Use of stiffness measure in dynamic analysis of reinforced concrete frame structures

A method used for measuring the stiffness of hinging reinforced concrete frame structures is developed. The structures suffer from a loss of stiffness during responses exceeding the yield deflection during earthquakes. The so called Stiffness Measure Approach is used to evaluate the tangent stiffness of hinge regions while the structure is responding in nonlinear ranges. Use of the stiffness measure approach for both direct and indirect methods of integration is tried.; Eigenvector methods for nonlinear response have not been especially popular because of the need for regenerating eigenvectors as the time history proceeds. In the present work the eigenvectors sets and corresponding nonlinear state variables, i.e., the tangent stiffnesses of the hinge regions, are stored. There is an expectation that previously generated eigenvectors can be reused as the analysis proceeds.; Nonlinear dynamic response analysis of a structure is usually performed by means of a step-forward or direct integration of the equations of motion expressed in real coordinates. The direct integration method requires the triangular decomposition and the backsubstitution of the effective mass matrix for each time step. By storing and reusing the previously decomposed effective mass matrix during the simulation, the efficiency of the analysis can be improved.; The stiffness measure is used to compare the current tangent stiffnesses of hinge regions with those of previously stored eigenvectors or decomposed matrix sets. The stiffness measure quantity can be used to decide if a previously generated information can be reused or if it is necessary to generate a new information for the current time step.; Since eigenvector calculations or the number of triangular decompositions of matrix are diminished the method is effective in reducing computational effort for reinforced concrete frame structures subjected to strong ground motions.