2 .a . 5

THE DETERMINATION OF STRESS/STRAIN RELATlONSHIP OF BRICKWORK B, POWEL L H,R, HODGKINSON

The British Ceramic Research Association, St oke-on - Trent, Creat Britain

THE DETERMINATION OF STRESS/STRAIN RELATIONSHIP OF BRICKWORK

BESTIMMUNC DES VERHALTENS SPANNUNC/VERFORMUNC DES

~UERWERKS

The stress/strain relationship of brickwork at or

Das Verha lten Sparmung/Verformung von Mauerwerk in

near its ultimate f~ilure load has been- investigated to provide necessary information 0'1 which to base the recommendations of a proposed Design Cuide for Reinforced and frestressed Clay Brickwork . Short duration axial compressive tests were -carried out 0'1

der Nahe der

~chbelastung

wurde untersucht , um die

notwendige Information zu bekol111len für das AufsteZZen einer praktischen Code für bewehrtes und vorgespanntes Mauerwerk . Axiale Druckversuche von kurzer Dauer

small brickwork columns built jrom four different

wurden durchgeführt CI'Af kZeinen Mauerwerksaulen aUB vier Sorten Ziegel und 1: ~ _:3 Mortel.

types of bricks and J:~:3 mortar. The development of the methods used for load application and the measure ment of the compression undergone by the column is described . Stress/strain relationships are demon -

Die Entwicklung der Methoden, die benutz t wurden für das Anbringen VOn BelaBtungen und das Messen des Drucks, wird beschrieben .

strated for the four types of brickwork tested and these have been used to determine both the secant modulus of elasticity at two - thirds of the ultimate stress level and the tangent modulus of elasticity at zero stress. The two values of the modulus of elasticity are shown to differ widely .

DETERMINATION DU RAPPORT

TENSION/DEFOR~TION

Das Ver halten Spannung/Verf ormung fü"r vier Ar ten von Mauerwerk wurde unteraucht und benuizt , um den Sekant - EZastizitatsmodul (auf zwei Drittel der ~ch­ laat) und den tangentiellen Modul (bei Nullspannung) festzustellen. Es erweist Bich, dass beide Modulwerte weit von einander entfernt liegen.

BEPALINC VAN DE VERHOUDINC SPANNINC/VERVOlMINC VAN METSELWERK.

DE LA MACONNERIE Le rapport tension/defo rmation de la maçonnerie, lors

De verhouding spanning/vervonning van metselwerk in

de la mise sous charge à la limite de la rupture, a été étudié afin d ' obtenir les informations nécessaires à la rédaction d 'un code d 'utiZité pratique concernant

de buurt van de breukbelasting werd onderzocht ten einde de infornutie te krijgen die nodig ia om een praktische aode op te stellen voor gewapend en voor-

l 'emploi de maçonnerie Cl1"1IIée ou précontrainte.

gespannen metselwerk .

Des

essais axiaux de courte durée furent entrepris sur des petites colonnes construites de quatre différentes espe--

Axiale drukproeven van kort e

duur werden uitgevoerd op kleine metselwerkkoZol111len uit vier soorten baksteen en 1 : : 3 mortelo

ces de briques maçonnées avec un mortier bâtard ayant les proportions 1:

~: 3 .

De ontwikkeling van de methoden gebruikt voor het aanbrengen van belastingen en de meting van de druk

Le developpement des méthodes employées pour obtenir Zes charges desirées et pour les mesurer, fait l ' objet

-d ' une description . Le rapport tension/deformation des quatre especes de maçonneries fut examiné et employé pour determiner la valeur sécante d 'élasticité établie au deux tiers de la charge maximale de rupture, ainsi que la vale ur tangentieZZe d'élasticité , sous tensi on nuZZe. IZ appert que les deux résultats sont fort dis semblab7.es .

wordt beschr~ven.

De verhouding spanning/vervorming

voor vier soorten metselwerk werd onderzoaht , en gebruikt om de secant - elasticiteitsmodulus -(op twee derde van de breuklast) en de tangentie1e modulus (bij nulspanning) te bepalen~ Het blijkt dat beide aijfers ver uit elkaar liggen.

2 . a.5-1 1.

I NTRDDUCT IDN

I n 1972 , the Structural Ce ramics Advisory Gr oup formed a Working Pa rty to draft a Design Guide f or Reinforced and Pre-stressed Clay Brickwork. One of the Working Party ' s terms of reference was to decide on any topics r equiring immediate research . It was conside red tha t one such topic , was the st ress/strain relationship of b r ickwork at a r near the ultimate failu re load . 2.

REVIEW DF THE LIT ERATURE

Many investigators . including th e authors , have in the course of comp r essive testing of wa ll s fitted compression gauges pri marily to establish uniformity of loa d dist ri bution . Invariably it was the procedu r e for these gauges to be removed for safety long before the expected ulti mate failure load , and thus the values of modulus of elasticity derived from these measurements are totally irreleva nt to the present investigation . Anderson and Hoffman 1 carried out s ev e ral ultimate compressive load tests on reinfo rced brickwork columns under both axia l loading an d different deg r ees of eccentr i c loading during which they t ook measu r ements of the compressive strain up to 70% of the ult imate l oad . They concluded that the ultimate strength design method used for r einfo rc ed conc r ete columns appeared to be capable of being app l ied to "r einfo r ced br ickwork mason ry columns, and postulated a compressive stressstrain r ela ti onship for bric k masonry which was parabolic up to the leveI of ultimate stress and r emained constant at this leveI up to the point of ultimat e strain .

3.

De termination of the stress/sLrain relationship was carried out on brickwork pillars . Each pillar , as shown in Figure 1 , was eight courses high with two bricks in each cou r se , t he bricks in each course be i ng lai d at right angl es t o those in the cou rse below . The pillar was built on a 400 x 400 x 150 mm deep reinforced concrete block and was capped with a similar conc rete block . The tests were performed in the 8. 97 MN capacity wall testing frame s , with the arrangement as shown in Figure 2 . To facilitate close control of the rate of loading when approaching the point ' of failure , two singleacting , 3MN capacit y , hydraulic jacks we re mounted , one on either side of t he test pillar acting in op posit ion to the loading jacks using a separate hyd ra ulic circuit from that of the loading jacks . This method of controlling the rate of loading , necess itated the use of a load cell to measure the resultant l oad on the pillar, the load cell being located direct ly be l ow the pil la r. It ,.,as cap able of measu ring loads up to 3 MN . The output f ro m the l oad cel l was mea sured by a Dig ital Voltmeter , and in all tests subsequent to the first four the output was r ecorded using a U. V. recorder . Measurement of the sho rt ening of the pilla r was made using dial gauges , capab le of measuring to 0 . 0025 mm du ri ng the second , third and fourth tests . In a l I fu r ther tests it wa s measured using Linear Displacement Transd uce r s , t he output from these being recorded by the U. V. record e r . 4.

Ha ller 2 developed a meth od of calculation for determining the loadbearing capac ity of brickwork , based on a st r ess -strain relationship determined expe ri mentally from axial compressive load tests on small test struc tures made up o f at l east five courses of brickwo r k and typica l of the structure und er considerati on . He demonstrated that this metho d yielded results which we re in ve r y close ag reement with experimental va lu es . He concluded that it was not possible to replace the experimentally de te rmined relationship by a curve of s imilar shape , for instance by a parabol a having the same va lu e of compressive strain at the point at which ultimate stres s is attai ned . Turnse k and Cacovic 3 demonstrated a generalized fo r m of the stress-strain relationship for brickwork obtained by regression analysis of fifty-seven test results in which the compressive deformations were measu r ed up to 80% of th e ultimate load . The relationship was parabo lic up t o the ultimate st r ess le ve l after which the stress decreased almost linearly to the point of ultimate strain . They showed a good agreement between the expe rimentally determined relationship and a calcula ted relationship by compa ring the areas under the cu rves. In a comparison between brickwork and concrete they demonstrated a difference in the stress-strain rela tion ships for the two materi als, the relationship f o r concrete te nd ing to be mo re linear up to about 75% of the ultima te load . Kirt schig , Cordes an d Schone r 4 state that the load bearing capacity of brickwork can be determined on t l e basis of the stress - strain relationship obtai ned from axial compressive load tests . They propose that the r e lationshi p should be determined for each class of brickwork and postulate an equat ion which uses the modulus of elasticity and the ultimate failure st res s to determine the stress-strain relationship . They demonstrate good agreement between theoretical results and th ose ob tai ned from actual compressive load tests, during which comp r essive strain measurements were made, but not up to the ultimate failure load.

