Stiffness Degradation Rate Research Articles

Experimental Seismic Performance Evaluation of Coupling Beams: Comparison of Old with Modern Codes

ABSTRACT This study presents the results of an experimental investigation on the seismic performance of two reinforced concrete coupling beams (CBs) for coupled shear walls, one with a conventional reinforcement layout designed according to the old National Building Code of Canada (NBCC) 1941 and the other one with a diagonal reinforcement configuration designed according to modern NBCC 2015 and Canadian Standard Association (CSA) A23.3 2014 requirements. Experimental tests were conducted to investigate the behavior of specimens under reversed cyclic loading. The experimental results reveal that the diagonal reinforcement configuration could increase the load-resisting capacity and energy dissipation capacity by 4.4 and 10.2 times, respectively. Moreover, the maximum rate of stiffness degradation decreased from 96% in conventionally reinforced CB to 57% in diagonally reinforced CBs. Furthermore, diagonal reinforcement layout led to more stable hysteretic behavior without considerable pinching. In contrast and as expected, the conventionally reinforced CB did not comply with the requirements of the new design code. Therefore, such CBs should be retrofitted to upgrade their seismic performance in conformity with updated standards requirements.

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.

Distinct element modelling of the in‐plane cyclic response of URM walls subjected to shear‐compression

SummaryThe in‐plane capacity of unreinforced masonry (URM) elements may vary considerably depending on several factors, including boundary conditions, aspect ratio, vertical overburden, and masonry texture. Since the overall system resistance mainly relies on the in‐plane lateral capacity of URM components when out‐of‐plane modes are adequately prevented, the structural assessment of URM structures could benefit from advanced numerical approaches able to account for these factors simultaneously. This paper aims at enhancing and optimising the employment of the distinct element method, currently confined to the analysis of local mechanisms of reduced‐scale dry‐joint blocky assemblies, with a view to simulate the experimentally observed responses of a series of URM full‐scale specimens with mortared joints subjected to quasi‐static in‐plane cyclic loading. To this end, a mesoscale modelling approach is proposed that employs a simplified microscale modelling approach to effectively capture macroscale behaviour. Dynamic relaxation schemes are employed, in combination with time, size, and mass‐scaling procedures, to decrease computational demand. A new methodology for numerically describing both unit, mortar and hybrid failure modes, also including masonry crushing due to high‐compression stresses, is proposed. Empirical and homogenisation formulae for inferring the elastic properties of interface between elements are also verified, enabling the proposed approach to be applied more broadly. Using this modelling strategy, the interaction between stiffness degradation and energy dissipation rate was accounted for numerically. Although the models marginally underestimate the energy dissipation in the case of slender piers, a good agreement was obtained in terms of lateral strength, hysteretic response, and crack pattern.

Hysteretic Behavior and Restoring Force Model of Reinforced Glazed Hollow Bead Insulation Concrete (GIC) Columns

Based on the research of mix ratio and mechanical properties of glazed hollow bead thermal insulation concrete (GIC), the quasi-static tests of six GIC frame columns and one normal concrete (NC) frame column are carried out. The stress of frame columns under earthquake is simulated by applying a constant vertical load and cyclic horizontal load, and the hysteresis behavior, skeleton curve, ductility coefficient, stiffness degradation, and energy dissipation capacity of frame columns are studied. Contrast variables include axial compression ratio, stirrup reinforcement ratio and concrete material. The results show that the seismic performance of GIC frame columns is similar to that of ordinary concrete frame columns and frame columns. The stiffness degradation rate and ductility of GIC column are higher than that of NC column with the same parameter; higher axial compression ratio can increase the initial stiffness of GIC and reduce ductility; higher reinforcement ratio can increase ductility, but can limit plastic hinge development and reduce energy dissipation capacity of GIC column. The results can provide theoretical basis for elastic-plastic analysis of GIC column under earthquake action.

Stiffness degradation of GFRP pipes under fatigue loading

Abstract This research on the stiffness of glass fiber reinforced plastics (GFRP) pipes constructed according to various types of winding patterns and under varied loading conditions, proposes a model of stiffness degradation for GFRP pipes and the parameters for a model of stiffness degradation. Based on a hoop winding GFRP pipe fatigue test, it was found that the stiffness reduction rate of the first half a million cycles is 0.67 times that of the last 500,000 cycles when maximum alternating displacement is 5 % of the diameter of the GFRP pipe. For the same type of winding GFRP pipe, the stiffness reduction rate at a maximum alternating displacement of its diameter'of 10 % and 15 % yields 1.34 and 1.59 times the stiffness reduction rate of a GFRP pipe with an alternating displacement maximum of its diameter of 5 %, respectively. For GFRP pipes of varied types of winding modes, when the maximum alternating displacement is 5 % of the diameter of a GFRP pipe, the rate of stiffness degradation of the helical winding GFRP pipe and hoop-helical combined winding GFRP pipe is 1.50 and 1.28 times that of a hoop winding GFRP pipe, respectively.

