单元体的平衡与其质点的平衡不等价

Inequivalence Between Unit Body Balance and Particle Balance

该文发现了单元体平衡与质点平衡不等价的新概念。通过研究等直杆拉伸发现,其斜截面上的正应力σα及剪应力τα是保证部分体平衡的应力,而不是保证其斜截面上质点的平衡应力。σα和τα都小于质点平衡应力。与此同时,二向纯拉伸应力状态,质点平衡应力是单元体平衡应力的槡2倍。单元体的主应力不是其上质点的极值应力,而质点平衡应力才是极值应力。由质点平衡推导出新的拉伸-剪切公式:σ'a=σ2+2στ+2τ2,从而解决了三百五十多年以来无法解释的拉伸-剪切比压缩-剪切更容易破坏的实验现象。通过清华大学国家破坏力学重点实验室的实验,证实此理论其与实际的误差仅为1%,而第三、第四强度理论误差分别为14.2%,18.2%。这也解释了大型桥梁坍塌事故的根本原因。

This paper presented a newconcept that unit body balance and particle balance were not equivalent. Through the research of the straight uniform tensioned rod,it is found that the oblique section normal stress σαand shear stress ταare to ensure the stress part of body balance,and they are not guaranteed by stress of particle balance on its oblique section,normal stress σαand shear stress ταare less than the balance stress of particle. At the same time,the 2-direction pure tensile stress state,equilibrium of a particle stress is2 times of the unit body balance stress. Extreme unit principal stress is not the particle on the stress,and the balance stress of particle is the extreme stress. In this paper,equilibrium of a particle is derived by the newtensile shear formula: σa' = σ2+ 2στ + 2τ2,so as to solve the 350-year-old problem that the tensile-shear state is more liable to destruction than the compression-shear state. The laboratory failure test in Tsinghua U niversity confirmed this theory with the actual error within only 1%,while the 3rd and the 4th strength theory have errors up to 14. 2% and 18. 2% respectively. This also explains the essential cause for large-scale bridge collapse accidents.