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Concept# Return period

Summary

A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or river discharge flows to occur.
It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis. Examples include deciding whether a project should be allowed to go forward in a zone of a certain risk or designing structures to withstand events with a certain return period. The following analysis assumes that the probability of the event occurring does not vary over time and is independent of past events.
Estimating a return period
Recurrence interval = {n+1\over m}
:n number of years on record;
:m is the rank of observed occurrences when arranged in descending order
For floods, the event may be measured in terms of m3/s or height; for storm surges, in terms of the height of the surge, and similarly for other events.

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Ahmed Mohamed Ahmed Elkady, Dimitrios Lignos

This paper investigates the effect of the gravity framing system on the overstrength and collapse risk of steel frame buildings with perimeter special moment frames (SMFs) designed in North America. A nonlinear analytical model that simulates the pinched hysteretic response of typical shear tab connections is calibrated with past experimental data. The proposed modeling approach is implemented into nonlinear analytical models of archetype steel buildings with different heights. It is found that when the gravity framing is considered as part of the analytical model, the overall base shear strength of steel frame buildings with perimeter SMFs could be 50% larger than that of the bare SMFs. This is attributed to the gravity framing as well as the composite action provided by the concrete slab. The same analytical models (i) achieve a static overstrength factor, Ωs larger than 3.0 and (ii) pass the collapse risk evaluation criteria by FEMA P695 regardless of the assigned total system uncertainty. However, when more precise collapse metrics are considered for collapse risk assessment of steel frame buildings with perimeter SMFs, a tolerable probability of collapse is only achieved in a return period of 50years when the perimeter SMFs of mid-rise steel buildings are designed with a strong-column/weak-beam ratio larger than 1.5. The concept of the dynamic overstrength, Ωd is introduced that captures the inelastic force redistribution due to dynamic loading. Steel frame buildings with perimeter SMFs achieve a Ωd>3 regardless if the gravity framing is considered as part of the nonlinear analytical model representation. © 2014 John Wiley & Sons, Ltd.

Hammad El Jisr, Dimitrios Lignos

Earthquake loss estimation in composite-steel moment resisting frames (MRFs) necessitates a proper estimation of the level of damage in steel beam-to-slab connections. These usually feature welded headed shear studs to ensure the composite action between the concrete slab and the steel beam. In partially composite steel beams, earthquake-induced damage in the shear studs and the surrounding concrete occurs due to shear stud slip demands. Within such a context, this paper proposes shear slip-based fragility functions to estimate the probability of being or exceeding four damage states in steel beam-slab connections. These damage states include cracking and crushing of the concrete slab in the vicinity of the shear studs, as well as damage in the shear studs themselves. The developed fragility functions are obtained from a gathered dataset of 42 cyclic push-out tests. They incorporate uncertainty associated with specimen-to-specimen variability, along with epistemic uncertainty arising from the finite number of available experimental results. An application of the proposed fragility functions is conducted on a six-story building with composite-steel MRFs. It is shown that steel beam-slab connections along the building height only exhibit light cracking (i.e., crack sizes of 0.3 mm or less) at design basis seismic events. At seismic intensities associated with a low probability of occurrence seismic event (i.e., return period of 2475 years) the nonlinear building simulations suggest that the 25% reduction of the shear stud resistance in steel beam-slab connections with beam depths of 500 mm or less is not imperative to maintain the integrity of the shear stud connectors.

2021João Miguel De Oliveira Durães Alves Martins

Safety assessments of road bridges to braking events combine the braking force, acting along the longitudinal axis of the deck, with a vertical load that accounts for the vertical component of the traffic action. In modern design standards the vertical load models result from probabilistic calibration procedures targeting predefined return periods. On the contrary, the braking force was derived from a deterministic characterization of the vehicle configurations and of the braking process. Therefore, the return period of the braking force is unclear and may not be consistent with that of the vertical load model. Significant deviations from the target return period might lead to either uneconomical decisions, e.g. uncalled-for retrofitting interventions, or to inaccurate structural safety verifications. This thesis presents an original stochastic model to compute site-specific values of the braking force as a function of the return period. The developed stochastic model takes into account the length of the bridge deck and its dynamic properties for vibrations in the longitudinal direction, as well as different sources of randomness related to braking events, all of which comply with real-world measurements, including: - vehicle configurations, resorting to a time-history of crossing vehicles; - driver response times, randomly generated from probability distributions defined in the scope of this project; - deceleration profiles of the vehicles, resampled from catalogues of realistic deceleration profiles. The stochastic model uses Monte Carlo simulation of braking events and computes the maximum of the dynamic response of the bridge to each event. The computed maxima are collected in an empirical distribution function of the braking force. In the end, the model returns the quantile of this distribution that is suitable for safety assessments. This value of braking force is specific to the bridge given properties, to the traffic characteristics, and to the target return period. An additional novelty of this research work is the estimation of a rate of occurrence on motorways of braking events per vehicle-distance travelled. This parameter enables the estimation of the period of time covered by the simulations of braking events as a function of traffic flow and of the total number of braking events simulated. This step is fundamental to determine the value of the braking force that has a given return period. The braking forces returned by the stochastic model show significant dependence on the bridge length, the natural vibration period of the deck in the longitudinal direction, and the number of directions of traffic on the deck. On the contrary, damping ratio, traffic on the fast-lane or on weekends, and an augmentation of traffic in 20% show no substantial influence on the braking force. Moreover, the two motorway locations considered as sources of traffic data, Denges and Monte Ceneri, both in Switzerland, yielded braking forces with similar magnitudes, despite the significant differences in traffic characteristics. Finally, the results compiled served to calibrate an updated braking force that depends explicitly on the parameters found relevant, as well as on the return period so that it can be adopted by different standards even if they enforce different safety targets. This updated expression evidences that the braking forces of current codes tend to be conservative and, hence, can be improved based on the findings of this project.