A second order beam theory

A second order beam theory which takes into account shear curvature, transverse direct stresses and rotatory inertia is presented. The governing differential equation is similar in form to the Timoshenko beam equation but contains two coefficients, one of which depends on cross-sectional warping just as does Cowper's expression while the second, although similar in form, also includes terms dependent on the transverse direct stresses. Comparison is made with exact and other approximate theories for particular cases.