The transfer matrix method for the bending and stability of the variable section beams with shear deformation is presented.

The element stiffness matrix of this variable section beam is derived based on principle of virtual displacement.

Moreover,according to this method,the deflection curve equation of other kinds of variable section beam will be also carried out.

In order to calculate rationally the shear stresses in prestressed concrete box beams with variable cross section and reflect objectively their distribution, general formulas for shear stresses of arbitrary non-uniform beams are derived.

Based on the method of integration operators, a new method of computing equivalent nodal forces and inner forces for prestressed non-uniform beams is presented in this paper.

The finite difference method is always used to solve the maximum lateral flexure and its position for a tapered beam.

A method is presented in this paper for calculating the d eflection of tapered beam with shear effects by choosing an appropriate deflecti on equation and an appropriate slope equation.

Analysis of beam with variable cross-section by using direct element-based equilibrium framework

Based on the bending theory of beam with variable cross-section in mechanics of materials,a novel integral formula for elliptical flexure hinge is deduced by introducing centrifugal angle as the integral variable.

Also a new method on shear stress in beams is advanced and the calculation formula of shear stress and bearing stress of arbitrary variable cross section beams is derived.