carter 1970

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UDC 624.012.82: 624.042

Synops isThe pa pe r i r s t de s c r ibe s he e x i s t ing me thod o f t es t ingbrickmasonry iscs to es tabl ish the iagon al e ns i l es t re ng th o f b r i c kwo rk .

The ana lysi s o f the s e non-homoge ne ous d i s c s by u s inga f in i t e e l eme n t p rog ra mm e i s in t roduc e d a nd th e n c a r r i e dou t o r a series of ives pe c ime ns wi th heb r i c k lmor ta rmodu la r r a t io va ry ing f rom 4.0 t o 0.4. The re s u l t s a re the nus e d to p lo t t he c on tou rs o f p r inc ipa l t e ns i l e s t r e s s , a nds how s ign i f i c an t d i ffe re nc es o f s t r e s s d i s t r ibu t ion f rom thehomoge ne ous c a s e .

B y c ompa r ingh expe r ime n ta le s u l t si thh etheore t ica l ana lyses i t s sho wn hat he diagon al ens i les t rength of br ic kwork is appr oximate ly equal to e i ther thetens i le s t re ng th o f he mor ta r or t he e ns i l e s t re ng th o fthe brick , whic hever is smal ler.

The in i t ee l e me n t me thod i s s hown o beavaluabletechnique for analys ingon-homoge ne ous ater ia lswh ic h c a n be ide al i s ed as a two d ime ns iona l p rob le m.

Althoughrickworks ne of the ldest uildingmaterials in curre nt use, relatively little s know n abo utitsdetaile d behaviour. Existing nform ation has beenobtained u sual ly by series of tests on brick assemb lagesarranged ndoadedn way appropriateoheparticularspect fehaviourndernvestigation;thus a number of empirical formulaeave been collectedrepresentingropertiesuch as theompressivestrength, shear strength and he one presently underconsideration,he iagonalensile trength.Whilstthese have contributed great ly towards the safe designof brickw ork they have in some instances show n incon-sistencieswhich,nhe absence f detailed tressanalyses of the assemblages, have not been resolved.

The main obsta cle o any detailed stress analysis ofbrickwork istsnon-hom ogeneity esul t ing rom hedifference in propert ies of the brickandmortar; hishas precluded the use f classical elastic methods. Nowhowever, the inite element method has provided an

opportuni tyorhenalysis of non-homogeneousmaterials and the authors demonstrate here its applica-t ion to brickwork.

by B. Stafford Smit h B Sc Ph D CEng MIStructEMICESenior Lecturer in Civil Engineering,Universi ty of SouthamptonC. Carter PhDJCEng MlStructEPrincipal Lecturer in Civil and Structural Engineering,Southampton Col lege of Technology

andJ. R. Choudhury BSc PhDAssistan t Profe ssor in C ivi l Engineering,East Pakistan University:of Eng inee ring and Te chn olo gy

The res ul ts of the invest igat ion fi rs t ly emphasise theneed for a more horough examinat ion of hestressdistribut ionn rickwork nd econd ly onfirmheaptness of he finite element meth od of he detailedstress analysis of maso nry systems.

Diametra l test ing of b r i c k w o r k d i s c sA method of test ing brickwork to establ ish i ts diagonaltensile trengthhas recently een pionee red by theStructural Clay Products Research Foundation of theUSA . 2 (SCR ): 381 mm (15 in) diameter circula r speci-mens are cut and ground rom 406 mm (16 in) squarebrick w allettes, 102 mm (4 in) hick, as shown n Fig 1.These specimens are tested o destruction by loadingin compression along a diameter at 45 to he mortarlayers, as show n n Fig 2. The oad s appl ied o hespecime n through a 3.17 mm i n) thick plywood strip,6.35 mm a in) wide, i.e. thespecimen diameter.

DISC 15 DIA.

a

16

L E VAT I O N S E C T I O

Fig 1

Theusual mod e of failure s by splittingalong heloaded diameter as a resul t of the nduced ransversetensi le s t resses. This est ing echniq ue wil l be recog-nised as s imilar to the so called Brazilian or indirect

method for determining the tensi le s t rengthf concrete3.The load at which the specimen spl i ts is used t o calcu-late the diagonal ensi le streng th of the brickwork by

THETRUCTURALNGINEER UNE 1970 o 6 OLUME 48 219

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its

Fig 6

t s

Fig 7

222 THETRUCTURALNGINEER UNE 1970 No L] VOLUME 48

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ts

Fig 8.

Discussion of analytica l resultsInahomogeneous specimen of the dimensionscon-

sidered, the ransv erse ensile stress due to a 0.44 kN(100 Ibf)diametralcompressive oad is, according oequation 1,0.0073 N/mm 2 (1.06 Ibf/in2). Th e es ult s ofthe finite element c ontrol analys is for a homogeneousdisc agree exactly with his value, as show n n Fig 6;therefore, the working and accuracy of the programm eare considered confirmed.

