Stiffness Deterioration Research Articles

Integrating of Nonlinear Shear Models into Fiber Element for Modeling Seismic Behavior of Reinforced Concrete Coupling Beams, Wall Piers, and Overall Coupled Wall Systems

Reinforced concrete (RC) coupled wall systems, compared with RC shear wall without opening, have more complex nonlinear behavior under the extreme earthquake loads due to the existence of coupling beams. The behavior characteristics induced by nonlinear shear deformation such as shear–flexure interaction, pinching effect, strength and stiffness deterioration are clearly observed in numerous cyclic tests of RC coupling beams and shear walls. To develop an analytical model capable of accurately and efficiently assessing the expected seismic performance of RC coupled wall systems, it is critical to define the appropriate key components models (i.e., nonlinear models of RC wall piers/shear walls and coupling beams). Classic fiber beam element based on the theory of Euler–Bernoulli beam is frequently adopted to simulate the nonlinear responses of slender RC wall piers and coupling beams in the literature because it is able to accurately model the response characters from interaction of axial–bending moment at the section level. However, classic fiber beam element cannot capture the nonlinear behaviors of non-slender structures mainly controlled by nonlinear shear deformation. To overcome this shortcoming, a modified force-based fiber element (MFBFE) including shear effect is introduced and used as the analysis element of non-slender RC coupling beams and shear walls. At the section level, a novel shear model for RC coupling beams and an existed shear model for RC shear walls are respectively added to this fiber element to simulate nonlinear responses of these two key components. The analytical model for RC coupled walls hence is formed through integrating the proposed models of these two key components. The validations with different experimental results of cyclic tests including key components and structural system reported in the literature using these proposed models are performed. Good agreements are achieved for all of these proposed models via comparisons between predicted results and experimental data.

Model-based damage detection using constraint forces at measurements

The number of measurement nodes of a finite element model for damage detection is fewer than the model order. Thus, measurement data should be expanded or the system order should be reduced for evaluating the structural performance. A local damage in the model leads to stiffness deterioration at the corresponding element and variations in the responses of the adjacent elements, including the damaged elements. The response difference between two intact and damage-expected states can be approximately predicted by the constraint forces acting at the measurement nodes. The damage at the element represents the abrupt change in the constraint forces. This work proposes static and dynamic methods to detect damages based on the constraint forces acting on the measurement nodes. It is shown that the damage can be explicitly detected by the constraint forces that satisfy each constraint or measurements separating the given constraints rather than the entire constraint set. The validity of the proposed method is illustrated in two numerical applications of static and dynamic systems, and the effect of external noise is also investigated.

Concentrated-plasticity modelling of circular concrete-filled steel tubular members under flexure

The research reported herein aims at the proposal of an accurate and efficient simplified numerical modelling approach for circular concrete-filled steel tubular (CFST) members under flexural loading. Experimental tests were carried out to characterize the bending behaviour of CFST members under monotonic and cyclic loading. The observed behaviour was characterized by strength and stiffness deterioration effects, as a result of the development of local buckling of the steel tube and cracking of the concrete core. Numerical simulations of these tests were conducted by resorting to existing modelling approaches, namely through Distributed Plasticity (DP) and Concentrated Plasticity (CP) models. It was found that existing modelling approaches failed to accurately capture the levels of strength deterioration and pinching effects observed in the tests. Thus, a novel CP-based simplified model, designated by matCFSTdet, was implemented in OpenSees. The hysteretic response of the CP model is based on a novel rotational spring model. An advanced calibration framework was introduced with targets to calibrate the accuracy of the model. The validation analyses indicate that the model is able to capture well the deterioration in both strength and stiffness of CFST members under cyclic flexural loading. Furthermore, the elastic stiffness, ultimate strength and the pinching effects of the hysteretic loops were also well simulated. The proposed CP model, coupled with the advanced calibration framework, thus results in a more realistic simulation of the cyclic flexural response of circular CFST members.

