Combined Axial Compression Loads Research Articles

More accurate design equations for cold-formed steel members subjected to combined axial compressive load and bending

Cold-formed steel (CFS) load-bearing members in multi-storey frame systems are subjected to combined actions sourced from gravity and lateral loads. However, limited information is available on the complex interaction behaviour of such elements affected by different buckling modes. This study aims to provide a better understanding of the behaviour and design of CFS sections under various combinations of compression and bending about both major- and minor-axes. Experimentally validated finite element (FE) models of CFS elements were developed in ABAQUS software, accounting for material nonlinearity and geometric imperfections. The validated models were then used to conduct a parametric study to assess the structural performance and failure modes of over 500 CFS elements with various lengths, thicknesses and cross-sectional dimensions under 19 different load eccentricities. It was demonstrated that the element and web slenderness ratios and the magnitude and direction of eccentricity are the key factors affecting the behaviour of the CFS beam–column elements. The accuracy of current design specifications, including American Iron and Steel Institute (AISI-S100), Australian/New Zealand Standard (AS/NZS-4600) and European standard (Eurocode-3) was then investigated. Subsequently, the results were used to propose a new design interaction equation as a function of element and web slenderness ratios. It was shown that the proposed equation could considerably improve the accuracy of the code strength predictions, especially in the case of medium to high slenderness elements. Finally, a reliability analysis was conducted within the framework of the AISI-S100 to ensure that the proposed design equation provides the required level of safety.

Underwater strengthening and repairing of tubular offshore structural members using Carbon Fibre Reinforced Polymers with different consolidation methods

Offshore structural steel members will need strengthening or repairing due to various reasons. Strengthening is often required due to work over demands or increased environmental loads. Repairing becomes essential as the steel members are usually severely corroded due to the marine conditions. Conventional hot work strengthening and repairing solutions become very expensive and retrofitting using Fibre Reinforced Polymers (FRPs) is an economical alternative. This paper investigates strengthening and repairing of offshore steel tubular members using Carbon Fibre Reinforced Polymers (CFRPs) with the help of experimental testing and an analytical study. Two different specimen sizes which were representative of members in offshore structures namely leg and brace were examined in the study. Partial length strengthening of steel tubular members subject to combined loading of axial compression and bending was carried out using different curing environments (in air and underwater curing). Strengthening and repairing of leg and brace specimens with multiple layers of CFRP retrofitted in underwater conditions were also investigated. Two different consolidation methods (underwater vacuum consolidation and underwater stricture consolidation) were compared with the help of full length strengthening of leg specimens. Although partial length strengthening proved to be less effective, partial length repairing of corroded tubular members were successful in restoring their intact capacity. Full length strengthening for underwater leg specimens were experimentally tested and it was found to improve the structural behaviour in many aspects like ultimate strength, load displacement behaviour, elastic slope, energy absorption, and ductility. A novel technique of underwater vacuum consolidation of retrofit laminates was demonstrated through a set of full length strengthened leg specimens. Underwater vacuum consolidation proved to be advantageous compared to the normal underwater stricture consolidation. An analytical check to identify whether a retrofitted tubular member would reach its target section properties was also introduced. Overall, the paper demonstrates multiple successful applications of FRP composites for underwater strengthening and repairing of offshore steel tubular members. Studies like this expanding the current knowledge on how the FRP retrofitted steel tubular behave within a real offshore structure are essential to increase the uptake of this technology in the oil and gas industry.

Seismic behavior of PVC-CFRP confined reinforced concrete columns: An experimental study

This paper presents an experimental study on the seismic behavior of PVC-CFRP confined reinforced concrete columns subjected to combined axial compression load and horizontal reversed cyclic loading. A total of six one-fourth scale PVC-CFRP confined reinforced concrete columns (PVC-CFRP) and two one-fourth scale PVC confined reinforced concrete columns (PVC) are fabricated. The flexural failure mode, which is characterized by the crushing of concrete and the yielding of longitudinal reinforcement, is found for all PVC-CFRP and PVC specimens. The effects of axial compression ratio and CFRP strip spacing on the secant stiffness, energy dissipation, etc. are investigated. The results show the secant stiffness decreases rapidly as the axial compression ratio increases, and the confining effect of the CFRP strip spacing on the secant stiffness evolution is more obvious for the specimen with higher axial compression ratio. The specimen with smaller CFRP strip spacing exhibits better energy dissipation capacity, and the strengthening effect of CFRP strips is more significant for the specimen with higher axial compression ratio. The effective CFRP strip spacing for the PVC-CFRP is suggested.

