11 th INTERNA TIONAL BRICKJBLOCK MASONRY CONFERENCE

TONGII UNIVERSITY, SHANGHAI, CHINA, 14 - 16 OCTOBER 1997

RESEARCH ON BENDING CAPACITY OF COMPOSITE MASONRY W ALL •

Ruifeng Wu2 Quanfeng Shen! Xianhui Cai! Xiaofeng Xi2 Mingyu Xie2

Qianguo Zhang' Qinguang Li' Degao Chen'

L ABSTRACT

The normal cross-sectional bending capacity of composite masonry wall under vertical and horizontalload has not been deeply researched. This paper presents the researeh of bending capaeity of eomposite masonry wall with the ratio of height to width varing from 2. 5 to 4·. o. which isbased on two groups of model wall tests with 3. 5 ànd 3. O tatio of height to width and with the help of elastie-plastie finite element method. two simplified fromulas are proposed in this paper.

2. INTRODUCTION

Generally. the ratio of height to width of a composite masonry wall building is not larg­er than 2. 5. so it is not necessary to eheck the tilting momento In the at ease. The shear effect plays a major role in wall's failure and the bending moment i~ not a main faetor. it just only has the effeets on the shear eapacity of the wall. When the ratio of height to width is larger than 2. 5. the effect of bending moment becomes more and more obvious. So it is nessary and important not only to consider the bending effects on the shear eapaeity but also ·to eheek the moment eapaeity of eomposite wall.

Keywords: Composite m&sonry wall; Elastie-plastie FEM; RC eonfined bearos and columns I Bending capacity

* Supported by CNNSF and Doctoral Program Fund for Special Discipline. 1 and 2 Ph. D. and Professor. Dept. of Engineering Mechanies. Dalian University of

Technology. Dalian. 116024. China. 3 Senior Engineer and Engineer. Building Design and Researeh Institute of Liaoning

Province. 84 Heping South St .• Shen yang 110005. China. 4 Senior Engineer. Design and Research Dept .• Shenyang Urban Construetion Com­

mission. 41 Heping North St .• Shenyang 110002. China.

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The stress state of composite masonry wall under vertical and horizontalload simultan­cously is a little similar to the state of reinforced concrete or reinforced shear masonry wall, but it is more complex because the concrete confined colurnns and brick/block masonry in the composite wall will participate in the working. The fundamental as­sumptions and method used by reinfered concrete or veinforced shear masonry wall can be adopted in founding simplified calculation formulas.

3. INTRODUCTION OF THE MODEL W ALL TESTS AND CHECKS OF ELASTIC-PLASTIC FEM CALCULA TION RESUL TS

Detailled portrait of the model wall tests can refer to the test report C2J and the brief introduction can refer to reference CU. A comparision of curve Q - t. between the test results and computational results is made, which is shown in Fig. 1. It can be seen that FEM computational results have acceptable accurency at the cracking strenth and ulti­mate strength of the wall. Utilizing the elastic-plastic FEM program C3J, a series of 10 to 16 storey building's wall members with the ratio of height to width varying from 2. 5 to 4. O are computed, and the stress state of masonry, concrete and reinforcement in confined columns are analyzed, especially the length of compression zone and tension zone and the" stress values of them are focused on; Based on these results. some param­eters of the simplified formula are determined and simplified formulas are put forward .

100

90

80

3 ~ 70 ~

] 60

] 50

40

30

20

10

___ (1)-LCH-l

(2)- LCH-2

_-(1)

-- (3)- FEM FOR LCH-l.2 (4)-WCH-l

- . - (5)-WCH-2

_ "_ (6)-FEM FOR WCH-l,2

O 246 8 W U U ~ u m 30

Diaplacement 01 Top Point (mm)

Fig. 1 Q-t. Curves of FEM Results and Model Wall Test Results

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4. NORMAL CROSS-SECTIONAL BENDING COPACITY OF COM­POSITE MASONRY W ALL A.ND SIMPLIFIED FORMULAS

Assunptions used here are similar to the ones used by and reinforced masonry shear wall's simplified formulas.

