Effect Of Stiffness Degradation Research Articles

Study on the equivalent coefficients of seismic-induced track dynamic irregularities based on post-seismic running performance

The deterioration of track surface smoothness after seismic action of the track-bridge system is a key factor influencing the post-seismic operating safety of high-speed trains. This study proposes a linear mapping relationship between seismic-induced irregularities and the operation performance of high-speed trains to simplify the calculation of the seismic-induced dynamic irregularity building upon the residual geometric irregularity. It introduces the concept of an equivalent coefficient for seismic-induced dynamic irregularities. Within the study context, the validity of this equivalent coefficient in the post-seismic operation performance analysis of high-speed trains on bridges is confirmed, taking into account the randomness of ground motions. In addition, the impact of ground motion intensity and the structural natural vibration period on the equivalent coefficient for seismic-induced dynamic irregularities is examined. The study findings revealed that the magnitude of seismic-induced residual geometric irregularities in the track-bridge system far exceeds that of dynamic irregularities induced by earthquakes. Damage to the track-bridge system under seismic action primarily presents as residual deformations, with stiffness degradation playing a secondary role. There is a significant correlation between the root mean square velocity of seismic-induced irregularities and the post-seismic operation level in high-speed trains. This correlation is a quantitative basis for establishing the equivalent coefficient of seismic-induced dynamic irregularities. Under identical peak ground acceleration (PGA) conditions, the equivalent coefficient for dynamic irregularities in the track-bridge system during NF (near-fault) earthquakes is considerably lower than that during MFF (mid-far-field) earthquakes. This underscores the notable impact of the velocity pulse effect on the equivalent coefficient of seismic-induced dynamic irregularities. An increase in ground motion intensity and the structural natural period leads to a rise in the equivalent coefficient of dynamic irregularities. Finally, the stiffness degradation effect in critical components of the track-bridge system shows greater sensitivity to the ground motion intensity and the structural natural period.

Reliability-based ductility reduction factors surfaces using the generalized bojorquez ground motion intensity measure IBg

In this work, reliability-based ductility reduction factors surfaces are obtained through uniform annual failure rate (UAFR) spectra. For this aim, several nonlinear single degree of freedom (SDOF) systems that include various hysteretic behavior models, constant ductility performance and structural reliability levels are subjected to two sets of ground motions recorded on Mexico City. The first set includes 50 ground motion records located on stiff soils, while the second set correspond to 50 soft soil ground motions. In order to compute the UAFR spectra, the ground motion records were scaled at different values of a particular case of the generalized intensity measure IBg named INp for spectral acceleration. The study discusses the influence of different post-yielding stiffness on UAFR spectra obtained for the selected Bojorquez intensity measure, through the bilinear hysteretic model. Additionally, the Takeda model is used to represent structures that exhibit the effect of stiffness degradation. This study is aimed to compute the effect to obtain ductility reduction factors for various uniform annual failure rates, different degrees of post-yielding stiffness, and different ductility capacity for various nonlinear structures. The analyses of the results indicate that strength reduction (through ductility reduction factors) is mainly influenced by parameters such as ductility, failure rate, period of the system and soil conditions. Finally, reliability-based ductility reduction factor surfaces for stiff and soft soil are provided for different UAFR. It is important to say that this is the first time that ductility reduction factors are proposed based on IBg or INp as intensity measure.

Seismic performance and hysteretic model of corroded steel frame columns in offshore atmospheric environment

Previous studies show that the offshore atmospheric environment corrosion gradually reduces the physical and mechanical properties of steel and eventually deteriorate the seismic performance of steel structures. This paper presents a comprehensive study on the seismic performance of corroded steel frame columns in offshore atmospheric environment. Artificial climate accelerated corrosion tests and cyclic loading tests were carried out on six steel frame columns. The effects of corrosion level and axial compression ratio on the failure mechanism and seismic performance of the columns were investigated in details. The test results indicate that with an increase in corrosion level or axial compression ratio, the displacements associated with plate local buckling, plastic hinge formation and final failure tend to reduce gradually. The bending capacity, ductility and energy dissipation capacity of columns also significantly decrease, and the strength and stiffness degradation effect intensify. Furthermore, a moment-rotation hysteretic model in plastic hinge zone for corroded steel frame columns, considering the cyclic deterioration in strength and stiffness, was established by introducing a two-parameter seismic damage model. The predicted moment-rotation curves and energy dissipations coincided well with the experimental results, verifying the rationality and applicability of the proposed hysteretic model. The research results provide theoretical support for elastic-plastic time history analysis and seismic risk assessment of existing steel frame structures in offshore atmospheric environment.