Flexural Strengthening of RC Columns with Low Longitudinal Steel Ratio using GFRP Bars

This research describes the results of an experimental work that aimed to investigate the flexural capacity of RC columns with low longitudinal reinforcement ratio that was strengthened with near surface mounted GFRP bars. The experimental program consisted of four square reinforced concrete columns, including one control specimen that were designed with a longitudinal reinforcement ratio below the minimum required ratio of 1% specified by RC design codes. Three of the four specimens were strengthened with different ratios NSM GFRP bar. The specimens were tested under a combined axial compressive load and lateral cyclic displacement to evaluate this retrofit method for the flexural improvement of RC columns. The efficacy of the proposed strengthening method on the flexural capacity, failure modes, hysteretic curves, energy dissipation capacity, and stiffness are discussed on the basis of the test results. The experimental results demonstrated that the contribution of GFRP bars to the flexural capacity of RC columns was significant. Also, an analytical procedure for calculating the bending moment capacity of RC columns strengthened with GFRP bars subjected to axial and lateral is proposed. The model accuracy is demonstrated by comparing the model predictions with the experimental results. The flexural capacity calculated by this method were in good agreement with the experimental results.

Stainless steel channel sections under combined compression and minor axis bending – Part 2: Parametric studies and design

Following the experimental study and finite element (FE) model validation described in the companion paper, numerical parametric studies and the evaluation of design provisions for stainless steel channel sections under combined axial compressive load and minor axis bending moment are presented herein. The parametric studies were carried out to generate additional structural performance data over a wider range of cross-section aspect ratios and slendernesses, loading combinations and bending orientations. The test data and numerical results have been carefully analysed to develop a comprehensive understanding of the structural performance of stainless steel channel sections under combined compression and minor axis bending moment, and to assess the accuracy of the existing design provisions in Europe and North America. Comparisons of ultimate loads from the tests and FE simulations with the codified resistance predictions revealed that the current design standards typically under-estimate the capacity of stainless steel channel sections under combined compression and minor axis bending moment; this is attributed primarily to the neglect of material strain hardening and the employment of conservative interaction formulae. Improved design rules featuring more efficient interaction curves, anchored to more precise end points (i.e. cross-section resistances under pure compression and bending moment), are then proposed and presented. The new design proposals are shown to yield both more accurate and more consistent resistance predictions over the existing design provisions. Finally, statistical analyses are presented to confirm the reliability of the new design proposals according to EN 1990.

Effect of Thermal Environment on Buckling of Thick Cylinder Subjected to Combined Axial Compressive and External Pressure loads

Buckling is a critical failure phenomenon in the columns and pressure vessels subjected to external pressure and axial compressive loads. Generally pressure vessels and submarines will subject to these type of loads and tends to buckle. According to formulation buckling load is the product of the buckling load multiplier and applied load. In the case of the cylinders the buckling load will be affected by many factors such as length, thickness, diameter, cross section and temperature etc. Typically fluids will be stored in the pressure vessels and then exposed to ambient environment or customized environment. In the present work real life conditions are applied as inner fluid temperature (T1), external convective heat transfer (h). Buckling load of cylinder subjected to combined axial compressive load and external pressure was studied by varying the length to thickness ratio(L/T), inner fluid temperature(T1), convection heat transfer co-efficient(h), ambient temperature(T2). Then the critical parameters which influence the buckling load multiplier are concluded.

12.08: Cross‐section stability of stainless steel channel sections subjected to combined loading

ABSTRACTThis paper presents a comprehensive experimental and numerical study of the cross‐section stability of stainless steel channel sections under combined axial compressive load and major axis bending moment. The experimental investigation included material coupon tests, initial geometric imperfection measurements and eight eccentrically loaded stub column (combined loading) tests, while the numerical modelling programme comprised a valiadtion study and a parametric study to generate further structural performance data. Both the experimental and numerical results were carefully analysed and then used to assess the accuracy of the current Eurocode design provisions for stainless steel channel sections subjected to combined loading. Generally, the Eurocode was found to result in unduly conservative and scattered strength predictions. Improved design rules have been proposed through extension of the deformation‐based continuous strength method (CSM) to the case of channel sections under combined loading. Comparisons between the proposal and the test and numerical results indicate a high level of design accuracy and consistency in the predictions. The reliability of the new proposal has also been confirmed by means of statistical analyses according to EN 1990.

