Abstract
The response of steel moment frames is estimated by first considering that the mass matrix is the concentrated type (ML) and then consistent type (MC). The effect of considering more than one element per beam is also evaluated. Low-, mid- and high-rise frames, modeled as complex-2D-MDOF systems, are used in the numerical study. Results indicate that if ML is used, depending upon the response parameter under consideration, the structural model, the seismic intensity and the structural location, the response can be significantly overestimated, precisely calculated, or significantly underestimated. Axial loads at columns, on an average basis, are significantly overestimated (up to 60%), while lateral drifts and flexural moments at beams are precisely calculated. Inter-story shears and flexural moments at columns, on average, are underestimated by up to 15% and 35%, respectively; however, underestimations of up to 60% can be seen for some individual strong motions. Similarly, if just one element per beam is used in the structural modeling, inter-story shears and axial loads on columns are overestimated, on average, by up to 21% and 95%, respectively, while the lateral drifts are precisely calculated. Flexural moments at columns and beams can be considerably underestimated (on average up to 14% and 35%, respectively), but underestimations larger than 50% can be seen for some individual cases. Hence, there is no error in terms of lateral drifts if ML or one element per beam is used, but significant errors can be introduced in the design due to the overestimation and underestimation of the design forces. It is strongly suggested to use MC and at least two elements per beam in the structural modeling.
Highlights
A considerable number of problems related to building analysis and design procedures have been studied for many years
One of the most widely used structural systems in steel buildings is that based on moment-resisting frames (MRFs), where the prismatic framed-type members are represented by beam and beam-column members
The most common and simplest procedure to define the inertial properties of a building is to consider the mass as a concentrated type at the translational degrees of freedoms (DOFs) defined in the structure; it will result in a matrix (ML ) with non-zero numbers in the diagonal corresponding to such DOFs
Summary
A considerable number of problems related to building analysis and design procedures have been studied for many years. It is important to mention that in seismic analyses of steel MRFs, the M and K matrices are usually formulated by considering only one element to represent each structural member [1,2,3], which may introduce inaccuracy in the results. Energy dissipation should be properly estimated to correctly simulate the structural behavior Since it can be generated from many sources, it is more important for steel structures. Damping, which consists of expressing the matrix C as a combination of the M and K matrices In this regard, two special cases of K need to be identified: the elastic (or initial) stiffness matrix (Ko ) corresponding to small or moderate levels of deformations and the tangent stiffness matrix (Kt ) corresponding to inelastic behavior. MRFs, considering different alternatives for the M matrix, as well as to evaluate the accuracy of considering one element to represent each beam
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