EXPERIMENTAL EQUIPMENT

EXPERIMEN TAL METHOD

Initially the method entai led mounting the load cell on the conc rete sub-structure , wit h a thin bed of cemen t fondu/g ran o dust mortar i n between them , s o that it was firm and leveI . The two 3 MN jacks we r e also mounted in the same manner . The test pi llar was then placed on top of th e load cell , again with a laye r af cement fondu/g r ano dust mortar in between to ensu re solid contact and good transmission of load from the pillar to the load cell . The sub-structure , complete with load ce ll, test pillar and side rams, was then whee l ed into the testing frame and pos iti oned with i ts base in firm contact with the floor of the test ill g frame . A layer of cement fondu/grano du st mortar was then plac ed between the top of the test pillar and the under side of the load spreader beam , to ensure good contact between them. Th e layers of cement fondul grano dust mortar were allowed to mature befo re the test was carried out . Durin g the test the pillar was loaded in steps to about three-quarters of its eXp'ected failure load , this having been determined previously on anot her pillar . The side rams were then used to relieve some of the load from the pillar . Then by altern at ely in creas1ng the load on the sp r eader beam and r elieving the load on the side rams , t he pillar was loaded in steps up to failure . In the first twelve tests st rawboard was used t o en sure good contact between the side rams and the spreader beam . In the later tests, however , this was replaced by a layer of cement fondul grano dust mortar . This l oading pr ocedure was modified after the first four tests , to avoid having the load on the pillar increasing , then decreasing a nd then increasing again . To do this the side rams were brought into use at the st a rt of the test and thus the load on the pillar was always increasing . In practice it was found that the operation of the two hydraulic jack circu its, in complete unison , was difficu lt at th e point of failure . For this reason it was decided not to use the side rams in tests 11 and 12,

2 . a.5-2 TABLE 1 but this was unsatisfactory and the former method was reverted to . At each step in increasing the load the vertical shortening of the pill ar was measured. In tests 2 , 3 and 4 this was dane using dial gauges . The use of these proved to be unsuccessful from two points of view, the first being the difficulty in taking readings when near to failure load as the pointer was moving rapidly , and secondly, it was considered to be unsafe for an operative to be in close proximity to the pillar when it was failing. It was therefore decided to measure the movement using linear displacement transducers, th8 output signal from which was recorded using a U. V. Recorder . This method permitted the operatives to stay well clear of the pi ll a r, as well as providing a permanent record of the shortening . It was a l so decided, at thi.s stage, to feed the output signal from the l oad cel l into the U.V. Recorder, 50 that the load corresponding to the various compression readings cou l d be determined. Two li near disp l acement transducers we r e used, one mounted on each of two opposite faces of the pillar , the mean of the two sets of readings producsd being taken. The transducers were mounted on two 7.94 mm diameter steel rods set in the pillar, in the joints between the second an d third courses and between the sixth and seventh courses . Th is gave a gauge length of approximately 300 mm. The use of these rods proved to be another source of trouble. During the construction of the first eleven pillars, before the rods were placed in the joints, the ends of the rods were covered with a thin p l astic sleeve , l eavi ng only the middle two inches of the rod clear. When the pillars had cured for a few days the plastic sleeves were removed thus leaving on ly the middle two inches of the rod held by the mortar. By doing this it was hoped to e nsure that the mean of the two transducer readings wo uld accurately give t he mo vement in the middle of the pil l ar . In pr actice some of the rods became loose and tilted due t o l ocal crushing of the bri c ks during t he testo Thi s made it appear ,in some cases , that one face of the pil l a r was underg oing tension, whi ch was not 50 . To avoid this the rods inse r ted in pillar 12 were he ld by the mortar across the full width of the pill ar . This did not , howsver, . improve the method of measurement as when the pillar was ne ar to failure the bars moved bodily in the pillar , thus invalidating any measurements made. Therefore it was decided that in tests 13 to 26 the transducers would be mounted between the top su rface of lower conc r ete block and the bott om s urfa ce of the upper concrete block . Thi s gave a new gauge length of approximately 610 mm. Th e results obtained from th ese t es t s were much be tter . 5.