Behaviour of concrete filled glass fibre-reinforced polymer tubes under static and flexural fatigue loading

Abstract Concrete-filled glass fibre-reinforced polymer tubes (CFFTs) have reportedly been considered for industrial applications such as fender piling for marine structures and bridge girders. Even though previous investigations of the flexural fatigue behaviour of circular sectioned CFFTs have been reported in the literature, no such study has been carried out for square or rectangular sectioned tubes. In order to address this research gap, an experimental programme was carried out to investigate the flexural fatigue behaviour of square sectioned CFFTs, considering fatigue deformation cycles equal to 75%, 80%, 85% and 90% of the deformation corresponding to the static flexural failure of the tested CFFTs. The used glass fibre-reinforced polymer (GFRP) tubes contained reinforcements at the longitudinal direction and ±45° to the longitudinal axis of tubes. They were also specified to have much larger longitudinal tensile and compressive strength compared to typical rectangular GFRP tubes. Self-compacting concrete was used for the core-infill of the tested CFFTs. In total, eight static flexural tests and sixteen flexural fatigue tests were conducted under displacement-control fatigue loading using two loading arrangements, namely three-point and four-point bending. All CFFTs beams subjected to the fatigue loading failed due to buckling of the compression flange of CFFT. It was observed that the number of cycles to failure for the employed fatigue deformation ranges were quite low and decreased with increasing the amplitude of fatigue deformation. The bending stiffness of the tested specimens was observed to decrease as the fatigue loading progressed. It was also found that the amount of dissipated energy in a given cycle and the rate of stiffness degradation increases with an increase in the amplitude of fatigue deformation, especially for specimens tested under four-point bending. Furthermore, the bending stiffness at failure for the specimens tested under four-point bending was found to be approximately 80–90% of its initial value.

The relative importance of strong column-weak beam design concept in the single-story RC frames

Although seismic codes have determined all the required details for achieving different ductility classes, the relative importance of such details has not been well understood. This study investigated the relative importance of Strong Column-Weak Beam (SCWB) design concept in comparison to other code-prescribed details for a reinforced concrete Special Moment Frame (SMF). Two full-scale Reinforced Concrete (RC) frames were constructed with similar reinforcement ratios, geometry, and material properties. The first frame (i.e. OBF) only complied with the code-specified requirement for the strong column-weak beam design concept. However, the second frame (i.e. SBF) satisfied all other code-prescribed requirements for an SMF. Frames were subjected to a similar reversed cyclic loading and their response was compared. Results indicated that compared with SBF, OBF had an almost similar ultimate load, effective stiffness, displacement at effective yield strength, and displacement ductility ratio. Conforming to all code-prescribed details improved the displacement at ultimate load and the effective yield strength by an average of 25%. Moreover, although SBF exhibited a slower stiffness degradation rate for small to medium drift ratios, both frames achieved a similar lateral stiffness at large drift ratios.

Effect of combining steel fibers with crumb rubber on enhancing the behavior of beam-column joints under cyclic loading

This investigation aims to study the structural performance of beam-column joints under reverse cyclic loading. Different self-consolidating concrete (SCC) mixtures with various percentages of crumb rubber (CR) and steel fibers (SFs) were tested. The effect of combining different lengths and volumes of SFs with CR on enhancing the ductile behavior of the tested joints was investigated. The main parameters were the percentage of CR (0%-25% by volume of sand), coarse aggregate size (10 mm and 20 mm), concrete type (SCC and vibrated concrete), length of SFs (35 mm and 60 mm), and volume of SFs (0%, 0.35%, and 1%). The structural performance of the tested beam-column joints was evaluated based on load carrying capacity, load deflection response, initial stiffness, rate of stiffness degradation, failure mode, cracking behavior, displacement ductility, brittleness index, and energy dissipation. The results indicated that combining SFs with CR significantly improved the deformability, ductility, energy dissipation, initial stiffness, cracking behavior, first crack load, and load carrying capacity of beam-column joints under reverse cyclic loading. The results also showed that at high percentage of CR (20%), using a larger coarse aggregate (20 mm compared to 10 mm) helped to improve the shear capacity of the joint and changed the failure mode from BJ-mode to B-mode, which enhanced the load carrying capacity, ductility, and energy dissipation of the tested joint.