Accurate and Efficient Simulation of Cyclic Behavior of Diagonally Reinforced Concrete Coupling Beams

Diagonally reinforced concrete coupling beams (DRCB) play an important role in coupled shear wall systems since these members dissipate most seismic input energy during earthquakes. For reliable seismic performance evaluation using nonlinear response history analyses, it is important to use an accurate analytical model for DRCBs. In this study, the Pinching4 model is used as a base model to simulate the cyclic behavior of DRCBs. To simulate the cyclic behavior of DRCBs using the Pinching4 model, the constituent modeling parameters for backbone curve, pinching, and cyclic deterioration in strength and stiffness should be computed. To determine the proper values of the constituent modeling parameters accurately and efficiently, this study proposes empirical equations for the modeling parameters using forward stepwise regression analyses. This study shows that the cyclic behavior of DRCBs is accurately simulated using the Pinching4 model with constituent parameters calculated from the proposed empirical equations.

Collapse capacity of reinforced concrete skewed bridges retrofitted with buckling-restrained braces

This study assesses the collapse capacity and failure modes of skewed bridges retrofitted with buckling-restrained braces (BRBs) at the column bent. The asymmetric configuration of these bridges requires a three-dimensional numerical model that considers uncertainties in the seismic ground motions. The factors controlling the seismic performance of these bridges are obtained from a case study of a three-span reinforced concrete box girder skewed bridge with varying skew angles of 0°, 18°, 36°, and 54°. Numerical models with distributed plasticity and concentrated plasticity are created considering material deterioration and plastic deformation properties. A numerical distributed plasticity model with strength and stiffness deterioration is calibrated with a concentrated plasticity model by performing two-dimensional incremental dynamic analyses (IDAs) on the straight bridges (i.e., 0° skew angle), using 21 far-field ground motions. Then, the collapse capacity of original and retrofitted skewed bridges is obtained from three-dimensional IDAs using the distributed plasticity model. The collapse capacity and failure modes of BRB components are summarized based on investigations from experimental data. Nonlinear time history analyses indicate that the BRB retrofit greatly improves the seismic performance of skewed bridges, but it has negligible effects on the bridge’s collapse capacity after BRB failure. However, the use of BRB greatly reduces the bridge’s probability of failure, and the mean annual frequency of global collapse, since the BRB components dissipate seismic energy as structural fuses. The proposed method of parameter calibration, including BRB failure, is found to be sufficiently reliable to perform satisfactory results.

Continuum damage mechanics-based ductile behavior and fatigue life estimation of low carbon steels: AISI 1020 and AISI 1030

This paper presents an experimental estimation of the ductile behavior and low-cycle fatigue life for widely used structural steels AISI 1020 and AISI 1030 based on continuum damage mechanics approach. This method identifies the deterioration in stiffness of a material arising from micromechanisms of formation, growth, and coalescence of microvoids. This helps the characterization of the ductile flow behavior of metals through a damage variable D, evaluated via load–unload cyclic tensile test. The influence of strain hardening exponent, commonly treated as a constant in ductile flow characterization, is also explored in the current investigation. Its determination uses the Hollomon constitutive relation. Estimated D at different strain levels defines the corresponding effective stress. Application of this stress to the strain equivalence theory then enables the prediction of the stress–strain curve. The model-based results closely approximate the experimental stress–strain curve up to the onset of necking. The agreement of experimental results for fatigue life of the materials from low-cycle fatigue tests with damage-based low-cycle fatigue model demonstrates the correctness of the experimental findings. The damage-based model additionally helps in the prediction of microcrack nucleation and crack propagation life separately. Fractographic examinations of test specimen exhibit usually observed morphology of involved failure mechanisms. The present study emphasizes the experimental means of damage-based ductile flow assessment involving strain hardening exponent term and also the low-cycle fatigue life estimation. The significance of varying strain hardening exponent is further expressed in terms of the corresponding damage magnitude. The material data obtained from this study depicts the damage state at different levels of plastic strain that may serve as a useful information for metal-forming process design.