EXPERIMENTAL RESULTS

Tes t s were carried out on twenty-six pillars built from four types of brick s , all using 1:~:3 mortar. The brick types are as follows: Type A:

16-hole perforated, having a compressive st rength of 69 . 64 N/mm 2 •

Typ e B:

Cl ass A, bl ue eng i nee ring, naving a compressive strength of 71.7 N/mm 2 and a water absorption of 3 . 4% .

~:

Fletton havi ng a compressive strength of 25.5 N/mm 2 •

Typ e D:

Double-frogged, stiff-plastic, ha vlng a compressive streng th of 45.3 N/mm 2 •

Table 1 shows for each test pillar, the type and compressive strength of the brick, the compres sive strength of the mortar and the ult imate compressive strength of ths pillar.

Brick Pillar No .

Type

Compressive Stren~th

N/mm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 24 22 23 25 26

Mortar Compressive Stren~th

N/mm

A

69 . 64

16 .1 1

B

71 . 70

16 . 11

C

25.5

14 . 62

A

69.64

14 . 62

B

71 . 7

14.76

D

45.3

15.2 1

Pil l ar Compressive Stren~th

N/mm

30 .00 24 . 87 34.98 26 . 68 26 . 70 28 . 80 33 . 78 29 . 05 27 . 05 26.49 27 .00 9.18 8 . 36 10.68 8.95 20 .04 2 1. 60 24.67 18.15 25 . 66 28 . 21 29.09 18 . 63 20.58 16 . 80 21 .10

TABLE 2

Pil l ar No. 13 14 15

Brick Type

C Mean

16 17 19

A Mean

20 21 24

B Mean

22 23 26

D Mean

Tangent Modulus N/mm 2

Secant Modu lu s N/mm 2

4490 5580 4810 496 0

3370 4110 3750 37 40

21620 16490 16580 18230

14330 105 10 10760 11900

15610 18800 17670 17370

10410 14460 13910 12930

17060 16940 16480 168 30

11480 11990 11350 11610

2 . a . 5-3 Pillars 1 and 8 were tested only to determine their failure loads. Shortening under comp r ession was mea sured on the remaining twenty-four pillars tested . The measurements in tests on pillars 2, 3 and 4 were made using dia 1 gauges , those in tests 6 to 26 were made using linear displacement transducers, whilst in test 5 both methods were used so that a comparison could be made . In tests 2 to 7 and 9 to 12 the measurements were made over a 300 mm gauge length and in tests 13 to 26 over a 610 mm gauge length . 6.

3.

Turnsek, V., and Cacovic , F., "Some Experimental Results on the Strength Df Brick ~asonry Walls " . Proc . Df Second International Brick Masonry Conference ., Edited by H. W. H. West and K. H. Speed , Stoke-on-Trent , B. Ceram . R. A. , 1971 , pp. 149-156.

4.

Kirtschig, K., Cordes , R. and Schoner , W., "Computation Df the Loadbearing Capacity Df Masonry by means Df Stress-Strain Cu r ves ". Proceedin gs Df Third International Brick Masonry Conference . Edited by L. Foertig and K. GabeI . Bonn, Bundesverband der Deutschen Ziegelindustrie, 1975 . pp . 120-123 .

5.

Hodgkinson, H. R. , and.Powell , B., "Design Df the B. Ceram . R. A. Wall-testing Machine and Results Df Calibration Tests on Three Machines ". Proc . Brit . Ceram . Soc . No . 11 , 1968 .

