Seismic Response of Variable Section Column with a Change in Its Boundary Conditions

The end conditions of columns constitute an important design parameter as they change their stiffness. The degree of restraint of the column modifies its fundamental frequency and mode of vibration. The rotational stiffness at its ends may transform from zero (hinged) to infinite (clamped). For intermediate values, the rotational movement is partially restricted, and it is classified as semi-rigid. In this work, the seismic response for a linearly variable section column and with gradual change in the rotational fixity is studied. A parametric solution is developed using the Rayleigh method, derived for cases of non-prismatic columns, and considering the axially distributed force along the column height. The obtained generalized stiffness and mass are used to perform approximate seismic evaluation at low effort and examine the influence of the changes to the structure. The analysis indicated that with a spring coefficient of 5 EI/l, the displacement drops by 50%, meaning that this range can produce significant influence on the structural response. The relationship between the top load and the column self-weight equal to 0.3 defines the limit for the hinged–hinged boundary condition to exist. As research recommendations, analysis of columns with variable cross-sections and different shapes, different distributed loadings, applying the rotational spring for both ends and over the shape functions, and analysis of buildings by an equivalent system are suggested. Experimental activity is indicated as a possibility for future investigations.