Experimental and analytical investigation on seismic behavior of Q690 circular high‐strength concrete‐filled thin‐walled steel tubular columns

SummaryThis paper proposed a new Q690 circular high‐strength concrete‐filled thin‐walled steel tubular (HCFTST) column comprising an ultrahigh‐strength steel tube (yield strength fy ≥ 690 MPa). A quasi‐static cyclic loading test was conducted to examine the seismic behavior, and the obtained lateral load‐displacement hysteresis curves, skeleton curves, and ductility were analyzed in detail. Then, a numerical model based on a nonlinear fiber beam‐column element incorporating the modified uniaxial cyclic constitutive laws for concrete and steel was developed mainly to predict the seismic behavior of the tested Q690 circular HCFTST columns. The effects of the concrete cylinder compressive strength (fc), steel yield strength (fy), axial compression ratio (n), and diameter‐to‐thickness (D/t) ratio on the seismic behavior were investigated through a parametric study. Finally, a simplified hysteretic model incorporating the moment‐resisting capacity and deterioration of the unloading stiffness in addition to a normalized skeleton curve and hysteretic criterion was established. The results indicate the following: the proposed Q690 circular HCFTST columns can display reasonable hysteretic behaviors to some extent; the use of high‐strength steel can lead to a significantly larger elasto‐plastic deformation capacity and delay the appearance of post‐peak behavior, even if a lower ductility capacity is provided; moderately loosening the limitations on the D/t ratio can also result in ideal hysteretic behaviors; and the established numerical model and simplified hysteretic model can satisfactorily predict the experimentally observed load‐displacement hysteretic curves, including the deterioration of the strength and stiffness and can, thus, offer design references for the elasto‐plastic analysis of circular HCFTST columns.

Experiment study on hysteretic behaviour of arch truss

The research carries pseudo-static test on 6m-span spatial arch truss specimen with three centers under vertical circle loading, and analysis on their failure process. The hysteretic loops, skeleton curves and stiffness deterioration is obtained. The experimental results showed that the failure of arch truss specimens starts buckling and cracking of lower chord, then the members gradually formed local cracking in this region, and finally the midspan with the greatest force cracking leads for the truss to form geometrical mechanism and collapse; When the structure fails, many members enter the plastic stage. The overall plastic deformation is large and the energy consumption performance is good.

Hysteresis modeling for cyclic behavior of concrete-steel composite joints using modified CSO

Concrete filled steel tubular (CFST) column joints with composite beams have been widely used as lateral loading resisting elements in civil infrastructure. To better utilize these innovative joints for the application of structural seismic design and analysis, it is of great importance to investigate the dynamic behavior of the joint under cyclic loading. With this aim in mind, a novel phenomenal model has been put forward in this paper, in which a Bouc-Wen hysteresis component is employed to portray the strength and stiffness deterioration phenomenon caused by increment of loading cycle. Then, a modified chicken swarm optimization algorithm was used to estimate the optimal model parameters via solving a global minimum optimization problem. Finally, the experimental data tested from five specimens subjected to cyclic loadings were used to validate the performance of the proposed model. The results effectively demonstrate that the proposed model is an easy and more realistic tool that can be used for the pre-design of CFST column joints with reduced beam section (RBS) composite beams.

Nerve conduction velocity is negatively associated with intima-media thickness and brachial-ankle pulse wave velocity in men with type 2 diabetes mellitus.

ObjectivePrevious studies suggest that the presence of diabetic peripheral polyneuropathy (DPN) is associated with atherosclerotic diseases; however, little is known about the relationship between diabetic nerve conduction velocity (NCV) versus arterial stiffness and atherosclerosis parameters.MethodsThe subjects in this study were 292 men with type 2 diabetes mellitus (T2DM). All subjects underwent NCV examination at median and tibial nerves as motor nerve (MCV) as well as median and sural nerves as sensory nerve (SCV). Brachial-ankle pulse wave velocity (baPWV) and carotid intima-media thickness (IMT) were evaluated as arterial stiffness and atherosclerosis parameters.ResultsPearson’s correlation coefficient showed that NCV at all sites negatively correlated with baPWV, maximal and mean IMT (IMT-Max and IMT-Mean), and plaque score (all p values p<0.01 at least). Multiple regression analyses adjusted for confounding factors such as age, duration of diabetes, body mass index, HbA1c, fasting C-peptide, systolic blood pressure, HDL-cholesterol, LDL-cholesterol and albuminuria showed that the association of NCV with IMT-Max, ITM-Mean, and plaque score remained significant (all p values p<0.05 at least) except that between SCV at median and IMT-Max. Moreover, SCV at median (forearm) and sural were significantly associated with baPWV (p = 0.023 and p = 0.027, respectively).ConclusionThe present study showed that DPN estimated by quantitative NCV is linearly associated with the deterioration of arterial stiffness and atherosclerosis parameters in T2DM independently of various diabetic and atherosclerotic factors.

