Calculation method for shear lag of rectangular section beam based on the shear deformation
Received:April 28, 2014  Revised:June 22, 2014
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KeyWord:shear deformation  shear lag warping displacement  energy variation  rectangular section beam  the shear lag coefficient
舒小娟 中南大学 土木建筑学院, 长沙 ;湖南科技大学 土木工程学院, 湘潭
钟新谷 湖南科技大学 土木工程学院, 湘潭
沈明燕 湖南科技大学 土木工程学院, 湘潭
张天予 湖南科技大学 土木工程学院, 湘潭
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      By assuming shear stiffness and additional average deformation of shear angle of cross-section in order to revise approximatively the problem that ignoring the shear deformation energy in elementary beam method,which is the main method in Timoshenko beam theory.But in fact,the shear stress along the beam height is variable.This article is based on material mechanics calculation formula of the shear stress and the corresponding shear deformation theory .Starting from the relationship between the shear deformation and displacement to deduce the function formula of longitudinal displacement along the height variation of rectangular beam when considering shear deformation,which has proved that the displacement can be decomposed into pure bending displacement and shear-induced displacement caused by shear lag warping.Based on energy variational principle,we can get shear lag differential equations and its general solutions of uniform section beam by applying concepts of shear lag generalized coordinates and generalized forces.The analysis of simply supported rectangular beam under uniform loads shows that stress and deflection of the shear lag coefficient are very close to exact solution of Elasticity.This algorithm has sufficient accuracy and is simpler than the Elasticity.