Stiffness matrix for beams with shear deformation and warping torsion
- Univ. of Virginia, Charlottesville, VA (United States)
A beam model which considers the warping effect in beams with arbitrary cross sections is discussed. This model takes into account bending, shear, and warping torsion. The derivation builds on a result in beam theory that, if shear is considered, for arbitrary cross sections the deflections in the different coordinate directions are not uncoupled as has been widely assumed. This conclusion follows from the calculation of the shear coefficients from an elasticity solution using an energy formulation. The shear coefficients form a symmetric tensor. The principal axes for this tensor are called principal shear axes. In Reference 2 structural matrices for the shear problem are derived using these shear coefficients. This paper extends these matrices to warping torsion. St. Venant`s semi-inverse method is applied to calculate warping shear stresses. The usual assumptions of the beam theory are made. The material is linear elastic. The loads may consist of shear forces, axial loads and twisting moments. Small deformations are considered. The cross section of the beam can be of arbitrary shape, thin-walled or solid. A deformation coefficient matrix is calculated which describes the relations between the deformations and the different load cases such as shear, torsion, and warping torsion. Numerical results for warping shear stresses and deformations are given. Also, a method to derive a stiffness matrix for a beam of arbitrary cross section under combined loading including warping torsion is presented.
- OSTI ID:
- 175457
- Report Number(s):
- CONF-950686--
- Country of Publication:
- United States
- Language:
- English
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