Kawaguchi et al. 1998
In this paper, a database study on beam-column tests of square and circular CFTs was presented. All the test data was gathered from the Japanese literature published between 1971 and 1997. Using the database, load capacities and chord rotation capacities of CFT beam-columns were examined. In addition, a multi-linear moment-rotation model for CFT beam-columns was proposed.
Analytical Study
The database consisted of 143 square and 66 circular beam-column tests. Length (L), depth (D) and thickness of the steel tube (t) were the main parameters to be recorded for the size of the specimens. Loading methods (cyclic or monotonic) and loading systems were specified in the database. The axial load over nominal axial strength ratios (P/Po) were also reported. Three types of loading systems were defined depending on the support and loading conditions. The first type (CL) was the cantilever beam-column system with a horizontal and vertical load applied at the free end. The second system (SS) was a beam-column having a fixed support at the bottom and a guided support at the top, putting the member into reverse curvature flexure . For this system, the horizontal and axial loads were again applied at the top end. The third system (TL) was a pin-ended beam-column with axial loads applied at the ends and a horizontal load applied at the mid-height. The yield strength (fy) and ultimate strength (fsu) of the steel, the modulus of elasticity (Es) of the steel, and the cylinder strength of the concrete (f’c) were kept in the database. From the experimental results, the maximum bending moment (Mu) values were recorded. The axial strength of the steel tube (Pso), nominal axial strength of the CFT section (Po), and ultimate bending moment (Mpc) were calculated according to the AIJ (1997) design code provisions using the measured material properties and placed in the database. The experimental rotation angles and secant stiffnesses at different levels of moment strength were also included in the database. The theoretical elastic stiffness (Ke) values were entered as well.
In the experiments, the L/D ratios were generally less than 7. A similar number of tests of the square CFTs were done for each of the three loading systems. However, CL type test setup was rarely utilized for circular CFTs. The values of the D/t ratios were usually less than 48 and 80 for square sections and circular sections, respectively. The range of concrete strength used in the experiments was large. However, in most of the cases, the concrete strength selected for circular CFTs was higher than that used in square CFTs. Steel strengths above 58.0 ksi were common in circular tubes. On the other hand, the steel strengths of the square tubes exhibited two trends. They were usually either less than 30.5 ksi or greater than 65.3 ksi.
The Mpc values for the specimens were calculated based on a full plastic stress state. It was found out that the Mu/Mpc ratios were usually greater than unity. The rotation capacities of the specimens were determined by using empirical equations from the literature. For square specimens, the theoretical results estimated the experimental rotation capacities fairly well. In case of circular sections, theoretical results provided a lower limit for the experimental rotation capacities.
A multi-linear moment-rotation relationship to be used in push-over analysis of CFT frames was proposed. It was composed of four linear regions. The first region had a slope equal to the theoretical elastic stiffness and it was continuing up to 1/3 of Mpc. The second and third parts of the curves had lower slope values, with upper limits of 85% of Mpc and Mpc, respectively. The fourth region was a horizontal line that continued until the ultimate rotation (Ru) was achieved. The rotation at 85% percent of Mpc (R85), the rotation at ultimate moment (Rmax), and Ru were all required to construct the proposed moment-rotation curve. The following formulations were used for this purpose (all stress values are in MPa):
Reference
Kawaguchi, J., Morino, S., Shirai, J. and Tatsuta, E. (1998). “Database and Structural Characteristics of CFT Beam-Columns,” Proceedings of the Fifth Pacific Structural Steel Conference, Seoul, Korea, October 13-16, 1998.