ULTIMATE STRENGTH DESIGN OF MASONRY STRUCTURES - THE NEW ZEALAND MASONRY DESIGN CO DE

M J N PRIESTLEY Reader in Civil Engineering, University of Canterbury, New Zealand

ABSTRACT The choice between elastic theory and ultimate strength theory for the design of masonry structures is discussed. It is shown that elastic theory provides an inconsistent level of protection against failure for both unreinforced and reinforced masonry.

Provisions of a new New Zealand Masonry Design code, which requires ultimate strength design for all masonry, are presented. Most of these provisions are based on seismic design requirements, and are intended to ensure dependable ductile behaviour under inelastic response to earthquakes.

1. INTRODUCTION : ELASTIC OR ULTIMATE STRENGTH?

Masonry has lagged behind other materials in the adoption of an ultimate strength, or limit states design approach, and is still generally designed by traditional methods to specified stress levels under service loads. The reason that codes have not moved to ultimate strength design appears to be the dubious belief that behaviour of masonry structures can be predicted with greater precision at service load levels than at ultimate.

There is, in fact, little evidence to support this belief. At service load levels, the influence of shrinkage (or swelling), creep and settlement will often mean that actual stress levels are significantly different from values predicted by elastic theory. Further, the 'plane-sections-remain-plane' hypo­thesis may be invalid in many cases, particularly for squat masonry shear walls under in-plane loading. Ultimate strength behaviour is, however, rather insensitive to these aspects, so ultimate moments and shears can be predicted with comparative accuracy. There is now adequate test information, particularly for reinforced masonry (e.g. 1-3) to support the application of ultimate strength methods developed for concrete, to masonry structures, whether brickwork or blockwork.

Elastic theory has other drawbacks. Many codes, in specifying elastic theory persist in treating the combination of axial load and bending moment on masonry compression members by requiring that stresses satisfy

( 1 )

where fa and fb are the computed stresses under the axial and bending moments, calculated independently, and FA and FB are the permitted stress levels for pure axial load and pure bending. As is well known, this approach, implying that direct superposition of stresses is applicable, is invalid when cracked-section analysis is used for flexure, and results in extremely conservative designs. Further inconsistencies of elastic theory are examined in the following three examples.

(a) Unreinforced Shear Wall Under Wind Loading Consider the four storey shear vlall shown in Fig. la, subjected to floor loads P1 to P4 and lateral wind loads H1 to H4' resulting in a total axial force Pe and moment Me at the wall base. Typically axial compressions under Pe will be light, and the maximum moment permitted by elastic design will depend on the maximum allowable tension stress ft. Thus

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H, -

===r~===

= ==1P,=== p.

M. , ~/w------I

Floor slabs

(0 1 Wall Elevat ion and Service Loads

0.9 Pa (b) Vert ica l Equilib rium for Stabil ity Ca lcul at ions

2.5 p.

f;"/w.t

2.0 0.10

Mu 0 . 20 M. 1.5

1. 0

0.01 0.5

O O 0.01 0.02 0.03

ft /f;"

(c I Moment Rat io

FIG. 1 - ELASTIC ANO ULTIMATE MOMENTS COMPARE O FOR UNREINFORCEO

(2 )

where ~w and t are the wall length and thick­ness respectively at the base.

For ultimate strength calculations it would be normal to check the moment capacity under reduced gravity load. Fig. 1b shows forces involved in vertical equilibrium under an ultimate stability state defined by

U = O. 9 O + 1. 3W (3)

which is commonly used for Ultimate Strength Oesign Wind loading (4). Assuming an average uniform compression stress of 0.85 fm at the toe, and noting that cracking is assumed to have occurred, the length of the compression zone, a, is given by

0.9 Pe a = 0.85 f~t

and the ultimate moment capacity by

~ - a Mu = 0.9 P e ( w 2 )

(4)

(5)

MASONRY SHEAR WALL Fig. 1c compares the ratio of ultimate moment

(b)

(Eqn. 5) to design elastic moment (Eqn. 2) for a range ofaxial load levels Pe/fm~t and allowable tension strength ft/f~. It will be seen that the level of protection against overturning afforded by elastic theory is inconsistent, but is generally very conserv­ative compared with typical ultimate strength designo However, for very low axial load levels, elastic theory may produce unconservative results, as shown by the curve for Pe/fm~t = 0.01 in Fig. 1c.

