Combined Axial Loading Research Articles

Structural performance of stainless steel circular hollow sections under combined axial load and bending – Part 2: Parametric studies and design

This paper reports the second part of the study on the structural behaviour of stainless steel circular hollow sections subjected to combined axial load and bending moment. A series of numerical parametric studies is presented, using the validated finite element (FE) models from the companion paper, with the aim of generating further structural performance data over a wider range of stainless steel grades, cross-section slendernesses and combinations of loading. The considered parameters include the outer cross-section diameter, the ratio of outer cross-section diameter to thickness and the initial loading eccentricity. Both the experimentally and numerically derived section capacities were compared with the strength predictions determined from the current European code, the American specification and the Australian/New Zealand standard, allowing the applicability of each codified method to be assessed. The comparisons revealed that the current design standards generally result in unduly conservative and scattered strength predictions for stainless steel circular hollow sections under combined loading, which can be primarily attributed to the neglect of strain hardening in the determination of cross-section resistances and to the use of linear interaction formulae. To overcome these shortcomings, improved design rules are proposed through extension of the deformation-based continuous strength method (CSM) to the case of circular hollow sections subjected to combined loading. Comparisons between the proposals and the test and FE results indicate a high level of accuracy and consistency in the predictions. The reliability of the proposed approach was confirmed by means of statistical analyses according to EN 1990.

Influence of creep on the geometrically nonlinear behavior of soft core sandwich panels

The effects of creep of the core material on the global and local geometrically nonlinear behavior of sandwich panels under axial and/or lateral loading conditions is presented, within the framework of the high-order sandwich theory (HSAPT). The theoretical model combines the concepts of the hereditary (convolution) integral of viscoelasticity based on the principle of superposition, with the HSAPT. From the expansion of the relaxation moduli into Prony series, an incremental exponential law that corresponds to the rheological generalized Maxwell model is obtained, and which allows for a step-by-step time analysis that accounts for the change in deformations and stresses with time. The results show that creep of the core leads to a significant reduction in the local and global buckling capacity of sandwich panels. It is shown that sandwich panels under a combined axial and lateral loading can undergo global buckling with time due to creep, under a sustained load that is less than 50% of their buckling load. Similar trend is also observed for the local buckling (wrinkling) of the compressed face sheet when the panel is subjected to a sustained uniformly distributed load. In both cases, buckling commenced at a relatively low stress levels but it is associated with an unlimited increase of the stresses with time that eventually lead to material failures and total failure of the sandwich panel.

STRUCTURAL PERFORMANCE OF DAMAGED OPEN-WEB TYPE SRC BEAM-COLUMNS WITH BOLT-CONNECTED BATTEN STEEL PLATES AFTER RETROFITTING

In this paper, structural performance of damaged SRC beam-columns with open-web type of batten steel plate after retrofitting was investigated. Three open-web type SRC beam-columns with bolt-connected batten steel plates were fabricated and tested under combined constant axial load and cyclic lateral load. At first, each beam-column was cyclically loaded to the targeted displacement. After the first loading, the test columns were retrofitted and reloaded till large deformation or failure. The damaged portion of each column was retrofitted with the polymer cement mortar and epoxy resin was injected into the cracks. The measured stiffness of retrofitted columns varied between 71.4% and 85.5% of the initial one. And, test results also indicated that the column which experienced the larger displacement and higher axial load showed lower load carrying capacity, but the others showed approximately the same capacities as the initial columns. Numerical analysis was also conducted to explain the retrofitted columns. Analytical results predicted the experimental behavior fairly well, which verifies the validity of the analytical models in low axial load.

