YieldLine Theory and Material Properties of Laterally Loaded Masonry Walls Brincker, Rune

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1 Aabrg Universitet YiedLine Thery and Materia Prperties f Lateray Laded Masnry Was Brincker, Rune Pubished in: Masnry Internatina Pubicatin date: 1984 Dcument Versin Pubisher's PDF, as knwn as Versin f recrd Link t pubicatin frm Aabrg University Citatin fr pubished versin (APA): Brincker, R. (1984). YiedLine Thery and Materia Prperties f Lateray Laded Masnry Was. Masnry Internatina, (1), Genera rights Cpyright and mra rights fr the pubicatins made accessibe in the pubic prta are retained by the authrs and/r ther cpyright wners and it is a cnditin f accessing pubicatins that users recgnise and abide by the ega requirements assciated with these rights.? Users may dwnad and print ne cpy f any pubicatin frm the pubic prta fr the purpse f private study r research.? Yu may nt further distribute the materia r use it fr any prfitmaking activity r cmmercia gain? Yu may freey distribute the URL identifying the pubicatin in the pubic prta? Take dwn picy If yu beieve that this dcument breaches cpyright pease cntact us at prviding detais, and we wi remve access t the wrk immediatey and investigate yur caim. Dwnaded frm vbn.aau.dk n: januar 25, 2018
2 Aabrg Universitet YiedLine Thery and Materia Prperties f Lateray Laded Masnry Was Brincker, Rune Pubished in: Masnry Internatina Pubicatin date: 1984 Link t pubicatin frm Aabrg University Citatin fr puished versin (APA): Brincker, R. (1984). YiedLine Thery and Materia Prperties f Lateray Laded Masnry Was. Masnry Internatina, (1), Genera rights Cpyright and mra rights fr the pubicatins made accessibe in the pubic prta are retained by the authrs and/r ther cpyright wners and it is a cnditin f accessing pubicatins that users recgnise and abide by the ega requirements assciated with these rights. Users may dwnad and print ne cpy f any pubicatin frm the pubic prta fr the purpse f private study r research. Yu may nt further distribute the materia r use it fr any prfitmaking activity r cmmercia gain Yu may freey distribute the URL identifying the pubicatin in the pubic prta? Take dwn picy If yu beieve that this dcument breaches cpyright pease cntact us at prviding detais, and we wi remve access t the wrk immediatey and investigate yur caim. Dwnaded frm vbn.aau.dk n: December 02, 2013
3 8 YiedLine The ry and Materia Prperties f La tera y Laded Masnry W a s Rune Brincker Department af Structura Engineering, Technica/ University af Denmark, DK2800 Lyngby, Denmark The behaviur f masnry was subjected t atera ads has b een studied by means f a arge number f specia tests. The fracture prcess has been studed in arder t find the answer t an imprtant questin: des masnry shw any duetie prperties that may justify the appicatin f yiedine thery as a design methd fr ateray aded ma snry was? Frm the resuts f the t e sts it is cncuded that the answer must be in the affirmative. The masnry materia shws distincty duetie prperties with respect t frces impsed by atera ads, and stressstrain reatinships arewe deseribed by an eastpastic mde. The fracture criteria, describing which cernbinatins f mments and vertica inpane frces give rise t faiure, appears t be apprximatey fracture criteria f the Cumb type. The test series and resuts reprted in this paper are deseribed in detai in Brincker [12]. I NTRODUCTI ON The tests deseribed in the fiwing derive frm the prbem f desicninc ateray aded masnry was and, especiay, the discussin regarding the appicatin f yiedine thery t such was. As ur starting pint et us cnsider a masnry wa as shwn in Figure. The wa is primariy subjected t atera frces acting hrizntay, but there may as be sme vertica frces actinc in pane (dead ad). The prbems invved in designing such masnry was have