Load-shortening Curves Research Articles

Axially-compressed behavior of carbon-FRP strengthening CFT short columns having circumferential void defects

To clarify the viability of externally bonding carbon-fiber-reinforced polymer (FRP) for strengthening the structural integrity of concrete-filled steel tube (CFT) short columns having circumferential void defects, this study comprehensively explores the strengthening effectiveness of various wrapping parameters (i.e., carbon-FRP strength, wrapping layers, and wrapping ratio) on the axially-compressed CFT short columns with various void ratios, material strengths, and geometric parameters by numerical method. Detailed mechanical responses, encompassing failure patterns, load-shortening (N-Δ) curves and stress distribution, are delved to reveal the strengthening mechanisms. Finally, strength prediction formulas for these composite columns are proposed rooted in the ring extension and local force transmission theories. Results show that the presence of initial voids delays the occurrence of steel-concrete contact stress (p) and weakens the p-value at peak load, thus reducing the axial resistance of column. Particularly when the void ratio exceeds 0.2%, the longitudinal strain when the concrete contacts with outer tube is beyond the concrete's peak compressive strain, thus the shape of the N-Δ curve is obviously changed, exhibiting two peaks. Externally bonding carbon-FRP strips can obviously improve the peak load of the column with a void ratio ≤ 0.2%. If the void ratio exceeds 0.2%, externally bonding carbon-FRP strips can also improve the column's second peak load, even exceeding the strength of pure CFT column, while it has no effect on the first load. The formulas proposed herein have a satisfactory accuracy based on the tested validation, which are expected to guide the design of strengthening scheme in engineering.

Behavior of CA-UHPC filled circular steel tube stub columns under axial compression

Ultra-high performance concrete with coarse aggregate filled steel tube (CA-UHPCFST) is a sustainable and high-performance structural form with high carrying capacity. This paper presents experimental and numerical investigations on the axial compressive behavior of circular CA-UHPCFST stub columns. Forty-four specimens were tested to determine the effects of concrete strength, steel fiber content, steel tube thickness, and steel yield strength on the axial compressive behavior. A finite element (FE) model was developed and validated for composite action analysis between steel tube and concrete core. The results show that the failure modes of CA-UHPCFST stub columns depend on confinement coefficient (ξ) categorizing as shear failure (ξ < 0.9) and bulge failure (ξ > 1.4). Correspondingly, as the confinement coefficient grows, the load-shortening curve after the ultimate resistance demonstrates three categories: descending, plateau, or hardening stage. The steel tube exhibits a prominent confinement effect on the CA-UHPC core, with a strength index ranging from 1.066 to 1.225; however, the enhancing effect is not as significant as that of the ordinary concrete-filled steel tubes. The incorporation of steel fiber can improve the ultimate resistance, but has a limited effect on strength index. By comparing the measured ultimate resistances to the predictions, the feasibility of current design codes for the prediction of load carrying capacity is evaluated, and a simplified model is proposed to predict the ultimate resistance of circular CA-UHPCFST stub columns under axial compression.

Compression behaviours of CFSTs using stainless-steel tubes at low temperatures

This paper made pilot studies on behaviours of concrete-filled stub square stainless-steel tubes (CFSSSTs) subjected to low-temperature compression. Firstly, 16 CFSSSTs were tested under low-temperature axial compression. This testing program studied the effects of testing temperature (T) and SS-tube wall thickness (t). The tests showed that local buckling, corner-region splitting fracture, and concrete crushing occurred to CFSSSTs. The compressive load-shortening curves behaved a four-stage manner, which behaved differently from those hollow stainless-steel tubes (HSSTs). Compared with the common concrete-filled steel tube columns, the CFSSSTs exhibit a higher ductility. Studies showed that reducing T improved the compression capacity (Pu) but compromised the ductility of CFSSSTs; increasing the t of HSSTs improved the compression behaviour of CFSSSTs; filling concrete to the HSSSTs significantly improved the compression behaviour of CFSSSTs. This study also developed 3D finite element models (FEM) for the CFSSSTs using the low-temperature mechanical properties of both HSSTs and concrete, which accurately predicted compression behaviours of CFSSSTs at low temperatures. Moreover, the prediction equations in different codes were also adopted to predict the low-temperature Pu of CFSSSTs. Validations showed that these code equations provided about 15% underestimations on Pu, and they were recommended to predict Pu of CFSSSTs at low temperatures.