Experimental Study on the Seismic Performance of a Partition Damped Wall‐Filled Frame Structure

In the past, earthquakes have caused significant damage to traditional masonry filler wall frame structures. To solve this problem, a new design scheme, the partition damping filler wall, is proposed in this paper to reduce the interaction between the filler wall and the frame structure. Low cyclic loading tests are carried out on the traditional and the new masonry filler wall frames. Besides, one full‐scale‐angled span layer frame without a filler wall is produced for comparison analysis. The mechanical performances of the different frames are studied, including the characteristics of the deformation failure modes, hysteretic curves, skeleton curves, rigidity degeneration, energy dissipation capacity, and the lateral displacement of the frame columns. The research results show that the partition damping filler wall can significantly decrease the diagonal bracing effect of the filler wall on the steel frame. Meanwhile, the setting of the low‐strength mortar between the filler wall and steel frame and the arrangement of the damping layer can improve the stress distribution and delay the crack development of the wall. Furthermore, the stiffness degradation rate of the partition damping filler wall is obviously slower than that of the traditional masonry filler wall frame structure. In this paper, the partition damped wall‐filled frame structure shows outstanding ductility and deformation capacity.

Nonlinear lateral stiffness and bearing capacity of suction caissons for offshore wind-turbines

The paper investigates the linear-elastic and nonlinear stiffnesses of a suction caisson used as monopod foundation for an Offshore Wind-Turbine (OWT). Starting from caissons at low working stresses, in which case the linear elastic theory provides an adequate engineering model for soil, analytical expressions for the elastic stiffness matrix of a flexible skirted foundation are proposed and validated. To account for the nonlinear foundation response, the paper proposes a simplified equivalent linear iterative approach where the effective foundation stiffness is expressed in terms of deformation amplitude. To this end, utilizing results from a 3D finite element parametric study, non-dimensional charts have been produced for caissons ranging from perfectly rigid to flexible with variable embedment ratios. To deal with uncertainty on the conditions at the soil-skirt interface, three idealized interface scenarios – “fully-bonded”, “tensionless”, “frictionless” – are implemented. Reduced values of foundation stiffness are computed for a frictionless contact. On the contrary, the impact of a “tensionless” interface, whilst trivial in elastic problems, is intensified with progressing soil inelasticity resulting in severely reduced stiffnesses and capacities. Moreover, with increasing relative skirt flexibility, the elastic stiffnesses of deep suction caissons tend to recede substantially, but the rate of stiffness degradation is fairly attenuated.

Influence of rubber content on enhancing the structural behaviour of beam–column joints

This investigation aimed to determine the optimum percentage of crumb rubber (CR) in self-consolidating concrete (SCC) to enhance the structural behaviour of beam–column joints under reverse cyclic loading. The investigated mixtures were developed with percentages of CR ranging from 0% to 25%. The beam–column joint contained 2% flexural reinforcement and 0·6% shear reinforcement. The structural behaviour of the tested beam–column joints was evaluated based on load deflection, initial stiffness, rate of stiffness degradation, failure mode, cracking behaviour, displacement ductility, brittleness index, energy dissipation, first crack load and load-carrying capacity. The results indicated that the optimum percentage of CR to be used in beam–column joint mixtures is 15%. Although using this percentage slightly reduced the load-carrying capacity, it greatly enhanced the ductility, brittleness index, deformability and energy dissipation. The results also showed that further increase in the percentage of CR (above 15%) changed the failure mode of the tested specimens and limited the deformation capacity, which negatively affected the ductility, brittleness index and energy dissipation.

