Abstract
This chapter discusses the similarity between the equations of the Euler-Bemoulli beam theory and the Timoshenko beam theory for isotropic, variable cross-section. Single span beams are used to develop expressions for deflection, slope, bending moment, and shear force of the Timoshenko beam theory in terms of the same quantities of the Euler-Bemoulli beam theory. These explicit and exact relationships are useful in elucidating the effect of transverse shear deformation on the bending of beams of uniform cross-section. This new set of general relationships is explained for statically determinate and statically indeterminate, single span tapered beams. The understanding of these relationships allows easy conversion of the well-known Euler-Bemoulli beam solutions to those for Timoshenko beams. They can also be used to check numerical solutions to Timoshenko beam problems and even to verify the solutions obtained from other Timoshenko beam formulations. Extension of the results to laminated beams is also discussed.
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