2 .a . 5

THE DETERMINATION OF STRESS/STRAIN RELATlONSHIP OF BRICKWORK

B, POWELL

H,R, HODGKINSON

The British Ceramic Research Association, Stoke-on-Trent, Creat Britain

THE DETERMINATION OF STRESS/STRAIN RELATIONSHIP

OF BRICKWORK

The stress/strain relationship of brickwork at or

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 Re­

inforced and frestressed Clay Brickwork . Short

duration axial compressive tests were -carried out 0'1

small brickwork columns built jrom four different

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 ­

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 elas­

ticity are shown to differ widely .

DETERMINATION DU RAPPORT TENSION/DEFOR~TION

DE LA MACONNERIE

Le rapport tension/deformation de la maçonnerie, lors

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

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

essais axiaux de courte durée furent entrepris sur des

petites colonnes construites de quatre différentes espe-­

ces de briques maçonnées avec un mortier bâtard ayant

les proportions 1: ~: 3.

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 tension

nuZZe. IZ appert que les deux résultats sont fort dis ­

semblab7.es .

BESTIMMUNC DES VERHALTENS SPANNUNC/VERFORMUNC

DES ~UERWERKS

Das Verha lten Sparmung/Verformung von Mauerwerk in

der Nahe der ~chbelastung wurde untersucht , um die

notwendige Information zu bekol111len für das AufsteZZen

einer praktischen Code für bewehrtes und vorgespann­

tes Mauerwerk . Axiale Druckversuche von kurzer Dauer

wurden durchgeführt CI'Af kZeinen Mauerwerksaulen aUB

vier Sorten Ziegel und 1: ~ _:3 Mortel.

Die Entwicklung der Methoden, die benutz t wurden für

das Anbringen VOn BelaBtungen und das Messen des

Drucks, wird beschrieben .

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 verhouding spanning/vervonning van metselwerk in

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

gespannen metselwerk . Axiale drukproeven van korte

duur werden uitgevoerd op kleine metselwerkkoZol111len

uit vier soorten baksteen en 1 : : 3 mortelo

De ontwikkeling van de methoden gebruikt voor het

aanbrengen van belastingen en de meting van de druk

wordt beschr~ven. De verhouding spanning/vervorming

voor vier soorten metselwerk werd onderzoaht , en ge­

bruikt 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.

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 LITERATURE

Many investigators . including the authors , have in the course of comp r essive testing of wa ll s fitted com­pression gauges pri marily to establish uniformity of load dist ribution . Invariably it was the procedu r e for these gauges to be removed for safety long before the expected ultimate failure load , and thus the values of modulus of elasticity derived from these measurements are totally irrelevant to the present in­vestigation .

Anderson and Hoffman 1 carried out s everal 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 rced 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 brick 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 .

Ha ller2 developed a method of calculation for deter­mining the loadbearing capac ity of brickwork , based on a st r ess -strain relationship determined expe rimentally 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 under considerati on . He demonstrated that this method yielded results which we re in ve r y close ag reement with experimental va lues . 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 comparing the areas under the cu rves. In a comparison between brickwork and concrete they demonstrated a difference in the stress-strain relationships for the two mater­i als, the relationship f o r concrete te nding 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 those 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.

2 . a.5-1

3 . EXPERIMENTAL EQUIPMENT

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 bei ng laid at right angl es t o those in the course 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 oppo­sit ion to the loading jacks using a separate hydraulic 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 lar. It ,.,as capable of measu ring loads up to 3 MN . The output f rom 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 was measured using Linear Displace­ment Transd uce r s , t he output from these being recorded by the U. V. recorde r .

4 . 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 the 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 itioned with i ts base in firm contact with the floor of the test illg frame . A layer of cement fondu/grano dust mortar was then placed 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 .

During 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 alternately 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 ensure 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 procedure was modi­fied after the first four tests , to avoid having the load on the pillar increasing , then decreasing and 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 circuits, in complete unison , was diffi­cu lt at the point of failure . For this reason it was decided not to use the side rams in tests 11 and 12,

2 . a.5-2

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 linear 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 cks during t he testo Thi s made it appear ,in some cases , that one face of the pil l a r was undergoing tension, whi ch was not 50 . To avoid this the rods in­ser 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 surface of lower con­cr ete block and the bottom s urface of the upper con­crete block . Thi s gave a new gauge length of approxi­mately 610 mm. Th e results obtained from these 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 bricks , all using 1:~:3 mortar. The brick types are as follows:

Type A:

Type B:

~:

Type D:

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

•

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

•

Double-frogged, stiff-plastic, havlng a compressive strength of 45.3 N/mm 2

•

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

Pillar Type No .

1 2 3 A 4 5 6 7

8 9 B

10 11

12 13 14 C 15

16 17 A 18 19

20 21 B 24

22 23 D 25 26

Pil l ar No.