Analytical and experimental investigation on axial compression capacity of carbon fiber-reinforced plastic-confined concrete-filled double-skin steel tube stub columns

Concrete-filled double-skin steel tubes (CFDSTs) are widely used in civil engineering. During the service life of CFDSTs, their bearing capacity can be easily weakened by the corrosion of outer steel tubes. This study investigated the interaction mechanism and reinforcement effects of carbon fiber-reinforced plastic (CFRP)-confined CFDSTs under axial compression. Typical failure modes, axial load-shortening curves, and axial load-strain behaviors of CFDST and CFRP-confined CFDST (CFRP-CFDST) specimens were obtained. The test results showed that the ultimate bearing capacity of stub columns with concrete strength of C40 and C60 increased by 19.78% and 15.12%, respectively, when wrapped with two layers of CFRP sheets, and by 41.60% and 37.99%, respectively, when wrapped with four layers of CFRP sheets. In addition, the FE modeling of CFRP-CFDSTs was established and validated by experimental results. On this basis, the parametric analysis was conducted. To avoid local buckling and yield failure of the inner steel tubes before the outer steel tubes, a calculation formula was proposed for predicting the minimum wall thickness of the inner tube. Furthermore, the prediction formulas for the bearing capacity of CFDSTs and CFRP-CFDSTs were proposed.

Post-buckling analysis of axially loaded two-dimensional quasicrystal cylindrical shells with initial geometric imperfection

In this paper, the nonlinear post-buckling analysis of imperfect two-dimensional quasicrystal cylindrical shells is performed. The nonlinear governing equations are established by considering initial geometric imperfection, higher-order shear deformation theory and phonon-phason fields coupling effect. The load-shortening curves and buckling modes are obtained by the Galerkin’s method. Numerical results are compared with the existing results and excellent agreements are obtained. Effects of geometrical parameters, initial imperfection and phonon-phason fields coupling effect on the critical load and imperfection sensitivity of two-dimensional quasicrystal cylindrical shells are discussed in detail.

Numerical investigation on the ultimate strength behaviour and assessment of continuous hull plate under combined biaxial cyclic loads and lateral pressure

The ultimate strength of continuous hull plate under combined biaxial cyclic loads and lateral pressure is investigated in the present paper by using nonlinear finite element method. Geometric nonlinearity due to large deflection and material nonlinearity induced by kinematic hardening and isotropic hardening are both accounted for. A parametric study is designed and completed to examine the longitudinal ultimate compressive strength behaviours in the cycles on the basis of a large number of load-shortening curves. Effects of series of parameters especially the plate slenderness ratio, transverse cyclic compression, lateral pressure and cycle number are analyzed with details. It is found that the strength characteristic and collapse mode are highly affected by the coupling influence of the mentioned factors as well material behaviours. A dimensionless unified formulation as a function of the decisive factors is empirically proposed to accurately assess the ultimate strength of continuous hull plate in various cycles.

Experimental and numerical studies on the axial compression performance of hexagonal stiffened CFDST stub columns

In this paper, the authors conducted sixteen axial compressive tests on the hexagonal ultra-high performance concrete-filled steel tubular stub columns. The parameters studied in this research program included the cross-sections, section width, the steel tube thickness, and the hollow ratio. Based on the experimental results, the failure modes, axial load-shortening curves, composite strength, and ductility coefficient of the column were illustrated and discussed. The results indicated that stiffeners can significant delay the local bucking of steel tube and improve the interaction between the ultra-high performance concrete (UHPC) and the steel tubes. To simulate the mechanical response of these new types of columns, the authors developed a fiber-beam model (FBM) including the local buckling of steel tubes and the confinement effect. Then, the authors conducted a parametric study to discuss the influence of the hollow ratio, the steel tube thickness, and the strength of steel and concrete. Finally, the authors proposed a new method for predicting capacity and verified it against the test/numerical results. With the comparison of the design rules recommended by the current design codes, the new method proposed in this paper showed a good agreement with the test/numerical results. It can provide a reference for related engineering design.

