摘要：根据材料力学的基本理论，分析了平面弯曲梁强度问题中的两个问题：截面形状对梁弯曲正应力强度的影响和工字型截面梁截面上的最大切应力与腹板名义平均切应力的关系。定量求出了各种截面形状对梁弯曲正应力强度的影响程度、工字型截面梁的截面尺寸变化对截面上最大切应力的影响规律。研究结果表明，当矩形截面横放且宽高比大于 时，其弯曲正应力强度差于圆形截面；当工字型截面竖放程度小于矩形截面的竖放程度时，如果工字型截面的腹板很矮或很宽，则工字型截面的弯曲正应力强度差于矩形截面；对于一般的截面尺寸，工字型截面上的最大切应力并不等于腹板名义平均切应力，仅在特定的截面尺寸条件下，工字型截面上的最大切应力才等于腹板名义平均切应力。研究结果修正了现行材料力学教学中的一些模糊概念，研究过程和研究方法为材料力学教学中提高学生的科学素养和培养学生的科学研究能力提供了一个良好的案例，对材料力学的教学具有重要意义。

Abstract: According to the basic theory of mechanics of materials, two problems in in-plane bending of the beam are analyzed in this study: the influences of different sections on the flexural normal strength of the beam and on the maximum shear stress of the cross section of I-beam, the level of the influence of various cross-section shapes on the flexural normal strength and the effect of various I – beam section sizes on the maximum shear stress were obtained quantitatively. The main results obtained are as follows: The flexural normal strength of rectangular section is lower than that of circular section when the rectangular section is transverse and the aspect ratio is greater than 1.36926; When the vertical degree of I-section is smaller than that of rectangular section, if the web of I-section is very short or very wide, the flexural normal strength of I-section is lower than that of rectangular section；For the general section size, the maximum shear stress on the I-section is not equal to the nominal average shear stress on the I-section web，Only under the specific section size, the maximum shear stress on the I-section is equal to the nominal average shear stress on the I-section web. The research results have corrected some vague concepts in the teaching of mechanics of materials, and the research process and the research method provide a good case for improving students' scientific literacy and cultivating students' scientific research ability in the teaching of material mechanics, which of great significance.

1. 2018年度广东省高等教育教学改革项目(x2tj/y1191701); 2.华南理工大学2019年度教研教改项目(x2tj/Y1190721)