1 Introduction
2 Background Theory: Evaluating Connection Shear Strength in RCS Composite Systems
ASCE |
\( V_{b} = \frac{{\left[ {V_{s} \cdot d_{f} + 0.75V_{n} \cdot d_{w} + V_{n}^{'} \cdot \left( {d + d_{o} } \right)} \right]}}{{\left[ {\frac{{L_{b} }}{{L_{c} }}\left( {L_{c} - d} \right) - jh} \right]}} \)
|
Kanno |
\( V_{b} = \frac{0.9d}{{L_{b} - h}}\left( {V_{s} + V_{sf} + V_{n} + V_{n}^{'} } \right) \)
|
M-Kanno |
\( V_{b} = \frac{{\left( {V_{s} \cdot d_{f} + 0.75V_{n} \cdot d_{w} + V_{n}^{'} \cdot d} \right)}}{{\left[ {\frac{{L_{c} }}{{L_{b} }}\left( {L_{c} - d_{f} } \right)} \right]}} \)
|
Parameters | Symbol | ASCE equation | Kanno equation | M-Kanno equation |
---|---|---|---|---|
b
o
|
C
|
C
wt
| max(C
wt
, C
t
) | max(C
wt
, C
t
) |
C
wt
|
\( \left( {x/h} \right) \cdot \left( {y/b_{f} } \right) \le 1 \)
|
\( \left( {\frac{x}{h}} \right) \cdot \left( {0.3 + 0.7\frac{y}{{\bar{b}_{f} }}} \right) \le 1 \)
|
\( \left( {\frac{x}{h}} \right) \cdot \left( {0.3 + 0.7\frac{y}{{\bar{b}_{f} }}} \right) \le 1 \)
| |
C
t
| – |
\( \frac{1}{2.5}\left( {\frac{d}{{b - b_{i} }}} \right) \)
|
\( 0.7\left( {\frac{x}{h}} \right) \cdot \left( {0.3 + 0.7\frac{y}{{\bar{b}_{f} }}} \right) \)
| |
b
m
|
\( \frac{{\left( {b_{f} + b} \right)}}{2} \)
|
\( \frac{{\left( {\bar{b}_{f} + b} \right)}}{1.5} \)
|
\( \frac{{\left( {\bar{b}_{f} + b} \right)}}{1.5} \)
| |
\( \bar{b}_{f} \)
|
b
f
|
\( max(b_{i} ,\bar{y}) \le 2b_{f} \)
\( \bar{y} = min\left( {y,b_{f} + n \cdot t_{s} } \right) \)
| max(b
i
, y) ≤ 2b
f
| |
V
s
|
jh
| Iteration procedure |
\( 0.8\;h\;({\text{No shear key}}) \)
\( h\;(E - FBP, \;{\text{Band Plate}}) \)
| 0.8 h
|
V
sf
|
V
sf
| – | 4M
pf
/d
f
| – |
V
sf
, V
b
|
d
j
| – | 1.25d
| 1.1d
|
V
n
’
|
V
c
’
|
\( 0.4\sqrt {f_{ck} } \cdot b_{o} \cdot h \)
|
\( 1.05\sqrt {f_{ck} } \cdot b_{o} \cdot h \)
|
\( 1.05\sqrt {f_{ck} } \cdot b_{o} \cdot h \)
|
3 A New Equation for Connection Shear Strength in RCS Composite Systems
3.1 Effect of Shear Key (E-FBP etc.)
Specimen | Test | Kanno equation | Proposed equation | ||
---|---|---|---|---|---|
Strength increment (%) |
C
wt
| Strength increment (%) |
C
wt
| Strength increment (%) | |
JL0-1 | 21.8 | 0.21 | 47 | 0.21 | 23 |
JL0-2 | 1 | 0.56 | |||
STI-1 | 15.2 | 0.21 | 53 | 0.21 | 22 |
STI-2 | 1 | 0.56 |
3.2 Transverse Beam Effect
Specimen | Test | Kanno equation | Proposed equation | ||
---|---|---|---|---|---|
Strength increment (%) |
C
t
| Strength increment (%) |
C
t
| Strength increment (%) | |
SNI-1 | 14.8 | 0.21 | 10.7 | 0.21 | 16 |
STI-1 | 0.51 | 0.64 |
3.3 Effect of Cover Plates
Specimen | Strength increment (test) | Strength increment (Kanno equation) | Strength increment (proposed equation) |
---|---|---|---|
LCS-1 | 26.2% | 4.98% | 27.53% |
LCC-1 |
3.4 Proposed Shear Strength Equation
-
Effective internal element width:$$ b_{i} = \hbox{max} (b_{p} ,b_{f} ) $$(5)
-
Effective external element width:$$ b_{0} = C(b_{m} - b_{i} ) < 2d_{0} $$(6)$$ b_{m} = \frac{{(b_{f} + b)}}{2} < b_{f} + h < 1.75b_{f} $$(7)$$ C = \hbox{max} (C_{wt} ,C_{t} ) $$(8)In the above equations, x = 0.7 h and y = 0 without a shear key, x = h and y = the width of the shear key when it is present. b is the connection width.$$ C_{wt} = \left( {\frac{x}{h}} \right) \cdot \left( {0.3 + 0.7\frac{y}{b}} \right)$$(9)$$ C{}_{t} = \left( {\frac{1}{2.0}} \right) \cdot \left( {\frac{d}{{b - b_{i} }}} \right) $$(10)
