梁的载荷、内力微分关系推导方法的改进

An improvement on the derivation of relationships between loads, shear forces, and bending moments in beams

摘要: 在推导梁截面上的剪力、弯矩与分布载荷集度之间的关系时, 流行的《材料力学》教材采用的推导过程在数学上失于严密. 根据导数定义和洛必达(L'Hospital)法则(或积分中值定理)给出了逻辑严密的推导.

Abstract: The derivation of the relationships between loads, shear forces, and bending moments in beams in current textbooks was not exact. Based on the definition of differential and the L'Hospital rule (or the mean value theorem of integrals), the complete demonstration of above-mentioned relationships was presented in this paper.