Crack Paths 2006

parameters that govern the subsequent secondary cracking, that is, in addition to those

already stated, bond between bars and concrete, dowel action, aggregate bridging,

aggregate interlock, degradation of concrete between cracks. In order to verify the

reliability and capability of the proposed approach, a comparison with observations of a

well-documented experimental test program [2-4] is reported.

1

V y

y

W yx

W xy

W xy

T n

t

i

A sn

(c)

V x 1

V x

T i

VcII

compre sion-tension

tension-tension

0.2

s

i

---00....82460

Vc,

tfeanilsuiroen

s

n

Vc,Vc,,

tension-compression

compression- compression Vc,DlimVcII

max,cI

max,cII 2

d D d

1 if 1 c t cmax,cI max,cII c lim E V

D

compression failure

A si

f f

, h f

1

D

V

V cII

cI

D

t

D E

x

V

V

V

cII

W yx

(a)

V y

V c,

3 . 6 5 k , 0 . 8 h

V c

f ct

H c1

H c1

H c

6 15.131 V D V D V d D d D if

max,cIlIim

-1.-41.20

E

H

c

c

E

H

V

maxc

cs

0c

V

H

c

c

cs ¨ ¨ © § c E E

¸ ¸ ¹ ·

H

H

0c

c

1

2

H

0c

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

> @ 1 1 - k 2 1 h 1 k 4 2 - h k 2 - h k - E ¸ ¹ · ¨©§ E E E D 2 lim

V

maxc

D=-0.15

cs E

H

0c

D= -0.06

V

cI

D

f c

V

D=0.0

cII

D=1.0

V cmax

(b)

D=0.52

Figure 1. (a) R/C membrane element: geometry and notation, (b) equivalent uniaxial

curves for tension and compression, (c) biaxial strength envelope.

M O D E L IONFGR E I N F O R CCEOD N C R E T E

Uncracked stage

A concrete membrane element, with thickness t, reinforced by ordinary steel bars,

arranged in i-series, characterised by direction Ti , cross-section area Asi , spacing si ,

smeared through the geometric steel ratio Ui=Asi/(si˜t), (i=1,n), is analysed (Fig.1a).