Compressive behavior of CFRP-confined concrete-filled double-skin stainless-steel tube stub columns

The axial compression behavior of CFRP-confined concrete-filled double-skin stainless-steel tube (CFDSST) stub columns were investigated through experiments and FE modeling in this study. The typical failure modes, axial load–shortening curves, and strain responses of CFDSST and CFRP-confined CFDSST specimens were determined. The test results showed that CFRP could effectively restrain the local buckling and evidently enhance the compression behavior of the specimens. FE models of the CFRP-confined CFDSST stub columns were established and then validated by comparing with the experimental results. On this basis, FE modeling was used to perform parametric studies. To avoid the local buckling and yield failure of the inner steel tube prior to that of the outer stainless-steel tube, a design model was suggested to calculate the minimum thickness and yield strength of the inner tube. Furthermore, to evaluate the ultimate bearing capacity of the CFRP-confined CFDSST stub columns, a prediction model based on the superposition principle was suggested. The calculation results of the prediction model were consistent with the test and FE results.

Axial compression behavior of stub square concrete-filled steel tubes with regional defect

This paper investigated the axial compression behavior of stub square concrete-filled steel tubes with simulated local corrosion damage through a series of tests. The local corrosion damage was simulated by machining a regional defect on the tube. Aiming at the test specimens, the noteworthy observations were recorded, the load-shortening curves were developed, and the influence of the defect dimensions on the compressive performance of the specimens was discussed. The results revealed that the local defect on the steel tube can lead to the loss of confinement on the core concrete and the centroid offset of the specimen. Therefore, the increase in the defect sizes decreased the ultimate resistance of the specimen. When the local defect sizes reached 150 mm (length) × 112.5 mm (width) × 3.5 mm (depth), the ultimate resistance and the ductility of the specimen decreased to 88.2 % and 65.8 % of the intact specimens, respectively. Furthermore, based on the experimental study and the theoretical analysis, with consideration of the cross-sectional area loss and the confinement loss, a method was proposed to predict the ultimate resistance of the specimens with the local defect, which also can be adopted to evaluate the residual resistance of the locally corroded members in service.

Uncertainty Of Ship Hull Girder Ultimate Strength in Longitudinal Bending

The engineering modelling of ship hull girder strength usually consists of global and local levels. The Smith-type progressive collapse method is a typical example of this kind, in which the global model requires input from the local model with the underpinning local structural behaviour, i.e., load-shortening curve (LSC). However, the modelling is prone to uncertainty due to the statistical variability of the basic variables (aleatoric uncertainty) and the inadequacy of engineering models in both global and local levels (epistemic uncertainty). The former can be well tackled by a probabilistic sampling, whereas dealing with the latter for ship hull girder strength lacks an established approach. There can be different sources of epistemic uncertainty. In the modelling of ship hull girder strength, this may be partially manifested as that caused by different choices of local engineering models for predicting the LSC. In the light of this, a probabilistic method is applied in this research to investigate and quantify the uncertainty related to the local models. The adopted approach is a hybrid method incorporating the Smith-type progressive collapse method with Monte-Carlo Simulation and an adaptable LSC algorithm. Case studies on four merchant ships show that the ultimate strength in sagging is subjected to the most significant computational uncertainty as compared with those in hogging and horizontal bending. In a bi-axial load case, the computational uncertainty estimated for vertical bending will be counteracted as the horizontal bending increases. Nevertheless, this change is not directly proportional to the bi-axial load component ratio and appreciably varies between different ship types. The insights and data provided by this study may eventually resolve the epistemic uncertainty in the modelling of ship hull girder strength. It would also be useful to improve the ultimate limit state-based reliability analysis with regards to the strength model uncertainty evaluation.

Axial compression behavior of CFRP-confined square concrete-filled double skin tube stub columns with stainless steel outer tube

Concrete-filled double skin tube (CFDST) stub columns with a stainless steel outer tube is a new kind of composite columns and potential to be widely utilized in ocean engineering owing to the excellent performance characterized by high corrosion resistance. To improve the ultimate bearing capacity and delay the local buckling of stainless steel tube, confining materials such as carbon fiber reinforced polymer (CFRP) can be adopted in these composite columns. Thus, this study conducted an experimental investigation on the axial compression behavior of CFRP-confined square CFDST stub columns with a stainless steel outer tube. The main variables were the width-to-thickness ratio of stainless tube and the number of CFRP layers. The typical failure modes, load-shortening curves, and load-strain curves of the CFDST and CFRP-confined CFDST columns were obtained. The test results indicated that the local buckling of CFDST columns can be well suppressed with CFRP wrapping, prior to CFRP rupturing. The CFRP can provide an effective confinement on the sandwich concrete and the ultimate bearing capacity enhancement increased with increasing the number of CFRP layers. Based on theoretical analysis a design model for the inner steel tube has been proposed to prevent the premature failure of the inner steel tube which can leads serious ultimate bearing capacity lose. Additionally, new methods for predicting the ultimate bearing capacity of the square CFDST and CFRP-confined CFDST are proposed based on the limit equilibrium method and twin shear unified strength theory. The predicted results are in good agreement with the experimental results and collected test data.

Post-buckling of two-dimensional decagonal piezoelectric quasicrystal cylindrical shells under compression

In this paper, a new theoretical model for post-buckling of two-dimensional decagonal piezoelectric quasicrystal (2D decagonal PQC) cylindrical shells under axial compression is proposed. The nonlinear post-buckling equations are established based on the high-order shear deformation theory and phonon-phason-electric coupling effect. A series of new displacement functions for both symmetric and asymmetric post-buckling modes are proposed to enhance the Galerkin's method. Therefore, the load-shortening curves with mode-jumping phenomenon and post-buckling deformations are accurately solved. Numerical results are compared with existing solutions and found to be in good agreement. A parametric study of geometrical parameters, phonon-phason-electric coupling effect and applied electric voltage on the post-buckling of two-dimensional piezoelectric quasicrystal cylindrical shells is carried out also. The results show that the geometrical parameters have a significant influence on both the post-buckling equilibrium paths and post-buckling deformations while the phonon-phason coupling effect and piezoelectric effect only lead to a shift in the post-buckling equilibrium path.

Postbuckling and secondary buckling of rectangular fiber-metal laminates and glass-fiber reinforced composites under uniaxial compression

This article deals with the postbuckling and secondary buckling response of simply supported and clamped rectangular fiber-metal laminates (FMLs) and glass-fiber reinforced composite plates subjected to uniaxial compression. A novel FEM procedure is proposed in order to locate their secondary buckling point. The procedure is validated by comparisons with established literature results.Using validated FEM models, diagrams of the secondary buckling coefficient versus the plate aspect ratio are constructed. It is found that the secondary buckling load strongly depends on the aspect ratio. New analytical formulas are also derived for the approximation of the postbuckling load-shortening curves of the FMLs.

Mechanical Performance of Circular Ultrahigh-Performance Concrete–Filled Double Skin High-Strength Steel Tubular Stub Columns under Axial Compression