Experimental Study on Ferritic Stainless Steel RHS and SHS Cross-sectional Resistance Under Combined Loading

The excellent corrosion resistance presented by all stainless steel grades, together with their appropriate mechanical properties, aesthetic appearance and easy maintenance, makes these metallic alloys perfect for sustainable structural performances. However, their nonlinear stress–strain behaviour, together with their strong strain hardening features, makes them different from carbon steel and makes the development of some specific guidance necessary. Although the compressive and flexural behaviour of stainless steel Rectangular and Square Hollow Sections (RHS and SHS) has been widely analysed and advanced design approaches considering strain hardening have been developed, more general loading conditions such as combined axial compression and bending moment loading conditions still need to be investigated. Within this scenario, this paper presents an experimental programme on several ferritic RHS and SHS stub column tests subjected to concentric and eccentric compression. The objective is to extend the recent research on austenitic and lean duplex stainless steel RHS under combined loading to ferritic grades by assessing the applicability and accuracy of the interaction expressions currently codified in EN1993-1-4 and those proposed in the literature.

Joint strength of gasketed bolted pipe flange joint under combined internal pressure plus axial load with different (industrial and ASME) bolt-up strategy

Gasketed bolted flange joints are used in process industry for connecting pressure vessels and pipes. Design procedures available in the literature mostly discuss structural strength, while sealing failure is still a big concern in industries. Similarly, limited work is found in the literature regarding performance of gasketed bolted joints under combined loading. A detailed 3D nonlinear finite element analysis is performed to study the strength and sealing of a gasketed bolted flanged pipe joint under different bolt-up strategy (Industrial and ASME) and under combined internal pressure and axial loading.

Lateral buckling of box beam elements under combined axial and bending loads

The effect of distortional deformation on the elastic lateral buckling of thin-walled box beam elements under combined bending and axial forces is investigated in this paper. For the purpose, an analytical model is developed for the stability of laterally unrestrained box beams according to higher order theory. Ritz and Galerkin's methods are applied in order to discretize the governing equilibrium equations and then the buckling loads are obtained by requiring the singularity of the tangential stiffness matrix. The different solutions are discussed and then compared to the finite element simulation using Abaqus software where shell elements are used in the mesh process. The numerical results reveal that classical stability solutions as those adopted in Eurocode 3 overestimate the real lateral buckling resistance of thin-walled box beam members, particularly for the ones with high ratios between the height and the thickness of the cross-section. Numerical study of incidence of compressive forces on lateral buckling resistance of thin-walled box beam is investigated.

Bulging bifurcation of inflated circular cylinders of doubly fiber-reinforced hyperelastic material under axial loading and swelling

In this paper, we examine the influence of swelling on the bulging bifurcation of inflated thin-walled cylinders under axial loading. We provide the bifurcation criteria for a membrane cylinder subjected to combined axial loading, internal pressure and swelling. We focus here on orthotropic materials with two preferred directions which are mechanically equivalent and are symmetrically disposed. Arterial wall tissue is modeled with this class of constitutive equation and the onset of bulging is considered to give aneurysm formation. It is shown that swelling may lead to compressive hoop stresses near the inner radius of the tube, which could have a potential benefit for preventing aneurysm formation. The effects of the axial stretch, the strength of the fiber reinforcement and the fiber winding angle on the onset of bifurcation are investigated. Finally, a boundary value problem is studied to show the robustness of the results.

Dimensionless analysis of composite rectangular and circular RC columns

A numerical procedure is presented that provides ultimate curvature and moment domains for composite rectangular and circular cross-sections of reinforced concrete columns with or without an embedded steel section subjected to combined axial loading and biaxial bending. The stress resultants for the concrete and reinforcement bars are calculated using fiber analysis and the stress resultants for the encased structural steel are evaluated using an exact integration of the stress-strain curve over the area of the steel section. A dimensionless formula is proposed that can be used for any section with similar normalized geometric and mechanical parameters. The contribution of each material to the bearing capacity of a section (resistance load and moments) is calculated separately so that the influence of each geometric or mechanical parameter on the bearing capacity can be investigated separately.

