Energy-consistent shear coefficients for beams with circular cross sections and radially inhomogeneous materials |
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| Authors: | A Steinboeck A Kugi HA Mang |
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| Institution: | 1. Automation and Control Institute, Vienna University of Technology, Gußhausstraße 27–29, 1040 Vienna, Austria;2. Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria |
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| Abstract: | 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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