Efficiency of glass-fiber reinforced-polymer (GFRP) discrete hoops and bars in concrete columns under combined axial and flexural loads

Abstract Discrete hoop reinforcement is preferable over continuous spiral reinforcement due to ease of construction in bridge applications. This research presents the experimental results of full-scale circular concrete columns reinforced with glass-fiber-reinforced-polymer (GFRP) bars and confined with GFRP discrete hoops subjected to combined axial compression loads and bending moments. The findings of the experimental work were integrated with a theoretical analysis based on the strain computability and force equilibrium to extend the parametric study. The lowest and highest bounds of the mechanical properties of GFRP reinforcement along with concrete strength and reinforcement ratio were employed. Sets of axial force–bending moment ( P-M ) interaction diagrams and indicative guide charts are introduced, and recommendations drawn. The compressive-strength contribution of GFRP reinforcement is reviewed and discussed. The results reveal that the GFRP bars developed compression and tension strains up to −0.003 and 0.008 at peak loads and up to −0.015 and 0.0135 at failure on the compression and tension sides, respectively. The confinement provided by GFRP discrete hoops (9.5 mm) spaced at 80 mm prevented the buckling of longitudinal GFRP bars up to and even past the peak load until failure occurred. Based on the experimental and theoretical results, the minimum GFRP longitudinal reinforcement ratio was found to be 1% in order to prevent tension failure (GFRP-bar rupture), provided that the mechanical properties comply with the limits of the available codes and standard.

Axial Load–Moment Interaction Diagram of Circular Concrete Columns Reinforced with CFRP Bars and Spirals: Experimental and Theoretical Investigations

AbstractNorth America’s current design codes and guidelines allow the use of fiber–reinforced polymer (FRP) bars as the primary reinforcement in concrete structures and provide design recommendations for using these bars. Because of a lack of experimental data, however, FRP bars have not been recommended for resisting compression stresses as longitudinal reinforcement in columns or compression reinforcement in flexural elements. This paper presents test results of an experimental program to investigate the structural performance of 10 full-scale circular concrete columns reinforced with carbon fiber–reinforced polymer (CFRP) bars and spirals subjected to combined axial compression loads and bending moments. The test variables include different eccentricity-to-diameter ratios and two types of reinforcement (CFRP and steel). The test results show that the CFRP- and steel-reinforced concrete columns behaved similarly up to their peak loads. The failure of the test specimens under different levels of eccentri...

Buckling of non-homogeneous orthotropic conical shells subjected to combined load

The buckling analysis is presented for non-homogeneous (NH) orthotropic truncated conical shells subjected to combined loading of axial compression and external pressure. The governing equations have been obtained for the non-homogeneous orthotropic truncated conical shell, the material properties of which vary continuously in the thickness direction. By applying Superposition and Galerkin methods to the governing equations, the expressions for critical loads (axial, lateral, hydrostatic and combined) of non-homogeneous orthotropic truncated conical shells with simply supported boundary conditions are obtained. The results are verified by comparing the obtained values with those in the existing literature. Finally, the effects of non-homogeneity, material orthotropy, cone semi-vertex angle and other geometrical parameters on the values of the critical combined load have been studied.

Sensitivity analysis on the elastic buckling and ultimate strength of continuous stiffened aluminium plates under combined in-plane compression and lateral pressure

In this paper, the results of an investigation into the post-buckling behaviour of high-strength aluminium alloy stiffened plates subjected to combined axial compression load and different magnitudes of lateral pressure using non-linear finite element approach is presented. Both material and geometric non-linearities have been taken into account. The principal variables studied are the plate thickness, boundary conditions and the stiffener geometries beside the geometrical imperfection, the width of the welding heat-affected zone (HAZ) and welding residual stresses. The influence of these variables on the post-buckling behaviour and ultimate strength of such stiffened plates has been investigated in details.