Studies on carbon fiber polymer confined slender plain and steel fiber reinforced concrete columns

This paper presents an experimental research to examine the behavior of carbon fiber reinforced polymer (CFRP) confined plain and steel fiber reinforced concrete columns. In this study, plain and steel fiber reinforced concrete columns were wrapped with CFRP material and experimentally tested to determine the effects of sheets on column behavior. It is revealed that the CFRP material is significantly effective on reinforced concrete columns with respect to strength, ductility and confinement. In addition, a numerical procedure is presented for the analysis of slender reinforced concrete columns confined with CFRP sheets subjected to combined axial load and biaxial bending. The CFRP confined slender reinforced concrete columns have been analyzed using geometric features and experimental parameters of concrete compressive strength, steel yield strength and CFRP material properties to predict the column structural behavior. The analysis and experimental results of CFRP confined slender plain and steel fiber reinforced concrete columns have been achieved in good accuracy in this study.

Collapse Resistance of Steel Columns under Combined Axial and Lateral Loading

AbstractThe collapse resistance of steel columns subjected to combined axial and reversed lateral loading is investigated computationally. Detailed finite-element models that are validated using available experimental data are presented. Simulation results using these models suggest that local buckling as well as lateral torsional buckling in deep, slender sections under combined axial and lateral loading can lead to a substantial reduction in column ductility. The results of an extensive parametric study suggest that the current design guidelines are potentially unconservative and are used to develop a simple-to-use design aid.

Surface stress effects on the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to combined axial and radial compressions

Because of surface free energy effects at nanoscale, study of the mechanical behavior of nanostructures including surface stress effects is a topic of substantial interest. Herein, the nonlinear buckling and postbuckling characteristics of geometrically imperfect cylindrical nanoshells under combined axial and radial compressive loads are investigated in the presence of surface stress effects. An efficient size-dependent shell model is proposed based on Gurtin–Murdoch elasticity theory and von Karman–Donnell-type of kinematic nonlinearity. On the basis of variational approach using the principle of virtual work, the non-classical governing differential equations are derived. Afterwards, a boundary layer theory is employed incorporating surface stress effects in conjunction with nonlinear prebuckling deformations, initial geometric imperfections and large postbuckling deflections. Then a two-stepped singular perturbation methodology is put to use in order to solve the size-dependent nonlinear problem corresponding to axial dominated and radial dominated loading cases. It is shown that in the case of radial dominated loading, the combination of hydrostatic pressure with axial compression causes to decrease approximately the effect of surface stress compared to the absence of axial load. However, for the axial dominated loading case, in comparison with no applied radial load, the surface stress effects is more significant in the presence of hydrostatic pressure.

Nonlinear buckling and postbuckling behavior of cylindrical nanoshells subjected to combined axial and radial compressions incorporating surface stress effects

In the present study, the Gurtin-Murdoch elasticity theory, as a theory capable of capturing size effects, is implemented to predict the nonlinear buckling and postbuckling response of cylindrical nanoshells under combined axial and radial compressive loads in the presence of surface stress effects. For this purpose, a size-dependent shell mode containing geometric nonlinearity is proposed within the framework of the classical shell theory. Because it is necessary to satisfy balance conditions on the surfaces of nanoshell, it is assumed that the normal stress component of the bulk varies linearly through the shell thickness. On the basis of a variational formulation using the principle of virtual work, the non-classical governing differential equations are derived. Subsequently, a boundary layer theory is employed including the nonlinear prebuckling deformations and the large deflections in the postbuckling regime. Then a two-stepped perturbation methodology is utilized to obtain the size-dependent critical buckling loads and the postbuckling equilibrium paths of nanoshells corresponding to the axial dominated and radial dominated loading cases. It is revealed that in the radial dominated loading case, a positive value of surface elastic constants leads to increase the critical buckling load but decrease the critical end-shortening of nanoshell. However, in the axial dominated loading case, surface elastic constants with positive sign causes to increase the both critical buckling load and critical end-shortening of nanoshell.

Application of third order shear deformation theory in buckling analysis of 2D-functionally graded cylindrical shell reinforced by axial stiffeners

This paper presents buckling analysis of a two-dimensional functionally graded cylindrical shell reinforced by axial stiffeners (stringer) under combined compressive axial and transverse uniform distributive load. The shell material properties are graded in the direction of thickness and length according to a simple power law distribution in terms of the volume fractions of the constituents. Primarily, the third order shear deformation theory (TSDT) is used to derive the equilibrium and stability equations. Since there is no closed form solution, the numerical differential quadrature method, (DQM), is applied for solving the stability equations. Initially, the obtained results for an isotropic shell using DQM were verified against those given in the literature for simply supported boundary conditions. The effects of load, geometrical and stringer parameters along with FG power index in the various boundary conditions on the critical buckling load have been studied. The study of results confirms that, stringers have significant effects on critical buckling load.

