Haider Al Abadi

A SIMPLE DISPLACEMENT-BASED MODEL FOR PREDICTING SEISMICALLY INDUCED OVERTURNING

The displacement-based modelling methodology which has been applied extensively to buildings and bridges is extended herein to model the over-turning behaviour of rigid free-standing objects. The acceleration-displacement relationship associated with the overturning motion is linearised in order that the maximum displacement experienced by the object can be estimated using the elastic displacement response spectrum of the building floor. Whilst overturning motion is characterised by highly nonlinear acceleration-displacement properties, it was observed that modelling errors arising from nonlinear behaviour can be effectively controlled through limiting the maximum displacement of the object to some 50% of the ultimate displacement for overturning. The 50% safety margin is one of the key features in the proposed model. Three rigid rectangular objects with depths of 100 mm, 300 mm and 500 mm were used initially to illustrate the use of the model. The height of these objects was 0.5 m, 1.5 m and 2.5 m respectively in order that every object has a common aspect ratio of 1:5. Despite that the aspect ratios of the objects were the same, they have very different levels of vulnerability to overturning. The proposed model was evaluated by nonlinear time-history analyses involving pulse-type excitations, recorded earthquake excitations and computer simulated earthquake excitations. Linear elastic models of buildings have also been used to simulate floor motions at the upper levels in the building. Predictions using the proposed linearised model based on the use of elastic response spectrum of the building floor was found to be very consistent with results obtained from nonlinear time-history analyses. Sufficient verification analyses have been carried out to provide the initial indications that the proposed linearised model seems to work well despite its simplicity.

A simple model for estimating shocks in unrestrained building contents in an earthquake

Building contents that include cabinets housing electronic equipment are typically not rigidly secured to the floor, nor to the adjacent wall except in regions of high seismic activities. The behavior of unrestrained building contents in an earthquake is a cause of concern because of the consequence of damage to certain equipment or other forms of fragile items. Much of the research reported in the literature has been devoted to studying the rocking and sliding motion behavior of base-excited rigid objects and their risks of overturning. In contrast, this paper is concerned with estimating the impact acceleration that can be generated by the pounding of the rocking object onto the floor. Algebraic expressions for predicting the acceleration level, which can be translated into dynamic force values, are derived and illustrated by case studies. Importantly, the proposed expressions have been verified by comparisons with results from both simulated and physical experiments. In illustrating the use of the proposed analytical procedure, a parametric experimental study has been undertaken on a cushion material to study the sensitivity of its static and dynamic stiffness to changes in the boundary conditions of the cushion. The proposed calculation procedure, while simple to apply, can be used as a means of predicting shock and the dynamic forces that can be generated in an object in the course of the response to an earthquake.

Rocking Behavior of Irregular Free-Standing Objects Subjected to Earthquake Motion

ABSTRACT Free-standing rigid objects and structures are dominantly found to exhibit rocking behavior and can be vulnerable to overturning during an earthquake as demonstrated by numerous past earthquake events. Such objects are typically considered to be displacement sensitive with their rocking response being well presented by the Peak Displacement Demand (PDD) parameter of the supporting floor’s motion. This in turn can be directly related to an object’s width (along the direction of motion) for assessing its vulnerability to overturn. Such findings have been sufficiently justified by refined dynamic analysis supported by experimental evaluations which were based on rigid blocks with uniform geometric format (i.e., regular in their mass distribution). However, vulnerable rocking objects can be asymmetric and accordingly their sensitivity to floor displacement cannot be directly related to their width. The key parameter which defines irregular objects’ response to rocking motion is represented by the degree of eccentricity of their center of mass. In this study, the well-known rocking equation of motion is reconfigured and devised to model the rocking responses for 280 irregular objects undergoing eight earthquake motions which included artificial and recorded earthquakes. Analytical results obtained from solving the adjusted equation of motion were evaluated with sophisticated finite element (FE) models simulating the 280 irregular cases. This experimentally validated FE modeling approach was found to be time- and cost-effective for understating the rocking behavior of asymmetric objects as well as clarifying an interesting relationship between the object’s damping level and the condition of the supporting base (i.e., whether being provided with supports at the points of rotation or not). The rocking response of irregular objects was found to be highly influenced by the level of eccentricity of the object when excited by motions with high displacement amplitudes, while such influence was not found noticeable by wider objects. Based on the developed trends between the maximum top displacement of irregular objects and the PDD, an expression for estimating the rocking amplitudes is proposed which is a function of the object’s eccentricity.