nt yet been satisfactriy sved. If the mernhers adjacent t the wa under cnsideratin are sufficienty stiff r if inpane extensins are in sme way prevented, we can assume arch actin, which prvides great resistance t atera ads. It is usuay easy t prve the necessary strength against atera ads in such cases. Hwever, in themanycases in which arch actin eannt be assumed, serius design prbems arise, a nd it is these we sha be deaing with in the fwing. Design methds based n e astic sutins have been prpsed, see Facner [1], Bradshaw and Entwise [2], Francis [3], and Haquist [5], but are generay nt easy t hande, and the ad determined n the basis f the thery f easticity aften represents a grss underestimatin f the strength. Mdified methds such as the strip methd h ave been prpsed, see Baker [6] and Hendry [8]. Here, t the resuts are aften t cnservative, and it is generay difficut t take accunt f different supprt cnditins and specia cnfiguratins such as hes. The yied ine thery has therefre been prpsed by sme authrs, see Lsberg and Jhanssn [4], Satti [7], Hasetine [9], Hendry and Kheir [10], Hasetine, West and Tutt [11], and Cajdert [13]. The yiedine thery is a fexibe design methd, especiay when rthtrpic and inhmgeneus prperties, hes and specia supprt cnditins, have t be taken int accunt. Accrding t the abve references, the yiedine thery shws gd agreement with experimenta resuts, but ne prbem is that there is at present n ratina justificatin fr its use. The main aim f the tests perfrmed has been t fcus n the physica prperties f the masnry matera against such sectina frces ccurring in ateray aded masnry was. The crack patterns f such was at faiure devep very much ike the yiedine patterns f reinfrced cncrete sabs. If the wa under cnsideratin is simpy supprted ang its fur edges, ike that shwn in Figure, bth hriznta and bique yi e d ines wi devep. Figure DL> ad ad. Obique yiedine. r,..l h r i z n t at r'''"'.. yied  ti n e. 1. Lnterny n<cd ma snry wn with bique and hr i znta yiedines. Latera ad. The materia's resistance t the actua sectina frces has been studed in a herizenta and an bique yied ine. In the case f the hrizn ~ ta yied ine, the criteria describing which cernb inatins f vertica inpane frces and bending mments give rise t faiure have been determined by experiments with eccentricay aded brick piers in which the tensie strength f the masnry was assumed t be zer (cracked sectin assumed). In the bique yied ine, the cnditins ~rp. much mre interesting and have therefre been studied in far greater detai. The fracture prperties f the materi a in an bique yied have been studied by me ans f an advanced test in which a speciay designed test speemen is subjected t a cernbinatin f bending, trsin and verticay acting inpane frces. This test is deseribed in detai ater.
4 9 In the prgramme tests were perfrmed n fur cmbinatins f materias, tw quaites f mrtar and tw types f brick. The bricks were Danish nrma size 55x108x228 mm; ne f them was sid, whie the ther had 55 hes distributed in five rws parae with the Ingest edge f the brick. The sid brick had a cmpressin strength f 48 MPa, and the brick with hes a cmpressin strength f 28 MPa. Thø tw mrtars werc bth rcativey weak. One was a pure ime ~rtar with a ime/sand rati f 100/1200 (uy weight), and the ther was a imecement mrtar, with a ime/cement/sand rati f 50/50/750. The cmpressin strengthf the rnrtars, determined by means f 40x80 cyindrica mrtar specimens, was fund t be MPa fr the ime mrtar and MPa fr the imecement mrtar. The fur cmbinatins f materiais have each been given a cde as shwn in Tabe. Sid brick Brick witi hes!. M<n:tar: Lime/sand: LS LH 100/1200 (by weight) Mrtar: Lime/cement/sand: L CS LCH 50/50/750 (by weight) TABLE  CODE NUMBERS AND COMBINATIONS OF MATERIALS USED IN THE TEST PROGRAMME TESTS RELATED TO HORIZONTAL YIELD LINES