13 14 15

16 17 19

20 21 24

22 23 26

TABLE 1

Brick

Mortar Pil l ar Compressive Compressive Compressive Stren~th

N/mm Stren~th

N/mm Stren~th

N/mm

30 .00 24 . 87

69 . 64 16 .1 1 34.98 26 . 68 26 . 70 28 . 80 33 . 78

29 . 05 71 . 70 16 . 11 27 . 05

26.49 27 .00

9.18 8 . 36

25.5 14 . 62 10.68 8.95

20 .04 69.64 14 . 62 21. 60

24.67 18.15

25 . 66 71 . 7 14.76 28 . 21

29.09

18 . 63 45.3 15.2 1 20.58

16 . 80 21 .10

TABLE 2

Brick Tangent Secant Modulus Modu lu s

Type N/mm 2 N/mm 2

4490 3370 C 5580 4110

4810 3750 Mean 496 0 37 40

21620 14330 A 16490 10510

16580 10760 Mean 18230 11900

15610 10410 B 18800 14460

17670 13910 Mean 17370 12930

17060 11480 D 16940 11990

16480 11350 Mean 16830 11610

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 . ANALYSIS DF RESULTS

The results for tests 13 to 17, 19 to 24 and 26 were analysed and the stress/strain relationship 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 . CONCLUS I ONS

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 rced Brickwork Working Party in drafting their design guide .

Irrespecti ve Df the method used , statistical analysis Df the modu li for the four bricks showed that there was no significant difference between the va lues 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 likely that in the design guide different values Df modulus will have to be used for different classes Df brickwork .

8 . 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 .

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

9 . RE FE RENCES

1 . 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 .

2 . 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 .

2 . a . 5-3

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 ". Proceedings

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 .

Reinforced - -- concrete block

-

300mm. gaug~

~glli

7·94mm. dia. metal rod

Reinforced concre te block

Figure I. Typical test pillar.

r Loading-2preader beam

l

, Load _ ----,- I

Lt::~U cell. Reinforced concrete

Rigid steel beam on jackable wheels

-]

3 MtL-hy'drGl ~k .Jac .

Figure 2. Schematic arrangement of test equipment.

2 . a . 5 - 4

30

28

26

24

22

20

18

16 r;;-'

E .!§. 14 z

L-...J 12

VI 111 (li

10 ... ... \11

o_-_. Pillar

If--- ---I( Pillar

0-- . --o Pillar

NO. 20} NO. 21

No. 24

Brick Type B

1:~:3 Mortar

8

6

4

2

0·002 5train

0·004 0·006

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

12

10 ,--, ..

E 8 E --Z L-.....I 6

111 111 4 C\I ... ... til 2

~x«-It/Ç..J(Jr""~"" ,/If ,.I!t.,II' ..

--~ -« , .Ht(''''' ___ ~õõiili o"iõ;õ ,-o-- . -0--. .... ......

",M ..J'-" ' • --... .~ -'" /" ·-.w··· •... . ~ -~~~ , ':----..

Ir" Ir' } J( or ~ • Pillar No 13 _,,( . . Brick Type C

",,,,'" o ... -----.., Pillar No. 14 I:Y4 :3 Mortar "A _ ._ .... Pillar No. 15

." o ~.

j(..

O 0·004 O'OOp 0·002 5train

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

22

20

18

16

14 ,..-, "E 12 E --~ 10

'" ., ... L­o' Vl

8

6

4

2

22

20

18

16

r:;-' 14 E ~ 12 z

L-I

10 z: ... !:; 8 Vl

6

4

2

o

28

26

24

22

20

18

16 ,....-,

E 14 ~

.3... 12

'" ~ 10 .. Ví

8

6

, \

'" '" \ \ \ \

\

Pillor No 16} 8rick Jt---- --x Pillor No. 17

1 : ~ : 3 0.-. --<) Plllor No 19

0 ·002 Stroin

---Pillor

,..-----« Pillor

_.--<) Pillor

0 ·002 Stroin

Brick 0-- ._ Brlck

0 ·004

No. 22} Brick

No. 23 1:~:3 No. 26

0 ·004

Type A \

Mortor

Type D

Mortor

Brick

Type B Type A)

I: y .. :3 Mortor Type e

0 ········· ····0 Brick Type D

0·006

0·006

0~----~----~0~·0~0~2~----~----~------~----~ 0 ·004 0006 Stroin

Z. a . 5- 5

2 . a . 5-5

Figure 5.

Stress/stroin relotionships for

Pillors Nos. 16,17 and 19.

Figure 6.

Stress/stroin relotionships for

Pillors Nos. 22,23 ond 26.

Figure 7.

Stress/stroin relotionships for

pillors built with

Bricks Types A,B,e ond D,

ond 1:v,.:3 Mortor.