Stability of single-walled carbon nanopeapods under combined axial compressive load and external pressure

In this paper, the axial stability of single-walled carbon nanopeapods is studied based on an elastic continuum shell model. In order to model the non-bonded van der Waals interactions between host carbon nanotube and guest fullerenes, an equivalent pressure distribution is proposed and incorporated in the model. Deriving an explicit equation for the determination of critical axial load, it is concluded that the axial stability of a single-walled carbon nanopeapod is less than that of a carbon nanotube under otherwise identical conditions. In addition, it is shown that applying external pressure to the carbon nanopeapod decreases the axial compressive stability through reducing the critical axial load and any increase in the external pressure appears to further weaken the carbon nanopeapod under axial loading.

Buckling and postbuckling of anisotropic laminated cylindrical shells under combined axial compression and torsion

Abstract A postbuckling analysis is presented for an anisotropic laminated cylindrical shell of finite length subjected to combined loading of axial compression and torsion. The governing equations are based on classical shell theory with von Karman–Donnell-type of kinematic nonlinearity and including the extension–twist, extension–flexural and flexural–twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells for different values of load-proportional parameters. The results show that the postbuckling characteristics depend significantly upon the load-proportional parameter. The results reveal that in combined loading cases the postbuckling equilibrium path is unstable and the shell structure is imperfection-sensitive.

Fatigue behavior of Ilizarov frame versus tibial interlocking nail in a comminuted tibial fracture model: a biomechanical study

BackgroundTreatment options for comminuted tibial shaft fractures include plating, intramedullary nailing, and external fixation. No biomechanical comparison between an interlocking tibia nail with external fixation by an Ilizarov frame has been reported to date. In the present study, we compared the fatigue behaviour of Ilizarov frames to interlocking intramedullary nails in a comminuted tibial fracture model under a combined loading of axial compression, bending and torsion. Our goal was to determine the biomechanical characteristics, stability and durability for each device over a clinically relevant three month testing period. The study hypothesis was that differences in the mechanical properties may account for differing clinical results and provide information applicable to clinical decision making for comminuted tibia shaft fractures.MethodsIn this biomechanical study, 12 composite tibial bone models with a comminuted fracture and a 25 mm diaphyseal gap were investigated. Of these, six models were stabilized with a 180-mm four-ring Ilizarov frame, and six models were minimally reamed and stabilized with a 10 mm statically locked Russell-Taylor Delta™ tibial nail. After measuring the pre-fatigue axial compression bending and torsion stiffness, each model was loaded under a sinusoidal cyclic combined loading of axial compression (2.8/28 lbf; 12.46/124.6 N) and torque (1.7/17 lbf-in; 0.19/1.92 Nm) at a frequency of 3 Hz. The test was performed until failure (implant breakage or ≥ 5° angulations and/or 2 cm shortening) occurred or until 252,000 cycles were completed, which corresponds to approximately three months testing period.ResultsIn all 12 models, both the Ilizarov frame and the interlocking tibia nail were able to maintain fracture stability of the tibial defect and to complete the full 252,000 cycles during the entire study period of three months. A significantly higher stiffness to axial compression and torsion was demonstrated by the tibial interlocking nail model, while the Ilizarov frame provided a significantly increased range of axial micromotion.ConclusionThis is the first study, to our knowledge, which compares the biomechanical properties of an intramedullary nail to an external Ilizarov frame to cyclic axial loading and torsion in a comminuted tibia shaft fracture model. Prospective, randomized trials comparing Ilizarov frames and interlocked tibial nails are needed to clarify the clinical impact of these biomechanical findings.

Experimental and Analytical Modeling of Concrete-Filled Fiber-Reinforced Polymer Tubes Subjected to Combined Bending and Axial Loads

This paper presents test results of an experimental program, and proposes an analytical model to describe the behavior of concrete-filled, fiber-reinforced polymer (FRP) tubes subjected to combined axial compression loads and bending moments. The experimental program included 10 specimens subjected to eccentric axial loads, 2 specimens tested under concentric axial loads, and 2 specimens tested in bending. Glass FRP tubes with 2 different laminate structures were considered, and axial load/bending moment interaction curves are given. An analytical model is presented that accounts for variable confinement of concrete as a result of the gradual change of the biaxial state of stresses developed in the tube as the eccentricity changes. A parametric study was conducted to evaluate effects of diameter-to-thickness ratio and laminate structure of the tube, including different fiber proportions in the axial and hoop directions. The study evaluated the confinement as affected by the eccentricity of the applied axial load as well as the influence of the FRP laminate structure. Findings indicate that the interaction curves are significantly affected by both the laminate structure and diameter-to-thickness ratios of the tubes.

