A companion paper presents the formulation of a fibre beam-column element for the non-linear static and dynamic analysis of R/C frames. This paper illustrates the application of the proposed element in the simulation of the hysteretic behaviour of several R/C beam and column specimens. The specimens are subjected to uniaxial and biaxial loading histories with varying axial load. The proposed element shows computationally stable and robust numerical behaviour, while being able to describe very well the hysteretic behaviour of the reinforced concrete members under the imposed complex loading histories.

Fibre beam–column model for non‐linear analysis of r/c frames: part i. formulation

This enduringly popular undergraduate textbook has been thoroughly reworked and updated, and now comprises twelve chapters covering the same breadth of topics as earlier editions, but in a substantially modernized fashion to facilitate classroom teaching. Covering both theoretical and applied aspects of geophysics, clear explanations of the physical principles are blended with step-by-step derivations of the key equations and over 400 explanatory figures to explain the internal structure and properties of the planet, including its petroleum and mineral resources. New topics include the latest data acquisition technologies, such as satellite geophysics, planetary landers, ocean bottom seismometers, and fibre optic methods, as well as recent research developments in ambient noise interferometry, seismic hazard analysis, rheology, and numerical modelling - all illustrated with examples from the scientific literature. Student-friendly features include separate text boxes with auxiliary explanations and advanced topics of interest; reading lists of foundational, alternative, or more detailed resources; end-of-chapter review questions and an increased number of quantitative exercises. Completely new to this edition is the addition of computational exercises in Python, designed to help students acquire important programming skills and develop a more profound understanding of geophysics.

Fundamentals of Geophysics

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Earthquake ground motion estimation using strong-motion records: a review of equations for the estimation of peak ground acceleration and response spectral ordinates

A differential equation model to describe pinching, degrading response of hysteretic elements is presented. The model consists of a nonpinching hysteretic element, in series with a “slip-lock” element. Zero mean response statistics for a single degree of freedom oscillator whose stiffness is described by the series model, computed by equivalent linearization and by Monte Carlo simulation, are compared. The model response statistics are seen to be reasonable estimated by equivalent linearization.

Random Vibration of Degrading, Pinching Systems

The structure's ability to survive an earthquake may be measured in terms of the expected state of damage of the structure after the earthquake. Damage may be quantified by using any of several damage indices defined as functions whose values can be related to particular structural damage states. A number of available response-based damage indices are discussed and critically evaluated for their applicability in seismic damage evaluation. A new rational approach for damage assessment is presented which provides a measure of the physical response characteristics of the structure and is better suited for non-linear structural analysis. A practical method based on the static pushover analysis is proposed to estimate the expected damage to structures when subjected to earthquakes of different intensities. Results of the analysis of ductile and non-ductile reinforced concrete buildings show that the proposed procedure for damage assessment gives a simple, consistent and rational damage indicator for structures.

Response-based damage assessment of structures

Seismic damage in reinforced concrete frames is predicted by analytical methods. Analytical models are developed which can reproduce the behavior of reinforced concrete members under cyclic loads. Accuracy of the analytical models is checked by considering a set of quasi-static cyclic load tests, and the models are found to be sufficiently accurate. Several damage indicators such as ductility, flexural damage ratio, dissipated energy, and cumulative plastic rotation are investigated for each experiment. Based on the test results and physical grounds, flexural damage ratio and dissipated energy are chosen as damage state parameters. The results of the present study are later used to develop a probabilistic model of member failure in reinforced concrete structures.

Seismic Damage in Reinforced Concrete Frames

Based on cyclic load tests of large-scale reinforced concrete elements and assemblages, a probabilistic model of member failure is developed. The model gives the probability of survival at time t as a functional of damage ratio and dissipated energy up to t. After extension to multivariate survival of several members with correlated resistance, the model is used to calculate the safety of reinforced concrete frames subjected to given input motions. Results are in terms of the probability of local failure and of no failure anywhere in the system.

Seismic safety of reinforced concrete members and structures

Statistical methods are available which predict the maximum response of simple oscillators given the peak acceleration (Ap), peak velocity (Vp) or peak displacement (Dp) of seismic ground motions. An alternative parameter, namely an ordinate (or ordinates) of the Fourier amplitude spectrum of ground motion acceleration, FS(f), may in fact be a preferred predictor of peak response, especially in a frequency range close to f. Other statistical methods (attenuation laws) use distance R and other parameters such as magnitude (M), Modified Mercalli epicentral Intensity (Io) and Modified Mercalli site Intensity (MMI or Is) to predict spectral velocity (Sv(f)), etc. In using such approaches, it is most desirable to know the total uncertainty in the predicted peak response of the system given the starting parameter values. An extensive strong motion data set is used to study these questions, The most direct prediction models are found to be preferable (have lower prediction dispersion) but data may not be available in all regions to permit their use.

Hooshang Banon

Papers

Seismic Damage in Reinforced Concrete Frames

Seismic safety of reinforced concrete members and structures

Seismic motion and response prediction alternatives