STABILITY AND SECOND-ORDER ANALYSIS OF TIMOSHENKO BEAM-COLUMN STRUCTURES WITH SEMIRIGID CONECTIONS: SLOPE-DEFLECTION METHOD

A new set of slope-deflection equations for Timoshenko beam-columns of symmetrical cross section with semi-rigid connections that include the combined effects of shear and bending deformations, and second-order axial load effects is developed in a classical manner. The proposed method that also includes the effects the shear component of the applied axial forces (Haringx Model) has the following advantages: 1) it can be utilized in the stability and second-order analysis of framed structures made up of Timoshenko beam-columns with rigid, semirigid, and simple end connections; 2) the effects of semi-rigid connections are condensed into the slope-deflection equations for tension or compression axial loads without introducing additional degrees of freedom and equations; 3) it is more accurate than any other method available and capable of capturing the phenomena of buckling under axial tension forces; and 3) it is powerful, practical, versatile and easy to teach. Analytical studies indicate that shear deformations increase the lateral deflections and reduce the critical axial loads of framed structures made of members with low shear stiffness.