Delamination Behavior of CFRP Laminated Plates under the Combination of Tensile Preloading and Impact Loading.

When subjected to impact loading, aircraft composite structures are usually in a specific preloading condition (such as tension and compression). In this study, ballistic tests were conducted using a high-speed gas gun system to investigate the effect of biaxial in-plane tensile preload on the delamination of CFRP laminates during high-speed impact. These tests covered central and near-edge locations for both unloaded and preloaded targets, with the test speeds including 50 m/s, 70 m/s, and 90 m/s. The delamination areas, when impacting the center location under 1000 με, show a 14.2~36.7% decrease. However, the cases when impacting the near-edge location show no more than a 19.3% decrease, and even more delamination areas were observed. In addition, in order to enhance the understanding of experimental phenomena, numerical simulations were conducted using the ABAQUS/Explicit solver, combined with the user subroutine VUMAT with modified Hou criteria. The experimental and simulation results were in good agreement, and the maximum error was approximately 12.9%. The results showed that not only the preloading value but also the impact velocity have significant influences on the delamination behavior of preloaded CFRP laminated plates. Combining detailed discussions, the biaxial tensile preload enhanced the resistance to out-of-plane displacement and caused laminate interface stiffness degradation. By analyzing the influence of the preloading value and impact velocity on competing mechanisms between the stress-stiffening effect and interface stiffness degradation effect, the complex delamination behaviors of laminates under various preloading degrees and impact velocities at different impact locations were reasonably explained.

Evaluation of post-storm soil stiffness degradation effects on the performance of monopile-supported offshore wind turbines in clay

Over their lifetime, offshore wind turbines (OWTs) will experience large storm surges that may negatively affect their structural performance. Current design codes do not provide sufficient guidance on tackling this problem. To address it, this study aims to provide a guideline on how shear stiffness degrades around monopiles in normally consolidated clays after a storm surge. High-fidelity finite element models of monopile-supported OWTs are built and validated with 5.5e-05 mean square error against centrifuge tests. Parametric analysis of 108 scenarios is conducted, considering different pile diameters, lengths, soil strengths, and loading scenarios. Pile toe displacements are recorded and used to define a system that can classify the OWT monopiles as flexible or rigid. Shear stiffness degradation ratios at 1D (pile diameter) depth are utilized to predict the change of natural frequency, given the mudline loads. The data suggest that over 5% or 10% decrease in natural frequency indicates that pile head deformations exceed serviceability or ultimate limit state criterion, respectively. A database of soil strain - stiffness degradation ratio pairs is tabulated along each simulated pile as a reference for degraded p-y curve calibration. The proposed method and database are crucial for safer design and quicker assessment of OWTs.

Nonlinear hysteretic behavior of wound reinforced composite pipe with steel strip in service

Steel strip wound reinforced composite pipe (SSRCP) is used for shallow sea oil and gas transportation. Its hysteresis characteristics under low-cycle cyclic loads can absorb external energy by deformation. That is beneficial to ensure the stability of ships, drilling platforms and other marine structures. Considering the nonlinear contact between layers, the nonlinear hysteresis characteristics of SSRCP under bending load were investigated. The results show that SSRCP has different strength change trends under different loading modes during the bending cycle loading process, but stiffness degradation characteristics occurs in all conditions. The frictional energy dissipation increases with an accelerated rate. The increasing of limit displacement is the main factor for the rapid accumulation of frictional energy. When the small displacement amplitude is not applied at the initial stage, the effect of stiffness degradation weakens with the internal pressure increases. The stiffness degradation rate decreases with the increasing of the internal pressure and friction coefficient between layers. When the internal and external pressures are both 3 MPa, a minimum point appears on the skeleton curve, which means that the SSRCP stiffness increases. Frictional energy dissipation increases nonlinearly with the increasing of diameter-to-thickness ratio, shelf friction coefficient and internal pressure. There is a critical spiral angle, which makes the ability of SSRCP increases suddenly for absorbing external energy.

