Effect of the Distribution of Mass and Structural Member Discretization on the Seismic Response of Steel Buildings

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.

Dynamic response of multi-degree-of-freedom systems with a Coulomb friction contact under harmonic excitation

This paper investigates the steady-state response of a multi-degree-of-freedom (MDOF) system with a Coulomb contact to harmonic excitation. Although discrete MDOF models are commonly used at early design stages to analyse the dynamic performances of engineering structures, the current understanding of the friction damping effects on MDOF behaviour is still limited due to the absence of analytical solutions. In this contribution, closed-form expressions of the continuous time response, the displacement transmissibility and the phase angle of each mass of the system are derived and validated numerically for 2DOF and 5DOF systems. Moreover, the features of the analytical response are investigated, obtaining the following results: (i) the determination of the minimum amounts of friction for which the resonant peaks become finite and (ii) for which stick-slip motion can be observed at high frequencies; (iii) an equation for the evaluation of invariant points for the displacement transmissibilities; (iv) a better understanding of phenomena such as the inversions of the transmissibility curves and the onset of additional resonant peaks due to the permanent sticking of the mass in contact. All these results show that MDOF systems exhibit significantly different dynamic behaviours depending on whether the friction contact and the harmonic excitation are applied to the same or different masses.

Multi-degree-of-freedom systems with a Coulomb friction contact: analytical boundaries of motion regimes

This paper proposes an approach for the determination of the analytical boundaries of continuous, stick-slip and no motion regimes for the steady-state response of a multi-degree-of-freedom (MDOF) system with a single Coulomb contact to harmonic excitation. While these boundaries have been previously investigated for single-degree-of-freedom (SDOF) systems, they are mostly unexplored for MDOF systems. Closed-form expressions of the boundaries of motion regimes are derived and validated numerically for two-degree-of-freedom (2DOF) systems. Different configurations are observed by changing the mass in contact and by connecting the rubbing wall to: (i) the ground, (ii) the base or (iii) the other mass. A procedure for extending these results to systems with more than 2DOFs is also proposed for (i)–(ii) and validated numerically in the case of a 5DOF system with a ground-fixed contact. The boundary between continuous and stick-slip regimes is obtained as an extension of Den Hartog’s formulation for SDOF systems with Coulomb damping (Trans Am Soc Mech Eng 53: 107–115, 1931). The boundary between motion and no motion regimes is derived with an ad hoc procedure, based on the comparison between the overall dynamic load and the friction force acting on the mass in contact. The boundaries are finally represented in a two-dimensional parameter space, showing that the shape and the extension of the regions associated with the three motion regimes can change significantly when different physical parameters and contact configurations are considered.

Inelastic Analysis of Mdof Systems Damaged by Earthquakes, Posteriorly Subjected to Wind Load

This paper deals with the analysis of the inelastic response of buildings originally damaged by earthquakes and subjected to earthquake aftershock and wind loading. The overall aim is to establish the effect of wind actions on structural stability. To that end, one four-story bare frame benchmarked by the European Laboratory for Structural Assessment, is subject to various levels of winds and earthquake joint load while monitoring changes on the ductility demand. In this paper is shown that the combined action of strong winds and earthquakes, however its low probability of occurrence, would cause a decrease of strength reduction factors and considerably increase the ductility demand of damaged infrastructure hence inducing additional risks that would otherwise remain unquantified. The paper examines the non-linear performance of Multi-degree of freedom systems subject to various levels of winds and earthquake load and deals with the estimation of strength reduction factors. This is a relatively unexplored area of research which builds on past developments whereby inelastic performance of buildings has been discussed. It also links to various other paths of development such as structural reliability, forensic and control systems engineering. Doi: 10.28991/cej-2021-03091675 Full Text: PDF