This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum and the time integral of the square of the ground acceleration ∫a2 dt. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio EHEI) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low-cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio EH/EI is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R, proposed in the companion paper, and the proposed values for γ and EH/EI

Consistent inelastic design spectra: hysteretic and input energy

In this paper, a method is proposed in order to obtain a simplified representation of hysteretic and input energy spectra. The method is based on the evaluation of the equivalent number of cycles correlated to the earthquake characteristics by the proposed seismic index ID. This procedure allows us to obtain peak values of the hysteretic and input energy that depend on the demanded ductility, on the seismic index ID and on the peak pseudo-velocity. The assessment of the input energy represents a first step towards the definition of a damage potential index capable of taking into account the effect of the duration of the ground motions. Copyright © 2001 John Wiley & Sons, Ltd.

Evaluation of seismic energy demand

The seismic input energy imparted to a structure is dissipated by hysteretic behavior and other nonyielding mechanisms usually represented by equivalent viscous damping. It is generally recognized that there is a strong correlation between the energy dissipated by hysteretic action and the seismically induced level of damage. While viscous damping has a small effect on the amount of energy imparted to a structure, it has a significant influence on the amount of hysteretic energy dissipation. A parametric study is presented on the influence of the mathematical modeling of viscous damping on seismic‐energy dissipation of multidegree‐of‐freedom (MDOF) structures. The damping is modeled using mass‐proportional, stiffness‐proportional, and Rayleigh damping computed from either the initial elastic or the tangent inelastic system properties. Various structural performance indices are evaluated for bilinear hysteresis model of simple MDOF structures with different strength levels, strain hardening ratios, and dam...

Seismic-Energy Dissipation in MDOF Structures

This article reviews the ground motion parameters than can be assumed as structural and non-structural damage measures. Measures of seismic damage potential based on ground motion records are first described, followed by a discussion of the damage measures relating to simple (linear) and more complex (non-linear) structural responses. The second section reviews the measures of damage phenomena which govern structural degradation and/or collapse, including experimental results and analytical models. The relationship between earthquake characteristics and type and level of damage on the seismic response of structures is examined, and data from different well-known destructive earthquakes are given.

Damage indices and damage measures

An energy-based methodology for the assessment of seismic demand

The recently performed experimental study indicates that the current Japanese steel design standards (AIJ) cannot be used to predict accurately the ultimate behavior of bolted connections loaded in static shear, which are fabricated from thin-walled (cold-formed) SUS304 austenite stainless steel plates and thus, modified formula for calculating the ultimate strength to account for the mechanical properties of stainless steel and thin-walled steel plates were proposed. In this study, based on the existing test data for calibration and parametric study, finite element (FE) model with three-dimensional solid elements using ABAQUS program is established to investigate the structural behavior of bolted shear connections with thin-walled stainless steel plate. Non-linear material and non-geometric analysis is carried out in order to predict the load–displacement curves of bolted connections. Curling, i.e., out of plane deformation of the ends of connection plates which occurred in test specimens was also observed in FE model without geometric imperfection, the effect of curling on the ultimate strength was examined quantitatively and the failure criteria which is suitable to predict failure modes of bolted connections was proposed. In addition, results of the FE analysis are compared with previous experimental results, failure modes and ultimate strengths predicted by recommended procedures of FE showed a good correlation with those of experimental results and numerical approach was found to provide estimates with reasonable accuracy.

http://www.labciv.eng.uerj.br/pgeciv/files/ThinWalled-45-issue-4-2007.pdf

Finite element modeling of bolted connections in thin-walled stainless steel plates under static shear

This paper aims to predict ductile fracture of mild steel under monotonic loading only from the test results of notchless tensile coupons. A simple fracture model based on the concept of a ...

Ductile Fracture Simulation of Structural Steels under Monotonic Tension

An ultimate limit state criterion is developed for the seismic reliability assessment of single-story structures. This criterion is: when the structural precollapse energy absorption capacity is greater than the earthquake energy input, the structure can survive. Thus, the load effect is the maximum earthquake energy input which the building is expected to encounter during its lifetime. For the determination of this load effect, the seismic hazard potential as well as the dynamic characteristics of the structure and the ground motion are considered in this study. The seismic hazard term is determined from seismic source and attenuation models, and the dynamic characteristic term is determined from the energy input spectrum of inelastic single-degree-of-freedom (SDOF) systems. The uncertainty involved in these terms is also investigated in order to calculate the failure probability.

Earthquake Load for Structural Reliability

In practice, engineers can usually only obtain material properties from monotonic tensile coupon tests. The aim of this paper is to predict cyclic plasticity of mild steel from coupon test results available. First, the theory of metal plasticity is generally reviewed, and selected models are introduced, i.e., Prager’s hardening rule, the Chaboche models, and the Yoshida-Uemori model. Calibration methods of the material parameters of each model are proposed and limitations of the models are addressed. Then, a modified Yoshida-Uemori model is proposed. Monotonic tensile coupon tests and a series of tests of hourglass-type specimens were carried out under different loading histories to fracture. Numerical simulations using the selected plasticity models and the modified Yoshida-Uemori model were carried out to simulate the cyclic behaviors of hourglass-type specimens using the material parameters calibrated by the monotonic coupon test results. The comparison results show that the modified Yoshida-Ue...

Prediction of Cyclic Behaviors of Mild Steel at Large Plastic Strain Using Coupon Test Results

Finite element analysis (FEA) procedures for predicting the structural behaviors of single shear bolted connections in cold-formed stainless steel have been recommended through previous numerical studies conducted by T.S Kim for Kuwamura's test results and are also introduced briefly in this paper. It was shown that ultimate behaviors such as ultimate strength, failure mode and curling occurrence by FEA were in a good agreement with those of test results. Based on the reasonable prediction accuracy of numerical approach, parametric studies on single shear two-row bolted connections with extended variables; plate thickness, end distance in the direction of load and edge distance perpendicular to the direction of load is conducted in order to consider the strength reduction effect due to curling. It can be found that Kuwamura's equations, which has been specified by Stainless Steel Building Association of Japan (SSBA) design manual are more valid for estimating the ultimate strength of bolted connections with no curling when compared to other design standards, whereas for connections curled in test and FEA results, since SSBA design standard does not consider the curling effect, the ultimate strength of connection was overestimated. Consequently, revised design formulae considering the effect of curling on bolted connection are proposed in this paper using correlations between strength reduction ratio and plate thickness. Furthermore, the validation of the design equations is verified through comparisons with existing test and additional FEA results.

Hitoshi Kuwamura

Papers

Finite element modeling of bolted connections in thin-walled stainless steel plates under static shear

Ductile Fracture Simulation of Structural Steels under Monotonic Tension

Earthquake Load for Structural Reliability

Prediction of Cyclic Behaviors of Mild Steel at Large Plastic Strain Using Coupon Test Results

Investigation on ultimate strength of thin-walled steel single shear bolted connections with two bolts using finite element analysis