Eccentrically Loqded Unreinforced ~ Sl ender Wa 11 Fig. 2 examines the behaviour of a slender unreinforced wall subjected to vertical load with end eccentri-city = e. Moments at midspan are I increased by the structural deflect- h I

4.0

3. 0

1. 0

in Pu only

ions !::. . Sahlin (5) presents an exactl solution for this case, but a simpler, approximate solution for load capacity based on elastic buckling may be found from the equati on \-I~

O'------'-----'----'------'----"'''-'----l_

f c h 2 6E Cf)

h 1 e. th d' . w ere y = - - - 1S e 1menS1on-less dista~ce from the extreme

O. 0 .1 0.2 0.3 0.4 0.5

Eccenlr ic ily . e/ I

(6) ( a ) (b ) Slrenglh Rali o for fe = 0.2 f'm . ~ = 25

FIG. 2 - ELASTIC ANO ULTIMATE LOAOS COMPARE O FOR ECCENTRICALLY LOAOEO UNREINFORCEO SLENOER WALL

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compression fibre to line of action of the load at the top and bottom of the wall, (h/t) is the slenderness ratio, and fc is the stress at the extreme compression fibre at midheight. Eqn. 6 applies for e > t/6, and is always accurate to within 4% of the exact solution. Eqn. 6 may be solved for a specified maximum allowable stress (elastic design), or solved for maximum P, either by using trial values of fc ' or by differentiating Eqn. 6 to find the value of fc for maximum P (ultimate strength) . Fig. 2b compares results for a wall of slenderness ratio h/t = 25, E = 600 fm, maximum allowable stress for elastic design = 0.2 fm, and different levels of end eccentricity. Two curves are shown, one where the maximum elastic design load Pe is based on solution of Eqn. 6 for fc = 0.2 fm, and the other where additional moments due to the P-6 effect are ignored. The ultimate value for zero eccentricity was based on the Euler buckling load. It will be seen that where P-6 effects are included in estimate of both elastic and ultimate load, the curve ends at e/t = 0.313, since Eqn. 6 indicates instability for maximum stress less than fc = 0.2 fm at higher eccentricities.

Again it is apparent that elastic theory provides inconsistant protection against failure, with elastic design becoming progressively unsafe as end eccentricity increases .

(c) Distribution of Flexural Reinforcement in Shear Walls As a third example of unsound results obtained from elastic theory, the behaviour of reinforced masonry shear walls is examined. Fig. 3 shows two walls of identical dimensions and axial load level, reinforced with the same total quantity of flexural reinforcement, Ast. In Fig. 3a, this reinforce­ment is uniformly distributed along the wal I length, while in Fig. 3b, the reinforcement is concentrated in two bundles of Ast/2, one at each end of the wall . Elastic theory indicates that the distribution of Fig. 3b is more efficient, typically resulting in an allowable moment about 33% higher than for the distributed reinforcement of Fig. 3a. However, for the typically low steel percentages and low axial loads common in masonry buildings, the ultimate flexural capacity is insensitive to the steel distribution. For uniformly distributed reinforcement (Fig. 3a) the small neutral axis depth will ensure tensile yield of virtually all vertical reinforcement, resulting in an ultimate capacity of

M

~ -2 -2 ~

st Ast

.....-Y1 :,I--1Hf-~-1d;f-~1H, IHf-'-1 """" ,~

g- . E _ ly E! .ew

8 4: Y-E"$ o '" ---f

~ ~ t~~' te t f--- j d = d ------l T _ Ast. l y + - 2

( a) Distributod Stoo l (b) Stool Concon t rotod ot E nds

FIG. 3 - EFFECT OF STEEL DISTRIBUTION ON FLEXURAL CAPACITY

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(7)

For reinforcement concen­trated near the ends of the wall, the tension force, at ~ Ast fy is approximately half that for the distri­buted case, but at roughly twice the lever arm, so the flexural capacity remains effectively unaltered.

In fact, there are good reasons for even distri­bution of the flexural steel along the wall. Distributed steel will result in a higher masonry fle xural compression force, and there­fore more efficient compres­sion shear transfer, and

provides a clamping force along the wall base joint, which is an area of potential sliding. Concentration of steel close to the wall ends results in high bond stresses on the limited grout area, and due to vertical cracking in the crushing zone, lateral stability provided by the masonry will often be inadequate to prevent the compression steel from buckling. Thus elastic theory encourages designs which may be detrimental to satisfactory ultimate behaviour. This is particularly important when seismic loading dominates design, as is invariably the case in New Zealand.

2. PHILOSOPHY FOR SEISMIC DESIGN

The considerations discussed above indicate that ultimate strength design is more likely to produce consistently safe masonry buildings than is elastic designo However, when seismic loading is considered, the case for ultimate strength design becomes overwhelming. Consider the smoothed composite acceleration response spectra of Fig. 4a, developed by Skinner (6) from eight Californian accelerograms scaled to the intensity of the El Centro 1940 N-S accelerogram, which is considered to have an annual probability of exceedance (annual risk) of

...... ' ·2 .. ~

!-o-,---,--'+-- Typicol pef'iod range­of Masonry Bu i ldings

2'·0 t &; o.e 2-'. of Criticai Damping

~ I"d-~-

0 ·4 0 ·8 ' ·2 ' ·6 2·0 2 ·4 2 ·8 Fundam~tQ I P~iod - (sr'Cl

t:.y

Lo~1 Displacrmeont

(o) CompOSI~ R~spons~ Speoctro trom Eight ACCf'I~grams (b) Peoak Lat~ral Lood using "Equol- d ispl~nt"

SCQ~d to Et Crntro 1940 N-S (aftrr Skinnrr) Principl@' .