The effects of hygrothermal conditions on the postbuckling of shear deformable laminated cylindrical shells

The effect of hygrothermal conditions on the buckling and postbuckling of shear deformable laminated cylindrical shells subjected to combined loading of axial compression and external pressure is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling is extended to the case of shear deformable laminated cylindrical shells under hygrothermal environments and a singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behaviour of perfect and imperfect, moderately thick, cross-ply laminated cylindrical shells under different sets of environmental conditions. The results show that the hygrothermal environment has a significant effect on the interactive buckling load as well as postbuckling response of the shell. In contrast, it has a small effect on the imperfection sensitivity of the shell with a very small geometric imperfection.

Ultimate load behaviour of welded thin-walled stub columns under combined loading of axial compression and bending

This paper describes a theoretical study on the post-buckling behaviour and ultimate strength of the welded thin-walled box-section and I-section stub columns under combined loading of axial compression and bending at the ends. A large-deflection elastic-plastic spline finite strip method associated with a more rigorous multi-layer integration is developed to analyse such a problem. Initial imperfections including the residual stresses and initial deflections of plate elements are considered. An iterative numerical procedure combining a modified arc-length method and Newton-Raphson iteration is presented to predict a complete load-deflection curve of the stub column. The analytic results obtained by the spline finite strip method is presented in the form of interactive diagrams for typical values of plate slenderness ratios. Comparison with the experimental results previously published is made and good agreement is obtained between both results [A. J. Davids and G. J. Hancock, J. Struct. Engng, ASCE 112, 960–976 (1986)].

Ultimate load behaviour of box-columns under combined loading of axial compression and torsion

This paper describes a study of the theoretical and experimental behaviour of box-columns of varying b/t ratios under loadings of axial compression and torsion and their combinations. Details of the testing rigs and the testing methods, the results obtained such as the load-deflection curves and the interaction diagrams, and experimental observations regarding the behaviour of box-models and the types of local plastic mechanisms associated with each type of loading are presented. A simplified rigid-plastic analysis is carried out to study the collapse behaviour of box-columns under these loadings, based on the observed plastic mechanisms, and the results are compared with those of experiments.

Axially Loaded Sandwich Panels

In recent years there has been a dramatic increase of interest in sandwich cladding panels consisting of metal faces and a rigid foam core. Previous studies have concentrated on the behavior of these panels when subject to bending action due to wind and snow load and under temperature gradient. Comparatively little is known about their behavior under axial compressive load when acting as load‐bearing wall panels. This paper first considers appropriate methods of analysis for sandwich panels subject to combined axial compressive load and bending moment and an exact finite element is derived. Some early and previously unpublished tests are described and the results compared with the theoretical values. It is concluded that great care must be taken in the design of load bearing wall panels because of the interaction between local and global buckling and their sensitivity to eccentricity of load.

Generalized Design of Columns Subjected to Combined Axial Load and Bending Moment

The design of wide-flange steel columns subjected to combined axial compression load and bending moment according to the AISC Manual of Steel Construction involves a trial-and-error procedure. In this method the applied bending moment is converted to an equivalent axial load by using a bending factor. This allows the selection of a trial section from the AISC Column Tables. Then, using the modified AISC interaction formulas, the required axial tabular load can be determined. From this load, another trial section is selected, and the procedure is repeated until a satisfactory section is obtained. The selected section must be checked for compliance with the AISC Formulas (1.6-1a), (1.6-1b), and (1.6-2). This process is often tedious and time consuming and is not efficient for usage in the design office. Several methods have been presented which tend to simplify the AISC design procedure for columns subjected to combined axial load and bending moment. These methods either modify the AISC column interaction equations to minimize the number of trials used in selecting the final section, or present design charts, graphs, and tables. This paper provides a rapid selection of steel wide-flange columns subjected to combined axial compression load and bending moment about the strong axis of the member, in compliance with the AISC Specification.