Effect of Reduced Beam Section Frame Elements on Stiffness of Moment Frames

The reduction of the flanges of steel wide flange beams near beam-column joints in special moment resistant frames is currently an acceptable alteration of a connection which connects a beam and column with complete-joint-penetration groove welded flanges and a welded or bolted web connection. Herein, the closed-form stiffness matrix of a two-dimensional frame element with radius flange reductions symmetric about the centroid of the element is derived using virtual work theories. Tip translations of a cantilevered $W24\times 103$ beam containing a maximum reduction in flange area of 44% are obtained using two methods: The analytically derived stiffness matrix of the reduced beam section (RBS) frame element and finite-element analyses of the beam discretized with solid elements. The differences between the results of the two analyses range from 0.3 to 3.9%. The stiffness matrix terms of a $W24\times 76$ beam with and without flange reductions are compared. Again, the frame element includes a 44% maximum reduction of beam flange area. The resulting reduction in stiffness terms ranges from 3.6 to 15.1%. The rotational stiffness decreased by 10.4%. The effects of changes in the dimensions and location of radius flange reductions on the stiffness matrix of the beam are investigated. Given a specific cut geometry and location, as the length of the beam increases, the effect of the cuts on all stiffness terms decreases. However, the relationships are not linear. The relationships between the reduced flange width and the stiffness terms are also nonlinear. As the length of the beam or the width of the reduced flanges increases, the reduction in all stiffness terms decreases at a decreasing rate. As the cuts are moved away from the ends of the beams, the reduction in shear and bending stiffness terms also decreases at a decreasing rate. The location of the reductions has no effect on the axial stiffness of the frame element. The results also show that as the length of the cuts is increased, the reduction in the shear and bending stiffness terms increases at a decreasing rate, and the reduction in axial stiffness increases at practically a constant rate. The results of parametric studies conducted on six-story two- and three-bay moment frames subjected to seismic base shears are also presented. Lateral story drift coefficients of moment frames with and without RBS beams are compared. The greatest reduction area investigated consisted of 40% maximum reductions in all the beam flanges. When compared to frames without cuts, these reductions resulted in a 10.6% increase in the story drift of the two-bay frame and a 10.3% increase in the story drift of the three-bay frame.