FIG. 4 - SEISMIC LOADS FOR MASONRY WALLS

about 0.007 for the more seismic regions of New Zealand. Masonry structures, being stiff, typically have fundamental periods in the range 0.1 - 0.85s, thus spanning the frequency range of maximum response. Assuming a 5% equivalent viscous damping, peak elastic response of the order of 0.8 9 can be anticipated.

Design for such high lateral force levels is not economically viable, and siesmic coeffici­ents included in most codes are reduced from the elastic

response levels, typically by a factor of about 4, implying considerable ductility demand, as shown in Fig. 4b. Consequently it is to be expected that under the design level earthquake, the structure will attain its ultimate strength, and be required to deform inelastically in a ductile manner without significant loss of strength. The equal displacement principle, illustrated in Fig. 4b implies that the maximum displacement response ]J is independent of the strength for structures of equal stiffness. Thus if a masonry building is designed to allowable stress levels at the code level of lateral load, it will still attain its ultimate capacity under the design earthquake, but with a reduction in the required structure ductility, given by ]J = 6U/6Y ' in Fig. 4b.

Design to elastic theory in such cases is a 'head in the sand ' approach, unless the structure is designed for the full lateral force level corresponding to elastic response. A more realistic approach is to accept that the ultimate capacity of the structure will be attained, and to design accordingly by ensuring that the materials and structural systems adopted are capable of sustaining the required ductility without excessive strength or stiffness degradation.

3. NEW ZEALAND MASONRY DESIGN CODE

3.1 Design Basis A new New Zealand masonry design code is due for publication late in 1984 (7). The document has been strongly influenced by the arguments developed above, and

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has been based on the following basic principles.

(a) Ultima te Strength Design All masonry design will be required to be on the basis of ultimate strength calculations. Elastic theory is not permitted, and allowable working stress limits are not mentioned anywhere in the code.

(b) Compatibi lity with Concrete Code Section design and analysis are virtually identical to normal concrete ultimate strength theory. Thi s means that there is a strong parallel between the masonry design code and the New Zealand concrete design code (8). In fact this parallel is emphasised in the document by frequent reference to the concrete design code, and by adopting a format and sequence of code provisions that closely follows the concrete code. Thus a designer familiar with the concrete code will find 'dri ving' the masonry code comparatively straightforward.

(c) Ductile Seismic Design Seismic design is based on the concept of ductile response under earthquake attack. Provisions are included to ensure the required ductility is available.

(d) Unreinforced Masonry As seismic considerations dominate masonry design in New Zealand, unreinforced mas onry is not permitted, except for low-rise veneer construction.

Some of the provisions of the code, and their background, are discussed in the following section, with particular reference to seismic aspects.

3.2 Structural Forms Fig. 5 shows the four most common masonry structural systems used in New Zealand. Although brick masonry has been used in all of these forms, it is more commonly used as reinforced cavity masonry (Fig. 5a) or veneer wall construction (Fig. 5d), with hollow unit masonry and infill normally constructed in concrete masonry.

3.2.1 Masonry walls. The preferred structural form for masonry subjected to seismic loading is the simple cantilever shear wall. Where two or more such walls occur in the same plane, linkage betweem them is provided by flexible floor

( a) Re-inforceod Groute-d Masonry. (RGM)

(c) Masonry In-fill Panel Construction

{b} Reoinforceod HOllow Unit Masonry(Rhum) (using open -e-nd bond-beoam units. )

T,rnb o:'r j boc k,ng

. ::k~n ll

U"C. '"'om' w.".,.,.. ,

'-----'::or-- F"oot ,n 11 -"

(d) Masonry Veone'e'r Wall Constructton

FIG. 5 - COMMON FORMS OF MASONRY CONSTRUCTION

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slabs (Fig. 6a) to ensure moment transfer between the walls is minimised. Openings within the wall elevation are kept small enough to ensure that the basic cantilever action is not affected. Energy dissipation occurs only in carefully detailed plastic hinges at the base of each wall.

