Bending Solutions of the Timoshenko Partial-Interaction Composite Beams Using Euler-Bernoulli Solutions

For partial-interaction composite beams, two beam theories (i.e., the Euler-Bernoulli and Timoshenko beam theories) are usually used to investigate their deflections, slips, and stress resultants. However, the relationships between the solutions of partial-interaction composite beams based on the two beam theories have not been discussed while the corresponding relationships for homogeneous beams have been investigated in detail for several years. By analyzing the constitutive relationships and equations of equilibrium, the authors derived the relationships of the solutions between single-span Euler-Bernoulli and Timoshenko partial-interaction composite beams. The integral constants are also presented for various boundary conditions. Through the presented relationships, the solutions of the Timoshenko partial-interaction composite beams could be readily obtained from the solutions of the corresponding Euler-Bernoulli counterparts. As a result, the more complicated flexural-slip-shear deformation analysis based on Timoshenko beam theory may be avoided for engineering designers.