This paper proposed a new type of stiffened circular ultra-high performance concrete-filled double skin steel tubular (UHPCFDST) column, in which stiffeners were applied to connect both inner and outer steel tubes. It efficiently delayed the local buckling of steel tubes and enhanced the integral of the section. This new type of UHPCFDST can be named multicells ultra-high performance concrete-filled double skin steel tubular (MUHPCFDST) column since the stiffener divided the sandwich space between the two steel tubes into multicells. Both the UHPCFDST and MUHPCFDST stub columns were fabricated and tested under centrally compression loading to investigate the axial mechanical behavior. The parameters considered in this study included specimen size, diameter-to-thickness ratio, the quantity of stiffener, and hollow ratio. Based on the tests, specimens’ column failure mode, axial load-shortening curves, local buckling behavior, compounding strength, strength index, and ductility coefficient were obtained and discussed. Then, the authors proposed a uniaxial stress-strain function of ultra-high performance concrete under compression and established three-dimension finite-element (FE) models with this stress-strain model to simulate the axial behavior of UHPCFDST and MUHPCFDST columns. Compared with the experimental results, the average deviation of the FE analysis in predicting the column bearing capacity and corresponding axial shortening was −3% and −5.5%, respectively. Finally, parametric studies were carried out, and a calculation method was proposed. The parametric analysis results and predictions from different methods (including the proposed method and methods suggested by existing design codes) were compared. The proposed method and calculating methods provided in AIJ-2008, EC4, and AS/NZS 2327 can reasonably predict the ultimate bearing capacity of both circular UHPCFDST and circular MUHPCFDST columns.

Prediction of the load-shortening curve of CFST columns using ANN-based models

Artificial neural network (ANN) as a machine learning (ML) technique has been successfully applied in engineering applications such as structural dynamics and structural design. It has also received considerable attention for the design of concrete-filled steel tube (CFST) columns. However, the application of ANN method to CFST columns is mainly restricted to the prediction of the ultimate strength. In this paper, a novel approach to predict and plot the complete axial load-shortening curve of concentrically loaded rectangular and circular CFST columns using ANN method is presented. To train the networks, a database including 392 test results of rectangular and circular CFST columns with their corresponding data points of the load-deflection curves is compiled. In addition, 1152 finite element models (FEMs) are generated and analysed using ABAQUS to expand the training data and address data gaps in the experimental database. The validity of the developed FEMs is verified by experimental data. Based on the trained ANN models, a MATLAB-based graphical user interface (GUI) is also developed to provide a convenient tool for users to predict and plot the axial load-shortening response of rectangular and circular CFST columns. Using the developed GUI, a parametric study is also conducted to verify the accuracy of the ANN models in predicting the behaviour of CFST columns fabricated with different geometric and material properties. The results show that the developed ANN models can accurately predict the load-deflection response of CFST columns.

Compression-after-impact effect on postbuckling behavior of thermoplastic composite laminated plates

This paper investigates the postbuckling behavior of carbon fiber reinforced thermoplastic composite (CFRTPC) laminated plates under uni-axial compression-after-impact (CAI). A physical model is proposed where both internal damage and local geometric imperfection of the plate caused by impact are taken into account. The distributed damage and impacted region of the plate are determined by using X-ray computed tomography analysis. An experiment-based approach is utilized to obtain the nonlinear constitutive law along with the stiffness degradation for the CFRTPC laminated plates. The experiments for two CFRTPC laminated plates under uni-axial compression-after-impact are carried out firstly. Then the experimental data are compared with finite element numerical results to validate the present method. The numerical results reveal that the postbuckling load-deflection curves of CFRTPC laminated plates under CAI are significantly influenced by the initial local geometric imperfection, impact point position, plate width-to-thickness ratio and boundary conditions. In contrast, the initial local geometric imperfection and impact point position only have a small effect on the postbuckling load-shortening curves of CFRTPC laminated plates under CAI.

Axial behaviour of square stub CFST columns strengthened with square steel tube and HPC jacket

This study examines the performance of 26 concrete-filled steel tube square stub columns strengthened with square steel tube and concrete jacket, 21 steel tubes were infilled with high-performance concrete (HPC) jackets and 5 were infilled with ordinary concrete (OC). The test results of the failure modes, load–axial shortening curves, ductility index, and strain analysis revealed that no evident effect was observed on the load-bearing capacity when steel fibre-reinforced concrete (SFC) or self-stressing concrete (SSC) alone was used; however, an enhancement was achieved with the combination, i.e., steel fibre-reinforced self-stressing concrete (SFSSC). The results also indicated that SFC demonstrated a positive effect on ductility, whereas SSC decreased the deformation capacity. A finite element model was established for further analysis of retrofitted columns and comparison of the failure modes and load-shortening curves with the experimental results. The model was used to analyse the confinement of the concrete jacket and inner concrete. The curves of the load on the components indicated that the contribution of the concrete jacket to the peak load was lower than that of the outer tube owing to the uneven confinement effect, and the different types of concrete jackets only affected the load they bore. Based on the numerical database, equations for predicting the ultimate strengths of retrofitted columns with OC were proposed. A coefficient related to SSC was considered in the equations for predicting the capacities of columns with HPC. The calculated results showed good agreement between the experimental and numerical results.

Analytical model for circular high strength concrete filled steel tubes under compression

It is well known that the effect of confinement in concrete filled steel tube (CFST) can enhance the axial compressive strength of the concrete core. The confining pressure is a key issue to determine the compressive strength of concrete while the development of confining pressure is related to the lateral responses of steel tube and concrete core. This paper firstly presents a review on the lateral behaviour of circular CFST and existing lateral-axial strain models for concrete. These models are assessed by the authors’ previous experimental observations. Assessment results reveal deficiencies of current lateral-axial strain models, especially on the CFST with high strength concrete. A modified lateral-axial strain model for both normal and high strength concrete core in CFST was then proposed to accurately capture the interaction behaviour of the steel tube and the concrete. An analytical model of CFST with uniformly confined concrete core (i.e. with circular section) was then proposed to capture the development of confining pressure in CFST. A reduction factor was considered when the high strength concrete was used. The proposed analytical model can well predict the load bearing capacity, load-shortening curve, axial strain-lateral strain relationship of CFST with normal and high strength concrete.

An adaptable algorithm to predict the load-shortening curves of stiffened panels in compression

ABSTRACT An adaptable algorithm is proposed in this study, which can predict the complete load-shortening curve of a stiffened panel subjected to uniaxial longitudinal compression. The algorithm provides an extension to existing empirical formulae initially derived for predicting the ultimate compressive strength of stiffened panels. Based on observations from a series of nonlinear finite element analyses, the compressive load-shortening behaviour of stiffened panels is idealised with a linear pre-collapse response, an arc-shaped nonlinear ultimate collapse region and an asymptotic post-collapse decay. The algorithm allows direct modification of the elastic stiffness, ultimate strain, ultimate strength and post-collapse characteristics of the load shortening curve. This enables the load shortening curve to incorporate characteristics specific to the type of stiffened panel under analysis. The capability of the algorithm is demonstrated through an application with the simplified progressive collapse method to calculate the ultimate ship hull strength of four merchant ships and one naval vessel.

Behaviour and design of high-strength concrete-filled rectangular ferritic stainless steel tubular (CFFSST) short columns subjected to axial compression

Concrete-filled stainless steel tubes (CFSSTs) are increasingly applied in current composite structures owing to their excellent performance characterized by aesthetic appearance, high corrosion resistance and durability, and ease of maintenance. Compared with austenitic and duplex stainless steels, ferritic stainless steels have not or contain very low nickel content, achieving lower and more stable material costs. This provides a more viable alternative for structural applications. Additionally, it has been used successfully in corrosive marine environment in a few countries, such as South Africa. However, structural applications of concrete-filled ferritic stainless steel tubular (CFFSST) columns are still limited owing to the dearth of performance data and design guidance. To understand their structural behaviour and to include relevant design recommendations in current design specifications, this paper aims at investigating the compressive behaviour of axially loaded rectangular CFFSST short columns using the nonlinear finite element (FE) modelling. The FE models are developed using ABAQUS software, where two different material constitutive models for the flat and corner portions of the rectangular ferritic stainless steel tubes are incorporated. Close agreement is found between the outputs of FE analysis and existing test results with respect to the failure modes, cross-sectional strengths and axial load-shortening curves. Parametric analysis is then conducted to ascertain the impacts of key variables on the compressive behaviour of the studied CFFSST columns. The obtained numerical results as well as available test results are employed to evaluate the feasibility of current design specifications to design the examined CFFSST columns. Finally, a novel strength design model is proposed and shown to achieve a higher degree of accuracy and consistency of the design predictions.