Experimental and Numerical Investigations on Seismic Performance of CFST Frame with External Diaphragm Joint

This paper aims to investigate the seismic performance of a steel frame with an external diaphragm joint between a concrete-filled steel tube (CFST) column and H-shaped steel beam through experiments and finite-element (FE) analysis. A quasistatic test was conducted on five steel frame specimens. The parameters involved in the test were joint stiffness, beam-to-column stiffness ratio and concrete strength. Based on the experimental results, failure mode, lateral load versus displacement hysteretic curve, skeleton curve, strength and stiffness degradation effects, ductility, and energy dissipation capacity were analyzed. The experimental results show the hysteretic curves have a plump shuttle shape; the strength degradation effect and stiffness degradation effect are relatively feeble; and the ductility and energy dissipation capacity are excellent. Therefore, the tested specimens have good seismic performance. Also, this suggests that larger joint stiffness brings about superior seismic performance; a stronger column leads to higher bearing capacity as well as inferior ductility and energy dissipation capacity; and a CFST frame performs better than a hollow steel tube column frame under cyclic loads. On the basis of the experimental results, the ABAQUS software version 6.14 was adopted to establish the FE models. The applicability and accuracy of FE simulation were first verified by experimental results. Then, quantitative parametric analysis was carried out to study the effects of different parameters on seismic performance of the CFST frame with an external diaphragm joint.

Mechanical performance and damping effect of multi‐stage yield metal sleeve damper

The traditional metal yield dampers such as buckling-restrained brace are designed only for strong earthquakes. Under small earthquake, it is difficult to dissipate the energy for common single-stage yield damper. In addition, it is difficult to observe its damage state after earthquake and inconvenient to replace the energy dissipation components separately. Therefore, a new metal sleeve damper which can dissipate the energy under all levels of earthquakes is proposed in this study. Due to the different yield displacements of the energy dissipation strips with different aspect ratios, the damper has multi-stage yield characteristics. Considering the stiffness degradation effect from the semi-rigid joints on both sides of the strips, the mechanical performance parameters of the damper are derived. The quasi-static experiment of the damper is carried out. Finite element method (FEM) is utilized to simulate the performance of the damper. At last, the damping effects of the multi-stage yield damper and common single-stage yield damper are compared. The results indicate that the accuracies of the mechanical performance parameters computation formulas are high. The energy dissipation performance of the multi-stage yield damper is excellent. The correctness of the finite element (FE) modeling method is verified. The seismic performance of the RC frame with the multi-stage yield damper is improved significantly under all levels of earthquakes. Comparing with the single-stage yield damper, the multi-stage yield damper is more effective in the vibration control of the reinforced concrete (RC) frame.

Numerical assessment of the effects of microcrack interaction in AM components

A combined analytical–numerical method to study the effects of linear microcracks and their interaction in additively manufactured components is presented. The 2-D method combines an analytical technique to solve the interaction of microcracks and a numerical RVE type technique to represent the microcracking within a finite element framework using Abaqus finite element software. The method is applied to both a unit cell and test specimen type geometries containing defect patterns generated based on general trends reported for AM materials. The approach is able to determine the local stress intensity factors for each microcrack and their stiffness degradation effects in the continuum. Parallel defect patterns, such as co-oriented lack-of-fusion defects between build layers in AM materials, induce the greatest interaction effects while overall interaction effects in random patterns tend to cancel out. Stacked surface defects produce shielding effects on each other, which may cause a neighbouring subsurface defect to be more critical than the surface defects. The results show that the common geometrical interacting defect re-characterisation rules may provide an incorrect prediction of the failure origin. Finally, the applicability of the method is demonstrated with an example AM component.