4 Statistically Evaluating Shear Strength Equations
4.1 Comparing Results from Shear Strength Equations with Test Results
4.2 Sample size
4.3 Statistical Analysis Results
Statistical parameter | ASCE | Kanno | M-Kanno | AIJ | M-AIJ | Proposed |
---|---|---|---|---|---|---|
Min. | 0.47 | 0.68 | 0.64 | 0.40 | 0.37 | 0.61 |
Max. | 1.16 | 1.29 | 1.20 | 2.51 | 1.98 | 1.11 |
Mean | 0.73 | 0.94 | 0.90 | 0.86 | 0.81 | 0.88 |
Std. error of mean | 0.02 | 0.02 | 0.02 | 0.05 | 0.04 | 0.02 |
Standard deviation | 0.14 | 0.12 | 0.12 | 0.37 | 0.27 | 0.11 |
Variance | 0.02 | 0.01 | 0.01 | 0.14 | 0.07 | 0.01 |
Skewness | 0.20 | 0.24 | 0.39 | 2.61 | 2.42 | 0.32 |
Kurtosis | 0.68 | 0.90 | 0.35 | 9.34 | 9.04 | 0.26 |
4.4 Factor Analysis
Test or equations | Group | Factor | ||||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | ||
Test | A | 0.17 | 0.00 | 0.20 |
0.96
| −0.05 |
B | 0.28 |
0.93
| −0.04 | 0.21 | 0.03 | |
C | −0.24 | −0.11 |
0.92
| −0.21 | 0.14 | |
D |
0.95
| 0.16 | −0.21 | −0.14 | 0.11 | |
ASCE | A | −0.26 | 0.26 |
0.63
|
0.61
| −0.21 |
B | 0.25 |
0.87
| −0.17 | 0.38 | 0.04 | |
C | 0.00 | −0.17 |
0.95
| 0.26 | 0.01 | |
D |
0.86
| 0.17 | −0.02 | −0.02 | 0.48 | |
Kanno | A | −0.09 | −0.03 | 0.59 |
0.78
| 0.17 |
B | −0.06 |
0.76
| −0.20 | 0.55 | −0.22 | |
C | 0.16 | −0.37 |
0.85
| 0.33 | 0.04 | |
D |
0.99
| −0.04 | 0.12 | −0.07 | −0.01 | |
M-Kanno | A | −0.20 | 0.37 | 0.21 |
0.88
| 0.11 |
B | 0.15 |
0.90
| −0.38 | 0.02 | −0.13 | |
C | 0.12 | −0.39 |
0.88
| 0.23 | 0.07 | |
D |
0.99
| 0.04 | 0.07 | −0.08 | 0.03 | |
AIJ | A | 0.29 | 0.36 | −0.20 | −0.75
|
0.41
|
B | 0.06 |
0.92
| −0.28 | −0.09 | 0.22 | |
C | −0.26 | −0.30 |
0.73
| 0.41 | 0.38 | |
D |
0.86
| 0.31 | −0.16 | −0.15 | −0.32 | |
M-AIJ | A |
0.74
| 0.23 | −0.08 |
0.48
| −0.40 |
B | 0.13 |
0.96
| −0.12 | −0.13 | −0.07 | |
C | −0.12 | −0.16 |
0.88
| 0.42 | −0.01 | |
D |
0.83
| 0.35 | −0.18 | −0.17 | −0.35 | |
Proposed | A | −0.20 | 0.37 | 0.21 |
0.88
| 0.11 |
B | 0.24 |
0.95
| −0.19 | 0.09 | 0.00 | |
C | 0.07 | −0.18 |
0.92
| 0.03 | −0.34 | |
D |
0.99
| 0.14 | 0.01 | −0.04 | 0.08 |
4.5 Correlation Analysis
Equations | Group | Test | |||
---|---|---|---|---|---|
A | B | C | D | ||
ASCE | A |
0.65
| 0.27 | 0.41 | −0.45 |
B | 0.35 |
0.97
| −0.41 | 0.36 | |
C | 0.44 | −0.14 |
0.84
| −0.26 | |
D | 0.11 | 3416.00 | −0.16 |
0.91
| |
Kanno | A |
0.84
| 0.10 | 0.41 | −0.30 |
B | 0.50 |
0.81
| −0.37 | 0.02 | |
C | 0.52 | −0.26 |
0.73
| −0.12 | |
D | 0.12 | 0.22 | −0.11 |
0.91
| |
M-Kanno | A |
0.84
| 0.47 | 0.03 | −0.28 |
B | −0.02 |
0.90
| −0.50 | 0.35 | |
C | 0.42 | −0.31 |
0.79
| −0.16 | |
D | 0.10 | 0.30 | −0.16 |
0.94
| |
AIJ | A |
0.74
| 0.28 | −0.09 | 0.52 |
B | −0.16 |
0.87
| −0.35 | 0.29 | |
C | 0.48 | −0.28 |
0.73
| −0.46 | |
D | −0.03 | 0.50 | −0.41 |
0.88
| |
M-AIJ | A |
0.59
| 0.52 | −0.43 | 0.65 |
B | −0.11 |
0.91
| −0.21 | 0.32 | |
C | 0.54 | −1318.00 |
0.74
| −0.39 | |
D | −0.06 | 0.52 | −0.42 |
0.86
| |
Proposed | A |
0.84
| 0.47 | 0.03 | −0.28 |
B | 0.09 |
0.98
| −0.35 | 0.40 | |
C | 0.25 | −0.18 |
0.80
| −0.20 | |
D | 0.12 | 0.41 | −0.22 |
0.97
|