction Guidelines forClay Masonry

5, and illustrated with

sample charts for quality control and assessment of compliance.

2.3 Effect of engaged piers

The thickness coefficient forengaged piers reflects the stiffening effect that piers have inincreasing the buckling resistanceby increasing the effective radius of gyration of the section. Thiscoefficient depends upon the relative pier thickness, pier widthand pier spacing. When applied tothe wall thickness, it gives an effective thickness of a rectangularsection having an equivalent radiusof gyration to the 'T' section.

For the stiffening to be effective, it requires full engagement of thepier, with bonding or tying asrequired by AS 3700 Clause 4.11.

Values are tabulated in AS 3700Table 7.2 for overall thicknesses (ofwall and pier combined) of two andthree times the wall thicknessalone. Figure 9 shows these valuesplotted against the ratio of pierspacing (centre to centre) and pierwidth. The pier width and spacingare illustrated on Figure 10.


Figure 10. Width and spacing of engaged piers

Figure 9. Thickness coefficients for engaged piers

width width width

spacing spacing

Compressive strength design in AS 3700 uses a tiered approachcomprising two levels – design by simple rules and refined calculation. Both use the samegeneral approach, but they differ in the method of allowance for slenderness and eccentricityeffects. The refined calculationmethod is more specific aboutthese factors and can producemore efficient designs, but at theexpense of greater calculationeffort.

Whereas some masonry codes inother parts of the world deal withcompression and bending effectsacting together by considering aninteraction diagram for the behaviour of the material, AS 3700deals with it by an equivalenteccentricity approach, in which thevertical load is considered to act at equivalent eccentricities at thetop and bottom of the wall. These equivalent eccentricities incorporate the effects of anyimposed bending actions.

AS 3700 sets out the general basisof design for unreinforced masonryin Clause 7.2. The approach is basedon the assumption that design forbending due to lateral forces anddesign for light compression loadscan be treated separately, ignoringany interaction. Consequently, provided the compressive stress isless than or equal to three timesthe characteristic flexural tensilestrength (f 'mt) design for bendingdue to lateral forces can be carriedout using the lateral load provisions in AS 3700 (see Manual4, Design of Clay Masonry for Wind &Earthquake1). Under these circumstances, the compressiondesign excludes forces andmoments arising from transientout-of-plane loads. In practice, thiscalculation will usually be carriedout using the simple rules procedure (see Section 5).

Where the level of compressivestress exceeds the limit of threetimes f 'mt, the bending provisions inAS 3700 do not apply and compression design must include allforces and moments. This is handledby converting the bending momentsto vertical loads at equivalent eccentricities. Thus a concentricload P acting simultaneously with amoment M will be replaced by theload P acting at an eccentricity e,where e = M/P (See Figure 11). Designfor compression in these situations can use the refined calculation procedure (see Section 6)but, in practice, the common caseswould be carried out more quickly(and conservatively) using the simple rules procedure (see Section 5).

3. General basis of design for compression


Figure 11. Equivalent eccentricity approach to combined compression and bending

P P

is equivalent to where e = M/P

M

e

The flow chart shown in Figure 12summarizes the general basis ofdesign as set out in AS 3700Clause 7.2 and discussed above.

Both the slenderness and eccentricity effects are incorporated into a single set ofreduction factors, which are provided separately for the simplified and refined calculationmethods. These reduction factorsare applied to a basic compressivecapacity (see Section 4) to give theload capacity of the member beingdesigned.

The simplified method is sufficientfor most cases commonly encountered and design charts forthis approach are provided in thismanual (see Section 5.2). In thesimplified method, the end eccentricities are dealt with bydefining three common cases ofend restraint and tabulating slenderness reduction factors forthese cases, based on all membersbeing in single curvature (a conservative assumption insome cases). Unlike the refinedmethod, this approach uses a single combined factor to cover lateral buckling and crushing failure. The simplified approach isdescribed in Section 5.

The method of refined calculationrequires the assessment of endeccentricities and takes fullaccount of the strengtheningeffect of double curvature, wherethe eccentricities at the two endsof a member are of opposite sign. A full range of slenderness coefficients is provided, dependingon the end conditions of the wallor pier. The refined method usesseparate reduction factors for lateral buckling and for crushingfailure. The method will thereforegive the most efficient design inany given situation. It can providea substantial strength increase incomparison with the simplifiedmethod, but it is complex to apply.The refined calculation method isdescribed in Section 6.


Figure 12. Flow chart for the general basis of compression design


Both the simplified and refinedmethods use a basic compressivestrength capacity, which is derivedas follows for ungrouted masonry:

Where:

Φ = Capacity reduction factor = 0.45 for compression in unreinforced masonry (see AS 3700 Clause 4.4)

f ‘m = Characteristic compressivestrength of the masonry

Ab = Bedded area

The design characteristic compressive strength f ‘m is eitherobtained from the default valuesgiven in AS 3700 Table 3.1 or fromtests on the actual materials andmethods to be used in the construction (see Section 2.2).

The bedded area Ab is calculated asspecified in AS 3700 Clause 4.5.4,allowing for any raking of the mortar joints. It is based on full bedding for solid or cored units andface shell bedding for hollow units.The length and width of the unitsused to calculate this area should always be based on the manufacturer's work size dimensions, not on actual measurement of individual masonryunits, as explained in Section 2.2.2.

Basic compressive load capacitiesare shown in Figure 13 for wall thicknesses of 90 mm, 110 mm and150 mm and for a range of masonrycompressive strength. The calculations are based on the fullbedded area with no joint raking.

4. Basic compressive strength capacity

Figure 13. Basic factored compressive load capacity


5.1 Procedure

It can be difficult to establish theend eccentricities for a given set ofwall support conditions and AS 3700 provides a simplifiedmeans of design to cover the mostcommon cases without the need tomake this assessment. In thisapproach, the slenderness andeccentricity factors are combinedinto a single set of coefficients,which are tabulated for three common end support cases. In doing so, simplifying but conservative assumptions aremade for end restraint conditionsand the deflected shape of the wallunder the applied end moments.This is called design by simple rules.

The design equation for the simplified method is:

Where:

Fd = Design compressive strengthcapacity of the wall

k = Slenderness and eccentricityreduction factor obtained fromAS 3700 Table 7.1)

Fo = Basic compressive strengthcapacity (see Section 4)

To find the slenderness and eccentricity reduction factor it isnecessary to establish the slenderness ratio of the wall. This is derived as follows (see AS 3700Clause 7.3.3.3).

Slenderness ratioFor a wall with no vertical edgesupport

Where:

av = Slenderness coefficient forvertical span

= 1.0 for top edge support

= 2.5 otherwise

H = Clear height between supports or the overall heightof the wall

kt = Thickness coefficient forengaged piers – see Section2.3

t = Thickness of the leaf

Consequently, for walls with onlythe top and bottom supported(one-way spanning walls) andwhere there are no engaged piers,the slenderness ratio is simply theheight-to-thickness ratio.

If there is no top support, the slenderness ratio is based on anequivalent height of 2.5 times theactual height. Such a cantileveredwall, with a vertical load appliedand yet no lateral support at thetop, is rare and its size is severelyrestricted by the high slendernessratio.

For a wall with at least one verticaledge supported, the slendernessratio is given by the lesser of theabove equation and the following:

Where:

av = Slenderness coefficient for vertical span

= 1.0 for top edge support

= 2.5 otherwise

H = Clear height between supportsor the overall height of the wall

ah = Slenderness coefficient for horizontal span

= 1.0 for both vertical edges supported

= 2.5 for one vertical edge supported

L = Clear length between supportsor the overall length of thewall

t = Thickness of the leaf

Note that in this equation the factorfor the stiffening effect of engagedpiers is not included, because theaction is a combination of the horizontal and vertical slendernesseffects as described below.

5. Design by simple rules


The purpose of this second equationis to allow for the so-called ‘two-waypanel action’, which has the effect ofstrengthening a wall against buckling when its length is shorterthan its height and at least one vertical edge is supported. The equation is an empirical approximation to the behaviour,which is illustrated in Figure 14.

Figure 14 shows an illustration ofpanel action in walls. If the bucklingload for a square panel supportedonly at its top and bottom is P, thenthe corresponding load for the samepanel with all four edges supportedis 4P. For a similar panel that is threetimes the height, the buckling loadis also 4P, because the length andnot the height governs the bucklingshape. The same would apply forany height of wall.

Figure 14. Panel action in walls undercompressive loading

Figure 15. Slenderness ratios for various length and support conditions (walls 2.4 m high and 110 mm thick)

P

P

4P

4P

4P

4P

Supported top and bottom

Supported on four sides

Supported on four sides

To illustrate how the slendernessratio is influenced by the walllength and support conditions,example slenderness ratios areplotted in Figure 15 for walls 2400mm high and 110 mm thick. It canbe seen that the slenderness ratiois limited once a certain length isreached.