The eccentric cmpressin tests t investigate the strength f the matera in respect f sectina frces acting in a yied ine were perfrmed as shwn in Figure 2, using t h e fiwing fur ad distributins: type 1: b t => e type 2: b 1/2 t => e = 1/4 t type 3: b 1/4 t => e = 3/8 t type 4: b 1/8 t => e = 7/16 t As a main ru e each test w as repeated five times. During each test crrespnding vaues f the axia ad K and the strains and E, defined 1 2 in Pigure 2 were measured. The unifrm stress a is given by: K a =.Q.b a nd the bending mment is given by M = K e () (2) The strain K crrespnding t the frce K (the strain f the ine f actin f K) is given by E 2 b K = E  2't (3 ) Typica O, K stressstrain reatinsbips fr the LCS cmbinatins f materiais (see Tabe ) are given in F.igures 3 t 7. J } e F arrm '! e: 1 Fgure 2. Eccentric cmpressin t est. ( x t x h = 22R x 108 x 1R9mm,h 8 = 134mm.) The ast pints n the curves, which shw strngy stchastic behaviur, shud nt be paid t much attentin, since the determinatin f the strain EK given by equatin (3) is based n the assumptin that pane sectins remain pane during defrmatin. This is nt true when the bricks fai. On the basis f the tests perfrmed it can be cncuded that the stressstrain reatins  and this appies t a fur cmbinatins f materiais  can be deseribed by dividing the reatinship int three phases: first a inear e astic phase, then a pastic phase with strainhardening, and ast, a fracture phase, with vaues equa t r ess than zer fr the spe d/d K. Accrding t the stressstrain reatinsbips the pint f faiure is defined as the first pinl between a phase 2 and a phase 3, see figure 6. The mduus f rupture c = Kc/b.Q. fund in this way may therefre sametimes be ess than the utimate breaking stress m ~ Tabe 2 shws mean vaues and standard deviaf1ns f the faiure ad Kc fr the different cases. Cmbinatiana f Lad distributin materia. type type type type !.Iean vaue (kn) c.v. (%) ) Mean va1ue (kn) c.v. (%) Mean vaue (kn) c.v. (%) Mean vaue (kn) c.v. (%) TABLE 2  VALUES OF FAILURE FOR THE ECCENTRICALLY ACTING AXIAL LOAD K. MEAN VALUE,S AND STANDARD DEVIATIONS OF FIVE EXPERIMENTS Crrespnding mean vaues f the bending mment M and th~ fdiure ad Kc are ptted in Figure 8. Fr each matera the fur pints are fitted with a secnd degree pynmia. Thus, the figure shws the faiure criteria fund in experiments reating the axia ad K and the bending mment M. Fr s ma axia ads K, where secnd rder effects can be negected,
5 10 25 er IMP a ) 0 L i/ +,t +.t z...,t ff ++i : +" i i.r ' ~.,..,! '', i i,, ; ; : +! '...,. 20! 25 O" IM Pa ) A F+ _t_ i :t J rr.ji. ff t: t! 1 _[~ 1 y / J s / ~ i++ i L IL c O Figurø J. Materta cmbinatin LC S, iad distributin type. Figure 4. The ad reieved three times. _j 20~~~~~~~'~/ 20 er IMPa) /: /V / : J '( 0~~~L~~~ n IO Ei<1%a er IMPa ) er c / ' i ++ '+ t #+.,.,.,. IO +f+++ Figure 5. Matera cmhinatin LCS ad distributin type 2. Figure 6. Matera cmbinatin LCS ad distributin type 3. 1 J O" IMPa ) f L f +..._... ~ i Figure 7. Matera cernbinatin LCS ad distribu tin type Figures 37 Stress reatinship fr eccentric cmpressin tests.
6 11 5 M knm) mater ie L materie L s H + materie maeri a Figur e R. Fniure critcra fr the diffcrent mat0rtns. LC  S LC  H the faiure eriterin wi be seen t be f the Cumb type: with zer chesin and a frietin f ~. The vaues f W fund in the experiments ~re given in Tabe 8. 