PRESENTED BY JOHN DOE

Shear Behavior of RC Tapered Beams with Stirrups

Tokyo Institute of Technology ○ SHUO TengTokyo Institute of Technology NAKAMURA TakuroTokyo Institute of Technology NIWA Junichiro

JSCE 72th Annual Conference

Background 1

The experimental data of RC tapered beams is rather insufficient.

Rational and economical design method for RC tapered beams in design specifications of Japan Society of Civil Engineers has not been established yet.

RC tapered beams

In the current constructionfield, RC tapered membersare widely used ascantilevers and footings dueto their economical andaesthetic advantages.

Previous research & objective 2

To investigate the effects of stirrups on shear behavior of RC tapered beams

Kakuta et al. (1977) and MacLeod et al. (1994)

a/d = 0.33 ~ 1.0Ishibashi et al. (1987)

a/d = 3.0 ~ 4.0

Vu_const < Vu_taper

There is effect of taper.There is no effect of taper.

d

a aa

d

a

Iwanaga et al. (2010)

a/d = 1.0 ~ 2.5

Less concrete

Higher capacityCompressive

strut

Objective

Constant depth beam Tapered beam

Experimental program 3

RW0

RW25-D6

RW18-D6

200300

30

225 a=875

d=250

100 75 50Test shear span

ASection A-A’

Unit: mm

RW33-D6

RW33-D10

a/d = 3.5RW○○-D△Stirrup ratio

0.○○%Nominal diameter of stirrups

35

200

A’

175 218

125 97

8.3°B

B’

Section B-B’

d0=130

20050

Stirrup

Stirrup

C.L. C.L.

C.L. C.L.

Load-deflection curves 4

35%

The stirrups started to carry load from the peak load of specimen withoutstirrups.

The shear capacity increased as the stirrup ratio increased, except forRW33-D10.

The shear capacity of RW33-D6 was 35% larger than that of RW33-D10.

2V= 311.0 kN

2V= 230.2 kN

𝑟 =0%: Failed suddenly at the occurrence of the diagonal crack

Initial crack

Stirrups started to carry load

RW: stirrup ratioD: stirrup diameter

Crack patterns at just after peak load 5

The critical diagonal cracks became flatter with the increase inthe stirrup ratio and the number of stirrups, implying thedifference in the formation of compressive strut.

RW0

P=151.8 kN

RW18-D6

P=247.2 kN

RW33-D10

RW33-D6

P=301.0 kN

RW25-D6P=311.0 kN

P=230.2 kN

RW: stirrup ratioD: stirrup diameter

Contribution of stirrups 6

In the conventional design method, the contribution of stirrups wasoverestimated, thus the contribution of concrete wasunderestimated in RC tapered beams. The extent increased withthe increase of the stirrup ratio and the spacing.

Determination of ε

𝑉 : 𝑉

𝑉 : 𝑉 𝑉 (Design method)

𝑉 : ∑ 𝐴 𝐸𝜀

𝑉 /𝑉

0 0.5 1 1.5 2

0 50 100 150 200 250

RW33-D10

RW33-D6

RW25-D6

RW18-D6

RW0

Vs-exp/Vs-ε

Shear capacity V (kN)

23.739.2

55.279.6

61.074.6

42.247.7

75.9

RW18-D6

RW: stirrup amountD: stirrup diameter

Conclusions 7

When the stirrups were arranged in larger spacing withthe same stirrup ratio, the shear capacity became smaller.

The stirrups started to carry load from the peak load ofspecimen without stirrups.

The critical diagonal cracks became flatter with the largerstirrup ratio and the larger number of stirrups.

The stirrups’ contribution would be overestimated by theconventional design method. The extent became largerwith the increase of the stirrup ratio and the spacing.

Regarding RC tapered beams: