where N is the axial force in the member (positive when the member is in tension).

Knowing that semirigid frames are more flexible than conventional rigid frames, the stability of semirigid frames becomes even more a concern in the design of such structures. Together with consideration of the nonlinear behavior of connections, the analysis of semirigid frames requires both geometrical nonlinearity (second-order) and material nonlinearity (semirigid connection behavior)

effects to be taken into account. The semirigid member stiffness matrices for second-order elastic analysis can be obtained by modifying the corresponding stiffness matrices of rigid members as follows [22]:

where the matrices S;, Ce_,-, and G, are as defined in Equations 23.12, 23.13, and 23.15, respectively, and is the correction matrix for the geometrical stiffness of the semirigid member and is expressed as

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