On the mechanical behavior of polypropylene, steel and hybrid fiber reinforced self-consolidating concrete

This article presents the results of an experimental investigation on the mechanical behavior of a self-consolidating concrete reinforced with steel, polypropylene and hybrid fibers. Hooked end steel fibers with different lengths and diameters were used as reinforcement in fiber volume fractions of 0.50%, 1.00% and 2.00%. Polypropylene fibers were used as reinforcement in volume fractions of 0.33%, 0.66% and 1.10%. Hybrid composites (HyFRC) were also developed to study the synergy effects of both fibers. The hybrid fiber self-consolidating concrete was produced with the addition of 0.50% of hooked-end steel fibers and 0.66% of polypropylene fibers.Pre-notched SCC prims where tested under monotonic and cyclic three-point bending. The tests where controlled by the crack mouth opening displacement in order to have a better analysis of the post cracking regime. The addition of polypropylene, hooked-end and hybrid fibers was effective in improving the post-peak strength of the composites, even though the use of steel fibers promoted higher values of flexural residual stress due to its geometrical and material properties. The same behavior was observed for the fracture parameters results with an improvement of the crack growth resistance for the analyzed composites.Finally, the effect of the fiber reinforcement on the flexural behavior was studied through structural tests on fiber reinforced self-consolidating concrete beams. Both hooked-end steel fiber and hybrid composites enhanced the resistance at yielding and promoted a lower rate of stiffness degradation, while the polypropylene fiber reinforcement presented an improvement in the ductile behavior of the structural composite. The present work gives an important contribution on the structural and cyclic behavior of steel, PP and hybrid fiber reinforced concrete. The paper makes a comparison on the mechanics of the different composite systems aiming its application in structural elements.

Effects of Variation of Axial Load on Seismic Performance of Shear Deficient RC Exterior BCJs

The focus of this paper is to investigate the effect of column axial load levels on the performance of shear deficient reinforced concrete beam column joints (BCJs) under monotonic and cyclic loading. The problem of interaction between shear stress in BCJ and axial load on column has been addressed in this work by initially postulating a mechanistic model and substantiated by an experimental test program. This was achieved by conducting appropriate tests on seven BCJ sub-assemblies subjected to monotonic and reversed cyclic loading, with varying levels of the column axial load. Experimental results were further validated using a finite element model in an ABAQUS environment. The effect of variation of compressive strength of concrete was considered in a subsequent parametric study, in order to obtain sufficient data, and utilized to develop a new shear strength model for BCJs which includes influences of all the important parameters required to predict the shear strength of BCJs. The results showed that column axial load affects the seismic performance of BCJs significantly. Experimental results demonstrated that at initial stages of loading, increase in axial load enhances the shear capacity of the joint and reduces its ductility. However, when the column axial load/axial strength ratio increases to about 0.6–0.7, shear strength starts to decrease rapidly, leading to pure axial failure of the joint. The magnitude of axial load/axial capacity ratio also dictates the failure mode and development of crack patterns in BCJs. Results of reverse cyclic tests on BCJs showed that high value of axial load/axial capacity ratio increases the initial stiffness of BCJ but rate of stiffness degradation is accelerated after peak strength attenuation.

Numerical analysis of a reinforced concrete beam under blast loading

The types of Dynamic loads that might face an engineer during any design procedure vary. One of these loads is the explosion's pressure on buildings which is in other words the blast load. This research has examined the possibility of using a finite element method as a tool for predicting the dynamic response of blast loaded reinforced concrete beams. In this study, the advanced software, ABAQUS is used in order to model materials and consider the material nonlinearity, stiffness degradation and strain rate effects. Experimental results for several beams under explosion are chosen to be modeled and verified using ABAQUS. These experiments were carried out at the National University of Defense Technology in China. The results show that the material properties of concrete under impact loads (high strain rates) can be well defined in ABAQUS. Also the built in model CONWEP for blast load in ABAQUS can be used in the simulation process with an acceptable error.

Numerical analysis of a reinforced concrete beam under blast loading

The types of Dynamic loads that might face an engineer during any design procedure vary. One of these loads is the explosion's pressure on buildings which is in other words the blast load. This research has examined the possibility of using a finite element method as a tool for predicting the dynamic response of blast loaded reinforced concrete beams. In this study, the advanced software, ABAQUS is used in order to model materials and consider the material nonlinearity, stiffness degradation and strain rate effects. Experimental results for several beams under explosion are chosen to be modeled and verified using ABAQUS. These experiments were carried out at the National University of Defense Technology in China. The results show that the material properties of concrete under impact loads (high strain rates) can be well defined in ABAQUS. Also the built in model CONWEP for blast load in ABAQUS can be used in the simulation process with an acceptable error.