0 TESTS WITH COMBINED TORSION AND BENDING (OBLIQUE YIELD LINES) The faiure prperties f the materia in an bique yied ine have been studed by means af a speciay designed test an sma piers s ubjected t atera ading, bending and trsiana mments. A specia testing machine was buit fr this purpse. The principe af the testbed is iustrated in Pigure The mec 1nnic.a principe fr tests wit1 cernbined bending and trsin. K crrespncts t the dead ad 2 1 and K 1 t th e atera and. ' (4) Here et us cnsider a masnry wa t hat is simpy supprted ang a fur edges and aded with its utimate atera ad. The bique yied ines wi be staircaseshaped because the fracture wi nrmay ccur ny in the jints. The fracture cnditins af the bed jints (the cntributins due t the crss jints are negected) are studed by the principes expained in the fwing. A vertica strip f the wa, cut thrugh by tw bique yied ines is cnsidered. The strip is divided int three pieces by the yied ines, each piece represented by a singe brick in the speciay designed test specimen. The upper piece af the strip rtates araund the hriznta ine in Pigure 9, the midde piece rtates araund the vertica ine 4 in the figure, and the battm piece rtates araund the hriznta ine 2 in the figure. Each f the bricks in the trsinbending speemen are nw frced t mave in a crrespnding way because each brick is camped t a rigid arm in the testbed, rtating araund either a hriznta ar a vertica ine accrding t the mvements af the piece f the strip crrespnding t the brick under cnsideratin, see Figure 9. Actuay, the testbed was aid hrizntay, whereby the atera ad an the wa became a verticay acting ad K 1 in the test, and the vertica dead ad n the wa became a hrizntay acting axia ad an the specimen, as shwn i n Figure ""...!.' Fi~LirP 10. Pz incipjc fr tests with cernbined bending a nd trsi ~. [IJD e i< During the tests, which were perfrmed with cnstant axia ad and cntinuusy increasing atera ad, measurements were taken af the bending mments M 11 and M 21 in jint and 2, respectivey, see Figure 10, and af the trsina mments M1 2 and M 22, tgether with ther quantities such as the crrespnding anguar strains ~ 11 ~21 ~ 12 and ~ 22, see figure 10. The anguar strains ~ 11, ~ 21, ~ 21 and ~ were 22 measured by means f speciay designed extensmeters paced acrss the jints. Tw extens~eters were paced at each jint, gued in pace an either side af the specimen, see Figure 11. Each extensmeter measured tw dispiacement cmpnents: ane perpendicuar t the jint, and ane parae t it. The bendingtrsin speemen was fastened t the arms af the test b e d by means af frietin jaws actinc an ppsite sides af each brick. The munting and starting ~rcedure was panned and carried ut t ensure minimum unintentina stress in the specimen. Unintentina prestress in the
7 12 specimen was as reduced t a minimum by means f hinges, which cud be eiminated by cking, and by very accurate shaping f the t es t specimens. The main gemetry f the testbed is shwn in Figure 12. It was designed s that the quantity (5) crrespnding t different spes f the yied ine, see Figure 9, cud be adjusted by mving the crsspiece n arm 2, s hwn in Figure 12. Bth the hriznta ad K 2 and the vertica ad K 1 were impsed n t he structure by hydraui c presses. The axia ad K 2 was kept cnstant by means f an i pressure cntr unit, and the atera ad K 1 was cntred by ' a serv pacer unit, in arder t achieve a rampshaped prgress fr the atera dispiacement crrespnding t the ad K1. In additin t the mments and the crrespnding anguar strains, a f which were measured as functins f the time 1, M11 = M 11 (1), ~ = ~ 11 (1), etc., the atera ad K 1 and the crrespnding atera dispiacement 1, were as measured. The fiwing parameters were varied in the test prgramme: The materia. Fur cmbinatins f materiais, LS, LH, LCS and LC H, see T ab e. The axia ad. The ad K 2 was varied thrugh five vaues frm zer up t abut 20% f Kzc where K is the cmpressin 2 faiure ad f the fest specimen. The spe f the yied ine. The quantity a was varied thrugh the vaues a= 1.149, 0.940, and As a principa rue, each test was repeated three times. The chsen vaues f the axia ad K 2, tgether with measured vaues f the cmpressin strength are given in Tabe 3. Figure 11. A sing e extensmeter (meas uring tw dispiacement cmpnents) munted n a test speci men. The data cected