A damping model for nonlinear dynamic analysis providing uniform damping over a frequency range

Nonlinear dynamic analysis provides the means for explicitly modeling structural behavior beyond the elastic range, including strength and stiffness deterioration associated with inelasticity and large displacement. Energy-dissipation mechanisms that cannot be explicitly modeled are represented by intrinsic damping. Existing observations suggest that the intrinsic damping of many solid materials is insensitive to frequency. These observations establish one of the primary requirements for a proper damping algorithm. The damping algorithms available in typical commercial nonlinear time-domain finite element codes fall short of this ideal and, in some cases, have other unrealistic effects such as damping of rigid-body modes.This paper presents a practical damping algorithm that offers advantages over existing approaches in its ability to accurately simulate realistic energy dissipation in analyses performed in the time domain. By leveraging filtering protocols, the proposed algorithm realizes frequency-insensitive energy dissipation over a frequency range. It is compatible with all constitutive models and element formulations. It provides orthogonality to rigid-body motion and diminishing damping force for material response beyond the elastic range. It allows different damping levels for individual components. The proposed algorithm is demonstrated to provide a versatile modeling approach for nonlinear dynamic analysis.

Seismic Analysis of Steel Solid Web Girder-RC Tubular Column Hybrid Structure

This paper aims to investigate the seismic performance of a novel type of steel–concrete hybrid supporting structure consisting of reinforced concrete (RC) tubular columns, steel solid web girder platform, and A-shaped steel frames. It is typically used to house air-cooled condensers (ACC) in thermal power plants (TPPs). First, the finite-element (FE) model was implemented in ABAQUS and the simulation approaches were validated by pseudo-dynamic test results of a scaled steel-concrete hybrid supporting structure. Then, the elasto-plastic time-history analysis of the steel solid web girder-RC tubular column hybrid structure was conducted. The El Centro (NS) record was scaled to peak ground acceleration (PGA) of 0.07, 0.20, 0.40 and 0.62 g to reflect the frequent, basic, rare, and very rare earthquakes. The dynamic characteristics, base shear force, lateral deformation performance, stiffness deterioration, and damage evolution characteristics were analyzed. The numerical results showed that the first vibration mode of this hybrid structure is torsion, due to its small torsional stiffness and the nonuniform distribution characteristics of stiffness and mass in the vertical direction; the lateral deformation shape is shear mode; and the damage mainly occurred on the RC tubular columns, while the steel components did not yield under severe earthquakes. In general, the overall seismic performance of the steel solid web girder-RC tubular column hybrid structural system could meet the seismic design requirements with respect to the high-intensity earthquakes.

Uncertainty Quantification in Seismic Collapse Assessment of Iranian Code-Conforming RC Buildings

Structural collapse is the main concern in the existing structures which are built in the seismic-prone regions. Therefore, the primary goal of the seismic provisions in building codes is to prevent the global collapse. Iran is located in the Alpine-Himalayan belt, and has experienced some of the most destructive earthquakes in the past century. To evaluate the extent to which the Iranian building code provisions meet this objective, the authors have conducted a detailed assessment of collapse risk on a set of moderate moment resisting reinforced concrete (RC) buildings. This study considers P-Delta effects, deterioration in strength and stiffness, and cyclic deterioration in structural components.Structural assessment is performed using OpenSees platform and the multiple-record incremental dynamic analysis (IDA). Results are presented in terms of the IDA capacity curves and the collapse fragility functions at different seismic hazard levels. Results show that probability of instability increases with height of the buildings. Moreover, the collapse confidence level was evaluated considering the available uncertainties. Assuming a minimum confidence level of 90% for the buildings, the collapse prevention limit state under the 2%/50 hazard level is not satisfied for the 9 and 12 story frames, and they need to re-designed.

