By Abramenko P., Van Maldeghem H.
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Extra info for 1-twinnings of buildings
8) where Eqs. 2) are used to derive the last equahty. To determine
SS, CF and FC beams. Also for these beams, the rotation of the Timoshenko beam is equal to the slope of the EulerBernouUi beam. For statically indeterminate CS, SC and CC beams, the stress-resultants are not the same, because the compatibility equation involving the effect of transverse shear deformation is required for the solution. The deflection relationships show clearly the effect of shear deformation. The shear-deflection component increases with increasing magnitude of the Euler-Bernoulli moment (or transverse load) and shear parameter.
The beam element has only four degrees of freedom^ namely^ deflection and rotation at each of its two nodes. Depending on the choice of the element type, the general stiffness matrix can be specialized to any of the three theories by merely assigning proper values to parameters introduced in the development. The element does not experience shear locking, and gives exact generalized nodal displacements for Euler-Bemoulli and Timoshenko beam theories when the beam is uniform and homogeneous. While the Timoshenko beam theory requires a shear correction factorj the third-order beam theory does not require the specification of such a factor.
1-twinnings of buildings by Abramenko P., Van Maldeghem H.