Traditional masonry construction has generally consisted of peri­pheral masonry shear walls pierced by window and door openings, as idealised in Figs. 6b and c. Under inelastic response to lateral load­ing, hinging may initiate in the piers (Fig. 6b) or the spandrels (Fig. 6c). In the former, and more common case, the piers will be required to exhibit substantial

(a ) Linkt2d Cont ilt2v ll r WolIs

Ouct rl ll RQsponS<2

DDD - ilIJil .... ~llnrr

.... , --co

~UTI .. nE1 kl ~

(b) Coupl l2 d Sh<lor Walls

PiQ:r Fei tura Spond rlll Fo rl url2

FIG. 6 - MASONRY SHEAR WALLS UNDER SEISMIC LOADING

of the piers is related to the structure ductility

~ = 2n ( ~ - 1) + 1 p

ductility unless designed to resist elastically the dis­placements resulting from the design earthquake. Plastic displacement (flexural or shear) will inevitably be concentrated in the piers of one storey, generally the lowest, with consequential extremely high ductility demand at that 1 eve 1. It can be shown (9) that for a regular wall where pier height is half the storey height, the displacement ductility factor ~p required

demand, ~, by the expression

(8)

where n is the number of storeys. Thus for a 10 storey masonry shear wall designed for ~ = 4, the pier ductility demand would be ~ = 61. Extensive experimental research at the University of California, B~rkeley (10) has indicated extreme difficulty in obtaining reliable ductility levels an order of magnitude lower than this value. It is concluded that the structural system of Fig. 6b is only suitable if very low structural ductilities are required. The New Zealand masonry design code limits use of this system to structures of only one or two storeys.

Occasionally, openings in masonry walls will be of such proportions that spandrels will be relatively weaker than piers, and behaviour will approximate coupled shear walls, with crack patterns as illustrated in Fig. 6c. Although well detailed coupled shear walls in reinforced concrete constitute an excellent structural system for seismic resistance, diagonal reinforcement of the spandrel beams is generally necessary to satisfy the high spandrel ductility demando Such a rein­forcement system is unsuitable for structural masonry, and strength and stiffness degradation of the spandrel is likely at moderate ductilities, causing the coupled shear wall to degrade towards the linked shear walls of Fig. 6a. Consequently the code limits use of this structural system to walls of 3 storeys or less, unless detailed calculations of available ductility are made.

3.2.2 Masonry infill. Masonry infill has been a common cause of poor performance of reinforced concrete frames under seismic loading, generally because the infill has been considered to be non-structural, and its effect on structural action ignored. The result has all too often been an unexpected shear failure of the columns, particularly when the infill has not extended the full storey height. It must be recognised that masonry infill panels modify the structural behaviour of the containing frame under lateral load, unless sufficient separation is provided at top and sides to allow free deformation of the frame to occur, in which case the panel may be designed as a partition, to carry face-loads only.

Where the infill is not separated from the frame, the code requires the composite action of frame and infill to be considered in analysis. Structural stiffness is greatly increased, and natural period reduced, which is significant to the deter­mination of the appropriate basic seismic coefficient. For purposes of stiffness and force distribution calculations, the infilled frame may be represented by an equivalent diagonally braced frame (Fig. 7), where the effective width of the diagonal masonry strut is one quarter of its length. Generally, the failure mechanism of an infilled frame involves a sliding shear failure along a mortar

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fI h

L • :~ . . '"l~

' d

. I. ld\"a l'$ \" d Wa ll

Brac\"

( Q) DfOformat ,Of"l UnO tof S h~ar loco (b) EQulVol \"nt Broce d Frome for 2 Bay 4 5lo re'Y lnf>ll \"d WoU

te) Kn\" \" Broced Froml" Conc C' p l fo r 511dl/'l9 Shl!'or Falluf \"

FIG. 7 - MASONRY INFILLEO FRAME UNOER LATERAL LOAO

bed, as shown in Fig. 7c. The ensuing ductility demand on the hinging storey, elasti c response levels, unless masonry base cantilever shear wall behaviour of

'soft-storey' mechanism again places high and the code generally requires design to shear stresses are sufficiently low that the infilled frame can be assured.

3.2.3 Secondary walls. Some shear wall structures do not lend themselves to rational analysis under lateral loading, as a consequence of the number, orient­ation and complexity of shape of the load bearing walls. In such cases the code permits the designer to consider the walls to consist of a primary system, which carries gravity loads and the entire seismic lateral load, and a secondary system which is designed to support gravity loads and face loads only. This allows simplification of the lateral load analysis in cases where the extent of wall area exceeds that necessary to carry the code seismic loads. However, although it is assumed in the analysis that the secondary walls do not carry any in-plane loads, it is clear that they will carry an albiet indeterminate proportion of the lateral load. Consequently they must be detailed to sustain the deformation to which they will be subjected, by specifying similar standards as for structural walls, though code-minimum requirements will normally be adopted. To ensure satisfactory behaviour results, the natural period should be based on an assessed stiffness of the composite primaryjsecondary system.

= p

= S e condary w olls

r

~ ( a ) Unsat I S fad or y

ISllffesl wall Ignared . P & S sys!ems E'ccentnc )

r

J'L

l

J

No secondary wall is permitted to have a stiffness greater than one-quarter that of the stiffest wall of the primary system. This is to ensure that the probability of significant inelastic deformation develop­ing in secondary walls is minimised, and integrity of secondary walls for the role of gravity load support is maintained.

