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Abstract An interested slender beam with constant section and material is established whose low and above surfaces are acted by reversed uniform distributed shear stresses. In engineering beam theory these loads are equivalent with uniform distributed couple. Timoshenko beam theory is used to develop the analytical results of the deflection and stress distribution of this model. And in comparison with the numerical results obtained by finite element method, some useful conclusions can be acquired: 1) when shear force is not equal to zero in boundary conditions, the shear effect need to be taken into account for the analyses of bending deflection and normal stress, i.e. Euler beam theory is not competent. 2) when boundary conditions contain zero shear force, Euler beam theory can be used in the analyses of bending deflection and normal stress. 3) The distribution of the shear stress in the cross-section is parabolic with the height coordinate as usual. When shear force is zero, the shear stress may be zero due to the effect of this surface load. The direction of the shear stress in same cross section can be altered.
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Received: 02 April 2010
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2011, Vol. 32 