4. 1 Fundamental Assumptions

(1) Plane sections remain plane (2) The stress-strain relationship of the materiaIs are: Concrete: _ {i ~(2 -=- - (-=-) 2), E::;;;; Eo = 0.002

(1, - Eo Eo

imo, €o < E ~ Eco = O. 0033 (1)

masonry

= 1 11. (1 - -460<.fT.) = O. 00521 a". . '" e , E_ r;:-vi ..

(2)

reinforcement (in tension zone) :

{EIEI , E::;;;; EO' <:3)

(1, = i", E" ~ E < E, •• = 0.01 (3) In ultimate state, the concrete and masonry in tension zone are to be neglected and the area of reinforcement in compressive zone is conversed into effective concrete area and copperates with concrete.

4.2 Effective Stress Figures and Its Proper Values

The actual distribution of the composite masonry wall is. rather complexo In order to

simplify calculation, reinforcement in tension zone is conversed into l.i.niformly distribut­ed and masonry and concrete in compression zone are also conversed into uniformly dis-. tributed (shown in Fig. 2).

Using C denotes the resultant force in compression zone, y. denotes the distance from the action point of C to the compressive side column, T denotes the reslttant force in tension zone. y. denotes the distance from the action paint of T to the tensile side .col: umn. we have

C = C ~ A,/ (lJ"", + ~ A"./ a..i .. Jô· y, = Clf31~"hO = C1Xc

T = a,fyAI1( ~) (x. = (1 - tb)ho

Y. = cz(ho - x") = cz(l - ~b)!ho

(4)

(5 )

(6)

(7)

Where am • ac and a, are the ratio of effective stress of compressive masonry, concrete and reinforcement to its ultimate strength respectively; Cl and Cz are the ratio of y, and y. to the effective rectangle stress distribution length x. and x, respectivelly; f31 and f3z are the ratio of x, and x, to the actuallength of compression zone, x •• and tension zone, (ho-x.) respectivelly. ~b is the limitted relative compression zone length. that means

~b =;. xb/ho all these coefficience are to be determined by FEM analysis.

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(a)

(b)

(c)

b TH----- ho -------,t +-______ h _____ --+

Fig. 2 Effective Stress Figure

4. 3 The Calculation of Relative Compression Zone Length

As is presented before that compressive reinforcement is to be conversed into effective concrete. So on1y two materials, masonry and concrete, would be considered in com­pression zone. In ultimate state, the tensile reinforcement yields and the masonry and concrete reach their ultimate strength respectively. They are to be used to determine the value of E.. The option should be the smaller one of which are relate<! to masonry strength and concrete strength:

1 E .. = f (8)

1 + O.OO§gEs

~ _ E_ ho - b· + ! (9) "'-e_+€y ho ho

Where . b is the width of confined column.

4. 4 Detérmination of Strength Proper Values a,. a~ and a,

The FEM computation is modelled from a composite masonry wall. of which the width is 13. 1m, the height of first storey is 3. 5m and the others' height is Z. 8m. The wall has 6 confine<! columns with cross-section of 240 X 600mm. each has reinforcement of 8 f 14mm. A uniform distribution of vertical load is exerted on each storey which is

O. 12MPa and a series of variable horizontalloads are exerted on each storey with the

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distribution shape of inversion triangle. The materiais are C30, Mu20 and M15.

The calculation showed that the waU's failure would take place in the bottom storey, 50

we selected the stress state in the middle cross-section of the bottom storey to determine a" a~ and a,. Calculated results are shown in Table 1.

From Table 1 we can see that when keeping the whole verticalload unchanging, the average values of these coefficience are a,=1. 05, a.=O. 86, a..=0. 72.

Table 1 Calculated Strength proper values a., a~ and a,

Ten.sile Reinforement Compressive Concrete and Masonary

Total T en.sile Side Column 1 Side Column 2 Average

Side Masonry Side Column Value

Storey TeMon Temion Compressive Compressive

Force a,. Force ao, a, a.. a,

(kN) (kN) Force (kN) force (kN)

16 505 1. 30 306 0.79 1.05 2400 0.74 4230 0.86

14 479 1. 24 356 0.92 1. 08 2440 0.74 4280 0.87

12 509 1. 31 290 0.75 1. 03 2320 0.71 3980 0.81

10 451 1.16 347 0.89 1. 03 2310 0.71 3640 0.74

So we use a,=1. O, .a .. =O. 72. ac=O. 85 to simplify analysis.