Ibl Sahsfaclory Long s ti ff secondary wa 11 s may be di vi ded ISllffeslwa ll s ulillsedP&S into a series of more flexible walls by the sYSlemShave s,milarcenlro,dsl incorporation of vertical control joints at

FIG. 8 - SUBOIVISION OF WALLS INTO PRIMARY ANO SECONOARY SYSTEMS

regular centres. A further requirement in selecting the primary and secondary systems of walls is that the centres of rigidity of the two systems should be as close as

possible to minimise unexpected torsional effects. Fig. 8 shows acceptable and unacceptable division of a complex system of walls into primary and secondary systems.

3.3 Masonry Strength Although the strength of masonry components, namely brick unit, grout and mortar, can be successfully monitored by performance tests. it is difficult to predict in-situ strength of the masonry from these results. since it depends on a number of other variables, including the critical influence of workmanship. Prism

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TABLE 1 - GRADE-DEPENDENT DESIGN STRENGTHS (MPa)

-Grade of Mason ry

Type of S tress A B C

Comp ression 8* 8 4

Shea r pr o vi de d by llIason ry j 0.30 0 . 24 0 .1 2 genera 1 cond i t i on s

Shear provi ded by llIa s onry

i O O -

plastic h i nges

Max i lllullI t ota l shea r , 1.60 1. 33 0 . 67 genera 1 cond i t ion s

I MaximullI tota l s hear . 1. 20 1.00 -plastic hinges

* A higher design f' may be used if substant iated by t est ing. III

testing is highly desirable to obtain realistic strength data, but is often impractical because of the size of prisms needed to provide representative results. Because of these aspects, the New Zealand Masonry Design Code (7) relates strengths to the degree of supervision, rather than to constituent properties.

As shown in Table 1, which lists grade­dependent design strengths, three grades of masonry are identified. Grade A masonry is intended for major structures, and requires continuous supervisiono Grade B is t he standard grade, used for most masonry build­ings of up to 3 storeys height, and requires inspection at cri ti cal stages, such as con­struction of plastic hinge regions. Grade C

masonry requires no supervlslon, and is considered satisfactory for designed structures (as distinct from small buildings not requiring specific design) only in exceptional circumstances . Minimum constituent strengths for masonry unit, mortar and grout as set at 12 MPa, 12 MPa and 17.5 MPa respectively, regardless of grade.

3.3.1 Flexure and axial compression. In Table 1, compression strength fm for Grades A and B masonry is taken as 8 MPa, with Grade C masonry at 4 MPa. These values apply whether the compression results from axial or flexural compression, or from a combination of these effects, as will generally be the case. Ultimate bearing stress is also limited to these values. For Grade A masonry f~ may be increased if substantiated by testing. The testing may be of representative prisms, or of constituent materials if a relationship between these and masonry compression strength has previously been established. At present such a relationship has been developed for concrete masonry, but is not yet available for brick masonry.

Computation of section strength under combined axial load and flexure follows the A.C.I. strength method for concrete members (4). The A.C.I. compression stress block is adopted, with an average stress of 0.85 fm over a length a = 0.85 c, where c is the depth of the compression zone at ultimate. An ultimate compression strain of 0.0025 is adopted to enable reinforcement strains to be calculated. This value is based on tests of concrete masonry (11) and is felt to be conserv­ative for brick masonry. Testing is planned to check this.

Dependable flexural strength is reduced from ideal strength (based on nominal material strengths) by a strength reduction factor ~f' whose value reduces linearly from ~f = 0.85 for a section in pure flexure to ~f = 0.65 for a section whose axial loaa equals (or exceeds) Nu = 0.1 f~Aq where Aq is the gross section area. These values are somewhat lower than commonly used for reinforced concrete.

On the basis of the arguments developed in l(c) above, the code requires flexural reinforcement in walls to be essentially uniformly distributed along the wall length, rather than concentrated towards the wall ends.

3.3.2 Shear. The code distinguishes between plastic hinge regions under seismic loading, and all other ('general') conditions. Within ductile plastic hinges, all shear must be carried by truss mechanism employing shear reinforcement, but in other regions a certain amount of shear may be carried by masonry shear resisting mechanisms (see Table 1). The reason for the distinction is that under ductile response loading, wide, crossed flexural-shear cracks develop in the plastic hinge

1456

region and the components of the masonry shear resisting mechanisms, namely compression-shear transfer, friction along the crack interfaces and dowel action of flexural reinforcement become progressively undependable. The distinction between plastic hinges and other regions is also made in the level of maximum total shear stress to which a section may be subjected. The level of 1.20 MPa for Grade A masonry is intended to ensure that stiffness degradation under cyclic inelastic response to seismic loading is not extensive.