Repair of severely-damaged RC exterior beam-column joints with FRP and FRCM composites

This paper presents the results of an experimental program aimed at comparing the cyclic behavior of three full-scale reinforced concrete (RC) exterior beam-column joints repaired with externally bonded composites. Preliminary, the specimens suffered significant damage, which resulted in a beam-joint (B + J) failure, i.e. shear failure of the panel joint after yielding of longitudinal reinforcement in the beam. The damaged specimens were then repaired using either Fiber Reinforced Polymer (FRP) or Fiber Reinforced Cementitious Matrix (FRCM) composites, and the same loading history was applied to the repaired specimens. The experimental behavior was compared with that of original specimens, and results are presented in terms of load-carrying capacity, stiffness deterioration, ductility, dissipated energy, and equivalent damping viscous ratio. Results allow to clearly identify the contribution of the externally-bonded composites to the overall behavior of the repaired specimens.

Computationally effective and accurate simulation of cyclic behaviour of old reinforced concrete columns

To evaluate the seismic performance of existing old reinforced concrete (RC) buildings, it is important to use an accurate analytical model. Most columns in these buildings do not satisfy the reinforcement details specified by current seismic design provisions. Columns that possess insufficient reinforcement details can exhibit significant pinching and cyclic deterioration in their strength and stiffness. They can also experience flexure-shear and shear failure during large earthquakes. The objective of this study is to simulate the cyclic behaviour of old RC columns accurately and efficiently with the Pinching4 model considering pinching and cyclic deterioration. Modelling parameters are calibrated based on the test results of 40 collected flexure-shear and shear critical columns. Columns failed by other failure modes rather than shear and flexure-shear failure are not considered in this study. Forward stepwise regression analyses are conducted to determine statistically significant variables from 34 candidate predictor variables and to propose the empirical equations of the modelling parameters. It is shown that the Pinching4 model with the proposed empirical equations accurately simulates the cyclic behaviour of both flexure-shear and shear-critical columns including pinching and cyclic deterioration in strength and stiffness.

Self-centering steel column base with metallic energy dissipation devices

Column bases of seismic-resistant steel frames are typically designed as full-strength to ensure that plastic hinges develop in the bottom end of the first-storey columns. Alternatively, column bases may be designed as partial-strength and dissipate energy through inelastic deformations in their main components (i.e., base plate, steel anchor rods). Both design philosophies result in difficult-to-repair damage and residual drifts. Moreover, the second design philosophy results in complex hysteretic behaviour with strength and stiffness deterioration. This paper proposes a partial-strength low-damage self-centering steel column base. The column base provides flexibility in the design as its rotational stiffness and moment resistance can be independently tuned. The paper presents an analytical model that predicts the stiffness, strength, and hysteretic behaviour of the column base. In addition, a design procedure and detailed finite element models are presented. The paper evaluates the effectiveness of the column base by carrying out nonlinear dynamic analyses on a prototype steel building designed as post-tensioned self-centering moment-resisting frame. The results demonstrate the potential of the column base to reduce the residual first-storey drifts and protect the first-storey columns from yielding.

Seismic-resistant self-centering rocking core system with buckling restrained columns

Conventional concentrically braced frame (CBF) systems have limited drift capacity prior to brace buckling, and related damage leads to deterioration in strength and stiffness. CBFs are also susceptible to soft-story failure. A pin-supported self-centering rocking core system with buckling-restrained columns (SCRC-BRC) is being developed to provide significant drift capacity while limiting damage due to residual drift and soft-story mechanisms.The SCRC-BRC system consists of beams, columns, and braces branching off a central column, with buckling restrained columns (BRCs) incorporated into the system at the first story external column positions. The BRCs and friction generated at lateral-load bearings at each floor level are used to dissipate energy to reduce the overall seismic response of the SCRC-BRC system. Vertically-aligned post-tensioning bars provide additional overturning moment resistance and aid in self-centering the system to eliminate residual drift. The pin support condition at the base of the central column and the lateral stiffness of the system enable it to exhibit a nearly uniform inter-story drift distribution.In this study, the suite of 44 DBE-level ground motions used in FEMA P695 is numerically applied to several SCRC- BRCs to demonstrate the seismic performance of the system. The results show that the SCRC-BRC system has a nearly uniform inter-story drift response, high ductility, and a high energy dissipation capacity, and is an effective seismic-resistant system.