Seismic retrofit of masonry wall infilled RC frames through external post-tensioning

In this study, an external post-tensioning technique was employed to enhance the seismic performance of infilled RC frames through preventing premature failure of infill walls and increase in their engagement with RC frames. Totally, six 1/3-scale single-story single-bay RC frames were constructed and tested. The frames were divided into two groups based on their aspect ratios. Each group consisted of a bare frame, an infilled frame and a retrofitted infilled frame. All specimens were subjected to a similar quasi-static cyclic loading and their responses were measured through load cells, strain gauges and linear variable differential transformers. Results indicated that the retrofitted infilled frames had higher initial stiffness, ultimate lateral strength and ductility ratio when compared with the bare and un-retrofitted infilled frames. The retrofitted infilled frames also showed a prolonged failure mode and a lower stiffness degradation rate compared to other frames. It was also observed that, compared to other frames, the retrofitted frames had smaller strain values at their critical zones.

Influence of Fiber Reinforced Concrete on Plastic Behavior on Exterior Beam Column Joint under Cyclic Loading

The plastic behavior of exterior beam-column joint with different fiber reinforced concrete (FRC) is explored experimentally under cyclic loading. Steel fiber and polypropylene fibers are used in fiber reinforced concrete and engineered cementitious composites respectively. A total of four specimens were prepared, among the four two specimens are conventional and remaining two are with different FRC. The hysteresis loop, stiffness degradation, energy dissipation and damage index are the considered parameters to quantify the plastic response of employed technique. The quantification of results shows enhanced load carrying capacity and energy dissipation capacity with lesser rate of stiffness degradation. The post failure analysis authenticates that the use of fiber improves the damage tolerance behavior and ductility enhancement without sudden loss in strength.

Progress on investigation on damage analysis in bonded polymer composites under fatigue

Several unexpected fatigue failures of polymer bonded joints used to repair damaged critical structures such as aircraft control surfaces have been reported in-service. The fatigue life and fatigue life scatter in polymer bonded joints was found to be highly dependent on the rate of stiffness degradation of the polymer adhesive layer under fatigue cycle. Since stiffness is a function of shape and boundary condition and not just material, this makes the static strength of bonded joints unsuitable for assessing and predicting fatigue life. The stiffness degradation of the polymer bonded joint led to in-homogenous strain hardening of the adhesive layer leading to eventual brittle fracture. The in-homogenous regional strain hardening in the polymer joint adhesive layer was caused by fabricated defects and anomalies. Residual strain effect was found in bonded joints after fatigue failure. This was extrapolated to reason that there may be a mean strain effect in adhesively bonded joints under uninterrupted fatigue leading to further research in this area. This research article completes knowledge created in two earlier ones, completing a necessary step in many steps towards addressing fatigue of bonded joints.

Method of reduced variables for stiffness degradation process of unidirectional CFRP composites subjected to alternating bending

The stiffness of carbon fiber reinforced polymer (CFRP) composites under alternating bending has been measured as a function of the number of loading cycles at various temperatures and deflection amplitudes. The stiffness of the specimens decreases gradually with an increase in the number of loading cycles. Such a stiffness degradation is closely correlated with the residual strength degradation, which suggests that the stiffness degradation process corresponds to the accumulation of microscopic damages under alternating bending. The stiffness degradation rate increases with an increase in temperature and deflection amplitude. By means of the method of reduced variables, a master curve for stiffness degradation that makes it possible to estimate the fatigue life has been composed from the stiffness degradation curves at various temperatures and loading stress levels. The activation energy and activation volume for the elementary process of the stiffness degradation are estimated to be 26 ± 3 kcal/mol and 1.1 × 10−28 m3, respectively. A molecular process for the stiffness degradation is discussed on the basis of the thermally activated process theory.

Experimental Evaluation of Seismically and Non-Seismically Detailed External RC Beam-Column Joints

An experimental investigation was undertaken to study the seismic performance of external reinforced concrete (RC) beam-column joints having representative details for mid-rise RC frame buildings in developing countries such as Iran that were designed and constructed prior to the 1970s. Three half-scale external RC beam-column joints were tested by applying lateral cyclic loading of increasing amplitudes. Tested specimens were comprised of one unit having seismic reinforcement detailing in accordance with the seismic requirements of ACI 318-11, and two units having non-seismic reinforcement detailing in accordance with the 1970s construction practice in many developing countries, such as Iran. Two typical defects were considered for the non-seismic units, being the absence of transverse steel hoops and insufficient bond capacity of beam bottom reinforcing bars in the joint region. Test results indicated that the non-seismically detailed specimens had a high rate of strength and stiffness degradation when compared to the seismically detailed specimen, which was attributed primarily to the joint shear failure or bond failure of the beam bottom bars. The non-seismically detailed specimens also showed a 30% reduction in both average strength and ductility and a 60% loss of energy dissipation capacity in comparison to the seismically detailed specimen.