A new method for cracks detection in beams is proposed by using the slope of the mode shape to detect cracks, and by introducing the angle coefficients of complex continuous wavelet transform. This study is aimed at detecting the location of the nonpropagating transverse crack. A series of beams with cracks that are simulated by rotational springs with equivalent stiffness are analyzed. The mode shape and the slope of this lumped crack model are calculated. Through complex continuous wavelet transform of the slope of the mode shape using Complex Gaus1 wavelet (CGau1), the locations of cracks are detected from the modulus line and the angle line of wavelet coefficients. By comparison, the singularity is much more apparent from the angle line of complex continuous wavelet transform. This demonstrates that the proposed method outperforms the existing method of wavelet transform of the mode shape with real wavelets. Also, this method can detect cracks in beams with different boundary conditions. The influence of crack locations and crack depth on crack detection is discussed. Finally, the noise effect is studied. Through the multiscale analysis, the locations of cracks may be detected from the angle of wavelet coefficients.

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This paper presents the results of experimental and theoretical studies undertaken to assess the flexural performance of high-strength steel-ultra-high-performance fiber reinforced concrete (HSS-UHPFRC) beams. A total of nine HSS-UHPFRC beams were tested, and the influence of fiber volume fraction, fiber type, longitudinal reinforcement ratio, and concrete strength on the flexural response was evaluated. The results indicate that sufficient longitudinal reinforcement should be provided in a UHPFRC beam to avoid abrupt failure and possible catastrophic collapse. After the loss of the fiber bridging effect, corresponding to the fibers being pulled out from the matrix, which occurs one by one with audible sound which is sizzling, redistribution, and homogenization of the concrete stress beside cracks, induced by the dispersed fibers, takes place and more flexural cracks with small spacing appear besides the existing cracks. The beam stiffness was about 85% of the initial beam stiffness at flexural cracking state and was only approximately 25% of the initial beam stiffness at the ultimate state. A constitutive model is proposed, including a bilinear model for compression and a drop-down model for tension, taking into account uniform distribution, embedment length, and orientation of fibers for the multi-scale mechanics analysis. A flexural strength model was subsequently derived on the basis of the proposed mesoscale constitutive model; strain compatibility and force equilibrium were taken into account. The prediction of the ultimate flexural capacity and the overall post-cracking response with the proposed model show a good agreement with the test results. K E Y W O R D Sconstitutive model, depth of compression zone, fiber orientation, flexural strength, high-strength steel (HSS), steel fiber, ultra-high-performance concrete (UHPC), ultra-high-performance fiber reinforced concrete (UHPFRC)

Post-cracking shear strength and deformability of HSS-UHPFRC beamsEleven T-beams, reinforced with high strength steel, were tested to failure to investigate the effect of shear span to depth ratio, fibre ratio, fibre type, concrete strength and stirrup ratio on the shear behaviour, especially post-cracking shear strength and deformability, of ultra-high performance fibre reinforced concrete (UHPFRC) beams. Test results indicated that fibres were efficient not only in enhancing the post-cracking shear strength, but also in improving the post-cracking deformability of UHPFRC beams. In addition, fibres could bridge the cracks and help in redistributing and homogenizing the concrete stress beside the cracks, allowing more short fine diagonal shear cracks with small spacing to develop around the existing cracks. A moderate amount of stirrups can effectively restrain shear cracks and allow more parallel diagonal shear cracks to develop and propagate thoroughly within the shear span. The stiffness of the UHPFRC beams at ultimate state was about 50 % of initial beam stiffness, which was considerable in strength calculations and ductility analysis, especially in seismic performance evaluation. Lastly, the current shear provisions were evaluated using the experimental results.

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