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3.3. Hysteresis behaviors
Fig. 5 shows the experimental results of four specimens in terms of the torque versus twist angle hysteresis curves(T–h relationship curves). Four specimens exhibited the same rule under combined bending, shear and cyclic torque actions. Before concrete cracking, box beam exhibited elastic properties with high torsional rigidity. With the increase of loading, hysteresis loop formed. After concrete cracking, especially after beam yielding, torsional rigidity reduced quickly and rotation angle increased obviously. The slope of curve in positive loading period was relatively small at first and then had a little improvement. This is because that during the unloading and reverse loading periods the opened cracks were closed partly which make it possible that concrete between cracks can touch with each other and transfer the forces.The hysteresis curves of all the four specimens experienced a significant pinching caused by the shear stresses. The hysteresis loops of strengthened beams exhibited a more rounded shape than the hysteresis loop of B-5,which indicates that CFS strengthening can improve the energy dissipation capacity of beam. At the same deformation stage, the corresponding torque moment in the second and third cycles were less than the torque in the first cycle, which is named strength deterioration. This is due to the accumulated damage at the yielding district
of the beam. For the box beams presented here, the accumulated damage are mainly caused by diagonal cracks development, concrete protective coating spalling in cracks and cohesion failure.
3.4. Skeleton curve
The skeleton curve is an envelopes developed from the torque versus twist angle hysteresis curve by joining together the peak value point of every cycle in the same loading direction. Fig. 6 shows the skeleton curves of four specimens.Before beam yielding, the skeleton curves of strengthened beams (B-6, B-7, B-8) exhibited nearly the same with the skeleton curve of referenced beam (B-5). After beam yielding, the corresponding torsional rigidities and torsional
strengths of strengthened beams were obviously improved. The ultimate twist angles of them were lager than that of unstrengthened beam. These results proved that the retrofit material begin to work only after sufficient cracking occurred and beam yielding. Comparing the skeleton curves of B-6, B-7 and B-8, it can be seen that transversal U-shape CFS strips strengthen more effectively than the longitudinal CFS strips on bottom surface.
3.5. Rigidity attenuation
Dividing the summation of absolute values of positive and negative peak torque in each cycle by the summation of corresponding absolute values of positive and negative twist angle, the result can be defined as the torsional rigidity in each cycle (Gi, i is the number of one loading cycle). G0 denote the initial torsional rigidity of specimen. The Gi/G0 versus twist angle curves of four specimens in this test are shown in Fig. 7.It can be seen that the rigidity attenuation of each beam became slower with the increase of twist angle. The torsional rigidity reduced rapidly along with the concrete cracking and beam yielding and slowly prior to complete failure. The rigidity attenuation was mainly induced by the plastic behaviors of box beam after its yielding and the accumulated damage, which includes concrete protective coating spalling due to appearance and development of cracks, the reducing of cross section due to the opened cracks, yielding and plastic behaviour of reinforcement and the slide between concrete and reinforcements. Applying CFS to strengthen box beam resulted in relatively slower rigidity attenuation. This proved that CFS strips wrapped on the beam can resist the applied load just as
reinforcements and provide confinement to cracks development. The use of transversal U-shape CFS strips may provide the more effective wrapping scheme to decrease the torsional rigidity attenuation than the use of longitudinal CFS strips on bottom surface.