Since shear failure is brittle, it must be avoided for structures required to exhibit ductility under seismic loading. For this reason, the co de requires a 'capacity design' approach for establishing the required shear strength. That is, the shear strength must exceed the shear corresponding to maxim um feasible flexural strength. Since flexural strength i s based on nominal (and therefore conservative) material strengths, and a strength reduction factor of 0.65 < ~f < 0.85, maximum feasible flexural strength may exceed the dependable strength by a substantial margin. Fig. 4 indicates that under seismic loading the actual strength is likely to be attained, albeit at a reduced ductility. Consequently the shear strength must exceed this possible fle xural strength to avoid the possiblity of brittle shear failure.

- - -

I V "w '" ~ I

I Po t e ntlc l

~, ..L . .

(o ) Slender waU I I'\., / lw > 1.0 1

A- ~ v - 41 s fy I0 8Iw J

Two possible situations are identified i n Fig. 9 for the design of shear reinforcement for shear walls. When the aspect ratio exceeds unity (Fig. 9a), a potential shear failure crack, inclined at 450 crosses the entire

~i=====~~== width of the wall. Normal reinforced - Po l , n"o l concrete theory gi ves the requi red

' "m IaM, steel area AV' at vertical spacing s,

(b) Squa t wa ll I hw / lw <1.01

Av : ~ ~sfylw

as

(9 )

FIG. 9 - SHEAR REINFORCEMENT FOR CANTILEVER SHEAR WALLS where Vo is the shear force required to

be carried by shear reinforcement, ~ s is the strength reduction factor for shear, and d is the effective depth, norma 11y taken 'as 0.8 2w for canti 1 ever shear wa 11 s.

When the aspect ratio is less than unity (Fig. 9b), the critical 450 crack intersects the wall topo Recent research on squat concrete walls (12) indicates that the shear entering the wall on the tension side of the 45 0 line from the compression toe can be transmitted by arch action involving the vertical flexural reinforcement, and inclined masonry compression struts. Shear reinforcement needs to be provided to transfer the shear entering the wall on the compression side of the potential initial crack, back across the crack into the body of the wall. Thus in Fig. 9b, assuming that Vo is distributed evenly across the wall 1 ength, the requi red s tee 1 area AV at spaci ng s i s

\'" s _ VO·s 9vw f yhw - ~ s f y9vw

(lO)

It will be noted that Eqns. 9 and 10 are inconsistent for an aspect ratio of 1.0, when both should theoretically apply. This is because of the different mechanisms involved, and clearly some judgement is required in determining which mechanism applies. For aspect ratios significantly less than unity, Eqn. 10 is likely to be conservative, as some shear will be transmitted back across the 45 0 crack at the top of the wall by a beam or roof slab. When the design shear force Vo in

1457

Eqns. 9 and 10 is based on the eapaeity design approaeh deseribed above, the strength reduetion faetor is taken as ~ s = 1.0. In all other eireumstanees, it is taken as ~ s = 0.80.

Tests on a wide range of masonry shear walls (1-3) have shown that if shear rein­foreement is designed in aeeordanee to the eode provisions outlined above, shear failure will be inhibited, and a duetile flexural hinging meehanism will develop, even for walls with aspeet ratios less than unity.

3.4 Duetil ity The design philosophy for seismie. resistanee outlined in Seetion 2 required the development of a duetile flexural meehanism under lateral loading that eould be sustained for displaeement that eould be as high as four times yield displaeement, without signifieant 10ss of strength. The maximum displaeement that a masonry strueture ean sustain will be a funetion of the ultimate eurvature ~u' whieh ean be expressed as

(11 )

where Eeu is the ultimate eompression strain for masonry, taken as 0.0025, and e is the distanee from the extreme eompression fibre to the neutral axis . Thus, to ensure adequate duetility is available, the eompression zone e must be kept as small as possib1e. The masonry eode reeognises this need by requirements limit­ing the value of e to the following levels:

For eantilever shear walls e = 0 . 4 9.w/fl (12)

For eolumns in whieh plastie hinges may oeeur 2 (13 ) e = 0 . 9 h /( fl~ n)

For beam hinges in frames or eoupled shear walls e = 2 1. 8 h / ( )l 9.n ) (14 )

where )l = 6u/ 6 is the strueture duetility faetor, 9.w is the length of a shear wall, 9.n is th~ elear length of spandrel beam or elear height of eolumn, and h is the depth of beam or eo1umn in the plane of loading. Eqns. 12-14 have been based on detailed ealeulations of duetility eapaeity, and are eonservative for struet-

12

10

~3 N u

---- - -, ~ 0 .0 'mAg

_-- ~=O.06 fm Ag

fy =380 M Pa

FIG. 10 - DUCTILITY OF MASONRY WALL~ FOR ASPECT RATIO A - 3 (f,Y. - 380 MPa)

ures up to 3 storeys in height.

As an alternative to this approaeh, or when the strueture exeeeds 3 storeys in height, detailed ealeulations for duetility eapaeity ean be earried out. Design eharts, sueh as Fig. 10 (13) have been provided to relate the available struetural duetility of masonry shear walls to the axial load ratio Nu/f~Ag' and the non­dimensionalised reinforeement ratio expressed as

(15)

where Ast is the total area of flexural rein­foreement, and 9.w and t are the wall 1ength and width respeetively.