were deat with as deseribed bew with a view t determining whether the masnry materia pssesses any duetie prperties against the effects cnsidered here. The wrk dne by the frces acting n ne f the jints, say jint ne, can, with gd apprximatin, be written as: r, if we chse the parameter instead f <j, w <~11> = 1 <M11 strain ~ as integratin the time, as: d~2 + M2~)d <j>11 (7) 11 On the basis f this resut it prves cnvenient t define a fictive stress paråmeter : (8) Axia ad K2 Cmpressin tauure adø 1 r by di*isin with the mrtar cmpressin strength f (The mrtar strength was measured by ' means f cytindrica test specimens made frm the same batch f mrtar as the cnsidered trsinbending specimen. The mrtar strength is shwn in Tabe 4) ad ad ad ad ad K2C c.v (kn) (kn) (kn) (kn) (kn) (kn) (~) (9) Materi a Simiary, fr jint tw: iaterta (O) Materi a 21 iaterta 22 TABLE COIIPRESSION STRENGTH AND IKPOSED VALUES OF AiAL LOADS FOR TUE DI!'FERENT TORSIONBENDING SPECIIIEHS. The stress strain reatinsbips s * and s *, ~ can be regarded as usua stresss~rain re~ati~! ships and prvide a direct iustratin f the behaviur f the materia, as if we were taking abut a cmpressin test, fr exampe. A inear reatinship indicates eastic behaviur, and a curve which changes frm cnstant spe t zer spe indicates pastic behaviur, etc ;
8 13 If we cud impse n t h e stru cture precisey the dispiacement fied wanted, we wud have: ( ) whic h means t h at the reatinship between t h e trsiana and the bedine anguar strain fr bth jints s h ud be inear. 800 In practice, f curse, t h e i mpsed disp i acement fied wi aways shw a certain deviatin frm the intended fied. In rder t see hw gd agreement t here was between t h e t heretica a n d the impsed dispiacement fied, the measured bending a nguar strain was fr bth jints p tted agai nst the measured trsina angu ar strain, tgether with the i n tended reatins h ip indicated by a straight ine. A typica res ut is s h wn in igure 13. As wi be seen, the agreement between t h e theretica and t h e i mpsed dispiacements was best in the atter part f the test. Th e stressstrain re at i nsbips s *, ~ and s~*, 1 ~ fr t h e same test are shwn in figure 14, 21 gether with the cntributins 6s * and 6s * due 1 2 t bending ane. M r  ~ t~ A 1100 arm Q} IPE 120 RHS r, X AL. LOAD K, ALL MEASURES IN mm. 3 M f t m 3 M21 f t m As wi be seen frm the figure, the matera shwed distincty pastic behaviur. ( 12) Finay, fr the same test, Figure 15 shws the atera ad K 1, ptted against the crrespnding di s pacgment. The resuts shwn here can generay be cnsidered as representative f a the tests, athugh there was a tendency fr tests with wer vaues f the axia ad K 2 t resut in mre irreguar curves (data shwing greater deviatins frm the mean trend), and vice versa i n cases f higher vaues, where the curves are even mre reguar. Hwever, the genera t e n dency is cear enugh: a stressstrain reatinsbips shw distincty pastic behaviur, as iustrated by th e test shwn in Figure 14. With respect t the impsed defrmatins, these seem t be in agreement with the intended defrmatins ny in the atter part f the test, when fracture had cmp}etey deveped, bec a~se the test specimens pssessed cnsiderabe r esistance t trsina strain in the eary stages f fr acture. On the basis f the reatinsbips btaine d, fai u r e vaues fr the atera ad Kc and fr t h e m ments Mc' M 12, ri '2c an d ' 11 22<;:' tgether w i t h t h e faiure benåina "' angu ar stra1n ~c were determined fr a tests. The faiure strain ~c was determined as t h e mean vaue f the bending anguar strains fr the tw jints, crrespndin~ t the kinkpint in the eastpøstic apprximatin f the measured stressstrain reatinships. N dependeuc:t: n the gemetrica parameter a cud be traced; therefre, a the faiure strains crrespnding t t h e same matera and the same axia ad have bee n ped. T he