Abstract
The exact bending stiffness matrix is developed for an arbitrary nonuniform beam including shear deformation. The current development is based upon Timoshenko's beam theory. The coefficients of the bending stiffness matrix require the evaluation of only three integrals. These coefficients are evaluated for a uniform beam (verification) and a nonuniform beam with either linearly or quadratically varying cross-section dimensions. Numerical results are presented to assess the interaction of taper rate and shear deformation on the behavior of short beams having a circular cross-section with linear taper and also short beams having a rectangular cross-section with either linear taper or two different types of simple quadratic taper.
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