Combined Axial Loading Research Articles

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.

On the local buckling of RHS members under axial force and biaxial bending

This paper presents the results of a large parametric study concerning the evaluation of the critical local buckling coefficient for thin-walled rectangular hollow section (RHS) members subjected to combined axial load and biaxial bending, accounting for web-flange interaction. The calculation of the half-wavelength leading to the minimum critical local bifurcation load is performed by means of a Generalized Beam Theory specialization, which makes it possible to quickly solve a large set of cases. In particular, taking advantage of the small half-wavelength of local buckling, it is assumed that the stresses are uniformly distributed along the member length, making it possible to resort to semi-analytical solutions using sinusoidal half-wave amplitude functions for the GBT cross-section deformation modes. On the basis of the results obtained, the key parameters governing local buckling are identified, leading to easy-to-use charts and closed-form formulae to determine the local buckling coefficient.

Elastoplastic response and recoil of lattice structures under hyperbolic hardening

Elastoplastic response and recoil analyses for hexagonal honeycomb lattice structures are presented when hardening is described by a hyperbolic law. By exploiting the translational symmetry of the problem, the analysis is reduced to that of a thin beam under combined bending and axial loading coupled with the kinematics of lattice deformation and its relationship with cell wall deformation. A closed-form solution for the load-curvature relationship of a beam with rectangular cross-section is obtained. A systematic study of beam response, as the stress-strain curve of the constituent material approaches an ideal elastic-perfectly plastic law, is presented. The analysis is then applied to an infinite honeycomb sheet under remote tensile load to obtain the apparent non-linear structural response. Apparent recoil of such a lattice material upon unloading is also calculated in closed form, when unloading is assumed to take place along a linear stress-strain curve. The analytical results are in excellent agreement with the numerical calculations.

High-Strength Concrete Masonry Walls under Concentric and Eccentric Loadings

AbstractMasonry walls and columns are common structural members that typically resist compressive loads, with a number of such members being required to resist combined axial load and out-of-plane ...

Interaction diagrams for FRP strengthened RC rectangular columns with large aspect ratio

The load carrying capacity of reinforced concrete columns (RC) shall be enhanced by providing lateral confinement using fiber reinforced polymer (FRP). As per ACI 440.2R-08 [1], external strengthening using FRP composites is more effective for circular columns than rectangular columns having an aspect ratio greater than 2.0. The main objective is to develop column interaction diagrams for RC rectangular columns having an aspect ratio greater than 2.0 externally strengthened using FRP composites without any shape modification and subjected to combined axial load (Pn) and bending moment (Mn) due to lateral loading. Tests are conducted and semi-empirical equations developed for FRP strengthened RC rectangular columns with large aspect ratio. Pn–Mn interactions diagrams are developed using the semi-empirical solutions and validated with 3D finite element analysis. The column interaction diagrams are developed by varying the unconfined compressive strength of concrete, yield strength of steel, percentage of steel reinforcement and thickness of FRP composite. These diagrams shall be used for the design of FRP strengthened RC rectangular columns with large aspect ratio.

Lateral buckling of tapered thin walled bi-symmetric beams under combined axial and bending loads with shear deformations allowed

In this paper, the effect of shear deformations on elastic lateral buckling of tapered thin-walled open and closed bi-symmetric section beams under combined bending and axial forces is investigated. For the purpose, a geometrical non-linear beam theory is presented according to a new kinematic model that incorporates shear flexibility components. Ritz method is applied to obtain the governing equilibrium equations, then the buckling loads are computed by solving the eigenvalue problem basing on the singularity of the tangential stiffness matrix. The elastic lateral buckling resistances given by the proposed method are generally in good agreement with the finite element simulation using Abaqus software. The numerical results for cantilevers and simply supported thin walled beams with open and box sections reveal that the classical stability solution tends to overestimate the real lateral buckling resistance of short tapered box cantilever beams.

