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4. Restoring force model
Based on the experimental results and the skeleton curves of four specimens, a simplified restoring force model, degenerated trilinear model, was put forward here to simulate the hysteresis behaviour of CFS strengthened box beams under combined bending, shear and cyclic
torque.(1) Skeleton line—skeleton line can be defined as a trilinear curve with four points, which are the origin point,the concrete cracking point (Tcr, hcr), the yielding point (TY, hY) and the ultimate point (Tu, hu).(2) Unloading line—the unloading line can be defined as a diagonal line with the slop of Gy. Gy is decided by the torque moment or twist angle at the begin point
of unloading. Before beam yielding, the unloading torsional rigidity is similar to the initial loading rigidity. After beam yielding, the unloading torsional rigidity reduced.(3) Reversed loading line—the unloading line in one direction intersects with the slide axis at one point with residual deformation and then develops along the line between this point and the point of torque
T* = cTY in the skeleton line in another direction. Then the reversed loading line will join together with the peak point of last cycle and then go along with the skeleton line in this direction. (TY is the yielding torque; c is the pinching effect factor, taken as 0.25–0.5, according to the experimental results. The bigger value of c means the more amount of CFS, the more rounded hysteresis loop of strengthened box beam and the improved energy dissipation capacity.).(4) Slide and pinching phenomena—in this restoring force model only the pinching effect after member yielding is considered. (shown in Fig. 8). The slide axis is a diagonal line through the original point with the slop of kG1, in which G1 is the torsional rigidity before concrete cracking and k is the slope factor denoting the extent of pinching phenomena. Based
on the test results, k can be taken as 0.075.(5) The torsional rigidity of each stage in the restoring
Before the concrete cracking eOAT : G1 ?T cr=hcr e1TConcrete cracking to beam yielding eABT : G2 ?
T Y _T cr
hY _hcr
e2T
Beam yielding to ultimate torque eACT : G3 ?
T u _T Y
hu _hY
e3T
Unloading rigidity :
Before beam yielding T 6 T Y; Gy1 ?G1 eaT
After beam yielding T Y _ T 6 T u; Gy2 ?aG1 ebT
_
e4T
in which, a ?ehY
hi
Tn, where, hi is the twist angle corresponding to the peak point of the torque moment at the i cycle after beam yielding; n is a experience factor, taken as 0.3 based on this test results.
5. Conclusions
In this study, the torsional behaviour, seismic behaviour and mode of failure of reinforced concrete box beam strengthened with carbon fiber reinforced sheets (CFS) under combined bending, shear and cyclic torque were investigated. The test results indicated that the externally
bonded CFS can be used to enhance the torsional capacity and deformation capacity of the beams. The strengthening effect is more obvious with the more layers of transversal U-shape wrapped CFS strips. The test results also indicated that the CFS strengthening reduce the ductility of the beams. So Special attention should be paid on the amount of CFS to avoid brittle failure. The test results were used to explore the restoring force model of CFS strengthened box beam under combined actions. This model provides a good reference to the study of seismic behaviors and wind vibration behaviors of CFS strengthened box beam under cyclic torque moment.
摘要
本文介绍了钢筋混凝土箱形梁的弯矩，剪力和反复扭矩的共同作用下，加强与外贴碳纤文增强聚合物板（CFS）的响应的实验研究结果。对三个加强型箱梁和一个参考箱形梁进行了测试。这个实验的主要参数是是CSF和包装方案的量。对失败的形状、抗扭能力，变形能力，刚度衰减和磁滞行为进行了详细研究。实验结果表明，外贴的CFS对箱型梁的抗震能力的提升效果是显著的。基于文本的结果和分析，恢复力模型的CFS加固钢筋混凝土箱形梁在联合行动的弯矩、剪力和扭矩是建立循环。