An analytical method for full-range mechanical behavior of continuous slab-deck in multi-span simply supported concrete bridges

Connecting the ends of girders with a continuous slab-deck to make a multiple-span simply supported girder bridge provides many benefits, but there is no suitable nonlinear analysis model which considers continuous slab-deck cracking under tension and bending. In this article, the rotational spring model is further refined to replace the restraining effects at both ends of the girder by the simplified mechanical model associated with axial stiffness, bending stiffness, and shear stiffness. Then, it is introduced into the analysis of continuous slab-deck. The more accurate rotations and displacements of both ends of continuous slab-deck are obtained to investigate the more precise moment and tension of the continuous slab-deck. Furthermore, this article presents an improved nonlinear analysis model of continuous slab-deck based on a detailed boundary rotational spring model. The displacements of important positions and the strain of key components in continuous slab-deck after cracking are investigated by numerical analysis and full-scale model test to verify the accuracy of the proposed nonlinear analysis model. The result shows that the nonlinear analysis model presented in this article could successfully evaluate the depth of cracks and the stress of rebars in continuous slab-deck, and it is instructional in predicting the cracking state of the continuous slab-deck and the reinforcement design.

Geometrically nonlinear free and forced vibrations analysis of clamped-clamped functionally graded beams with multicracks

Geometrically nonlinear free and forced vibrations of clampedclamped Functionally Graded beams with multi-cracks, located at different positions, based on the equivalent rotational spring model of crack and the transfer matrix method for beams is investigated. The FG beam properties are supposed to vary continuously through the thickness direction. The theoretical model is based on the Euler-Bernoulli beam theory and the Von Karman geometrical nonlinearity assumptions. A homogenization procedure, taking into account the presence of the crack, is developed to reduce the problem examined to that of an equivalent isotropic homogeneous multi-cracked beam. Upon assuming harmonic motion, the discretized expressions for the total strain and kinetic energies of the beam are derived, and through application of Hamilton’s principle and spectral analysis, the problem is reduced to a nonlinear algebraic system solved using an approximate explicit method developed previously (second formulation) to obtain numerically the FG multi-cracked beam nonlinear fundamental mode and the corresponding backbone curves for a wide range of vibration amplitudes. The numerical results presented show the effect of the number of cracks, the crack depths and locations, and the volume fraction on the beam nonlinear dynamic response.

Effect of Rotational Stiffness Evolution at Crack Part on Critical Crack Size in SFR

This paper describes the efficiency of the deployment of rotational stiffness evolution model in the critical crack size evaluation for Leak Before Break (LBB) assessment of Sodium cooled Fast Reactor (SFR) pipes. The authors have developed a critical crack size evaluation method for the thin-walled large diameter pipe made of modified 9Cr-1Mo steel. In this method, since the SFR pipe is mainly subjected to displacement controlled load caused by thermal expansion, the stress at the crack part is estimated taking stiffness evolution due to crack into account. The stiffness evolution is evaluated by using the rotational spring model. In this study, critical crack sizes for several pipes having some elbows were evaluated and discuss about the effect of the deployment of the stiffness evolution model at the crack part on critical crack size. If there were few elbows in pipe, thermal stress at the crack part was remarkably reduced by considering the stiffness evolution. In contrast, in the case where the compliance of the piping system was small, the critical crack size could be estimated under displacement controlled condition. As a result, the critical crack size increases by employing the model and LBB range may be expected to be enlarged.

Identification of Small Crack in Beam Structures Using Anti-Resonant Frequency and Wavelet Analysis

Structural crack identification has been received considerable attention in recent decade. A lot of different techniques like acoustic emission, ultrasonic, or X-ray, etc have been used for structural crack detection. However, it is still difficult to identify the small crack in structures. A new method for identification of small crack in beam structures using the first anti-resonant frequency curve is proposed in this paper. The method makes use of the driving-point mechanical impedance characteristics of beam structures and a simplified rotational spring model to model the edge crack of beam. After the first anti-resonant frequency curve is obtained, signal process based on wavelet transformation will be carried out and the small crack in beam structures can be explored. The proposed method is validated by a numerical example of cracked beam with pinned-pinned or fixed-free boundary. It is concluded that not only the location of beam crack can be determined, but also the extent of crack damage can be identified qualitatively based on the first anti-resonant frequency curve and wavelet analysis.

Incipient Crack Identification in Beam Structures Using the Slope of the Anti-Resonance Curve

Crack damage brings a serious threat to the safety of mechanical and civil structures, and the problem of incipient damage identification of structures has been paying attention as a puzzle by many researchers in recent years. To seek for an alternative solution of the problem, a method for incipient crack localization using the slope of the anti-resonance curve is proposed in this paper. The method makes use of the driving-point mechanical impedance characteristics of cracked beams stimulated by harmonic force. To characterize the local discontinuity due to the presence of crack, a simplified rotational spring model is presented to model the crack. Subsequently, the proposed method is verified by a numerical example of cracked beam under simple support or cantilever boundary conditions.

Vibratory Characteristics of Axially-Loaded Timoshenko Beams With Arbitrary Number of Cracks

A simple and efficient analytical approach is presented to determine the vibrational frequencies and mode shape functions of axially-loaded Timoshenko beams with an arbitrary number of cracks. The local compliance induced by a crack is described by a massless rotational spring model. A set of boundary conditions are used as initial parameters to define the mode shape of the segment of the beam before the first crack. Using this, the remaining set of boundary conditions and recurrence formula developed in the study, the mode shape function of vibration of the beam containing multiple cracks can be easily determined. Four different classical boundary conditions (pinned-pinned, clamped-pinned, clamped-free, and clamped-clamped) are considered. Elastically-restrained support condition with concentrated masses is also considered. Three crack depths and five axial force levels representing the conditions under service loads are used. A parametric study is carried out for each case of support conditions to investigate the effect of crack and axial load on the vibrational properties of cracked Timoshenko beams. The influence of crack on the buckling load of the beam is also studied statically. Part of the results obtained is checked against the published values. The study concludes that the crack location, crack severity, and axial force level strongly affect the eigenfrequencies.

Wave Propagation Based Multi-Crack Identification in Beam Structures through Anti-Resonances Information

Cracks bring a serious threat to safety of structures. Most of the failures and fractures of engineering structures are due to initial cracks or fatigue cracks of materials. So it is very important to analyze the vibration characteristics and to identify the damage of cracked structures. A method for multi-crack identification based on wave propagation is proposed in this paper, which makes use of the driving-point mechanical impedance characteristics of the cracked beams stimulated by harmonic force. The proposed identification method is used to characterize the local discontinuity due to cracks, and a simplified rotational spring model is introduced to model cracks. Subsequently, the proposed method is verified by a numerical example of a simply supported steel beam with three cracks. The effect of crack depth on driving-point impedance is investigated. Combined with the first anti-resonances information, the proposed method can identify the presence of cracks, localize the multiple cracks, and qualitatively identify the extent of the crack damages.