The calculation formulas of the end moments,the rotation rigidity and the transmission coefficient were derived by using three parameters mechanical model to simulate the moment rotation of beam-column connections of semi-rigid steel frame and helical spring to simulate semi-rigid connections of the nodes.

The coupling element-free Galerkin with finite element method for semi-rigid steel frames is given.

Employing finite element method,influence of beam-to-column connec- tions rotational stiffness on lateral deformation of regular semi-rigid connected frames is analyzed.

Beam-to-column connection with cantilever beam high-strength bolted-splicing in rigid steel frame is widely used in multi-stories or high-rise buildings and industry workshops in the USA and Japan, which is also the recommended connection type in our Technicall Specification for Steel Structure of Tall Buildings and Code for Seismic Design of Buildings.