The results for the non-homogeneous analyses showsignificantdifferencesofstress distr ibution rom hehomogeneous case. Fig 4 and 5 demonstrate that in theusual practical case when the brick s stiffer han hemortar, concentrations of high principa l ensile stressare induced n the mortar layers. The higher the brick/mortarmodular ratio, the igherheocalensilestresse s; or example, in he cases considered withmodular ratios of 4 and 2 he corresponding maximumpri nc ipa l ten sil e str es se s are O.O112N/mm2 1.63 Ibf/in *)and 0.0106 N/mm2 (1.54 Ibflinz), i.e. respectively, 54 percent and 45 per cent higher han in the hom ogen eou scase. In these two cases a concentration of high tensilestress also occurs in th e b rick at one end of the loadeddiagona l; however, since it is clearly a resu lt of the loca lgeometry of the brickw ork close to the applied load, itmay be assumed not to have any general im plications.

In the other two ases, where the mortar s stiffer thanthe brick, region s of high tensile stress are induced nthe brick, as show n n Fig 7 and 8. However, as suchmodular atios are unlikely to be met npractice, heresults are primarily o f academic interest.

Comparison with exper imenta l resultsIf equation 1 s rewritten as

NPnDt

f d t = ~ . .

then, using the maximum principal tensile stresses fromthe contou r diagrams, values of N can be derived fo rdifferent brick/mortar modular ratios; these analyticallydetermined values of N are plotted as a unction ofEB/E.W n Fig 9.

4 c

N 3 c

2 0

Fig 9.

FORANYVALUE OF THE BRICK:MORTARMODULAR RATIO Ed EM THE CURVEGlVES THE VAWE OF N WHICHSHOULD BE USED TO DETERMINE f d t

THE MAXIMU M PRINCIPAL TENYLE STRESSIN THE MORTAR.

P

Cons idering the experimental results of the d isc te stsconducted by the SCR, four different ypes of mortarwere used n com bination with a standard brick. Th equoted mortar strengths were obtained at 28 days using

cube and briquet tests for the compressive and tensilevalues respectively. The standard brick had an averagestrength of 81.2 N/m m2 ( l 1 770 Ib/in2) and mea sured


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approximately 203 m m x 102 m m x 57 m m 8 in 4 inx 2+ in) ; it was laid with 9.5 m m (# in) thick joints.

Usinghemodularatios fhe ifferentests,correspon ding values o N can be obtained from Fig 9 ;these are given n Table 1.

T A B L E 1

Fo r t a r

10-33/mm2 1.02 N/mm2.3 kN/mrn2 2-98(1500 bf/in2)1(148 bf/in2)1 ( 1 . 2 ~06 Ibf/in2)

5.52 N/mm 2 0.60 N/mrn 2 4.4 kN/m m2 5-50(800 Ib f /in2 ) (87 Ib f /in2 ) ( 0 . 6 4 ~06 Ibf/in2)

4-14 N/mm 2 0.44 N/mm 2-3N/mm2 7.30(600 Ib f /in2 ) (64 Ib f /in2 ) ( 0 . 4 8 ~06 Ibf/in2)

N

2-2

3.0

.2

.25

Hence he oad o cause spli t t ing may be used withequation 2 to determine a value of the diagonal tensile

20c

150

100

5

350

3

250

Y

>

Fig 10.

224

strength of thebrickworkon hebasisof henon-hom ogeneo us analysis.

It is useful to compare thealues for diagonal strengthdetermined on the bases of the homogeneous and non-hom ogeneo us analyses, i.e. with N = 2 and N as givenin Fig 9, respectively. This com pariso n is ade in Tableand also demons trated graphically n Fig 10 by plott ingthe diagonal tensile strength against the tensile strengthof the mortar, in th e fo rm given by SCR.

T A B L E 2

MortarTy p e

M

S

N

f l d t ( N = 2 )

2-16 N/mm 2(313 Ib f/in2)

1.74 N/rnm2(252 bf /i n2)

1.21 N/mrn 2(176 Ibf/in2)

0.64 N/mm 2(93 Ibf/in2)

f ’ d t N r o m f ’ tFig 8)

2-00 N/rnm2

(168 Ibf/in2)1.02 N/rnm 2-16 N/mrn 2

(309 Ibf/in2)290 Ibf/in2)2.13 N/mrn2

(64 Ibf/in2)58 Ibf/in*)0.44 N/mm 2.40 N/mm 2

(87 Ibf/in2)110 Ibf/in2)0.60 N/rnm2.76 N/rnrnz

(148 Ibf/in2)

C U RV EU G G E S T E DBYS.C. R. B A SE D ON /

t F R o M mP

I I

5 100 150 200 250 300 350

M O RTA R T E N S I L E S T R E N G T H LBF I N/THESTRUCTURALENGINEER UNE 1970 o 6 OLUME 48

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Whenplottedon he basis of henon-homogeneousanalysis the results indicate that diagonal tensile fai lureoccurred when the principal tensile stress in the mortarreached its tensile strength. The subsequent extensionof the crack throug h the stronge r brick, which oc curredin some tests, could probably be explained in term s ofcrack propogation hrough a brittle material.