Once the slenderness ratio is calculated, the slenderness andeccentricity reduction factor isfound (see AS 3700 Table 7.1). These factors are tabulated forthree different end support conditions, thus avoiding the needfor the designer to calculate endeccentricities. Slenderness ratiosup to 36 are provided for.

thickness based on a combinationof the two leaf thicknesses wasused for such a case. However,later research showed that eachleaf acts independently and thereis no mutual support available toenhance load capacity. AS 3700therefore requires that each leaf bedesigned separately for its share ofthe vertical load. In the majority ofcases, the vertical load is takenentirely by the inner leaf of the cavity wall and the outer leaf actsonly as a cladding.

Figure 20 is a flow chart summarising the design processfor compression by simple rules.

Worked Example 9.1 shows thedesign by simple rules of a wallgoverned by panel action.

End support conditionsFigure 16, Figure 17 and Figure 18illustrate the three end supportconditions covered by the simplemethod. These are a wall supporting a concrete slab, a wallsupporting a roof or floor otherthan a concrete slab, and a wallwith a side-attached load (such as a floor) and at least one storeyheight of masonry above thatlevel. In the last case, the wallmust be at least 140 mm thick.

Figure 19 shows the slendernessreduction factors for the three support cases illustrated on Figure 16, Figure 17 and Figure 18.Note the higher factors for a wallloaded by a concrete slab, compared with those for a wall supporting another type of load.This is because the concrete slabimposes a greater degree of endrestraint, causing the equivalentload to act at a smaller eccentricity

than for other types of load. Thefactors for a load attached at theside of the wall are very lowbecause of the high eccentricity. In this case, since the load beingapplied to the wall is outside thewall thickness, the load from aboveis critical in moving the resultant of the two forces within the wallthickness and thus avoiding inherent instability. This is the reason for the requirement of atleast one storey of masonry (andthus superimposed load) above the level under consideration.

In the past, it was assumed thatthe two leaves of a cavity wall provided mutual support againstbuckling and an equivalent


Figure 16. Wall loaded by aconcrete slab

Figure 17. Wall loaded byother than a slab

Figure 18. Wall loadedon one face

Minimum140 mm

Minimum ofone storey


Figure 19. Slenderness reduction factors for design by simple rules

Figure 20. Flow chart for compression design by simple rules


5.2 Design charts

The following design charts can beused for design according to simplerules for walls with slab or otherloading and with supports on fouredges or on three edges with oneend free. For the use of these charts,the loading conditions must correspond with one of the casesillustrated in Figure 16, Figure 17 andFigure 18. The applicable case is indicated on each chart by an icon.

Charts are provided for thicknessesof 90 mm, 110 mm and 150 mm incombination with heights of 2.4 mand 3.0 m. For the case of face loading, the only thickness providedfor is 150 mm because AS 3700requires the wall to be at least 140 mm for this loading case.


Figure 22. Compressive load capacities for walls 2.4 m high and 90 mm thick, with three edges supported and loaded by a concrete slab

Figure 21. Compressive load capacities for walls 2.4 m high and 90 mm thick, with four edges supported and loaded by a concrete slab

5.2.1 Walls 2.4 metres high


Figure 24. Compressive load capacities for walls 2.4 m high and 90 mm thick,with three edges supported and loaded by a roof or floor other than a slab

Figure 23. Compressive load capacities for walls 2.4 m high and 90 mm thick, with four edges supported and loaded by a roof or floor other than a slab


Figure 25. Compressive load capacities for walls 2.4 m high and 110 mm thick, with four edges supported and loaded by a concrete slab

Figure 26. Compressive load capacities for walls 2.4 m high and 110 mm thick, with three edges supported and loaded by a concrete slab



Figure 27. Compressive load capacities for walls 2.4 m high and 110 mm thick,with four edges supported and loaded by a roof or floor other than a slab


Figure 29. Compressive load capacities for walls 2.4 m high and 150 mm thick,with four edges supported and loaded by a concrete slab

Figure 30. Compressive load capacities for walls 2.4 m high and 150 mm thick,with three edges supported and loaded by a concrete slab



0



Figure 33. Compressive load capacities for walls 2.4 m high and 150 mm thick,with four edges supported and loaded by a floor attached to the face

Figure 34. Compressive load capacities for walls 2.4 m high and 150 mm thick,with three edges supported and loaded by a floor attached to the face

0




5.2.2 Walls 3.0 metres high


Figure 48. Compressive load capacities for walls 3.0 m high and 150 mm thick,with three edges supported and loaded by a floor attached to the face

Figure 47. Compressive load capacities for walls 3.0 m high and 150 mm thick,with four edges supported and loaded by a floor attached to the face

Design of Clay Masonry for Compression /39

In the method of design by refinedcalculation, the slenderness andeccentricity reduction factors arecalculated considering the actualsupports of the wall and makingan assessment of eccentricities atthe top and bottom and theireffect on the wall deflected shapeand buckling capacity.

