Energy-consistent shear coefficients for beams with circular cross sections and radially inhomogeneous materials

An exact computational method for the shear stiffness of beams with circular cross sections and arbitrarily radially inhomogeneous Young’s modulus is presented. We derive the displacement and stress field of a cantilever beam according to 3D theory of elasticity, which requires to solve just a 1D linear boundary value problem. The shear stiffness is obtained by setting the shear strain energy from the exact solution equal to that from technical beam theory. Results and closed analytical formulae are given for several functionally graded and layered cross sections.

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► The shear stiffness of radially inhomogeneous circular cross sections is computed.
► The 3D flexure problem reduces to a linear 1D multi-point boundary value problem.
► The exact computation of the shear stiffness is based on equal strain energies.
► For equal bending stiffness, effects of shifting stiffness to the core are studied.