Abstract: A second-order nonlinear analysis is presented for the designof a semi-rigid steel frame, which includes the effects of the flexibilityof the connections and the geometric nonlinearity of the members. Thebeam-column element stiffness matrix and the semi-rigid beam elementstiffness matrix are given. The fixed-end moments equilibrium forthe semi-rigid beam holds for concentrated, uniform, and linear loads onmembers. In the semi-rigid steel frame, the effective column-lengthfactor must be considered. The connection flexibility has a significanteffect on the drift in unbraced frames. It is shown that economical designs may be realized with semi-rigid connections by avariation of connection stiffness that balances the span and endmoments in a beam.