resuts btained are shwn in Figure 16. Here, the faiure strains are ptted against the stress eve K 2 /K2c where K is the actua axia ad, and K 2 2 c is Fig rc 12. The mai n g e mctr y f thc t es t bed. 10 'P 2 (%) d ~ the cmpressin faiure ad. It wi be seen that with the data d epicted in this way, there seems t be n dependence n the c hice f materia, but with gd a p prximatin i neai dependence n the axia ad. Hwever, the mst imprtant aspects f the tests reprted here are t h e vauatin f t h e measu red fai ure DD JOINT JOINT 2 / / / ' /' // /,L  r / _./ ~...::: / Q/ ~.v... Fgure 13. Trsina anguar strain ptted ngainst t 1 c bending anguar strains fr t 1e LC  ff cmbinatin f materiae wit1 K = kn, and n = 0. 9 ;G, 2 20,, =,..,, S; (% ) ,. "r V:: m' v f A' f r f v/ f+~4~~~=+~~  ~~ rc ~~t=~~~~ v... r rf J"' J "./ ~x _.;,( >~ x ~ x r:1.' r;. "'.c:~: >L"1_r'... =_"'f~_.;! :::....===4.==f=r..,'"''+ +..,... ~f!:= tt J i... ti/ f t1 ifj : r <j),j(%) 10 ~~~~~~ A JOI IT 2 + JO N 2 Pigure 14. Stress strain r e atinships sr rf 11 nn d S~, ~ 21 tget i e r wth t h e cntributtns frm bending ane fr the LCH cmb inatin f ma teria wi th K 1 = kn, and et=
9 K 1 (kn) 2 Tes~ stpped. 5, L L (mm) Figure 15. SimutRneJS pt f the ate t a ad K v. ate ra dispiace ment 6 fr 1 1 the test s hwn in Figures 13 and 14, a fr the vaues f a cnsidered here, it is at any rate weak and f minr significance. It can be negected, and we have therefra rnned a data crrespnding t the same materia and the same axia ad. Readers wh are interested in further investigatins regarding this assumptin are referred t the test reprt Brincker [12]. The reasnabeness f the assumptin can be checked by appying the ped faiure vaues fr the b e nding and trsina mments t btain a pastic sutin fr the dependence f the atera ad K 1 n the gemetrica parameter a, and cmparing this resut with the measured faiure vaues fr the atera ad. A the data required can b e btained frm Tabes 5, 6 Mater i L S Maeria L  H Materiet LC S Materie LC  H x A ' ' 5 Materie L  S + Mater i L.  H x Materie LC S A Materie LC H v + 4>c (%) f Figure 17. Fai ure criteria fr dfferent mat e ra s. Figure 16. The depenrenc e f the fa i u re strain upn the s tress e ve R ;K c. 2 2 vaue s fr the atera ad and the bending and trsina mments, and their dependence upn the materia, the axia ad, a nd the gemetrica parameter a representing the spe f bique yied ines. It is nt difficut t see that the masnry materia can b e ascribed tw yied mments based n the ideas and resuts given here characterising the abiity f the materia t resist atera ading  a nd this is essentia if we wi s h t appy the yied ine thery in the usua way  ny if the faiure vaues fr the bending and trsina mments measured by the tests can be assumed t be independent f the gemetrica parameter a. In faet, this seems t be the case. The tests shw that if there is any dependence n a at and 7, giving the resuts f the measured faiure vaues fr the atera ad and the mments. This investiga tin  which serves t s upprt the assumptin  is as perfrmed in the repart Brincke r r 12. In Pigures 17 and 18 th e faiure vaues fer the bending mments and the trsina mments are each ptted against the axia ad. The figures s hw the faiure criteria fr the diffcrent materia s fr b e nding and trsin measured by the t ests. These curves are ne f themst imprtant resuts f the test prgramme. The measured faiure criteria fr the b endi ng mm e nts can be deseribed in the fiwing way. Fr sma vaues f the axia ad, K 2, the criteria seem t be the same, independent f the chice f materia, a nd the criteria are a f the Cumb type with zer chesin. Fr h igh er vaues f K 2 (va ues f K 2 greater than, say, 10% f the cmpressin strength), secnd rder effects reduce the faiure vaues fr the bending mments cmpared with the extrapated inear behaviur fund fr s ma vaues f K 2.