Fig. 10 applies for walls of aspeet ratio (height/length) = 3, and flexural reinforeement yield strength f = 380 MPa. It will be seen that the availab1e duetility deereases with i nereasing reinforeement ratio and with inereasing level of axial load. For a wall of aspeet ratio A

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the available ductility ~A may be related to the ductility W3 given by Fig. 10, by the expression

3 . 27 ( W 3 - 1) (1 - O. 25/ A) WA = 1 + A (16 )

Eqn. 16 and Fig. 10 are based on the assumption of elasto-plastic load-deflection behaviour, and an equivalent plastic hinge length of half the wall length. Other charts for different reinforcement strengths are also available.

If either the simplified approach of Eqns. 12 to 14, or the more detailed approach based on ductility charts indicate that the available ductility is insufficient, the designer has three main options.

(1) The compression strength of the masonry, fm, may be increased. This Will reduce c in Eqns. 12 to14, and will reduce the non-dimensionalised rein­forcement ratio and axial load ratio in Fig. 10, thus improving ductility. However, the consequences may be a requirement to carry out prism tests to confirm the higher design strengths.

(2) The wall width can be increased, reducing c proportionately, and again increasing ductility in Fig. 10. This will have obvious economic consequences.

,..-- Platez rQcczssad 10mm [' I-bIQS for I . ) t o ollow pointing { morto r k" ying

(3) The cri ti cal compression zones within the plastic hinge regions may be confined, to increase the ultimate compression strain. Con­finement of concrete columns and shear walls by transverse hoops or ties is now accepted as a necessary requirement for providing ductility under seismic loading, and can

FIG. 11 - CONFINING PLATE FOR REINFORCED BRICK CAVITY MASONRY SHEAR WALL (PLAN VIEW)

result in ultimate compression strains exceeding 5%. A degree of confinement can be provided for

masonry walls and columns by placing thin stainless steel or galvanised steel plates in critical mortar courses. As shown in Fig. 11 for reinforced brick cavity masonry, the confining plate has a width about 20 mm less than that of the wall to permit pointing, and has large cut-outs over the cavity to facilitate placement of vertical reinforcement and grout. Note that the cross links shown across the cavity are essential as these provide the transverse confining action. Holes drilled in the plate provide keying of the plate with the mortar bed.

Under axial compression, the plates resist the lateral expansion of the mortar and grout, applying passive transverse compression to the masonry. Tests on brick masonry walls (1) and on masonry prisms (10) have shown that the con­fining plates inhibit the vertical splitting failure mechanism characteristic of masonry in compression, enhance the crushing strength by 15-20%, and greatly increase the ultimate compression strain. On the basis of these tests the code allows an ultimate compression strain of 0.008 to be used for confined masonry, increasing the available ductility to more than three times that for unconfined masonry. Since it is only the cri ti cal compression regions that are likely to fail under combined axial load and flexure, the code requires con­finement only of the outer 2/3rds of the compression zone (i.e. 0.67c), and only within potential plastic hinge regions.

3.5 Detailing It could be argued that sound detailing is even more important to satisfactory seismic performance of masonry structures than the provision of adequate shear and

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flexural strength. Because of this importance the code includes fairly stringent detailing requirements. Some of these are briefly mentioned below.

Slenderness ratios . Within plastic hinge regions the ratio of clear storey height to wall thickness must not exceed 13.3 unless the structure is less than three storeys high, or has a compression zone shorter than c = 0.3 ~w or c = 4 t where ~ and t are the wall length and thickness respectively. This requirement is to prevent buckling of the compression end of the wall under inelastic cyclic loading. For short walls, or walls where the compression zone is small, buckling is less likely to occur. In most other cases, the minimum structural wall thickness is 110 mm, provided the slenderness ratio does not exceed 20.

Reinforcement ratio . The sum of the horizontal and vertical reinforcement ratios for walls must be at least 0.2%, which can be divided up to 2/3 , 1/3 in the two directions . Maximum reinforcement ratio is related to the cavity size, and must not exceed D = 8/fy (or 13/fy at laps) at any part of the wall . Bar diameter must not exceed 1/4 of ~he cavity width. Maximum spacing between adjacent bars in both horizontal and vertical directions varies with the seismicity of the site and the importance of the building, and in the most stringent case is 400 mm each way. An exception to the requirement for two-way reinforcement is made for minor structures in the less seismically active regions of New Zealand, provided the structures are designed for the elastic response levels of seismic lateral force, and are subject to design shear stress which does not exceed the appropriate value for masonry shear mechanisms in Table 1, in which case horizontal reinforcement may be ommitted.

Anchorage. Wherever possible, the des i gner is encouraged to avoid lapping rein­forcement within plastic hinge regions. The basic development lengths of 40 db and 54 db for bars of diameter db and yield strength 275 MPa and 380 MPa respect­ively are increased by 50% where lapping within the plastic hinge region cannot be avoided.