FRP Strengthened RC Rectangular Columns Under Combined Axial and Lateral Loading: Analytical Study

Semi-empirical solutions are proposed to predict the axial and lateral capacities of reinforced concrete (RC) rectangular columns having aspect ratio greater than 2.0 strengthened using fiber reinforced polymer (FRP) composites without any shape modification and subjected to axial, lateral and combined axial and lateral loading. 3D finite element models are generated for the analysis of FRP strengthened RC columns. Semi-empirical solutions and finite element models are validated with the test results. Column interaction diagram between axial capacity Pn and bending moment Mn is generated using the proposed semi-empirical solutions and compared with Pn - Mn interaction diagram generated as per ACI 440.2R-08 [1] procedure. From this study, it is concluded that the proposed semi-empirical solutions shall be used for the design of RC rectangular columns having aspect ratio greater than 2.0 strengthened with FRP composites and without any shape modification.

Cyclic behavior of concrete-filled steel tubular column–reinforced concrete beam frames incorporating 100% recycled concrete aggregates

Concrete-filled steel tubular structural members can be recognized as an effective mean to improve the mechanical behavior in terms of strength, stiffness, ductility, and energy dissipation for the initial recycle aggregate concrete deficiencies compared with natural aggregate concrete. A small-scale model of square concrete-filled steel tubular column–reinforced concrete beam frame realized employing 100% recycled coarse aggregates was tested under combined axial loads and cyclic reversed lateral flexure. The failure modes, plastic hinges sequence, hysteresis loop, skeleton curve, stiffness degeneration, energy dissipation capacity, and ductility of the frame were presented and analyzed in detail. The structural behavior of square concrete-filled steel tubular column–reinforced concrete beam frame with 100% recycled coarse aggregates was compared with circular concrete-filled steel tubular column–reinforced concrete beam frame made with 100% recycled coarse aggregates. A fiber-based program model for the nonlinear analysis of concrete-filled steel tubular column–reinforced concrete beam frames incorporating recycled coarse aggregates was developed using SeismoStruct, to highlight the effect of recycled coarse aggregate content on mechanical behavior of recycled aggregate concrete and the confinement effect provided by outer tubes on core concrete. The analysis results show that the numerical model can well simulate and predict the seismic behavior of concrete-filled steel tubular column–reinforced concrete beam frames with 100% recycled coarse aggregate content. Both experimental and numerical results demonstrate that concrete-filled steel tubular column–reinforced concrete beam frames with large content of recycled coarse aggregates have a receivable seismic performance, and it is feasible to apply and popularize recycled aggregate concrete into concrete-filled steel tubular structures in seismic regions.

Biomechanical Analysis of the Proximal Femoral Locking Compression Plate: Do Quality of Reduction and Screw Orientation Influence Construct Stability?

To investigate biomechanically in a human cadaveric model the failure modes of the proximal femoral locking compression plate and explore the underlying mechanism. Twenty-four fresh-frozen paired human cadaveric femora with simulated unstable intertrochanteric fractures (AO/OTA 31-A3.3) were assigned to 4 groups with 6 specimens each for plating with proximal femoral locking compression plate. The groups differed in the quality of fracture reduction and plating fashion of the first and second proximal screws as follows: (1) anatomic reduction with on-axis screw placement; (2) anatomic reduction with off-axis screw placement; (3) malreduction with on-axis screw placement; (4) malreduction with off-axis screw placement. The specimens were tested until failure using a protocol with combined axial and torsional loading. Mechanical failure was defined as abrupt change in machine load-displacement data. Clinical failure was defined as 5 degrees varus tilting of the femoral head as captured with optical motion tracking. Initial axial stiffness (in N/mm) in groups 1 to 4 was 213.6 ± 65.0, 209.5 ± 134.0, 128.3 ± 16.6, and 106.3 ± 47.4, respectively. Numbers of cycles to clinical and mechanical failure were 16,642 ± 10,468 and 8695 ± 1462 in group 1, 14,076 ± 3032 and 7449 ± 5663 in group 2, 8800 ± 8584 and 4497 ± 2336 in group 3, and 9709 ± 3894 and 5279 ± 4119 in group 4. Significantly higher stiffness and numbers of cycles to both clinical and mechanical failure were detected in group 1 in comparison with group 3, P ≤ 0.044. Generally, malreduction led to significantly earlier construct failure. The observed failures were cut-out of the proximal screws in the femoral head, followed by either screw bending, screw loosening, or screw fracture. Proper placement of the proximal screws in anatomically reduced fractures led to significantly higher construct stability. Our data also indicate that once the screws are placed off-axis (>5 degrees), the benefit of an anatomic reduction is lost.

