Uniform Damping Ratio For Non-Classically Damped Hybrid Steel Concrete Structures

Steel–concrete hybrid systems are used in buildings, in which a steel structure has been placed on a concrete structure to make a lighter structure and have a faster construction. Dynamic analysis of hybrid structures is usually a complex procedure due to various dynamic characteristics of each part, i.e., stiffness, mass and especially damping. Dynamic response of hybrid structures has some complications. One of the reasons is the different stiffness of the two parts of structure and another reason is non-uniform distribution of materials and their different features such as damping in main modes of vibration. The available software is not able to calculate damping matrices and analyze these structures because the damping matrix of these irregular structures is non-classical. Also an equivalent damping should be devoted to the whole structure and using the available software. In the hybrid structures, one or more transitional storeys are used for better transition of lateral and gravity forces. In this study, an equation has been proposed to determine the equivalent uniform damping ratio for hybrid steel–concrete buildings with transitional storey(s). In the proposed method, the hybrid structure containing concrete, steel and transitional storeys appropriately substituted with 3-DOF structure. A wide range of eigenfrequency and mass ratios is examined for each ratio pair, and given the characteristics of the primary system, the complete 3-DOF structure can be formed. Equivalent uniform damping ratio is derived by means of a semi-empirical error minimization procedure. The multiple nonlinear regressions are used for determination of equations of modal damping ratios of hybrid buildings.