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: