Load-displacement Relationship Research Articles

Axial local bearing behavior of circular reinforced concrete filled steel tube stub columns

In this work, the axial local compression of circular reinforced concrete-filled steel tube (CRCFT) stub columns is studied. Sixteen specimens, including one circular reinforced concrete stub column (CRCC) specimen and fifteen CRCFT specimens, were prepared, considering different variables, such as the local compression area ratio β, sectional steel ratio α, volume stirrup ratio ρv, longitudinal reinforcement ratio ρ, and concrete strength fc. The axial local compression of specimens were experimentally investigated in terms of the damage process, failure mode, load-displacement relationship, ultimate bearing capacity, stiffness, deformation capacity, and strain characteristic. The finite element model of the CRCFT was also developed and validated. The parametric analysis of the local compression area ratio β, sectional steel ratio α, and volume stirrup ratio ρv facilitated the further investigation of the axial local compression behavior of CRCFT. The results showed steel tube buckling and concrete shear failure exhibited by CRCFT specimens. With the increasing local compression area ratio β, the ultimate bearing capacity reduced by 3.6–47.9 %, whereas the local compression strength improvement coefficient βcl increased by 11.8–273.9 %. With the increase in section steel ratio α and volume stirrup ratio ρv, the ultimate bearing capacity, stiffness, and deformation capacity were improved. Longitudinal reinforcement ratio ρ and the concrete strength fc also influenced the stiffness of CRCFT specimens. A simplified calculation method for the ultimate bearing capacity of CRCFT specimens was also presented.

Reconstruction and prediction of Mode-I cohesive law using artificial neural network

Cohesive zone model (CZM) is a widely used tool for simulating both static and fatigue damage propagation for bonded area in composite materials. Under static loading, the damage propagation behavior is governed by a cohesive law (CL), the shape of which is an important property especially when non-linear damage mechanisms such as fiber bridging is involved. In this work, a CZM driven by artificially neural network (ANN) for simulating mode-I damage propagation is proposed, where the traction-separation relationship is calculated by a multi-layer perceptron (MLP). More importantly, a reconstruction method is proposed to extract the CL through the training of the neural network using a simple load-displacement (P–U) relation of a double cantilever beam (DCB) as the only inputs, without the need to measure the crack opening displacement (COD). The proposed method is first validated using finite element generated virtual experimental data with various CL shapes before being applied to experimental data, where good correlations are obtained, proving the effectiveness of the proposed method.

An experimental study of cold-formed steel connections with screwed clip angle under tension and shear loads

This paper aims to investigate the performance of typical cold-formed steel (CFS) beam-to-beam connections between floor bearers and floor joists through a series of full-scale experiments. The investigated connections consisted of a lipped channel (floor joist), an unlipped channel (floor bearer), a thin-walled clip angle (connector), and a self-drilling screw (fastener). In this study, customised T-shaped and H-shaped CFS connection specimens were tested to examine the performance under tension and shear loads, respectively. Two sizes of self-drilling screws, 10 G and 14 G, were used with the selected load bearing clip angle. The fabricated connection specimens were subjected to displacement-controlled tension and shear loads. The experiments uncovered the ultimate connection strengths, load-displacement relationships, and failure mechanisms of the designed CFS connections under the applied loads. Moreover, the experimental tensile and shear strengths of the connections were compared with the strengths predicted by the standard design equations. It was found that the screw pullout on the anchored leg of the clip angle was the main mode of failure under the tensile load. On the other hand, two different failure modes—fracturing of 10 G screws or shear buckling of the cantilevered leg of the clip angle with 14 G screws—were observed in the H-shaped specimen under the applied shear load. Among the designed connection specimens, the maximum tensile load capacity was 30.86 kN and the maximum shear load capacity 88.15 kN. The standard design calculations predicted screw pullout failure under tension, while the shear bucking failure mode of the clip angle under shear load was overlooked.

Structural Performance of Ferrocement Hollow Shear Walls Subjected to Lateral and Compressive Axial Loads

In this study, ten shear walls were experimentally tested to examine behaviour of ferrocement hollow shear walls subjected to axial and lateral loads. Ferrocement mortar (FM) was used to build eight walls, while normal concrete (NC) was used to build two controls. Walls were lateral reinforced using conventional stirrups, two layers of welded wire mesh (WWM), and expanded steel mesh (ESM). Two specimens lacked lateral reinforcement except for one transverse web in the center of the inner hole. Two symmetric groups of five walls each were created by dividing the walls. While the other group was loaded laterally, one group was loaded axially. In each group, the load–displacement relationship, maximum load and associated displacement, stiffness, ductility, and failure mechanism of FM and NC walls were compared. The results showed that FM walls provided with ESM and WWM had ultimate axial loads that were, respectively, 36% and 19% higher than NC control walls. Ultimate lateral loads and related ultimate drifts of FM walls reinforced with two layers of WWM and ESM were, respectively, 68% and 39%, 96% and 43.5%, larger than control NC wall. For lateral loads greater than those applied to the NC control wall, stiffness increase ratios for FM walls ranged from 2.5% to 89.5%, and for axial loads, they ranged from 20% to 150.5%. The ductility of FM walls increased when compared to NC walls by 58.5% and 158.8% for axial and lateral loading, respectively, when two layers of WWM were utilized to lateral reinforce FM walls. When two layers of ESM were applied to laterally reinforce FM walls in comparison to an NC wall, this increased the walls' ductility under axial and lateral loads by 110.5% and 214.7%, respectively.

Fast analysis approach for instability problems of thin shells utilizing ANNs and a Bayesian regularization back-propagation algorithm

Abstract This research develops a data-driven methodology for structural instability problems with highly nonlinear, difficult, noisy, and small data. A fast analysis and prediction (FAP) approach for instability problems of thin shells is first proposed. This approach contains two phases: the fast numerical analysis and the pure prediction utilizing artificial neural networks (ANNs) incorporated with the Bayesian regularization (B-R) algorithm as follows: (1) in Phase 1 (the fast numerical analysis), post-buckling analysis is conducted utilizing a minor amount of load steps. The load–displacement relation achieved from Phase 1 is not exact because of the small number of load steps utilized; (2) in Phase 2 (the prediction), the loads and deflections achieved from Phase 1 were employed as the data for training ANNs. The trained networks, including the load and displacement networks, were employed to fast predict loads and deflections at any step of the post-buckling analysis. After utilizing Phase 2, a smooth, complete and exact load–displacement curve was achieved. In Phase 1, the available formulation for post-buckling analysis of thin shells in the literature was utilized. Five popular types of instabilities chosen to confirm the effectiveness and exactness of the FAP were snap-through, snap-back, softening–hardening, kink instabilities, and delamination buckling and post-buckling of composites. The high exactness and effectiveness of the FAP were confirmed in the numerical verification section. The present approach saves a huge computation compared to the other ones. It was found that ANNs incorporated with the B-R algorithm have notable advantages compared to numerous neural networks. The proposed approach is applicable to simulations or experiments where data are “expensive”, highly nonlinear, difficult, and limited. Utilizing the proposed approach for these fields can dramatically save time and money.

Parametric study on the flexural behavior of steel fiber reinforced concrete beams utilizing nonlinear finite element analysis

Reinforced concrete beams undergo significant internal forces and deformations under extensive loading and have flexural or shear failure based on the reinforcement detailing and geometric properties. The addition of steel fibers increases the deformation and load carrying capacities that leads to ductile behavior. The main contribution of fibers is the improvement of the composite tensile capacity, which results in improved flexural and shear responses. This study numerically investigates the effect of fiber properties on the flexural behavior of steel fiber reinforced concrete (SFRC) beams for both compression and tension failure. First, three specimens from prior experimental studies are modeled using the nonlinear finite element program ABAQUS and the analytical results are verified by comparison with the test results. Contrary to prior nonlinear models, the developed model accurately predicts the damage pattern, descending portion of the load-displacement relationship, and ultimate displacement, which lead to a reliable estimation of energy dissipation capacity and ductility. A comprehensive parametric study is then conducted to examine the effect of tension reinforcement ratio, fiber volume fraction, and fiber aspect ratio on the flexural behavior of both reinforced concrete and SFRC beams. The influence of these key parameters is investigated by comparing the peak load, displacement ductility, peak stiffness, service stiffness, energy dissipation capacity, and damage pattern for both reinforced concrete and SFRC beams. The analytical results indicate that the addition of steel fibers up to 2.0 % leads to a slight increase in the load carrying capacity, while the displacement ductility and energy dissipation capacity are significantly improved. Furthermore, the utilization of 1.0 % steel fibers is observed to be sufficient to modify the failure mode of over reinforced concrete beams from brittle compression failure to tension failure.

Shear performance and failure mechanism of socket CFST column-beam connection with UHPC grouting

Prefabrication assembly technology has been widely recognized due to its rapid construction, minimal environmental impact, and superior quality of precast components. The reliability and construction convenience of the connection joints of precast components are particularly important. In this paper, a novel Ultra High-Performance Concrete (UHPC)-filled concrete-filled steel tube (CFST) socket connection (UCSC) was proposed for the column-beam connection. To explore the shear behavior and shear load transfer mechanism of UCSC joints, four direct shear experiments were conducted in terms of different parameters (socket depth, presence of studs). Meanwhile, ABAQUS was used to perform a systematic parametric analysis (socket length, embedded length, outer diameter of CFST, thickness of steel tube). The results indicated that the shear performance of UCSC joints was significantly influenced by both the socket depth and the outer diameter of CFST. The proposed finite element model (FEM) can predict the load-displacement relationships of UCSC joints with a maximum peak load error of 2.3 %. Combining the experimental results and numerical results, a simplified calculation model was formulated to accurately estimate the shear bearing capacity of UCSC joints, and was verified by numerical and experimental results with a maximum error of 8.6 %. The research results have practical implications for the preliminary design of UCSC joints to avoid non-ideal failure mode.

Behavior of hybrid R.C. columns under the effect of fire furnace (experimental and numerical study)

ABSTRACT When fire exposes the hybrid reinforced concrete R.C. columns, it seriously damages the mechanical qualities of steel bars, concrete, and glass fiber reinforced polymer G.F.R.P. bars. This study focused on hybrid reinforced concrete R.C. columns’ behaviour and failure modes that were eccentrically and concentrically loaded during the fire until a failure. The behaviour of these R.C. columns will be quantified by demonstrating and going over the load-displacement relationships, failure mechanisms, crack patterns, strain distribution at failure, ductility, and stiffness. The number and width of cracks in the columns heated to 300 ºC, 500 ºC, and 700 ºC were significantly more than in the unheated columns. When the specimen is exposed to high temperatures, less force is needed to cause a first crack, and the ultimate strength decreases as the applied load and eccentricity ratio values increase. Hence, all specimens’ axial and lateral displacement values increase. This can be explained by two factors: the depth of the practical section because of the thermal expansion effect and the cracking expansion of concrete when subjected to high temperatures, and heating causes a loss in stiffness of column because the elasticity of concrete’s modulus of elasticity drops.

A developed soil reaction model for large- diameter monopiles in sand based on hyperbolic curves

Given the preference as the foundation for offshore wind turbines, this paper focuses on large-diameter monopiles and presents a series of finite element analyses to investigate the response to lateral loads. The contribution of four soil reactions, including distributed lateral load (p-y), distributed moment (m-θ), and base shear force and base moment, to the lateral resistance encountered by monopiles is quantified. It can be found that apart from the distributed lateral load, the contribution of distributed moment exceeds 14 %, while the proportion of base shear force and base moment is less than 5 % and is considered negligible. This research investigates how the diameter and embedded length of monopiles impact the load-bearing characteristics. A 'p-y + m-θ' model based on the two-parameter soil reaction curve is proposed. This model is not only straightforward and easy to use for engineering design but also considers the effect of rotational deformation on the soil reaction curves. Additionally, a relationship between ultimate lateral soil resistance and relative density is established, leading to an analysis model suitable for sands of various relative densities. Finally, the model effectively predicts the load–displacement relationship for large-diameter monopiles under lateral loads, providing valuable support for monopile design in the offshore wind industry.

Using crack width for shear, stiffness, and stirrup strain history predictions for reinforced concrete beams

Shear failures in reinforced concrete structures occur with little or no warning. Reinforced concrete members with shear cracks should be evaluated to ensure safety. Existing evaluation methods have large variability, require time-consuming modeling or expert opinion. This study uses machine learning to investigate correlations of crack width with shear loading, stiffness, and stirrup strain histories. Experimental literature enables the assembly of a database of rectangular reinforced concrete slender beams with crack width measurements for beams with shear reinforcement amounts smaller and larger than the minimum required by ACI 318-19. Measured data include crack widths from 122 beams, load–displacement relationship from 100 beams, and stirrup strains from 46 beams. Gaussian Process Regression is used to correlate crack width and geometric, material and design properties to shear loading, stiffness, and stirrup strain histories. Ten-fold cross validation training shows mean absolute percent errors of 18, 33 and 77% for shear, stiffness, and stirrup strain history predictions. The proposed algorithms can be used to accelerate the evaluation of in-service structures and can be updated upon availability of additional data.

Fatigue characteristics of rubber isolation layers used in high speed railway ballastless tracks: A theoretical and experimental study

In order to enhance operational conditions for high-speed trains on long-span bridges, the utilization of rubber under-ballast mats were taken as a novel isolation layer in ballastless tracks. Due to the increased train axle load, it is imperative to conduct investigation into the fatigue properties of the rubber isolation layer, so as to ensure the smoothness of the railways. In this work, a series of fatigue tests were performed on the rubber isolation layer to obtain the influence of stress amplitude and loading cycles on its fatigue performance. The results demonstrate a pronounced non-linear load–displacement relationship of the rubber isolation layer with increasing load, while the fatigue endurance significantly decreases with escalating the stress amplitude. Moreover, considering the hyperelastic properties of rubber material, the Mooney-Rivlin constitutive model was employed in finite element simulations. Subsequently, the stress distributions of the rubber isolation layer were analyzed, and the fatigue life was evaluated based on Luo stress method. The rubber isolation layer exhibits localized damage that does not affect the overall performance after 32 years of normal service condition. Therefore, the fatigue performance of the rubber isolation layer remains reliability, providing assurance for the application in ballastless tracks on high-speed railway long-span bridges.

Flexural performance and damage of reinforced fly ash and slag-based geopolymer concrete after coupling effect of freeze-thaw cycles and sustained loading

To better represent field conditions, the bending performance of reinforced geopolymer concrete (GPC) beams after the coupling effect of freeze-thaw cycling and sustained flexural load was investigated. Two types of GPC (G10 and G50) with different content of fly ash and slag were included and compared with ordinary Portland cement concrete (OPC). The mechanical strength of concrete and bond strength of rebars in concrete before and after freeze-thaw cycles were measured. It was found that the frost resistance of G10 was the weakest followed by OPC and G50. Three scenarios of bending tests on reinforced concrete beams were included: (1) control (without freeze-thaw damage); (2) individual freeze-thaw cycling; (3) coupling effect before bending. Rebound tests were conducted to evaluate frost damages at different areas of the beams as the base to analyze bending behaviors of the beams. The failure mode, load-displacement(strain) relationship, ultimate flexural strength, and bending stiffness of beams from bending tests are analyzed. All beams in scenario (1) were dominant in flexural failure. For scenario (2), G10 and G50 failed in debonding failure due to significant reduction in bond strength, while OPC failed in diagonal tension failure as OPC could sustain bond stiffness, thus preventing debonding failure. For scenario (3), damages in GPC were exacerbated, while damages in OPC were limited.

The Analytical Model and Horizontal Resistance of the Column-Head Dou-Gong in the Traditional Chinese Timber Structure

ABSTRACT To study the horizontal resistance of the column-head Dou-Gong (CHDG) in the traditional Chinese timber structure, the analytical model of CHDG without or with horizontal gap was proposed in this study. According to the structural form analysis of CHDG, the analytical model of CHDG considers the contact relationship between the components. CHDG has several distinct layers, of which the first layer is modeled as a rotation spring element and the second layer and above of CHDG are modeled as shear spring elements. Then, the horizontal resistance of CHDG was analyzed, and the horizontal load-displacement relationship of CHDG with horizontal gap appears triple polyline, while CHDG without horizontal gap is bilinear. Finally, the effects of parameters, including the length or width of Dadou bottom, height of Mantousun (MTS), width of horizontal gap, and vertical load, on the horizontal resistance was analyzed. The horizontal resistance of CHDG increases significantly with the length or width of the Dadou bottom, height of MTS, and vertical load increase, while the horizontal resistance of CHDG decreases significantly with width of horizontal gap increases.

Progressive damage analysis of embedment of metal washer into timber

ABSTRACT Metal washers are widely used in joints of timber structures. Thick washers embed fully into timber, whereas thin washers partially embed into timber due to their bending deformation. For thick washers, physical models have been proposed to estimate the stiffness and strength of timber. However, for thin washers, these estimation methods are insufficient. The objective of this study is to propose a finite-element analysis (FEA)-based approach to predict the stiffness and strength of wood during washer embedding, as well as forecast plasticity and damage behaviours of timber, regardless of the washer size. The FEA used a constitutive model with plastic and damage criteria for timber. In the FEA, an explicit dynamic solution method was used to prevent solution divergence. The FEA reproduced the embedment load–displacement relation and damage behaviours of three species. In addition, the FEA predicted the initial stiffness, second stiffness, and yield load with error margins of 12%, 16%, and 7%, respectively. The influences of the loading speed and mesh fineness on the FEA were investigated numerically to validate the results. In addition, parametric studies on contact stiffness and damage constants were conducted to understand the influences of material constants on the embedment behaviours of FE models.

A novel constitutive law of confined grouted rock bolt under pull-out load based on a fully nonlinear bond-slip model

Rock bolts are widely applied in deep underground excavations for rock reinforcement. Here, a constitutive model that quantifies the pull-out load-displacement relationship of the grouted rock bolt has been developed though theoretically analyzing the load transfer behaviour along the bolt-grout interface. An improved nonlinear continuously yielding criteria was employed as a bond-slip model where the role of confining pressure playing in slip was accounted. The performance of the proposed constitutive model was demonstrated by comparing with three sets of laboratory pull-out tests on the fully grouted rock bolts under different confining pressure levels (including a short-encapsulated pull-out test designed in our laboratory). The input parameters in the model were determinable within the laboratory environment. The analytical simulation results of pull-out load-displacement performance, the axial stress in the rock bolt and shear stress along the bolt-grout interface agreed well with the laboratory data. We also found that the confining pressure significantly affects the critical embedment length and the higher the confining pressure, the shorter the critical embedment length. The findings enrich the understanding on the mechanical properties of grouted rock bolts and hence aid the rock engineers in rock reinforcement design in underground excavations.

Moment redistribution in continuous reinforced concrete beams: Experimental study and analytical investigation

This paper presents the results of experimental and analytical studies carried out on continuous reinforced concrete (RC) beams to determine moment redistribution in statically indeterminate RC structures. For this purpose, continuous RC beams were produced with varying tensile reinforcement ratio at the intermediate support, which are shown as the parameters that affect moment redistribution the most in the literature. One of the main goals of this study is to check if the formulations in the design code provisions and in the literature give a safe estimate, and in order to perform this check, a dataset consisting of the experimental results of 141 beams in the literature has been used for validation and the moment redistribution ratios of this dataset have been estimated with all these formulations. The obtained results have been compared using various statistical indices such as the mean value (MV), standard deviation (SD), coefficient of variation (COV), the root mean square error (RMSE), mean absolute percentage error (MAPE). In particular, the formulations in the literature that take into account many parameters affecting the moment redistribution have been found to give better results than the formulations in the design code provisions. The results of this study confirm that elastic moment redistribution, which occurs in the process from the moment when the concrete cracks until the tensile reinforcement yields and constitutes a significant part of the total moment redistribution, is also important. Moreover, the properties of continuous RC beams related to their general behaviors, such as load-displacement relationships, ductility and moment-curvature relationships have been also investigated in detail.

Time-dependent soil–structure interaction analysis using a macro-element foundation model

The delayed settlement of foundations due to soil consolidation, creep or particle breakage can alter the internal load distribution and differential settlements in a superstructure through soil–structure interaction (SSI). The study introduces a novel methodology to simulate time-dependent SSI that overcomes the complexity of incorporating the time-dependent behaviour of foundations into routine SSI analysis. The proposed approach represents the superstructure as a condensed stiffness matrix, and replaces the foundations and underlying soils with macro-element foundation models that encapsulate the foundation–soil interaction into load–displacement relationships derived from constitutive models. To examine the performance of the proposed method, a macro-element model for time-dependent analysis of shallow foundations on sand was integrated with structural analysis to simulate two tests performed in a geotechnical centrifuge on a 3D-printed aluminium framed structure supported by footings on sand. The simulated responses of the superstructure and foundations were found to agree well with those observed in the centrifuge tests. Parametric analyses were conducted to investigate the effect of loading history, load level on the superstructure, and creep tendency of soil on post-construction load redistribution and differential settlements. The findings suggest that creep of foundations on sand facilitates load redistribution in the structure from heavily loaded sections to lightly loaded sections. Moreover, post-construction load redistribution depends on the differential creep between footings and should be considered for structures that are quickly constructed or at high levels of strength mobilisation (low factor of safety). Overall, the study highlights the potential of the proposed methodology in analysing the time-dependent SSI and its applicability in practical SSI analysis.

Experimental investigation on influence of vertical stirrup legs to shear failure behavior in RC beams

Conventional close stirrup has been widely used in RC beams to avoid shear failure behavior but the effect of internal vertical stirrup legs on the shear strength and the initiation of three-dimensional diagonal shear crack in RC beams is still debatable. In this study, three-dimensional crack evaluation was conducted to determine the shear failure mechanism of RC beams with different (two, three and four) vertical stirrup legs across beam width, with almost same stirrup contribution in design equation, using three-point loading test. The load displacement relationship, surface crack initiation and propagation, internal cracking patterns in cross section, vertical stirrup leg strain and concrete strain relationships, shear resistance components were discussed in detail. It was concluded that the presence of two equally spaced internal vertical stirrup legs with conventional close stirrup restricts the initiation and propagation of internal cracks to side surfaces of tested RC beams and influenced the shear strength.

The Stability of Corroded Circular Steel Tubes Under Axial Compression Investigated Through Testing, Finite Element Analysis and Theoretical Approaches

Circular steel-tube members are extensively used in various large-scale steel structures. The detrimental effects of corrosion on the ultimate bearing capacities of these structures require urgent attention. This study designed six circular steel tube specimens to explore the degradation pattern of the ultimate bearing capacity of corroded circular steel tubes under axial compression; three were subjected to accelerated corrosion by electrification, and the other three were used as the control group. Following the accelerated corrosion test, both groups of specimens were subjected to material-property and axial-compression tests. These tests provided data on the bearing capacity and midspan displacement of the corroded circular steel tubes, allowing for the construction of load–displacement relationship curves. The test results demonstrate that corrosion significantly affects the bearing capacity of circular steel tubes. As the severity of the corrosion increased, the bearing capacity and stiffness of the corroded circular steel tubes progressively weakened. To simulate the behavior of circular steel tubes, a numerical model was established that provided the ultimate bearing capacity under axial compression and generated load–displacement curves. The simulation results closely aligned with the test results. This study introduced a novel approach for accurately computing the stability-bearing capacity of circular steel tubes subjected to corrosion and axial compression. Comparative analyzes with test results validated the superior performance of the proposed method in accurately predicting the ultimate bearing capacity.

Experimental study and efficient shear-flexure interaction model of reinforced concrete shear walls with UHPC boundary columns

Traditional reinforced concrete (RC) shear walls have insufficient deformation capacity under strong earthquake conditions and are difficult to repair due to severe post-earthquake damage. Ultra-high performance concrete (UHPC) is a cement-based composite material with high strength and toughness, which can be applied to shear walls. Therefore, a new type of RC shear walls with UHPC boundary columns was proposed. A rectangular-shaped shear wall and two shear walls with barbell-shaped sections were tested under axial force and lateral cyclic load, and the effects of UHPC distribution, sectional shape and stirrup strength were studied. The hysteresis characteristics, ductility behavior, energy dissipation and stiffness degradation of all the specimens were analyzed and discussed. The test showed that the shear wall with UHPC boundary columns had good crack-width control ability and the damage degree was greatly alleviated even under large axial forces. The addition of UHPC could enhance the ductility and energy dissipation capacity of shear walls, especially for rectangular-shaped walls. Besides, an efficient shear-flexure interaction (SFI) model was developed for the shear walls and it could accurately capture the lateral load versus lateral displacement relationship and crack orientations. This nonlinear analysis model had fast calculation speed and effective results, with a prediction error of less than 5 % for peak loads.