Bringing Probabilistic Analysis Perspective into Structural Engineering Education: Use of Monte Carlo Simulations

In structural engineering education, particularly at the undergraduate level, it is customary to teach analysis of structures with a deterministic approach where applied loads are assumed to be constant. The possibility of variability in these loads is typically taken into account by using load amplification factors at the design stage. Unfortunately, these load factors are accepted by students without questioning what they really are. Besides other complex methods, use of Monte Carlo Simulation Method has the potential to teach students probabilistic structural analysis without expecting a solid background in the theory of probability. As a final outcome, it is expected that structural engineering students will gain a new perspective aside from their traditional deterministic perception of structural analysis. In this article, use of Monte Carlo Simulation Method in teaching probabilistic structural analysis is demonstrated via examples with different complexity levels including a simple beam under gravity loading and a frame under combined gravity and earthquake loads. Proposed subject was taught at different classes of different levels varying from Sophomore to Graduate level students and a very positive feedback was obtained. It is concluded that Monte Carlo Simulation can be used to bring a probabilistic analysis perspective to structural engineering education

Seismic isolation performance sensitivity to potential deviations from design values

Seismic isolation is often used in protecting mission-critical structures including hospitals, data centers, telecommunication buildings, etc. Such structures typically house vibration-sensitive equipment which has to provide continued service but may fail in case sustained accelerations during earthquakes exceed threshold limit values. Thus, peak floor acceleration is one of the two main parameters that control the design of such structures while the other one is peak base displacement since the overall safety of the structure depends on the safety of the isolation system. And in case peak base displacement exceeds the design base displacement during an earthquake, rupture and/or buckling of isolators as well as bumping against stops around the seismic gap may occur. Therefore, obtaining accurate peak floor accelerations and peak base displacement is vital. However, although nominal design values for isolation system and superstructure parameters are calculated in order to meet target peak design base displacement and peak floor accelerations, their actual values may potentially deviate from these nominal design values. In this study, the sensitivity of the seismic performance of structures equipped with linear and nonlinear seismic isolation systems to the aforementioned potential deviations is assessed in the context of a benchmark shear building under different earthquake records with near-fault and far-fault characteristics. The results put forth the degree of sensitivity of peak top floor acceleration and peak base displacement to superstructure parameters including mass, stiffness, and damping and isolation system parameters including stiffness, damping, yield strength, yield displacement, and post-yield to pre-yield stiffness ratio

Probabilistic sensitivity of base-isolated buildings to uncertainties

Characteristic parameter values of seismic isolators deviate from their nominal design values dile to uncertainties and/or errors in their material properties and element dimensions, etc. Deviations may increase over service life due to environmental effects and service conditions. For accurate evaluation of the seismic safety level, all such effects, which would result in deviations in the structural response, need to be taken into account In this study, the sensitivity of the probability of failure of the structures equipped with nonlinear base isolation systems to the uncertainties in various isolation system characteristic parameters is investigated in terms of various isolation system and superstructure response parameters in the context of a realistic three-dimensional base-isolated building model via Monte Carlo Simulations. The inherent record-to-record variability nature of the earthquake ground motions is also taken into account by carrying out analyses for a large number of ground motion records which are classified as those with and without forward-directivity effects. Two levels of nominal isolation periods each with three different levels of uncertainty are considered. Comparative plots of cumulative distribution functions and related statistical evaluation presented here portray the potential extent of the deviation of the structural response parameters resulting from the uncertainties and the uncertainty levels considered, which is expected to be useful for practicing engineers in evaluating isolator test results for their projects

Protecting vibration-sensitive contents: an investigation of floor accelerations in seismically isolated buildings

For the public welfare and safety, buildings such as hospitals, industrial facilities, and technology centers need to remain functional at all times; even during and after major earthquakes. The values of these buildings themselves may be insignificant when compared to the cost of loss of operations and business continuity. Seismic isolation aims to protect both the integrity and the contents of a structure. Since the tolerable acceleration levels are relatively low for continued services of vibration-sensitive high-tech contents, a better understanding of acceleration response behaviors of seismically isolated buildings is necessary. In an effort to shed light to this issue, following are investigated via bi-directional time history analyses of seismically isolated benchmark buildings subject to historical earthquakes: (i) the distribution of peak floor accelerations of seismically isolated buildings subject to seismic excitations in order to find out which floors are likely to sustain the largest accelerations; (ii) the influence of equivalent linear modeling of isolation systems on the floor accelerations in order to find out the range of possible errors introduced by this type of modeling; (iii) the role of superstructure damping in reducing floor accelerations of seismically isolated buildings with flexible superstructures in order to find out whether increasing the superstructure damping helps reducing floor accelerations notably. Influences of isolation system characteristics and superstructure flexibility are both taken into account