Proposal of an equivalent linearization method to predict seismic hysteretic energy demand considering stiffness degradation effects

SummaryTo overcome complexities and shortcomings of previous studies, a new method is proposed to derive an equivalent linear model for predicting seismic hysteretic energy demand of bilinear single degree of freedom (SDOF) models. A new displacement spectrum is defined, which represents hysteretic energy. It is found that by increasing initial period and damping of a nonlinear system in the correct proportion and defining a linear model with these characteristics, the new developed displacement can be achieved. Error minimization is applied through an algorithm to find the optimum equivalent period corresponding to an equivalent damping utilizing two sets of far‐field and near‐field earthquakes. To analyze the effects of stiffness degradation, the proposed algorithm has been implemented on modified Clough hysteretic model as well. Comparing the results, effects of stiffness degradation on the ratio of equivalent to initial period is evident in the short period range, while with increasing initial period, the effect can almost be neglected at higher values of ductility. Nonlinear regression analysis is carried out to provide the equations for predicting equivalent linear parameters as a function of ductility. Despite the previous predictive equations, the proposed model is independent of earthquake characteristics and response‐related parameters, which has increased efficiency as well as simplicity.

Stiffness degradation effects on disk-shaft connection behavior of a three-dimensionally carbon-fiber-reinforced composite rotating disk

High-speed rotation tests of a three-dimensionally reinforced annular disk were conducted with specimens, but were suspended at a speed below that predicted for disk fracture by high-amplitude vibrations. As described herein, the vibration source was assumed to be disk stiffness degradation. This study examined the validity of this mechanism. First, laser devices were used to measure elastic displacement at the disk periphery and to estimate global disk stiffness. Second, static ring burst tests using circular ring specimens machined from composite disks were conducted to evaluate the circumferential stiffness. Compression tests were done using rectangular parallelepiped specimens for the radial stiffness. Results show that the circumferential stiffness was 67% of the prediction by the rule of mixture. The radial stiffness was 85% of that. Locally wavy carbon fiber bundles were responsible for stiffness degradation. Stiffness degradation effects on the shaft–disk connection were specifically examined based on those results.

Stiffness degradation of shear walls under cyclic loading: experimental study and modelling

Stiffness is an important parameter for the seismic design of shear walls, which is related to the shear force distribution of each wall member. The stiffness degradation occurs in shear walls under the effect of earthquakes, and the effect of stiffness degradation is considered by a constant reduction factor in many design codes. However, the constant reduction factor cannot consider the whole stiffness degradation process of shear walls. The aim of this paper is to experimentally study and model the stiffness degradation of shear walls under cyclic loading. Five wall specimens were tested under cyclic loading to study the influence of reinforcing bar strength, axial load ratio, failure mode, and cross-section type on the stiffness degradation. Based on the experimental stiffness degradation curves of rectangular shear walls failing in flexure, a four-line stiffness degradation model controlled by crack, yield, peak, and ultimate points was proposed, and the calculation methods for the values of each point were established. The four-line stiffness degradation model was used to obtain the analytical stiffness degradation curves of the wall specimens, which were compared with the experimental stiffness degradation curves. Study shows that increasing reinforcing bar strength decreases the initial stiffness, and increasing axial load ratio significantly improve the initial stiffness while accelerating the stiffness degradation rate with drift ratio. The stiffness of shear walls failing in flexure is more fully degenerated than that of shear walls failing in shear. The stiffness of T-shaped shear walls is larger loaded in the positive direction than that loaded in negative direction. The flange improves the stiffness while accelerates the stiffness degradation rate with drift ratio. The analytical and experimental stiffness degradation curves were in the reasonable agreement.

Proposed Input Energy-Based Damage Index for RC Bridge Piers

In this paper, a new damage index is proposed for RC bridge piers using the concept of earthquake input energy distribution in a structural system. The damage index was defined as the ratio of the hysteretic energy to the earthquake input energy to take into account the cumulative effects of stiffness degradation, inelastic deformation, and material nonlinearities throughout the loading history. A damage-assessment method was also developed in accordance with material strain. For this purpose, a set of circular RC bridge piers tested under cyclic/seismic loadings was simulated to calibrate the reliability of the proposed damage index and strain-based damage limit states. The results confirmed the ability of the damage index to predict the damage levels of piers under cyclic and seismic loading. The damage index was also compared to some existing damage indices. The comparison showed that the proposed damage index is a relatively simple and practical approach that can provide a reasonably gradual progression of damage throughout the loading history more convincingly than other damage models.

