矩形截面悬臂梁斜弯曲应力分析和实验探讨

Analysis and Experimental Exploration of Oblique Bending Stressin Rectangular Cross-Section Cantilever Beams

以矩形截面悬臂梁为研究对象,研究其斜弯曲时的应力分布和中性轴位置。首先分析了矩形截面悬臂梁自由端受倾斜力作用时的挠度,定义了斜弯曲的概念;然后对矩形截面悬臂梁斜弯曲进行应力分析和中性轴位置分析,得到了矩形截面悬臂梁斜弯曲时正应力的计算公式和中性轴位置方程;最后采用电测法实验,探讨不同夹角φ对矩形截面悬臂斜弯曲梁正应力大小的影响。结果表明:随着作用力F的方向与z轴平行轴夹角的不断增大,各测点应力的理论值和实验值的相对误差越来越大。矩形截面悬臂梁斜弯曲时任一横截面形心合力方向不一定垂直于中性轴,并且由于切应力很小,其对弯曲梁强度的影响往往忽略不计。

Taking a rectangular cross-section cantilever beam as the research object,the stress distribution and neutral axis position of the rectangular cross-section cantilever beam during oblique bending are studied.Firstly,the concept of oblique bending is defined by analyzing the deflection of a rectangular cross-section cantilever beam under an inclined force at the free end;then,by conducting stress analysis and neutral axis position analysis on the oblique bending of a rectangular cross-section cantilever beam,the calculation formula for the normal stress and the neutral axis position equation of the rectangular cross-section cantilever beam during oblique bending are obtained;finally,an electrical measurement experiment is conducted to explore the influence of different anglesφon the magnitude of normal stress in a rectangular cross-section cantilever oblique bending beam.The results indicate that as the angle between the direction of the applied force F and the parallel axis of the axis z increases,the relative error between the theoretical and experimental values of stress at each measuring point increases.When a rectangular cantilever beam is diagonally bent,the direction of the resultant force of the centroid of any cross-section may not be perpendicular to the neutral axis,and due to the small shear stress,the influence of shear stress on the strength of the bent beam is often ignored.