## 5 Concentrated vs. Consistent Mass
### Comparison for Local Parameters
The flexural moments of the models with \(M_{L}\) were also compared to those of \(M_{C}\), for the case of exterior and interior beams but, the results are not presented. It is important to mention, however, that underestimation is less significant even than that of interior columns. The earlier results indicate that the effect of the mass matrix model can significantly vary from one parameter to another. There are many reasons for this; axial loads for example are directly affected by the vertical modes of vibration, which is not the case for interstory shears. Another reason is that due to the fact that the numerical values of the elements of the \(M_{L}\) matrix associated to vertical vibration are greater than those of the \(M_{C}\) matrix, the larger inertial vertical effects, and consequently larger axial loads on columns, are expected for the case of \(M_{L}\). For the case of bending moments the opposite occurs, that is, the bending moments are larger for the \(M_{C}\) matrix because the rotational inertias are larger in comparison with those of the \(M_{L}\) matrix. The overestimation tends to increase as one moves up the model, since the contribution of the higher-mode response may have enhanced for the case of the \(M_{C}\) matrix. Figure 8: Mean values of \(R_{A}\), \(NS\): (**a,c,e**), exterior columns of Models 1-2-3, respectively; (**b,d,f**), interior columns of Models 1-2-3, respectively. In summary, depending upon the response parameter under consideration, the structural model, the seismic intensity and the structural location, the responses can be precisely calculated, considerably overestimated, or considerably underestimated when \(M_{L}\) is used. The inter-story shears, on an average basis, are underestimated by up to about 15%, but for individual strong motions they are underestimated by up to 30%. It can be said that the underestimation is negligible for lateral drifts. The axial loads at exterior columns are significantly overestimated by up to 100% and 60% for individual strong motions and on an average basis, respectively; the corresponding values for the interiors are 44% and 30%. Flexural moments at exterior columns may be underestimated by up to 60% and 35%, individually and on average, respectively; the corresponding values for interior columns are about 21% and 11%. On the other hand, there is no error in the estimation of flexural moments at beams if \(M_{L}\) is used. Structural members in MRFs are designed as beams or beam-columns. In traditional seismic design procedures of steel buildings around the world [48], the members are first designed following the strength concept and then the drifts are revised. It is shown in this paper that there are no significant errors in drifts if the \(M_{L}\) matrix is assumed in the analysis. For inter-story shears and flexural moments, on the other hand, significant non-conservative  
Figure 9: Mean values of \(R_{B}\), _NS_: (**a,c,e**), exterior columns of Models 1-2-3, respectively; (**b,d,f**), interior columns of Models 1-2-3, respectively. errors may result in the design. Hence, it is strongly suggested to use the \(M_{L}\) model while numerically modeling the structural system (steel MRFs) considered in the study. One of the main justifications in the past to avoid the use of the consistent mass matrix was the greater computation (implying greater cost) time demand. However, these days this justification is no longer valid; using modern computers together with efficient modern operating systems, the differences between the computer time requirements of the concentrated and the consistent mass matrices are tremendously reduced.