3.6 Non-Structural Walls The code includes specific provlslons for veneers and partitions for designed buildings, even though these are considered to be non-structural. Partitions have a minimum thickness of 90 mm or 0.035 h, where h is the unsupported height, increased to 120 mm where the partition is a wall of an exit way, or is adjacent to a public place, where consequences of failure are more serious. Sufficient separation between partitions and thestructure's lateral load resisting system must be provided to prevent contact during the design level earthquake. This is to avoid loading of the partition, and structural modification of the primary seismic system.

Because of the severe consequences of veneer shedding into streets from upper floors during an earthquake, a height limitation is placed on unreinforced veneer, the value of which depends on the seismic zone of the building site. Where the veneer is at an egressway, a blanket restriction of 2.4 m is made. Reinforced veneers may be used without height restriction, provided adequate basketting reinforcement (vertical reinforcement plus horizontal joint reinforcement in the form of galvanised lattice) or close spaced vertical reinforcement is provided, and vertical support is provided at not more than 10 m centres vertically.

4. CONCLUSIONS

The need for a realistic assessment of masonry performance under seismic design has resulted in ultimate strength design being specified in the New Zealand masonry design code. Examination of non-seismic behaviour of masonry leeds to the view that in these cases also, ultimate strength design will result in a more consistent and coherent design approach. For seismic design the ultimate strength

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approach is coupled with code prOV1S10nS which will ensure that adequate ductility is provided to enable the structure to respond inelastically to the design earth­quake without significant loss of strength or stiffness.

Inherent in the approach adopted in drafting the code was a desire to depart from constraints imposed by traditional masonry designo The code emphasises that some traditional structural masonry forms are not suitable for modern design, particularly when seismic loading dominates, and simple structural systems with clearly identifiable behaviour under lateral loading are essential. Preliminary response from the design profession in New Zealand indicates that the new code will result in more economical structures thanwas previously the case, and will thus make masonry more competitive in the structural market place.

5. ACKNOWLEDGEMENTS

Many people have been involved in the development of the new New Zealand Masonry Design code. Their contribution to the subject matter of this paper is acknowledged, as is the financial support of the University of Canterbury.

6. REFERENCES

(1) PRIESTLEY, M.J.N. and BRIDGEMAN, 0.0. "Seismic Resistance of Brick Masonry Walls", Bullo NZ Nat. Soc. for Earthquake Engineering, Volo 7, No. 4, De c. 1974, P P . 167 -18 7.

(2) PRIESTLEY, M.J.N. "Seismic Resistance of Reinforced Concrete Masonry Shear Walls", Bull. NZ Nat. Soc. for Earthquake Engineering, Vol. 10, No. 1, March 1977, pp.1-16.

(3) PRIESTLEY, M.J.N. and ELDER, D.McG. "Cyclic Loading Tests fo Slender Concrete Masonry Shear Walls", Bullo NZ Nat. Soc. for Earthquake Engineering, Volo 15, No. 1, March 1982, pp.3-21.

(4) "Bui 1 ding Code Requi rements for Reinforced Concrete - ACI 318-83", American Concrete Institute, Detroit, 1983.

(5) SAHLIN, S. "Structural Masonry", Prentice-Hall Inc., Englewood Cl iffs , New Jersey, 1971.

(6) SKINNER, R.I. "Earthquake Generated Forces and Moments in Tall Buildings", DSIR Bulletin 166, Wellington, 1964, 106p.

(7) "The Design of Masonry Structures", NZS 4210P, SANZ, Wellington, 1984.

(8) "The Design of Concrete Structures", NZS 3101, SANZ, Wellington, 1982.

(9) PRIESTLEY, M.J.N. "Seismic Design of Masonry Buildings - Background to the Draft Masonry Design Code DZ 42l0", Bull. NZ Nat. Soc. for Earthquake Engineering, Vol. 13, No. 4, Dec. 1980, pp.329-346.

(10) MAYES, R.L., OMOTO, Y. and CLOUGH, R.W. "Cyclic Shear Tests of Masonry Piers", University of Calif., Berkeley, Report EERC 76-8, May 1976, 84p.

(ll) PRIESTLEY, M.J.N. and ELDER, D.M. "Stress-Strain Curves for Unconfined and Confined Concrete Masonry", Jour. ACI, Vol. 80, No. 3, May/June 1983, pp. pp .192-201.

(12) PAULAY, T., PRIESTLEY, M.J.N. and SYNGE, A.J. "Ductility of Earthquake Resisting Squat Shear Walls", Jour. ACI, Vol. 79, No. 4, July/Aug. 1982, pp.257-269.

(13) PRIESTLEY, M.J.N. "Ductility of Unconfined and Confined Masonry Shear Walls", Masonry Society Journal, Vol. 1, No. 2, July/Dec. 1981, pp.T28-T39.

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