DYNAMIC STABILITY OF EMBEDDED SINGLE WALLED CARBON NANOTUBES INCLUDING THERMAL EFFECTS

A nonlocal beam model based on the Bernoulli-Euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (SWCNTs) in thermal environment under combined static and periodic axial loads. The dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. The equation of motion is reduced to the extended Mathieu-Hill equation, the stability of which is analyzed through the Floquet-Lyapunov theory as well as bounded and unbounded solution theory. The instability regions obtained from both theories are examined and compared with each other. Also, the effects of the small-scale parameter, temperature change, elastic medium, compressive static axial load and excitation frequency on the dynamic stability of SWCNTs are discussed in detail. The prediction of dynamic instability of carbon nanotubes enables one to eliminate this phenomenon in cases that may fall within the range of practical significance.

Experimental investigation on the seismic performance of steel–polypropylene hybrid fiber reinforced concrete columns

Addition of fibers into cementitious composites has raised concern over decades, which enables considerable improvement in mechanical and dynamic properties of reinforced concrete (RC) members. In this paper, we present an experimental study on the seismic performance of steel–polypropylene hybrid fiber reinforced concrete (HFRC) columns, which is of vital significance to postearthquake serviceability of structures. A total of 24 specimens subjected to combined constant axial load and cyclic lateral force were investigated. The main variables involve fiber type, shear span ratio, axial compression ratio, and reinforcement ratio (longitudinal and transverse). The failure modes, ultimate bearing capacity and deformation capacity were analyzed. The experimental results showed that the presence of hybrid fibers in RC columns had positive influence on improving the seismic bearing capacity. The improvement ratio could reach to 15–20% when a relative high axial compression was applied. Moreover, in comparison to RC columns, HFRC columns exhibited a notable synergetic effect in terms of ductility and energy dissipation capacity, particularly for columns with a higher axial compression ratio. Subsequently, on the basis of principles of equilibrium and compatibility, analytical equations to estimate the seismic bending moment capacity and shearing force capacity were developed, which took into account the synergetic effect of hybrid fibers. The analytical solutions were then validated by the test results, and the correlations were observed in reasonable accuracy.

Simplified design method for slender hybrid columns

This paper deals with numerical investigations on second-order effects in slender RC columns reinforced by several steel sections, namely hybrid columns, subjected to combined axial load and uniaxial bending moment. A FE model is developed in which geometrical and material nonlinearities as well as the partial interaction effect between the steel profiles and the surrounding concrete are taken into account. This model is then used to perform an extensive numerical parametric study on the ultimate load of hybrid columns considering 1140 different data sets. The comparison between the results obtained with FE analysis and Eurocode simplified methods (moment magnification approach) shows that EC2 and EC4 methods give wide discrepancies where half of case-studies are unsafe. The aim of the paper is to extend the use of the Eurocode moment magnification method to slender hybrid column design. In this method, the second-order bending moment is calculated by multiplying the first-order one by a magnification factor k that depends on the flexural stiffness EI and the equivalent moment distribution. New expressions for the correction factors involved in the determination of the effective flexural stiffness EI are proposed and calibrated by the results of the extended parametric study with 2960 data sets. The comparison of the predictions given by the new expressions against the FE analysis shows that the proposed new expressions of correction factors for moment magnification method provides largely safe designs for slender hybrid columns.