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.

Experimental and Numerical Study of Octagonal Composite Column Subject to Various Loading

In this study, experimental tests of the behaviour of steel and partially encased composite (PEC) columns subjected to compressive loading is performed. Evaluation of this type of composite column under axial loading and numerical analysis of its behaviour under combined torsional and axial loading are the main objectives of this study. At first, a parametric study of PEC columns under axial loading was performed in order to find the relationship between flange slenderness ratio of steel column section and concrete confinement. Width-to-thickness ratio of the flange, diameter and spacing of the transverse links were considered as variables in this study. It was observed that dimension of transverse links had almost no effect on the capacity of the specimens, however smaller transverse links spacing increased both capacity and deformability of the specimens. The comparison of the code equations given in CSA S16-14 and EN 1994-1-1 revealed that the equation in CSA S16-14 underestimates the capacity. Furthermore, different types of retrofit of cross-shaped steel column including concrete encasement, use of stiffener plates and transverse links were investigated in this research. Results revealed that concrete confinement and use of transverse links had respectively the most and the least effect on increasing torsional capacity of the specimens.

Hysteretic Model for Flexure-shear Critical Reinforced Concrete Columns

ABSTRACTA model for predicting the cyclic lateral load-deformation response of flexure-shear critical reinforced concrete (RC) columns subjected to combined axial load and cyclic shear is proposed. Strength deterioration in the primary curve due to the effect of shear after yielding is considered by a modification coefficient. Rules for unloading and reloading branches of the hysteretic curve are obtained from regression analysis of test results. Unloading stiffness is fitted as a function of displacement ductility and secant stiffness of the point with maximum displacement in the primary curve. Pinching is simulated by changing the slope of reloading branch. Path-based cyclic strength deterioration is incorporated in the proposed model. In the expression of cyclic strength deterioration, the effects of aspect ratio and axial-load ratio are considered. Comparison between the predicted cyclic response and experimental results indicates that the proposed model can predict the observed hysteretic response of flexure-shear critical RC columns well.

Inelastic Buckling of FGM Cylindrical Shells Subjected to Combined Axial and Torsional Loads

A semi-analytical procedure is presented to solve the elastoplastic buckling problem of cylindrical shells made of functionally groded materials (FGMs) under combined axial and torsional loads. The elastoplastic properties are assumed to vary smoothly according to the power law distribution rule, introduced in the J2 deformation theory for formulation of the constitutive relation of FGMs in the framework of the Tamura–Tomota–Ozawa (TTO) model, which is a volume fraction-based material model. The critical condition is deduced by the Ritz method. Assuming the uniform prebuckling strain, a biaxial stress state analysis is conducted to determine the analytical position of the elastoplastic interface, which is used in the integration of the elastoplastic internal force and all the material-related structural parameters. Finally, an iterative procedure is adopted to find the exact elastoplastic critical load. Numerical results indicate the effects of the inhomogeneous parameter and the elastoplastic material properties of their constituents on the stability region and plastic flow region of the materials.

Stress-strain relationship of FRP confined concrete columns under combined axial load and bending moment

Abstract The stress-strain relationship of FRP confined concrete columns under eccentric loading is different from that under concentric loading. However, eccentric loading can have different load paths, e.g. constant axial force with increasing load eccentricity or constant load eccentricity with increasing axial load. The effect of different load paths on the stress-strain behavior of eccentrically loaded columns has remained unclear to date. It was believed previously that such difference in load paths could be insignificant for the stress-strain behavior of FRP confined concrete columns under eccentric loading. Unexpectedly, the study in this work on two different load paths demonstrates that the stress-strain behavior can be very different. A new stress-strain model for FRP confined circular concrete columns under constant axial force and increasing load eccentricity is developed in this work for engineering applications.