Development and verification of large deformation model considering stiffness deterioration and shear dilation effect in FLAC3D

The existing constitutive models of rock with strain softening cannot successfully reflect the damage-induced anisotropy and nonlinearity of the post-peak failure behavior under progressive loading. In order to better reflect the nonlinear stress-strain behavior of rock, especially for the post-peak failure behavior, with expected stiffness degradation and large deformation, a modified constitutive model of rock considering stiffness degradation and dilatation behavior at large deformation was proposed in this study. This study analyzes and discusses various attenuation parameters in the proposed nonlinear plastic constitutive model using FLAC3D software. The excavation-induced stress in rocks was calculated by FLAC3D using the Mohr-Coulomb model, conventional strain model, and the proposed modified model. The obtained results of these models were analyzed and compared with field data. This study shows that the simulated results using the proposed new constitutive model matched much more closely with the measured field data, with an average error less than 5%. This new model can successfully reflect the damage-induced stiffness degradation at large deformation, and can provide a theoretical basis for stability design and evaluation of underground excavation.

Pinching in Steel Rack Joints: Numerical Modelling and Effects on Structural Response

The structural behaviour of beam-to-column joints plays a key role in the seismic response of frame structures. Regarding to steel storage pallet racks, experimental tests have highlighted that the hysteresis loop of their joints is characterized by the pinching, with the consequence of a reduction of the dissipated hysteretic energy and load carrying capacity. In this paper the authors propose a simplified numerical pinching model capable to simulate the mechanical response of beam-to-column joints under cyclic loads. To develop and check this model, several comparisons are performed with both literature data and experimental results of laboratory tests. The proposed model is characterised by three links placed in parallel: two “composed links” describe the non-linear bending moment-rotation curve of the joint, and a linear elastic link transfers the axial and shear force from the beam to the column. The model is appropriate for predicting the down-aisle seismic response of rack systems and it can be easily implemented in commercial software packages, commonly used for non-linear seismic vulnerability analyses. Moreover, features of the model can be estimated from a few structural data and it does not require to perform expensive cyclic experimental tests. For a deeper understanding of the effects of pinching in the seismic response and to highlight the potentiality of the proposed model a case-study example is also considered. The case-study concerns a rack system, whose beam-to-column joints are modelled using two numerical approaches which differ in the deterioration of the rotational stiffness of joints. Non-linear dynamic analyses, with simulated ground acceleration time-histories, have been carried.

Effect of salt water conditioning on novel fiber metal laminates for marine applications

One of the issues with the widespread use of polymer matrix composites in marine applications is their high susceptibility to environmental degradation, particularly hygrothermal conditions. Therefore, the present research intends to contribute to the better protection of the marine polymer matrix composites through the introduction of a newly developed fiber metal laminate for marine applications. This type of fiber metal laminate consists of a marine aluminum alloy of 5083 alternating with glass fiber reinforced epoxy composite layers. In order to evaluate the characterization of the environmental durability of this novel material, the specimens made of fiber metal laminates as well as commercial woven glass–epoxy composites were exposed to hygrothermal aging and hygrothermal cycling in boiling salt water. Then, to study the structural degradation caused by exposure to salt water, the mechanical properties of fiber metal laminate and woven glass–epoxy specimens under three-point bending and impact loading were evaluated. Results show that exposure to the saline environment generally decreased the flexural strength of woven glass–epoxy and fiber metal laminate specimens, whereas a smaller deterioration in flexural stiffness of both laminate types was found. Moreover, it was observed that the hygrothermal conditioning in salt water did not affect significantly the impact properties of both the fiber metal laminate and woven glass–epoxy specimens as compared to the flexural properties.