考虑界面滑移效应的组合裂纹梁弯曲解析解

将上部子梁的裂纹等效为线性扭转弹簧，考虑组合梁连接面的滑移位移，建立了以组合裂纹梁挠度和滑移位移为基本未知量的组合裂纹梁弯曲变形一维数学模型．利用Laplace变换及其逆变换，给出了组合裂纹梁弯曲变形一维数学模型的解析通解．在此基础上，研究了均布载荷作用下简支组合裂纹梁的弯曲变形问题，数值分析了连接面剪切刚度、裂纹深度、数目和位置等参数对组合裂纹梁弯曲变形的影响，结果表明：在裂纹处，组合裂纹梁挠度曲线存在尖点，而横截面转角曲线存在跳跃，且随着裂纹数目和深度的增加，挠度和横截面转角跳跃值增大；随着连接面剪切刚度的增加，挠度和横截面转角减小，并最终趋于定值．并且，随着组合梁跨高比的增加，连接面剪切刚度对梁挠度影响逐渐减弱．

Analytical Solution of Bending of Composite Cracked Beam with Effect of Interface Slip

Regarding crack in top sub-beam as a linear torsional spring and considering slip displacement on interface of the composite beam, a one-dimensional mathematical model for the bending deformation of a composite cracked beam was established with the beam deflection and the slip displacement as the basic unknown variables. A general analytical solution of the one-dimensional mathematical model was obtained using the Laplace transform and its inverse form. On this basis, the bending deformation of a simply-supported composite cracked beam subjected to an uniform load was investigated. The influences of the interface shear stiffness, as well as the depth, qunantity and location of the cracks on the bending deformation of the composite cracked beam were analyzed numerically. It is revealed that, at the crack location, there exist a cusp on the deflection curve and a jump on the rotational angle curve. The magnitudes of the deflection and the jump of the rotational angle increase with the increase of crack quantity and crack depth, while dcrease and finally converge to constant values with the increase of interface shear stiffness. Furthermore, the influence of the interface shear stiffness on the the deflection gradually decreases with the increase of the span-height ratio of the composite beam.