4. 5 Determination of the Values of Clt Plt CZ' Pz,

From the FEM analysis we abtained that the reinforcement in two tensile columns yielded its tension strength and some compressive masonry failed during ultimate state. 50 the limitted compression zone length can be determined by

~_ e..+e, ~ho - b - ho - b - s

Where s is the distance between columns.

From Eq. (2) and (3). we get e,.....:..0. 002 and €,=I,/Es"':"O. 0015. Thus ~ho= 5. 54m and these coefficienc CI' PI' C2' P2 can be deduced from FEM results, as are shown in Table 2.

From Table 2, we can see that the average values of these coefficience are PI = O. 536. CI=O. 549, P2=0. 657, C2=0. 414. In order to simplify calculation, we use PI=CI= 0.54, cz=O. 42. P2=0. 67.

Thus, ali coefficience are determined. We write two equations considering verticalload and lateralload are exerted simultaneously:

N = 0.852: (A; 1 em + 0.851 .. • A .. / )~, - (/"A'l + I"A.o ~) (10)

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Table 2 Deduced Coefficience of Cl' {3l' CZ' {3z

Tension Zone (l-E)h.=7. 257m Compression zone Eh" = 5. 543

'Total Tension Compressive Storey Force

y. x. fl, Forec

y. x. fJI (m) (m)

c, (m) (m)

Cl

(kN) (kN)

16 113.6 2.030 4.820 0.658 0. 421 9950 1. 604 2.99 0. 546 0.536

14 114.5 2. 053 4. 878 0.666 0. 421 9607 1. 56 2,94 0.536 0. 531

12 112.2 1. 933 4.729 0.646 0.409 9223 1. 671 2.886 0.527 0. 579

M = o. 85 ~ (A;; 1 ao + 0.851 .. • A,./ )0« % - Yc) + ( !,Al + /Ao :;) ( h ~ b - y,) (11)

When N is given, the bending capacity M can be 'determined by Eq. (11) and can be used to check bending capacity, or we can use Eq. 11 to determine reinforcement area if design moment is provided.

4.6 Effects of Wall's Flange on Coefficiences.

While calculatjng the composite masonry walPs bending capacity the flange's effect is obvious, and the width of the flange will infulence some coefficiences. So it should be considered. We can revise the two formulas (11) and (12) after series of calculations of walls with different flanges. It can be dane easily.

5. CONCLUSION

CD Composite masonry wall with the ratio of height to width varying from 2.5 to 4. O under vertical and horizontalload can use the proposed formulas (11) and (12) as fun­damental formulas for calculation.

CID There are many factors which infulence normal cross-sectional bending capacity of the walls, such as the number of confined columns, the area ratio of concrete to whole wa11, the distance between columns, the ratio of reinfercement to concrete, the match of masonry and concrete, and so on. But the formulas presented in this paper, are not theoretical, buf semi-empirica!. So it is necessary to consider a11 factors which influ­cence a11 selected coefficiences. These works are to be necessary advanced.

CID This paper and reference (lJ and (4J are a set of formulas to calculate the capacity of compression, lateral resistance and bending resistance, they can be used for design and seismic resitant check to high-rise composite masonary wall building after modifica­tion according to engineering needs.

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6. REFERENCE

(lJ Shen,Q. F. , et aI. , "Elastic-plastic Analysis of Lateral Bearing Capacity of Com­posite Masonry Wall and Simplified Calculating Formulas," Published in This Pro­ceeding.

(2) Wu, R. F., LU, H. X. and Xi, X. F. , "Elasto-Plastic Analysis and Crack Gracth Analysis of Reinforced Masonry Shear Wali," ]. of Dalian Institute of Technology, No. 3, 1979, pp.60-72

(3) Shen, Q. F. , et aI. , "Compression Capacity Calculation of Composite Masonry Wali," Published in This Proceeding.

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