Shear model with shear-flexure interaction for non-linear analysis of reinforced concrete frame element

This paper presents the shear constitutive model for the reinforced concrete (R/C) frame structures analysis under monotonic and cyclic loading. The proposed model is adopted and modified from Mergos and Koppos model [1] that accounts the shear stiffness degradation effect by the shear-flexure interaction in the plastic hinge region. Firstly, the proposed shear model starts from the primary curve without the damages due to the shear-flexure interaction effect. Then, the shear-flexure interaction effect is taken into consideration at the locations of plastic hinges and this effect leads to the degradation of the shear strength and shear stiffness on the undamaged primary curve that is replaced with the damaged primary curve. To determine the sectional shear stiffness with the shear-flexure interaction, an alternative way of the iterative procedure is proposed here. Finally, a numerical example is used to verify the characteristics and behavior of the R/C frame system and confirm accuracy and computational efficiency of the proposed model among the experimental data.

Hysteretic Models Considering Axial-Shear-Flexure Interaction

Most of the existing numerical models implemented in finite element (FE) software, at the current state of the art, are not capable to describe, with enough reliability, the interaction between axial, shear and flexural actions under cyclic loading (e.g. seismic actions), neglecting crucial effects for predicting the nature of the collapse of reinforced concrete (RC) structural elements. Just a few existing 3D volume models or fibre beam models can lead to a quite accurate response, but they are still computationally inefficient for typical applications in earthquake engineering and also characterized by very complex formulation. Thus, discrete models with lumped plasticity hinges may be the preferred choice for modelling the hysteretic behaviour due to cyclic loading conditions, in particular with reference to its implementation in a commercial software package. These considerations lead to this research work focused on the development of a model for RC beam-column elements able to consider degradation effects and interaction between the actions under cyclic loading conditions. In order to develop a model for a general 3D discrete hinge element able to take into account the axial-shear-flexural interaction, it is necessary to provide an implementation which involves a corrector-predictor iterative scheme. Furthermore, a reliable constitutive model based on damage plasticity theory is formulated and implemented for its numerical validation. Aim of this research work is to provide the formulation of a numerical model, which will allow implementation within a FE software package for nonlinear cyclic analysis of RC structural members. The developed model accounts for stiffness degradation effect and stiffness recovery for loading reversal.

The Effect of Using Hysteresis Models (Bilinear and Modified Clough) on Seismic Demands of Single Degree of Freedom Systems

Based on nonlinear inelastic dynamic analysis of Single Degree Of Freedom systems (SDOF), this work investigates the effect of different parameters on the seismic response of these systems. Generalized SDOF systems that present both short and long period structures are subjected to two sets of synthetic ground motions according to the site condition; stiff rock site and stiff soil one, each contains three records. The structural period vary from (0.1 to 2) seconds and the post yielding stiffness ratios vary from (0.0 to 0.2) with two hysteresis models. Modified Clough and Bilinear models have been utilized in the analysis to illustrate the effect of stiffness degradation. The relationship between the force modification factor (R) and the global ductility demand (μ) tends to be more affected under different post yielding stiffness ratios in the structures of short period more than long period structures, where the effect is negligible. Furthermore, while the post yielding stiffness ratio increases, the ductility demand of the structure decreases under all different periods and models. The effect of hysteresis models at all ranges of period is observed while the modified Clough model shows a higher ductility demand than the force modification factor in comparison with the bilinear model. The site condition influence indicates that short period structures have higher ductility demand in stiff soil sites. However, long period structures have higher ductility demand in stiff rock sites.