10 15 Simiar cncusins appy t the faiure criteria fr the trstna mments, except that in this case, the chice f matera pays an imprtant re, even fr sma vaues f K, 2 sinc e here, the faiure criteria, which are as f the Cumb type, are nt equa, but differ as regards bth chesin and frietin parameters. It is particuary interesting t see that the chesin appears t differ significanty frm zer. I f secnd rde r effec t s a re negected, t hen the Iaiure vaues fr the bending mments can be written and simiary fr the trsina mments (13) (14) The vaues measured fr the chesin and frietin parameters are given in Tabe 8. s CONCLUSIONS On the basis f the tests deseribed in t h e fre ging, which were carried ut t investigate the fracture cnditins in herizenta and bique yied ines, the fwing cncusins can be drawn: That the masnry matera in a herizenta yied ine is abe t resist a bending mment independant f the chice f materia, which  fr sma vaues f axia ads  can be written as an expressin f the Cumb type with the chesin c =O and thc frietin W = 0.90 t/2; That the materia at each f the herizenta segments f the staircaseshaped bique yied ine is abe t resist a bending mment independant f the chice f materia, which  fr sma vaues f the axia ad  can be written as an expressin f the Cumb type, wit h the cnstant c = O and the frietin ~ = 0.75 t/2; That the matera at e ach f the hrizanta segments f the staircaseshaped bique yied ines is abe t resist a trsiana mment, which  fr sma vaues f the axia ads  can be written as an expressin af the Cumb type, where the chesin and frietin parameters depend n the chice f materia; That, fr the s pes f the yi e d ine cnsidere d here, the abvementined faiure vaues fr the bending and trsiana mments in an bique yied ine can b e assumed t be c nstant, independent f the spes; Materie Materi a Materie Materia L  S L  H LC  S LC  H + x A ' That the abvementine d faiure vaues fr the bending and trsina mments c a n be r e garded as yied mments since they are pre s ent in a wide range f strain va ues ; Fgure 18. Fature crite ria fund fr th e diffe re nt materiais by expe rime nts re nting th e trstna m ment M 2 and th e axia ad K 2. That the faiure bending strain in an bique yied ine ca~ b e assume d t be a ine ar fun c tin f the cmpre s s in stre s s eve, a nd inde p e ndent f the chice f materia; a. 149 a a C. = Materia 11 & & & & & & & & 22 Axia ads f f f f f f f f m m m m m m m m acc. t tabe 3 (MN/m 2 ) (MN/m 2 ) (MN/m 2 ) (MN/m 2 ) (MN;m 2 ) (MN/m 2 ) (MN/m 2 ) (MN/ru 2 ) ad ad ad ad :J ad , , The standard deviatin is f the rde r f 10% f the mean vaues. TABLE 4  MEASiRED MORTAR STRENGTH (COMPRESSION STRENGTH) f FOR THE DIFFEI!ENT TORSIONBENDING SPECHIENS. SPECIMENS MADE OF THE SAME BRICKS AND USED IN TEs'\s WITH THE SAME AXIAL LOAD AND THE SAME VALUE OF a (SLOPE OF YIELDLINE), WERE MADE FROM THE SAME BATCH OF MORTAR.
11 16 That secnd rder effects, which reduce the faiure vaues fr the mments in bth hriznta and bique yied ines, shud be taken int accunt in cases f greater vaues f the axia ads. A things cnsidered, it can be cncuded that the resuts f the investigatin supprt the appicatin f yiedine thery as a design methd fr ateray aded masnry was. Nevertheess, it must be admitted that the inves tigatin and its resuts aremre f a quaitative than a quantit~v& nature, and even thugh we have supprted the assumptin that masnry was d pssess sme duetie prperties against atera ads that may justify the use f yied ine thery, the resuts are imited by si~~i fying pints f view, as fr instance the faet that we ignre the cntributins t the atera strength due t the crss jints. Hwever, this des nt weaken the main resuts f the investigatin, which prve that ateray aded masnry was d have duetie prperties, and prve that  and expain why  the bique yied