On the relative position of twist and shear centres in the orthotropic and fiberwise homogeneous Saint–Venant beam theory

The relationship between twist and shear centres in an orthotropic Saint–Venant beam, with fiberwise homogeneous elastic moduli and constant Poisson ratios, is investigated. Arbitrary cross-sections are considered. As a new result the relative position of these points is expressed in terms of the scalar potential whose gradient is the rotated field of twist tangential stresses. Its evaluation requires the solution of n+1n+1 boundary value problems, being n⩾0n⩾0 the number of holes in the cross-section. In an isotropic and homogeneous beam the potential is Prandtl stress function and known formulae, providing the relative position of twist and shear centres, are recovered. Explicit expressions of sliding-torsional compliance blocks for Timoshenko beams, defined by an energy condition of equivalence with the orthotropic and fiberwise homogeneous Saint–Venant theory, are provided. Coincidence of twist centre and Timoshenko shear centre is proven. Numerical computations on homogeneous and composite orthotropic L-sections are performed.

► Linearly elastic, orthotropic and fiberwise homogeneous beams are dealt with.
► The intrinsic expressions of displacement, strain and stress fields are given.
► The classical problem of Prandtl stress function is generalized.
► A general formula for the relative position of twist and shear centres is provided.
► Numerical evaluations are performed.