Seismic performance evaluation of mid-rise shear walls: experiments and analysis

Seismic performance evaluation of shear wall is essential as it is the major lateral load resisting member of a structure. The ultimate load and ultimate drift of the shear wall are the two most important parameters which need to be assessed experimentally and verified analytically. This paper comprises the results of monotonic tests, quasi-static cyclic tests and shake-table tests carried out on a midrise shear wall. The shear wall considered for the study is 1:5 scaled model of the shear wall of the internal structure of a reactor building. The analytical simulation of these tests is carried out using micro and macro modeling of the shear wall. This paper mainly consists of modification in the hysteretic macro model, developed for RC structural walls by Lestuzzi and Badoux in 2003. This modification is made by considering the stiffness degradation effect observed from the tests carried out and this modified model is then used for nonlinear dynamic analysis of the shear wall. The outcome of the paper gives the variation of the capacity, the failure patterns and the performance levels of the shear walls in all three types of tests. The change in the stiffness and the damping of the wall due to increased damage and cracking when subjected to seismic excitation is also highlighted in the paper.

Element mesh, section discretization and material hysteretic laws for fiber beam–column elements of composite structural members

A fiber beam–column element for nonlinear analysis of composite structural members is developed in this paper. The programing of complex material uniaxial constitutive laws and the implementation of the developed element into a general commercial standard finite-element package are discussed. Intensive parametric studies on the modeling strategies of element mesh, section discretization and material hysteretic laws are carried out to develop fiber element with sufficient accuracy, efficiency, stability and practicality for composite structural members. Rational element mesh scheme is recommended to capture the sharp jump of the curvature value at the plastic hinge region and to effectively overcome the numerical difficulty of pathological mesh-sensitivity brought about by the strain softening effect. Efficient section discretization schemes are proposed to give results of sufficient accuracy for the hysteretic behavior of composite members under complex cyclic load histories. The Bauschinger effect of the steel is found to be the most significant factor dominating the accuracy, and the hysteretic law of the concrete can be simplified by ignoring the complex strength and stiffness degradation effects with little influence on the accuracy. Finally, the developed program COMPONA-MARC and the recommended modeling strategies are validated by extensive experimental results of composite structural members.

Springback Predictions of a Dual-phase Steel Considering Elasticity Evolution in Stamping Process

Mechanical properties of a dual-phase steel of 0.8 mm thickness are investigated with uniaxial tensile loadings at room temperature. Standard tensile tests are conducted to determine Young’s modulus, flow curves and plastic strain ratios in rolling, transverse and diagonal directions, respectively. Moreover, uniaxial tensile loadings with unloading–reloading cycles are performed to determine the elastic modulus evolution. Anisotropy of DP600 steel is described using isotopic hardening plasticity in junction with Hill’s orthotropic yield function and applied in finite element (FE) stamping analysis of an automotive structural member. In sheet metal deformation modeling, material models with both constant and variable Young’s moduli were considered to assess the effect of stiffness degradation on FE springback predictions. Effective plastic strain and part thickness distributions calculated with both models were fairly similar and maximum differences were determined to be 4 and 6 %, respectively. A similar situation holds for predicted springback distributions, but springback magnitudes calculated with variable modulus model were constantly higher. Computed geometries with both FE models were, furthermore, evaluated with surface scanning of manufactured parts. While stamping geometries predicted with both models underestimate actual shape distortions determined in manufactured parts, calculations with variable modulus have reduced maximum geometric deviation by 20 % and constantly improved shape correlation.

Bayesian parameter identification of hysteretic behavior of composite walls

A Bayesian probabilistic approach is applied for parameter identification of a hysteretic model using laboratory test data in this paper. A hysteretic model for multi-grid composite walls is proposed to model the behavior of multi-grid composite wall specimens under lateral cyclic loading. Effects of stiffness degradation, strength degradation and pinching are considered. The test data consists of observed hysteretic curves of precast composite wall specimen, composite wall specimen reinforced by light steel, retrofitted composite wall specimen and cast-in-place composite wall specimen. Using the Bayesian approach, the identification results are presented in terms of the most probable value and posterior covariance matrix of model parameters. The implied hysteretic and backbone curves with their uncertainties identified based on the test data are compared with their observed counterparts.