ines greaty increase the atera strength f such was, especiay in cases f sma vaues f the inpane frces. ACKNOWLEDGEMENTS Financia supprt frm the Danish Cunci fr Scientific and Industria Research is gratefuy acknwedged. REFERENCES [] B.H.Facner (1962). Engineering design in brickwrk. Cay Prduets Buetin, New Zeaand Pttery and Ceramics Research Assciatin (PACRA), Pub. N. 22. [2] R.E. Bradshaw and F.D. Entwise (1965) Wind frces n nnadbearing brickwrk panes. Cay Prduets Technica Bureau, Techn. Nte, (6), Lndn, 8pp. [3 ] A. J. Francis (1964) The SAA Brickwrk Cde  The research backgrund. The Civi Engineering Transaetins f the Institute f Civi Engineers, Austraia, pp [4] A.Lsberg and S. Jhanssn (1969) Sidewavs pressure n masnry was f brickwrk. CIB Sympsium n Bearing Was, Warsaw. [5] A. Haquist (1970) Latera ads n masanry was. Nrwegian Buiding Research Institute (NBI). Reprint N Os. [6] L. R. Baker (1972) Brickwrk panes subjected t face wind ads. Thesis fr degree f Master f Engineering Science, University f Meburne, 204 pp. [7] K. M. H. Satti (1972) Mde brickwrk pane s under atera ading. Ph. D. thesis, Edinburgh. [8] A.W. Hendry (1973) The atera strength f unreinfrced brickwrk. The Structura Engineer, pp [9] B. A. Hasetine (1974) Design f atera1y aded wa panes. Prc. Fifth Sympsium n Ladbearing Brickwrk, British Cer. Sc., Lndn, pp [10] A. IV. Hendry and A. M.A. Kheir (1976) The atera strengthf certain brickwrk panes. Prc. Furth Int. Drick Masnry Cnf, Brug~e. [11] B.A. Hasetine, H.W. West and J.N. Tutt (1977) Design f was t resist atera ads. The Structura Engineer, Octber 1977, 55 (10) pp [12] R. Brincke r (1979) The atera strength f masnry was. An investigatin f the physica prperties f masnry. (In Danish) Structura Research Labratry, Technica1 University f Denmark, Reprt N. R111, 210 pp. [13] A. Cadjert (1980) Lateray aded masnry was. Ph.D. thes is, Chamers University f Techngy, Div. Cnc. Struct., Pub. 80 : 5, Gtebrg, pp. 283.
12 1 TAiLE 5  VALURS OF FAILIIRE S:tC!'O TI!K!J.T!AL LOAD Kt FOR 'i: DIF!'!RENT COIIBiiATIONS OP iatbi I ALS. UIAL LOADS, Af V ALUJ!S r a 'r!& GEOKETRIC PARAnE :. TADLE 6  VALUES OF FAILURE MC FOR THE BENDING MOMENT FOR THE DIPYERENT COMBINATIONS OF IIATERIALS, AXIAL LOADS, AND VALUES FOR TIIE GEOiETRIC PARAMETER a. 17 iaterta Gt.49 adi0,94.0 a O. 79~ CL K1 1 1c K1C K1C K1C (ko (ko (ko (ko (k.'i) $ U;78 2. ~ * ;.;$5 4.8$ ,$8* ** ' * s $ s $ * The standard deviatins are t the arder t 13~ t the maan vauea. :.>ny tw tests ny ne te a t :t tests U e an vsues U'"1.149 a=o. 940 ~. 795 C=O. 689 ped data Mteria K2 11 1c MIC 11 tc 11 1c MC (kn) ( k~m ) (knm) (knm) (knm) (knm) ~ ~ ~ , JOB B ~ ~ O.OH ~ t ~40. 61~ ~ ~ ~ The standard deviatins ar e t the rde r f 51, f tbe mean v aes, Ineudine the øtandard devnttua tr the ped data. AJ te ~t t.ø with!tae 11atrta and øam~ axa ad are p~d. TABLE 7  VALUES OF FAILURE M 2 c FOR THE TOiSIONAL MOMENT FOR THE TABLE 8  COHESION AND FRICTION PARAMETERS DIFFERENT COMBINATIONS OF MATERIALS, AXIAL LOADS, AND. FOR THE DIFFERENT TEST SITUATIONS VALUES FOR THE GEO!iTRIC PARAMETER a. AND MATERIALS. Mean vaueø <"". 14Q (1 1:1 9,010 a::to. 795 < t pf)d data Materta k2 M 2C 11 2c M2C 11 2c jj2c (kh) (khm) (khm) (k NM) (kne) (kna ) ~ ' ~ ~ ~ 2. H ~ ~ O.M IG ' ?.5 O. SAO. ~ ~ R G ,.,  The øtandnrd cteviøt tn~ ar e t the rde r f 10$ the mean va1ues, ncudt ng t he etandnrd ch!\'.t\ttns fcsr :.the ped fh.ta. A tesf:p with R\me mnterta and I!IIU!Ie axta ad nre ped. Materi a Chesin Frietin c \ (N m) (mm) Hriznta.11 O* 44.8 yiedine 12 O* 54.1 Bending 21 O* 49.9 mment 22 O* 45.7 Obique 11 O* 42.2 yiedine 12 O* 44.3 Bending 21 O* mment 22 O* 38.6 Obique yiedine Trsina mment * The chesin is put equa t zer in agreement with the resuts f the investigatin.
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