Abstract
AbstractStiffness matrices for three‐dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators. Using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member‐by‐member basis, an elastic ‘warping’ support is introduced to represent conditions of partial warping restraint at the member ends. The concept of a ‘warping indicator’ is then introduced to facilitate use of warping springs. Following this, static condensation is used to eliminate the restrained warping degrees‐of‐freedom. The condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix. In the global matrix, continuous warping degrees‐of‐freedom, that is, those internal to a member represented by several elements, are expressed in local co‐ordinates. The remainder are expressed in global co‐ordinates. In the force recovery phase, it is shown that an ‘indirect’ method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial. Solutions to examples of linear elastic analysis are compared with well‐known analytical solutions to demonstrate the application of the method.
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