ANALYSIS DF RESULTS

The results for tests 13 to 17, 19 to 24 and 26 were analysed and the stress/strain relation ship determined . These relationships are presented graphically in Figure 3 to 6 . Figure 7 shows , for comparison purposes, the mean curves for each brick type, as determined from Figures 3, 4, 5 and 6 . The Modu lus Df Elasticity values have been determined using two methods . The first method , which assumes that the stress/strain curve is pa rabolic up to the point Df maximum stress , gives the tangent modulus at the origin based on twice the maximum st r ess . The second method gives the secant modulus based on twothirds Df the maximum stress . Both sets Df Modulus Df Elasticity figures, as determined from Figures 3 , 4 , 5 , 6 are shown in Table 2 . 7.

-

Reinforced - - concrete block

300mm.

CONCLUS I ONS

gaug~

~glli The values Df modulus Df elasticity for a gi ven brick derived from the tangents and secants differ widely . The implications Df this difference wil l be considered by the Reinfo rc ed Brickwork Working Party in drafting their design g uide .

7· 94mm. dia. metal rod

-

Irrespecti ve Df the method used , statistical analysis Df the modu li for the four bricks showed that there was no signi ficant difference between the va lu es for bricks A, B and O. The re is a factor Df approximately 31:1 between the value for ~rick C and the mean Df the other three bricks . It is therefo r e lik ely that in the design guide different values Df modulus will have to be used for different classes Df brickwork . 8.

Figure

r

This paper is published by pe rmissi on Df Mr A. Oinsdale Oirector Df Research , Bri tis h Ceramic Rese'arch Association .

1.

2.

Typical test pillar.

ACKNOW LEOGEMENTS

This work was supported by funds provided by the Brick Oeve l opment Association . The authors wish to thank Mr . G. A. Weeks Df B.R . E. who devised the method Df l oad control and Mr J . Lomax for help in the experimental work .

9.

I.

Reinforced concre te block

RE FE RENCES

-

l

3 MtL-hy'drGl

~k .Jac .

, Load _ cell.

Anderson , O. E., and Hoffman , E.S . , "Design Df Brick Masonry Co lurnns " . Designing, Engineering and Con-' structing with Masonry Products , Edited by F. B. Johnson , Houston , Texas ., Gu lf Publishing, 1969, pp . 94-100 . Haller, R., "Load Capacity Df Brick Masonry ", . Designing , Engineering and Constructing with Masonry Products . Edited by F. B. Johnson , Houston, Texas ., Gulf Publishing , 1969 , pp. 129-149 .

]

Loading-2preader beam

- - - -,-

I

Lt::~U

Reinforced concrete Rigid steel beam on jackable wheels

Figure 2 .

Schematic arrangement of test equipment.

2 . a . 5-4

30 28 26 24 22 20 18 r;;-'

16

E

.!§. 14

o_-_. Pillar

z

L-...J

12

VI

---I(

Pillar NO. 21

0-- .

--o

Pillar No. 24

111

...... \11 (li

10

NO. 20} Brick Type B

If---

1:~:3

Mortar

8 6 4 2 0·002

0·004

5train

0·006

Figure 3. 5tress/strain relationships for Pillars Nos. 20.21 and 24.

12

.

,--, E E

-Z

10 , .Ht('''''

6

111 111 C\I

4

......

",M

-'" /"

8

L-.....I

til

--~

"A 2

."

~x«-It/Ç..J(Jr""~""

___ ~õõiili

..J'-" '

-~~~ J( or ~ _,,( Ir" . Ir' ",,,,'" o

,/If

o"iõ;õ

,-o-- . •

·-.w··· •... .

• Pillar No 13 } . ... -----.., Pillar No. 14 _ ._ .... Pillar No. 15

,.I!t.,II'. .

-« -0--.

..........

--... . ~

~

,

':----..

Brick Type C I:Y4 :3 Mortar

o

~.

j(..

O

0·002

5train

0·004

O'OOp

Figure 4. 5tress/strain relationshlps for Pillars Nos. 13,14 and 15.

Z. a . 5- 5

22 20

2 . a . 5-5

,

18

\

'"

16

'" \

,..-,

"E

-E

\

\

14

\

\

12

~ 10

.,'" ...

8

Vl

6

Figure 5. Pillor No 16} 8rick Type A Jt---- --x Pillor No.

Lo'

0 . - . --