Similar to the simplified designapproach, the slenderness ratio iscalculated using a vertical coefficient av and a horizontal coefficient ah in combination withthe height and length of the wall.The stiffening effect of anyengaged piers is also considered.The horizontal coefficient dependson whether one or both verticaledges of the wall are supportedand is identical to that used forsimplified design. It is never considered justified to assume anydegree of rotational restraint tothe vertical edges of a wall.

For a support to qualify as effectiveit must satisfy the AS 3700 conditions for load resistance, butno stiffness requirement isimposed. The vertical coefficient iscalculated taking into account thedegree of lateral support and rotational restraint at the top andbottom of the wall, rather thanbeing based on a few commoncases as it is for simplified design.The calculation of slendernessratios for the refined method isdescribed and illustrated in Section 6.1.

In addition to calculating the slenderness ratio, the refined calculation method requires anassessment of end eccentricities at the top and bottom of the wall. AS 3700 permits this to be done by a rigorous calculation methodor by certain simplifying assumptions. The assessment of eccentricity is illustrated in Section 6.2.

Once the slenderness ratio and endeccentricities have been determined,the reduction factor is calculated asthe lesser of two factors. The first ofthese accounts for the possibility oflateral buckling of the wall and thesecond accounts for the possibility of local crushing in the masonry. The worst of these two possibilitieswill govern in any particular case.The calculation of slenderness andeccentricity reduction factors is illustrated in Section 6.3.

Figure 49 is a flow chart summarisingthe design process for compressionby refined calculation.

Worked example 9.2 shows thedesign of a wall in a residential walk-up building, illustrating that a more efficient solution can beachieved by refined calculation than by simple rules.

6. Design by refined calculation


Figure 49. Flow chart for compression design by refined calculation


6.1 Slenderness ratio

For walls designed by refined calculation, the slenderness ratio iscalculated using similar expressionsto those used for simple design, butwith a broader range of possible values for the slenderness coefficientav. This reflects a broader range ofsupport conditions considered in the design.

The possible values for av are as follows:

0.75 Where the wall is assessed ashaving lateral support and partial rotational restraint atboth top and bottom.

0.85 Where the wall is assessed ashaving lateral support at bothtop and bottom and partialrotational restraint at onlyone of them.

1.0 Where the wall is assessed ashaving lateral support and norotational restraint at bothtop and bottom.

1.5 Where the wall is assessed ashaving lateral support andpartial rotational restraint atthe bottom and only partiallateral support at the top.

2.5 Where the wall has no support at the top, in otherwords it is freestanding.

Cases of walls where the varioussupport and restraint conditionsare deemed to be satisfied are illustrated in AS 3700 Figures 7.1 to 7.5.

Figure 50 and Figure 51 show theslenderness ratios applicable forwalls 2400 mm high and 110 mmthick with support on three sidesand four sides respectively. The limitation of slenderness ratiobased on height and the effect of the slenderness coefficient,which depends on the support conditions at top and bottom, can be clearly seen.

Figure 50. Slenderness ratios for walls 2.4 m high and 110 mm thick,with three edges supported


Figure 51. Slenderness ratios for walls 2.4 m high and 110 mm thick, with four edges supported

6.2 Assessment of eccentricity

The effective eccentricity at a jointbetween a masonry wall and abeam or slab that it supports isdetermined by the relative stiffnessof the members and the degree ofjoint fixity that exists. Factors thatinfluence the effective eccentricityinclude local crushing in the joint,opening up of the joint (relativerotation between wall and floorslab), non-linear material properties and two-way slab action.The degree of joint fixity is also influenced strongly by the magnitude of compressive loadtransmitted from the levels above.

Ideally, for a wall supporting a slab or beam, with additionalmasonry above the level under consideration, assessment ofeccentricity requires an equivalentframe analysis, which involves calculation of the masonry stiffnessabove and below and calculation ofthe slab or beam stiffness and therelative rotation between it and thewall. This calculation is relativelycomplex and AS 3700 permits asimple assumption that, where afloor or roof frames into a wall, itsload can be considered to act at aneccentricity of one-third of thebearing thickness. If the floor orroof is continuous across the wallthen each side is considered to besupported on half of the bearingthickness. In this approach, the vertical load coming from the levelabove is assumed to be axial at thelevel under consideration.


