1 Introduction
2 Previous Experimental Studies
Tests specimens (total 16) | E1–E4: Eccentric axial load tests (Eccentricity = 120 mm)
C1–C5: Concentric axial load tests F1–F7: Flexural tests |
Dimensions (square section) (see Fig. 2) | \( b \) = 260 mm, \( b_{c} \) = 230 mm, \( L_{k} \) = 2620 mm for E’s \( b \) = 500 mm, \( b_{c} \) = 400 mm, \( L_{k} \) = 1500 mm for C1–C3 and F1–F4 \( b \) = 400 mm, \( b_{c} \) = 300 mm, \( L_{k} \) = 1500 mm for C4–C5 and F5–F7 |
Concretea | \( f^{\prime}_{c,u} \) = 103.6 MPa, \( \varepsilon_{co,u} \) = 0.0027, \( \varepsilon_{cu,u} \) = 0.003 for E1 \( f^{\prime}_{c,u} \) = 96.6 MPa, \( \varepsilon_{co,u} \) = 0.003, \( \varepsilon_{cu,u} \) = 0.003 for E2 and E3 \( f^{\prime}_{c,u} \) = 98.7 MPa, \( \varepsilon_{co,u} \) = 0.0032, \( \varepsilon_{cu,u} \) = 0.0032 for E4 \( f^{\prime}_{c,u} \) = 23.5 MPa, \( \varepsilon_{co,u} \) = 0.002, \( \varepsilon_{cu,u} \) = 0.003 for C’s and F’s |
Steel angles (equal-leg)a | \( f_{ys} \) = 812 MPa, \( f_{us} \) = 868 MPa, \( b_{s} \) = 60 mm, \( t_{s} \) = 15 mm for E1 \( f_{ys} \) = 759 MPa, \( f_{us} \) = 884 MPa, \( b_{s} \) = 60 mm, \( t_{s} \) = 15 mm for E2 – E4 \( f_{ys} \) = 444 MPa, \( f_{us} \) = 689 MPa, \( b_{s} \) = 90 mm, \( t_{s} \) = 7 mm for C’s and F’s |
Transverse reinforcement (see Fig. 3)a | Lattices of \( \phi 7 \) Bars (\( f_{yt} \) = 531 MPa, \( s_{t} \) = 50 mm) for E1 Links of D13 Bars (\( f_{yt} \) = 481 MPa, \( s_{t} \) = 100 mm) for E2 Battens of 6 \( \times \) 60 mm Plates (\( f_{yt} \) = 418 MPa, \( s_{t} \) = 210 mm) for E3 Spirals of D13 Bars (\( f_{yt} \) = 567 MPa, \( s_{t} \) = 100 mm) for E4 Links of D10 Bars (\( f_{yt} \) = 522 MPa) for C’s and F’s \( s_{t} \) = 100 mm for C2, C4, F2, and F5 \( s_{t} \) = 200 mm for C1, C3, C5, F1, F3, and F6 \( s_{t} \) = 300 mm for F4 and F7 |
Longitudinal reinforcementa | 8-D13 (\( f_{yl} \) = 513 MPa, \( f_{ul} \) = 634 MPa) for E1 4-D19 (\( f_{yl} \) = 523 MPa, \( f_{ul} \) = 650 MPa) for C1 and F1 |
3 Nonlinear Numerical Analysis
3.1 Concrete and Confinement
3.2 Steel Angles and Local Buckling
Stress distributiona | Local buckling coefficientb, \( k_{b} \) (modified) | Elastic effective widthc, \( b_{{s,{\text{eff}}}} = \rho b_{s} \) (\( \rho \le 1 \)) | |
---|---|---|---|
SS \( \ge \) Free |
\( \psi \ge 0 \)
|
\( k_{b} = \left({\frac{0.578}{\psi + 0.34}} \right) + C_{k} \left({\frac{{b_{s}}}{{s_{t}}}} \right)^{2} \)
\( C_{k} = 2.5 - 2.5\,\psi + \,1.0\psi^{2} \)
|
\( \rho =\frac{{\left({1 - \alpha \frac{1}{\lambda}} \right)}}{\lambda} \)
|
\( \psi < 0 \)
|
\( k_{b} = \left({1.7 - 5\,\psi + \,17.1\psi^{2}} \right) +C_{k} \left({\frac{{b_{s}}}{{s_{t}}}} \right)^{2} \)
\( C_{k} = 2.5 - 1.2\,\psi - 0.6\psi^{2} \)
|
\( \rho =\left({1 + \psi} \right)\frac{{\left({1 - \alpha \frac{1}{\lambda}} \right)}}{\lambda} \)
| |
Free \( \ge \) SS |
\( \psi \ge 0 \)
|
\( k_{b} = \left({0.57 - 0.21\,\psi + \,0.07\psi^{2}} \right) + C_{k} \left({\frac{{b_{s}}}{{s_{t}}}} \right)^{2} \)
\( C_{k} = 1.25 - 0.25\,\psi \)
|
\( \rho =\frac{{\left({1 - \alpha \frac{1}{\lambda}} \right)}}{\lambda} \)
|
\( \psi < 0 \)
|
\( \rho =\left({1 - \psi} \right)\frac{{\left({1 - \alpha \frac{{\left({1 - \psi} \right)}}{\lambda}} \right)}}{\lambda} \)
|
3.3 Longitudinal Bars and Local Buckling
3.4 Bond Strength between Concrete and Steel
3.5 Second-order Effect
3.6 Verifications
Specimens | Maximum load, \( P \) (kN) for E1–E4 and C1–C5 or \( M_{m} \) (kN-m) for F1–F7 | Secant stiffness at maximum load, \( P /\varepsilon_{c} \) (kN) for E1–E4 and C1–C5 or \( M_{m} /\kappa_{m} \) (kN-m2) for F1–F7 | ||||
---|---|---|---|---|---|---|
Ta | Aa | A/T | Ta | Aa | A/T | |
E1 | 3343 | 3587 | 1.07 | 637700 | 491312 | 0.77 |
E2 | 3614 | 3328 | 0.92 | 449287 | 416056 | 0.93 |
E3 | 3472 | 3344 | 0.96 | 462683 | 405290 | 0.88 |
E4 | 3598 | 3366 | 0.94 | 371730 | 420757 | 1.13 |
C1 | 8081 | 8101 | 1.00 | 2711782 | 4050492 | 1.49 |
C2 | 7684 | 8267 | 1.08 | 2677178 | 2755614 | 1.03 |
C3 | 6722 | 7581 | 1.13 | 3280720 | 3790417 | 1.16 |
C4 | 5842 | 5941 | 1.02 | 1794820 | 1980334 | 1.10 |
C5 | 5680 | 5405 | 0.95 | 1897557 | 2702699 | 1.42 |
F1 | 572 | 572 | 1.00 | 11838 | 20637 | 1.74 |
F2 | 497 | 498 | 1.00 | 12697 | 7866 | 0.62 |
F3 | 412 | 487 | 1.18 | 31588 | 12820 | 0.41 |
F4 | 394 | 486 | 1.23 | 8649 | 13098 | 1.51 |
F5 | 377 | 338 | 0.90 | 6816 | 6014 | 0.88 |
F6 | 345 | 326 | 0.95 | 8133 | 9904 | 1.22 |
F7 | 351 | 325 | 0.92 | 8718 | 9911 | 1.14 |
Accuracy | Mean and standard deviation of A/T = 1.02 and 0.10 | Mean and standard deviation of A/T = 1.09 and 0.35 |