I f the brick had been of a ower elastic modulus andlowerensile trength han he mortar, it could beassumedhatiagonalensileailure ould haveoccurred when the principal tensiletress, as determinedfromheon-hom ogene ous analysis, equalled hetensile strength of the brick.

It seems probable, therefore, th at the diagona l tensilestrength of brickwor k s approximately equal o eitherthe tensile strength of the mortar or the tensile strengthof the brick whichever is less.

The resu l t s of this inves tigation focu s attention o n theneed for more detailed consideration of he behaviourof any non-homogeneou s structural m aterial in attempt-in g to make a rational prediction of its strength.

The finite element method s show n to be a valuabletechnique oranalysingnon-homogeneousmaterialswhich can be idealised as a wo-dime nsional problem;it is part icular ly appropriate o brickwork and the authors

material such as brickwork,an analysis based ontheassum ption of ahomogen eous material maylead to a substa ntial u nderes timationf the maximumstresses.

(2) The inite element method s an appropriate ech-nique oranalysingnon-homogeneous materials,especially in caseswhere the roblem may beassumed to be two-dimensional and where the sizeof he egion o be consid ered s not of a widelydifferentorder o he size of he elements in hematerial.

(3) In heparticularproblem of a diagonally loadedbrickwork isc, oncentrations of high r incipaltensile tress were found o be induced n heelements of lesser stiffness; the greater the mod ularratio of the materials, the arger he peak tensilestresses.

(4) The diagonal tensile strength f br ickwork is approxi-mately equal o he ensile strength of he mortaror brick, whichever is the weaker.

References1. ProgressReport No. 1 : Small-scalepecimen Testing,

StructuralClayProducts ResearchFoundation, Geneva,

nationalConference nMasonryStructural-Systems,

3 Wright, P. . F. ‘Comm ents on an Indirect Tensile Test onConcreteylinders,’ Magazine o Concreteesearch.

Conclusions Austin, Texas.ov. 1967.

The conc lusions may be summarised as follows:( l )nhe stress nalysis of aon-homogeneous Vol. 7. No. 20, July 1955.

(26.9 per cent) pass ed out of a totalof 952.

Examinationsanuary 1970 Associate-Membership

Pa r t 2 Examina t ionTheoorerformance of mostcandidates nhisexamination re-

These reports upon the performanceof candidates in the Insti tution P arts2 and 3 examinations held in January1970 are based upon the com me nts fexaminers. T he review is offered asa guide to those who are preparingfor future examinations and to thosemembersndthersesponsiblef o r h e e a c h i n g o r r a i n i n g o fpotential candidates.

It will be recalled tha t the Institu -tionPart xam ination has eenreplaced by the Part1examinationof the CEI; the nstitutionPart2examinationeadingoAssociate-Membershipwill beeplaced fterJuly 1970 by the CEI Part 2 examina-tion.

Candidateswho have completedthe Insti tution Parts 1 and 2 xamina-tions by the end of 1970 or who havebeen exempted therefrom by obtain-ing ualification therhan anapprovedengineering degree, mus tcomplete the Part 3 examination andbe elected to corporate membership( a n d h e r e b y a c h i e v e C h a r t e r e dEngineer registrationwith he CEI)

by 31 December 1973. Such can-didates will not be required o meetthis dead-line if they op t to take (andpass) the CEI Part 2 ‘two-subject-test’. Full details of this con ces sionmay be obtained onapplication othe Secretary of the In stitution.

The Insti tution Part 3 examinationwill be continued substantially n tsp resen t o rm; n he papers o be

set in January and uly 1972 and1973 the ues tion hoicewill beextended by the inclu sion of a ques-t ion n which he structural mater ialused s ef t o he discretion of hecandidate. A fter Ju ly 1973 cand idateswill have the cho ice of one of fourquestions:onen tructural teel;one in tructural oncrete ;one nwhich hestructura l material is no tspecified;andonedealingwith anaero-structure.

To return to the examinations heldin January 1970;09 candidatesattempted the Part 2 examination ofwh om onl y 62 (15.1 per cent) p ass ed;10 were eferred in one subject . nthe Part 3 xamination 256 candidates

flects an understandable anxietyto com plete the examination b efore itiswithdrawnnts resent orm.Worked scripts evealed poor prepar-ation and knowledge s o l imited as toraiseoubts whether many can-didates can ever expect to reach therequired academic standard or ad-mission to a professional Insti tution.

Propert ies of materialsA general criticismmus t be thatcandidates oncentrated n ues-t ionscall ing ordescriptive essay-typeanswers; hat few offered anyinformationorproperties ofmat-erials, moistureontentrhelike, and thos e hat did requentlygave inaccurate values. In to o manycases handwriting was almost il-legible and, combinedithadspelling nd grammar, resulted insome criptsbeingalmost ncom-prehensible.

Few candidates attemptedQues-tion 1; of those who did about one-

halfknew theequilibrium diagram.Others howed he iagram as a

continued on page 6


carter 1970

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