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Or, more concisely,

Substituting for the element loads column matrix using a relation of the form of eqn. (9.13) gives

which is the same form as eqn. (9.16) and [H/(e)] is the stress matrix with respect to local coordinates. Evaluating [h(e)\[k'<e)] gives the stress matrix as

Transformation of displacements and loads

Relations of similar form to those of eqns. (9.18)-(9.23) but with additional rotational dof. terms, previously not included in the rod element transformation, will enable the above element stiffness and stress matrices to be transformed from local to global coordinates. The expanded form of eqn. (9.18) for the beam element will be given as

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