Time history nonlinear analysis for 2D modelization of an existing building using flexibility and displacement-based formulation

The object of the research is the response of a structure in time between formulations, namely force-based (flexibility-based) and displacement-based. An existing two-story reinforced concrete structure subjected to three earthquakes separately is presented in order to carry out a comparative study in terms of time history structure response between the two formulations cited above namely force based (flexibility based) and displacement based. This research aimed to compare between two formulations namely displacement based and force-based (flexibility-based), in order to show the accuracy and the reliability of the second one. In the case of nonlinear time history response of a residential two-storey reinforced concrete building, which is representative of typical residential building construction in Italy in the 1970’s and 1980’s with the aim of taking advantages of flexibility-based formulation if the comparison proves conclusive. In the course of the research, the former approach is a classical two-node, displacement-based, Euler-Bernoulli frame element with the disadvantage of discretizing the structure thus increasing the number of degrees of freedom and equation, in order to achieve the required precision. The latter is a two-node, force-based, Euler Bernoulli frame element. The main advantage of the second element is that it is «exact» within the relevant frame element theory. This implies that one element per frame member (beam or column) is used in preparing the frame mesh, thus leading to a reduction of the global number of degrees of freedom. Therefore, a reduction in number of equations to solve, resulting in a saving of time with increased precision. An existing two-story reinforced concrete structure subjected to three earthquakes separately is presented in order to carry out a comparative study in terms of time history structure response between the two formulations cited above namely force based (flexibility-based) and displacement-based. As a result of the research, it is shown that with flexibility-based approach no discretization error occurs and all governing equations are satisfied exactly, making a possibility of simpler and faster numerical modeling. In the proposed approach will be of great use in the field of numerical modeling due to its ease and accuracy. This elegant formulation is promising for future work thanks to its advantages.