Modeling of Externally Prestressed Beams until Fracture in Non Linear Elasticity

In this paper, we present an analytical model to analyze reinforced and prestressed concrete beams loaded in combined bending, axial load and shear, in the frame of non linear elasticity. In this model, the equilibrium of the beam is expressed by solving a system of equations, governing beams equilibrium, based on the stiffness matrix of the beam, which connects the load vector to the node displacements vector of the beam. It is built from the stiffness matrix of the section which takes into account a variation of the shearing modulus (depending on the shear variation) instead of assuming a constant shearing modulus as in linear elasticity. For the internal tendons, the stiffness matrix is completed by the terms due to the prestress effect in flexural equilibrium and by the balancing of one part of the shear by the transverse component of the force in the inclined cables.

Experiments and FE modeling of stress–strain state in ReBCO tape under tensile, torsional and transverse load

For high current superconductors in high magnet fields with currents in the order of 50 kA, single ReBCO coated conductors must be assembled in a cable. The geometry of such a cable is mostly such that combined torsion, axial and transverse loading states are anticipated in the tapes and tape joints. The resulting strain distribution, caused by different thermal contraction and electromagnetic forces, will affect the critical current of the tapes. Tape performance when subjected to torsion, tensile and transverse loading is the key to understanding limitations for the composite cable performance. The individual tape material components can be deformed, not only elastically but also plastically under these loads. A set of experimental setups, as well as a convenient and accurate method of stress–strain state modeling based on the finite element method have been developed. Systematic measurements on single ReBCO tapes are carried out combining axial tension and torsion as well as transverse loading. Then the behavior of a single tape subjected to the various applied loads is simulated in the model. This paper presents the results of experimental tests and detailed FE modeling of the 3D stress–strain state in a single ReBCO tape under different loads, taking into account the temperature dependence and the elastic-plastic properties of the tape materials, starting from the initial tape processing conditions during its manufacture up to magnet operating conditions. Furthermore a comparison of the simulations with experiments is presented with special attention for the critical force, the threshold where the tape performance becomes irreversibly degraded. We verified the influence of tape surface profile non-uniformity and copper stabilizer thickness on the critical force. The FE models appear to describe the tape experiments adequately and can thus be used as a solid basis for optimization of various cabling concepts.

Seismic behavior of concrete-encased steel cross-shaped columns

Experiments were performed to investigate the seismic behavior of concrete-encased steel cross-shaped (CESC) columns. Four specimens subjected to combined constant axial load and cyclic lateral load were tested to study the effects of the axial compression ratio, the steel ratio, and the loading angle on the behavior (strength, stiffness, ductility, and energy dissipation capacity) of CESC columns. Experimental results suggest that the maximum lateral load increases with an increase in the axial compression ratio, while the displacement ductility decreases, and the stiffness degrades seriously. The maximum lateral load and the displacement ductility increase significantly with an increase in the steel ratio, whereas the stiffness degrades slightly. The maximum lateral load at the loading angle 45° is larger than that at the loading angle 0°, but the displacement ductility at the loading angle 45° is lower than that at the loading angle 0°. CESC columns exhibit good ductility, deformation capacity and energy dissipation capacity. Furthermore, a finite element analysis was also carried out to simulate the behavior of the specimens. The results obtained from the finite element analysis agree well with the experimental results. Compared with reinforced concrete cross-shaped columns, CESC columns show higher lateral bearing capacity and better seismic performance.

Finite Element Evaluation of Blast Design Response Criteria for Load-Bearing Precast Wall Panels

An impediment to using total precast construction for government, diplomatic and defense buildings is that load-bearing walls are defined as primary components and are therefore subject to significantly more restrictive blast response limits than non-load-bearing walls. These requirements are particularly restrictive for prestressed load-bearing wall panels. This paper presents analytical research used to define the behavior of precast/prestressed panels under combined axial loading and lateral impulse loading and to assess the current response criteria. Particular focus is placed on the ductility of load-bearing wall panels in comparison to non-load-bearing panels. The analytical procedures primarily rely on high-fidelity finite element methodology (nonlinear static and explicit nonlinear dynamic) that has been thoroughly validated through full-scale laboratory testing. The study indicates that under elevated axial load the response limits of prestressed and conventionally reinforced wall panels are comparative and could be increased from current limits, and revised response limits for future blast design of load-bearing precast wall panels are recommended.