Figure 52 illustrates these simplifiedassumptions for assessment ofeccentricity. For the case of a slabframing into either a solid wall orone leaf of a cavity wall (shown onthe left) the resultant eccentricityis:

For the case of a slab continuousacross a solid wall (shown on theright) the resultant eccentricity is:

In cases where the vertical stresscoming into the joint from the wallabove exceeds 0.25 MPa, a frameanalysis can be carried out to determine the moment, and hencethe equivalent eccentricity, at thejoint. This frame analysis can takeinto account a partial fixity of thejoint between the masonry and thesupported member. For this frameanalysis the remote ends of themembers attached to the wallbeing designed can be assumed as pinned (see Figure 1). The commentary to AS 3700 illustratessome typical joint fixity factorsfrom research on walls compressedbetween concrete slabs. These factors can be used to modify theresults of a rigid-frame analysis.

In extreme cases, very high eccentricities can arise. These canbe dealt with by inserting a strip offlexible packing material under theslab at the edge of the wall. Thishas the effect of permitting a higher joint rotation and relievingsome of the effect of eccentric loadon the wall below the slab. Forcases where high eccentricity is arisk, it is considered good practiceto restrict the maximum eccentricity to one-third of the wall thickness by this method.

Figure 52. Simplified assessment of eccentricity

from above from above

from slab


6.3 Reduction factors for slenderness and eccentricity

Reduction factors for slendernessand eccentricity are calculated fromseveral equations given in AS 3700Clause 7.3.4.5. The equations for lateral instability (buckling) takeinto account slenderness ratio, theratio of the larger end eccentricity towall thickness (e1/tw), and the ratioof the smaller end eccentricity tothe larger end eccentricity (e2/e1)that is, the deflected shape of thewall. There is a lower cut-off foreccentricity of 5% of the wall thickness, which is considered to bethe inherent limit of construction

accuracy. In other words, no wall isassumed to have perfectly alignedend bearings.

If the wall has one or both verticaledges supported, the slendernessratio is calculated assuming panelaction. It therefore cannot deformin double curvature and the reduction factor for lateral instability is based on e2/e1 = 1.

The equations for local crushingtake into account the eccentricityratio (for the larger end eccentricity) and, in the case of hollow units with face-shell bedding, the ratio of face-shellthickness to wall thickness.

The overall reduction factor for any given case is the lower of the separate factors for instability andlocal crushing.

Figure 53 shows the overall reduction factors for walls withsupports to one or both verticaledges (that is, single curvature)and built with solid units, plottedagainst slenderness ratio. A rangeof eccentricity ratios from the minimum of 0.05 to the practicalmaximum of 0.45 is shown. Thehorizontal cut-off at the left-handside of each line on the chart corresponds to the factor for localcrushing.

Figure 53. Slenderness and eccentricity reduction factors for walls with edge supports (single curvature)


Similar relationships hold for wallswith no support on their verticaledges, including cases of equaleccentricity at top and bottom,eccentricity at either top or bottomonly, and opposite eccentricity attop and bottom (leading to doublecurvature). A typical example isshown in Figure 54 for walls builtwith solid units where the ratio ofthe larger end eccentricity to thewall thickness is 0.2 and the eccentricity at the other end isequal but opposite in sign (doublecurvature), zero, or equal and having the same sign (single curvature). The strengtheningeffect of double curvature can be seen.

Figure 54. Slenderness and eccentricity reduction factors for e1/tw = 0.2 showing

the effect of end restraints and double curvature

46/ Design of Clay Masonry for Compression

Figure 55 shows the concentratedbearing factors for solid, cored orgrouted masonry walls and piers.The factor is plotted against theratio of the loaded area Ads to themid-height area of the dispersionzone Ade. Two example cases areshown, namely the case of a concentrated load bearing at thecentre of a wall a1/L = 0.5 and thecase of a load bearing at the end ofa wall a1/L = 0. The curves showthe lower of the two equations ineach case. All other cases will liebetween these two extremes. Thefactor kb is always greater than orequal to one.

