PROPOSED METHOD FOR EVALUATING THE DIAGONAL COMPRESSIVE CAPACITY OF REINFORCED CONCRETE BEAMS

1
PROPOSED METHOD FOR EVALUATING THE DIAGONAL
COMPRESSIVE CAPACITY OF REINFORCED CONCRETE BEAMS
Final Presentation of Master Course, 10th
February 2009

• Chikaharu KOBAYASHI
• Supervisor
• Prof. Junichiro NIWA

2
Background
Recently, bridges with slender and longer span
are required for economical design.
RC beam
?Very thin web
The diagonal compressive failure will occur.
The web concrete crushes prior to the yielding of
stirrup, resulting in a brittle failure.
The accurate calculation method for the diagonal
compressive capacity is needed.
3
Necessity for Evaluating Equation
There is few research for the diagonal
compressive failure.
JSCE Standard
VJSCE1.25f'c1/2bwd

• Quite conservative for safety reasons

• Covered only for concrete not exceeding
  fc50N/mm2

Purpose
To propose the equation for evaluating the
diagonal compressive capacity
4
Outline of Specimens
bf250
B
A
250
a660990
d220
bw40
s
A-A
A
B-B
B
Stirrup(fy953N/mm2)
Tensile bar(fy930N/mm2)
Unit mm
No yield in steel bars
Diagonal compressive failure
Experimental parameters
In addition to fc, rw, s and a/d, the effect of
bf /bw (flange width to web width ratio) was
discussed by comparing previous researches with
these experiments.
5
Evaluation of Diagonal Compressive Capacity
6
Capacity Evaluation Procedure
Assuming a free body
Assumptions
C
Steel
L
C'
The failure of member is caused by web concrete
crushing.
s'd
D'
jd
The stirrup does not yield.
?
The concrete between C and T resists against the
diagonal compressive force.
T
V
Cutting plane
j 7/8, q 30
It was discussed how much sdmax was affected by
the parameters (fc, rw, s, a/d, and bf/bw).
7
Effect of fcLoad-Displacement Curves
Sharp drop
fc165N/mm2
fc165N/mm2
fc133N/mm2
fc98N/mm2
fc62N/mm2
fc35N/mm2
fc35N/mm2
rw3
The peak load continued to increase as fc
increased.
The diagonal compressive failure occurred in a
brittle way, especially the higher fc was, the
brittler the failure became.
8
Effect of fc
The diagonal compressive capacity continued to
increase as fc increased.
rw3
In addtion, the incremental ratio of the capacity
decreased as fc increased.
9
Effect of fc
The diagonal compressive capacity continued to
increase as fc increased.
In addtion, the incremental ratio of the capacity
decreased as fc increased.
10
Effect of Stirrup Spacing s
fc3035N/mm2
fc100115N/mm2
Placas et al.(rw3.3)
rw4
rw3
Placas et al.(rw2.2)
rw2
Author
The amount of effectiveness by s is related to
fc.
With high-strength concrete (fc100115N/mm2),
the wider s was, the lower the diagonal
compressive capacity was.
11
Effect of Stirrup Spacing s
fc3035N/mm2
fc100115N/mm2
Placas et al.(rw3.3)
rw4
rw3
Placas et al.(rw2.2)
rw2
Author
12
Reason for Capacity Reduction
Stirrups arranged closely (s is small)
fc100115N/mm2
rw4
rw3
rw2
Stirrups arranged widely (s is large)
13
Proposal for Evaluation Method
Reduction factor bn
Apparent compressive strength of concrete fcs
Effect of a/d
Effect of bf /bw
fc100N/mm2
Vexp/(0.379f"csßvbwd)
Vexp/(0.379f"csßvßabwd)
fc35N/mm2
Proposed equation
14
Accuracy of Prediction Equations
Proposed equation
JSCE equation
n27
n27
avg.1.25, C.V.17.3
avg.1.01, C.V.6.9
JSCE equation cannot evaluate the diagonal
compressive capacity accurately.
Proposed equation can predict the diagonal
compressive capacity with good agreement.
15
Conclusion
Existing prediction equation cannot evaluate the
diagonal compressive capacity accurately.
As a result of evaluating effect factors on the
diagonal compressive capacity, the proposed
method can predict the diagonal compressive
capacity with good agreement (avg.1.01,
C.V.6.9).
16
Thank you for kind attention!
17
Accuracy of Prediction Equations
Placas equation
Eurocode equation
n27
n27
avg.0.96, C.V.31.6
avg.0.99, C.V.16.0
18
Capacity Evaluation Procedure
Steel
C'
s'd
w
D'
jd
?
b
T
Diagonal crack
V
Cutting plane
Stirrups resist against the crack opening.
s'dmax and q will be affected by f'c, crack
patterns (ex. w, b), a/d (shear span to effective
depth ratio) and bf/bw (the ratio of flange
breadth to web breadth).
The diagonal compressive capacity will be
affected by fc, stirrups (ex. area ratio rw,
spacing s), a/d, and bf/bw.
19
Effect of s
stirrup
There is a close link between crack width w and
the diagonal compressive capacity.
Stirrup do not yield.
w increases with distance from stirrups.
20
Mix Proportion of Casting Concrete
21
Effect of fcCrack Patterns
fc35N/mm2, rw2, a/d3.0
fc100N/mm2, rw2, a/d3.0
22
Influence of Parameters
fc35MPa
fc100MPa
N06
N1
N2
N3
UH2
UH3
UH4
UH2f7
UH2S160
N2AD40
N2AD45
UH2AD35
UH2AD40
Average 62.7kN, CV 5.7
Average 136.9kN, CV 17.6
There is a possibility that influence of
parameters depend upon fc.
23
Diagonal Compressive Strength - Normal Strength
Concrete
Critical Average Compressive Stress in Web, sdmax
sd
sc
fc
ec
sdmax
sd
sc
ed
ed
sd
ecu
edmax
ed
Vecchio, Collins (1986)
24
Outline of Specimens
a/d3.0
A-A
B-B
B
A
a660
250
250
50
h260
d220
40
70
s80
A
B
146
146
a/d4.0
B
A
a880
d220
s80
A
B
Unit mm
Parameters

