Center Of Rigidity Research Articles

The influence of torsion on acceleration demands in low-rise RC buildings

AbstractThis paper presents a study of acceleration demands in low-rise reinforced concrete (RC) buildings with torsion, evaluated by quantifying peak floor accelerations (PFAs) and floor response (acceleration) spectra (FRS). The study was performed with the aim to provide simple empirical formulas to quantify the amplification effects due to torsion, which can occur in most of the existing and new RC buildings. With this goal in mind, a set of eight archetype buildings was selected, characterized by an increasing floor eccentricity obtained by moving the centre of rigidity (CR) away from the centre of mass (CM). Numerical models of the proposed set of archetype RC buildings were considered in both linear elastic and nonlinear configurations. For the latter, the properties of models were widely varied, by systematically modifying parameters of plastic hinges, in order to obtain a sample of 1000 models. Non-structural components (NSCs) were considered linear elastic in all cases. To investigate acceleration demands, a set of forty Eurocode 8 spectrum-compatible ground motion records were used as input. For linear elastic building models, it was observed that the change of demands depends on the position of the NSC (in-plan and in-height), and on the distance between CR and CM. On the other hand, for nonlinear models, additional parameters must be considered, such as the building ductility (μ) and yielding force (Vy). New regression models were proposed for quantifying the observed differences in PFAs and FRS when torsion occurs. The efficiency of the proposed models was assessed by testing the new formulas on an existing case study building, as well as on the well-known SPEAR building.

Seismic retrofit of two-way unsymmetric-plan buildings with added masses

A new methodology for retrofitting unsymmetric-plan buildings against earthquakes is proposed. When such buildings are subjected to ground acceleration, the lateral inertial forces created at the floors’ center-of-mass (CM) induce torsional moments about the center-of-rigidity (CR). The retrofit approach introduces masses to the building floors and places them so that the CM is moved closer to the CR to decrease the lever-arm of the torsional moment. The mass placement is challenging since adding mass also increases the lateral inertial forces linearly and changes the natural mode-frequencies nonlinearly. In order to determine the optimal mass placement, the proposed methodology seeks to develop a new sequential search algorithm. A transfer-function matrix, relating the interstory drifts of the floor-plan edges to the ground acceleration components, is presented and used to obtain the magnitude of the peak gains. The search algorithm examines the performance index (PI) of the square-root of the sum of the squares (SRSS) of the magnitudes of the peak gains over a range of added mass quantities, starting from the top-floor and sequentially stepping towards the first-floor. Thanks to the proposed transfer-function matrix, the minimum PI is obtained very quickly, saving computation time. The developed methodology is examined for retrofitting a three-story building of shear-frames, a ten-story building of moment-resisting-frames and an inelastic ten-story building of yielding shear-frames. The results show that the maximum interstory drifts within the structure, the maximum story shear-forces applied to the lateral-load carrying frames, and the maximum absolute acceleration are reduced by moving the CM closer to the CR, which mitigates the threat of structural failure and demonstrates the effectiveness of the proposed retrofit approach. The developed methodology introduces a new sequential search algorithm that calculates optimal mass quantities, and their location in the horizontal-plane, to minimize the frequency-response of the new transfer-function matrix, while subjected to side-constraints. This is a novel approach to the utilization of systematic search algorithms.

Back-of-the-Envelope analysis of plan-asymmetric confined masonry buildings for force-based seismic design

Location of centers of rigidity (CR) in a confined masonry building is sensitive to the aspect ratio of constituting walls and wall-piers (in case of wall with openings). These centers, generally, do not lie on one vertical line. In contrast, the mass centers (MC) are nearly vertically aligned for a regular confined masonry building. Assuming an average vertical line for the CRs (elastic axis), this paper first presents a simplified framework to arrive at the design force resultants for the force-based seismic design. The framework uses a set of 2D Finite Element (FE) analyses (that can be performed using any commercial software) and some nominal spread sheet calculations. Case study on a recently constructed confined masonry building at Indian Institute of Technology Gandhinagar (India) campus is considered for the purpose of illustration. This framework leads to the design member force resultants close to that calculated using a detailed 3D FE analysis. Next, the framework is converted into a Back-of-the-Envelope method that does not require any FE analysis and yet leads to the member force resultants acceptable for all practical purposes. This is particularly suitable for routine seismic design, especially at the preliminary stage, provided none of the constituting walls comprises of a squat wall-pier.

An analysis of the dynamics of seismically isolated structures taking into account its torsional vibrations

In this paper are researched torsional fluctuations of structure located on the pendulum system of seismic isolation (SIS). Torsional oscillations are caused by the incongruence of the center of rigidity (CR) with the center of mass (CM) of the structure and influence of rotational ground motions. In the calculations given below is considered only the first reason. The lack of coincidence of CR and CM leads to an asynchronous motion of different pendulum devices and to their different longitudinal deformation. Thereby, the tension and compression forces of the devices are different. This leads to the torsion, rocking and vertical displacement of the seismically isolated structure. This paper investigates the influence of the above-mentioned effects.

A yield displacement distribution‐based approach for strength assignment to lateral force‐resisting elements having strength dependent stiffness

AbstractRecent studies have shown that for many lateral force‐resisting elements (LFRE) stiffness is dependent on strength, and as a result strength assignment to these elements would affect both the strength and stiffness distributions in a structure. Consequently, stiffness distribution cannot be considered known prior to strength assignment. This paper presents a yield displacement distribution‐based strength assignment strategy that does not require the knowledge of stiffness distribution prior to strength assignment. It is shown that structural systems with their center of rigidity (CR) and center of strength (CV) located on the opposite sides of the center of mass (CM) will have small torsional responses under seismic excitation. Copyright © 2003 John Wiley Sons, Ltd.

Design of torsionally unbalanced structural systems based on code provisions I: Ductility demand

AbstractUsing a three element single mass model, this paper presents the ductility demands on the elements of torsionally unbalanced systems when subjected to strong earthquake shaking. Torsionally unbalanced systems based on nine structural configurations are considered, ranging from torsionally stiff systems with the centre of rigidity (CR) centrally located to torsionally flexible systems with CR eccentrically located. The strength of the elements is designed based on the Canadian and New Zealand codes, and the Uniform Building Code (UBC) of the United States. It is shown that all three codes can limit the ductility demands on the elements to that of a similar but torsionally balanced system when the system is torsionally stiff. However, substantial additional ductility demands on the element at the stiff edge of the system exist for torsionally flexible systems when the New Zealand code or UBC is used. The large ductility demand is caused by the low strength of the stiff‐edge element permitted by these codes.