When a concentrated load is appliedto a masonry element, there is anenhancement of the compressive(bearing) capacity immediatelybeneath the load because of therestraining effect of the surrounding, more lightly stressed,material. In AS 3700 a strengthenhancement factor is used whenchecking the capacity of walls andpiers supporting this type of load.Although the basic compressivecapacity is used for design, failureunder this type of loading wouldusually be by splitting as a result ofinduced tensile stress. The strengthenhancement depends on the sizeof the loaded area as a proportion ofthe area of the member, as well asthe location of the load, measuredas the closest distance to the end orside of the member. Empirical equations are given in AS 3700Clause 7.3.5.4 for this strengthenhancement factor.

In addition to checking for crushing,the overall performance of the wallor pier must also be checked,assuming the concentrated load tobe spread over a dispersion zone atmid-height.

This treatment of concentratedloads applies equally to situationswhere a load is supported by a wallor pier, in which case the load disperses downwards, and caseswhere a wall is supported on a smallbearing area, in which case the loaddisperses upwards through the wall.The discussion here concentrates onthe more common case of a loadbearing downwards on a wall.

In summary, design for concentrated loads requires twothings:

• Check for crushing on the bearing area under the load(allowing for strength enhancement).

• Check for buckling in the dispersion zone at mid-height(overall member performance).

At the present time, the bucklingcheck requires the refinedapproach to compressive strengthdesign, the principles of which areoutlined in Section 6.

The crushing capacity under a concentrated load is kb Fo

Where:

kb = concentrated bearing factor

Fo = basic compressive strengthcapacity (see Section 4)

The effect of the code provisions isto limit the concentrated bearingfactor kb as follows:

• 1 for hollow masonry (because ofthe absence of load dispersion)

• not < 1 in any case

• not > 2 in any case

• not > 1.5 for a load at the end of amember (because of the limitedpossibility for dispersion)

This is achieved by taking the concentrated bearing factor as thelesser of the following equations:

and

Where:

a1 = distance of the bearing areafrom the end of the wall orpier

L = the length of the wall or pier

Ads = the bearing area

Ade = the area of dispersion at mid-height (see Figure 56)

7. Concentrated loads


Figure 55. Concentrated bearing factor for solid, cored or grouted masonry

Figure 56. Dispersion zones for concentrated loads acting on a wall

Figure 55 shows that the enhancement starts to operatewhen the loaded area falls belowabout 30% of the area in the dispersion zone for centre loadingand about 15% of the area for endloading. Cut-offs apply for loadedareas below about 5% of the dispersion zone area.

Dispersion zones are calculatedbased on a 45° angle of dispersion.They must also not overlap eachother or extend beyond the end ofa member. Various cases are illustrated on Figure 56. The area ofthe member in the dispersion zoneat mid-height is the parameter Ade used for calculating the concentrated bearing factor andfor checking the member againstbuckling under the concentratedload.


Buckling checks are carried out inaccordance with the compressiveload design (Section 6). The appropriate end eccentricity (orend support conditions) must beused as with the case of compressive load design.

The flow chart shown in Figure 57summarizes the procedures forconcentrated load design.

Worked example 9.3 shows thedesign check of the bearing capacity for a beam supported on a masonry wall.

Figure 57. Flow chart for concentrated load design


When a masonry wall is supportedon a beam or slab of concrete orother material, the wall can actcompositely with the supportingmember to resist vertical loads.The resulting action is complex anddepends on the relative stiffness ofthe wall and the supporting member. A common example ofthis is a lintel over an opening in amasonry wall, where the composite action is likely to be partial and is usually ignored.Another situation where composite action arises is for aninfill wall supported on a slab orbeam in a multistorey structure.For this case, assuming that thebeam will support the full load ofthe wall can be unnecessarily conservative, and it can be advantageous to design for composite action.

A full design procedure for composite action is beyond thescope of this manual, but an outline of the behaviour and theimportant design parameters isgiven. Further information and adesign procedure are discussed inThe Australian Masonry Manual6.

8.1 Wall-beam interaction

A simple model of the interactionbetween a loaded wall and its supporting beam would be to consider that the beam supportsonly a triangular portion of thewall, and that the remainder of themasonry and the load from above is supported by arching betweenthe supports. Figure 58 shows schematically this model of behaviour.

However, such a model is of limitedvalue because it does not provideinformation on the compressivestresses in the wall or an accuratepicture of the forces in the beam,either of which can be critical todesign. This model would significantly overestimate theforces in the beam.

Figure 59 shows a wall carrying ver-tical load supported on a beam andillustrates the main characteristics of the behaviour.Arching action develops in the wall,supported by a combination of theabutments (not shown in Figure 59)and the horizontal forces thatdevelop at the wall-beam interface.

These horizontal forces are concentrated towards the ends of the beam and rely on friction developed at the interface. The resulting action is to develop a tensile force in the beam, superimposed on its bending actionunder the vertical load from the wall.As the vertical load progressivelyincreases, a point is reached wherethe friction capacity is insufficient tomaintain the horizontal force andcomposite action is lost. The masonrywill then suffer tensile failure near thecentre at the base of the wall and thebeam will deflect excessively and fail.

The degree of arching depends on therelative stiffness of the wall and thebeam. Both the flexural and axial stiffness of the beam are relevant. In the case of a stiff wall and a veryflexible beam, the latter is actingalmost entirely as a tie to balance thehorizontal compressive stresses in thewall. This is the action for a simple arch bar used over small openings. At the opposite extreme,where a flexible wall is supported on astiff beam, the beam resists the loadprimarily by bending and the wall issubject to much lower stresses.

8. Composite action between walls and beams

Figure 59. Composite action behaviourFigure 58. Simple model of compositeaction behaviour


Another important consideration isthe relative proportion of verticalload transmitted through the walland that applied directly to the beamor slab. If the latter is high, the beamcan separate from the base of thewall and the development of frictionforces to promote arching can be compromised. The resulting horizontal crack at the base of thewall can be unsightly and the lack of sufficient arching might lead tooverstressing of the masonry in tension and result in a vertical crackat this point.

The main parameters for design ofthis combination can be listed as follows:

• Vertical stress in the wall, resistedby the masonry compressivestrength. The critical location forthis action is adjacent to the supports and immediately abovethe beam. If the wall is heavilyloaded in comparison to its compressive capacity this concentration of stress at the supports can lead to crushing.

• Axial force in the beam, resisted by its tensile strength. The tensileforce in the beam will be a maximum at mid-span.

• Shear stress at the interface, resisted by friction between themasonry and the beam. The friction capacity of the interface is influenced by the materials of thewall and beam and the level of compressive stress at the interface.Higher friction is usually likely for aconcrete supporting member thanfor steel.

• Bending moment in the beam, resisted by its bending capacity. The beam must be designed for thecombination of this bendingmoment and the superimposed tensile force.

In addition, the shear and tensilestrengths of the masonry must beconsidered and the constructionsequence can have a significant effect,because failure to prop the beam priorto building the masonry wall willincrease the bendingmoments in thebeam and reduce the capability fordevelopment of composite action.

Most design procedures for compositeaction are limited to cases where theheight of the wall is at least 60% ofthe span for the supporting member.Below this level, the composite actionis usually considered to be partial andnot reliable for design.

8.2 Composite action inwalls with openings

Where walls with openings are seated on flexible supports, theresulting action depends on thelocation of the opening within thewall as well as its size. Central openings have only a small effect,because the wall has a capacity toarch above the opening and stilldevelop the necessary compositeaction.

In the case of an opening near theends of a wall (near the beam supports), the effect of the openingon the potential for compositeaction can be severe. In these cases,it has been suggested that themasonry between the opening andthe end of the wall be designed as acolumn to withstand half of the vertical load transmitted throughthe wall.

Figure 60 shows schematically thedistribution of vertical stressesimposed on a beam as a result ofarching over a central opening andFigure 61 indicates the approximateshape of the distribution for an offset opening.

Figure 60. Composite action with a central opening

Figure 61. Composite action with anoffset opening


9.1 Simple wall governed bypanel action

Design a wall 4m long and 2.7mhigh carrying a concrete slab witha total factored load on the wall of50 kN per metre. Support is provided by intersecting walls atthe sides and the slabs above andbelow. The material is 90mm thickmasonry with M3 mortar (1:1:6) andbrick strength f ‘uc of 20 MPa.

Masonry strength f ‘m = 6.3 MPa (AS 3700 Table 3.1).

Bedded area:

Basic compressive capacity (AS 3700 Equation 7.3.2(1)):

There are no engaged piers, so kt = 1.0

Vertical slenderness coefficient av = 1.0

Slenderness ratio based on height(AS 3700 Equation 7.3.3.3(2)):

Horizontal slenderness coefficientah = 1.0

Slenderness ratio based on panelaction (AS 3700 Equation 7.3.3.3(3)):

Therefore the governing slenderness ratio = 25.6

Slenderness and eccentricity factor= 0.44 (AS 3700 Table 7.1)

Wall capacity (AS 3700 Equation7.3.3.2):

9.2 Ground floor wall in athree-storey residentialwalk-up

Design a cavity wall 5m long and2.7m high, supported on one vertical edge with a window at theother edge. The wall is at theground floor level of an apartmentbuilding with a tiled roof and supports two higher floors havingconcrete slabs, which span 6 monto the inner leaf of the cavitywall and are subjected to floor liveloads of 2 kPa. The factored load onthe top of the ground floor wall is100 kN per metre, comprising 60 kN/m from above and 40 kN/mfrom the first floor slab. Theground floor slab is on fill and isolated from the wall. The wallmaterial is clay masonry with M3mortar (1:1:6) and brick strength f ‘uc of 20 MPa.


9. Worked examples


Try a 90 mm leaf:





Slenderness and eccentricity factor(AS 3700 Clause 7.3.3.2(a)(i)):


For the refined calculationmethod:

Vertical slenderness coefficient av = 0.75 (AS 3700 7.3.4.3(b) & Figure 7.1)


Horizontal slenderness coefficient ah = 2.5

For a 110 mm leaf:

Bedded area:


There are no engaged piers, so kt = 1.0

For the simplified method:

Vertical slenderness coefficient av = 1.0


Horizontal slenderness coefficient ah= 2.5


Therefore the governing slendernessratio = 24.5

Slenderness and eccentricity factor(AS 3700 Clause 7.3.3.2(a)(i)):





Assuming that the load from theslab acts at one-third of the bearing area from the loaded face of the wall (AS 3700 7.3.4.4), theeccentricity of slab loading:

Load from above the first floor slab= 60 kN/m (assumed axiallyapplied).

Load from the first floor slab = 40kN/m acting at an eccentricity of18.3 mm.

Therefore, the effective eccentricityat the top of the wall:

Eccentricity ratio:

At the base of the wall, no momentis introduced from the ground floorslab, so

Therefore

Reduction factor for instability (AS 3700 Equation 7.3.4.5(2)):

Note: this factor could beinterpolated from AS 3700 Table 7.3.

Reduction factor for crushing (AS 3700 Equation 7.3.4.5(3)):

Therefore the governing reductionfactor = 0.546


Try a 90 mm leaf:



Slenderness ratio based on panelaction (AS 3700 Equation7.3.4.3(3)):


The eccentricity of slab loading:


9.3 Concentrated load

Check the bearing capacity for abeam resting on a 110 mm leaf ofclay masonry, 2.4 m high and 3.0 mlong and applying a factored loadof 75 kN. The length of the bearingis 200 mm. The material is claymasonry with M4 mortar (1:½:4½)and brick strength f ‘uc of 30 MPa.


Bedded area:


Distance from the edge of bearingto the end of the wall

With load dispersion at 45º, theeffective length of dispersion atmid-height is 1200+200 mm, sothe ratio of bearing area to area of dispersion:

Concentrated bearing factor (AS 3700 Clause 7.3.5.4) is not lessthan 1.0 and is the lesser of 1.5 and(AS 3700 Equation 7.3.5.4(1)):

Therefore, bearing capacity (AS 3700 Equation 7.3.5.3(1)):

Note: the overall adequacy of thewall under the concentrated loadplus any other applied loads mustalso be checked using the refinedcalculation method as described inSection 6 and illustrated inExample 9.2.

Therefore, the effective eccentricityat the top of the wall:

Eccentricity ratio:

At the base of the wall, assume

Therefore

Reduction factor for instability (AS 3700 Equation 7.3.4.5 (2)):

Reduction factor for crushing (AS 3700 Equation 7.3.4.5(3)):

Therefore the governing reductionfactor = 0.426


This illustrates that a better resultcan be achieved by using refinedcalculation because, using thatapproach, a 90 mm leaf will resistthe applied loads, whereas by thesimple method a 110 mm leaf isrequired.


1. Manual 4, Design of Clay Masonryfor Wind & Earthquake, Clay Brickand Paver Institute, Sydney,1999.

2. Manual 7, Design of Clay Masonryfor Serviceability, Think BrickAustralia, Sydney, 2008 (pending).

3. AS 3700-2001: MasonryStructures, Standards Australia,Sydney, 2001.

4. AS 3700 Supplement 1: MasonryStructures – Commentary,Standards Australia, Sydney,2004.

5. Manual 10, ConstructionGuidelines for Clay Masonry, ThinkBrick Australia, Sydney, 2008.

6. Baker, L.R., Lawrence, S.J. &Page, A.W. Australian MasonryManual, Joint Committee of theNSW Public Works Departmentand the Association ofConsulting Structural Engineersof NSW, Sydney, 1991.

10. References

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