• pw 8.8
• rw 2.0

25
Influence of a/d (fc35MPa)
a/d3.0, fc35.8MPa, rw2.0
a/d4.5, fc34.9MPa, rw2.0
Diagonal cracks are almost the same angle.
Under using normal strength concrete (fc35MPa),
diagonal compressive capacities are nearly
constant regardless of a/d changing.
a/d3.0
a/d4.0
a/d4.5
Nearly constant
fc is needed to consider the influence of a/d.
26
Influence of a/d (fc100MPa)
a/d3.0, fc102.4MPa, rw2.0
a/d4.0, fc104.3MPa, rw2.0
a/d3.5
a/d3.0
decreasing
a/d4.0
27
Outline of Specimens
s50mm
f7.1mm
A-A
B-B
B
A
a660
250
250
50
h260
d220
40
70
s50
A
B
146
146
s90mm
f10mm
Unit mm
B
A
a660

• pw 8.8
• rw 2.0

d220
A
B
s90
s160mm
f13mm
Parameters
B
A
a660
d220
s160
A
B
28
Angle of Principal Strain
a/d4.5, fc34.9MPa, rw2.0
a/d3.5, fc109.6MPa, rw2.0
a770
a990
Before diagonal cracks occurred, angle of
compression was around 40 degrees.
Angle of compression became 30 degrees right
before the peak load.
29
Load-Displacement Curves
fc100MPa
fc35MPa
rw4
rw3
rw2
rw3
rw1
rw2
Load (kN)
Load (kN)
rw0.63
Displacement (mm)
Displacement (mm)
The less amount of stirrup, the more brittle the
compression failure was.
Under using high-strength concrete (fc100MPa),
peak load increased as rw increased.
30
Uniaxial Compression Experiment
Stress N/mm2
N
UH
Strain 10-6