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| Study on modification term for normal stress of short beam with arbitrary cross section by applying formula in material mechanics |
| Received:March 12, 2014 Revised:June 25, 2014 |
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| DOI：10.7511/jslx201503014 |
| KeyWord:short beam modification stress shear deformation stress function compatibility equation bending-shear warping |
| Author | Institution |
| 刘亮 |
兰州交通大学 土木工程学院, 兰州 |
| 胡玉茹 |
兰州交通大学 土木工程学院, 兰州 |
| 张元海 |
兰州交通大学 土木工程学院, 兰州 |
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| Abstract: |
| The formula of bending stress of beam in mechanics of materials is modified by introducing a stress term to reflect the effects of bending-shear warping deformation on the stress distribution.Based on the boundary shape of cross section of a short beam and the Airy stress function,a method for solving the modification stress is proposed.The fundamental equations for determining the stress term and the shear stress of a short beam with arbitrary cross section are established by applying the general theory of spatial problem in Elasticity,where the stress equilibrium equations,the strain compatibility equations and the stress boundary conditions in Elasticity are simultaneously applied.The specific formulas of the stress term of the short beams with rectangular and circular cross section are derived on the basis of the fundamental equations established.The stress term is proportional to the magnitude of uniform load and the ratio of elastic modulus to shear modulus,but inversely proportional to the inertia moment of cross section.Numerical example shows that the stresses calculated by the present method are in a good agreement with those by the general finite element software ANSYS,which validates the correctness of the analytical method and the fundamental equations established. |