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.