Experimental investigation of seismic behavior of ultra-high performance steel fiber reinforced concrete columns

This paper presents an experimental study on seismic behavior of ultra-high performance steel fiber reinforced concrete (UHPSFRC) columns. Based on a series of cyclic loading tests on 14 UHPSFRC specimens subjected to combined static axial loading and cyclic lateral loading, the investigation and analysis have been carried out on crack status, failure modes, hysteretic loops, skeleton curves, strength and stiffness degradation, energy dissipation capacity and ductility of UHPSFRC columns. The influence of stirrup spacing, type of stirrup, axial compression ratio and shear span ratio on the seismic performance of UHPSFRC columns was also investigated in details. The experiment results show that three typical failure modes are observed, i.e., flexural, flexural-shear and shear failure mode. The existence of steel fiber could prevent the cracked concrete from spalling efficiently and delay the bulking of longitudinal reinforcement further. It noteworthy that the limit plastic drift ratio of all columns changes from 0.036 to 0.061, indicating that the UHPSFRC columns represent a good ductility which is obviously different from the conventional high strength concrete columns that exhibit much more brittleness with the increase of strength.

Experimental testing and numerical modelling of steel moment-frame connections under column loss

The beam-to-column connections of moment-resisting steel frames should exhibit capacities that allow them to transfer the forces that develop under normally expected loading conditions. However, when a column is lost owing to accidental loading, these conditions change, and the forces are redistributed to the adjacent beams and columns. In such cases, the connections must be capable of resisting the combined axial and flexural loads and allow for the redistribution of the loads, so that progressive collapse development is prevented. In this study, we investigated the performances of four types of beam-to-column connections, namely, the welded cover plate flange connection (CWP), the haunch end plate bolted connection (EPH), the reduced beam section welded connection (RBS), and the unstiffened extended end plate bolted connection (EP), against progressive collapse. Two span frames were constructed and tested under a central column removal scenario until failure. The results from the experimental tests were used to validate finite element models. The CWP, EPH, and RBS specimens showed good ductility, with the catenary action making a significant contribution to the ultimate load resistance. Further, the ultimate rotations of the beams were greater than the deformation limit given in the latest Unified Facilities Criteria guidelines for design of buildings to resist progressive collapse. Specimen EP showed the lowest ductility and ultimate load resistance, with the bolts in the rows under tension fracturing before the catenary action could develop. Further, the failure mode for specimen EP indicated that bolt strengthening is necessary for improving its progressive collapse resistance.

14.01: Influence of beam‐to‐column joints on the robustness of earthquake‐resistant moment‐resistant frames

ABSTRACTRobustness of Moment Resistant Frames (MRFs) designed according to current seismic codes and subjected to a loss‐of‐column scenario is strictly linked to the deformation capacity of beam‐to‐column connections, which are usually subjected to combined axial and bending loads. In the seismic design of steel frames, once avoided the yielding of columns, a global dissipative collapse mechanism has to be ensured by imposing the formation of plastic hinges at the ends of the beams or in the connections and guarantying, provided that the elements involved in plastic range have an adequate energy dissipation capacity. Within this framework, the aim of this paper is to analyse the influence of the response of the connections designed for seismic application on the global behaviour of MRFs under a loss‐of‐column scenario providing an accurate modelling of connections subjected to combined axial and bending loads. To this scope four different beam‐to‐column joints designed for seismic actions, previously tested under cyclic load history at the STRENGTH laboratory of Salerno University, have been modelled and introduced in a case‐study structure, whose response has been assessed by means of push‐down analyses. The performances of the analysed frames have been analysed and is compared using the Residual Reserve Strength Ratio (RRSR) index combined with the energy balance method.

P11.02: Experimental analysis and FE modeling of square hollow sections under combined axial and bending loads

ABSTRACTThe seismic performance of steel frames strongly depends on the non‐linear behaviour of beams and column because the plastic zones are concentrated in beams’ ends and at the base of the columns of the first storey. Therefore, in order to guarantee an appropriate behaviour of the whole frame, it is necessary to characterize the response of steel member up to failure. Dealing with the characterization of the non‐linear response of beams, many experimental works are currently available both for I and hollow sections. In addition, predictive models based on regression analyses able to provide both the ultimate resistance and rotation capacity of steel members, even though they always make reference only to the case of pure non‐uniform bending. As previously mentioned, the overall frame response is strongly influenced also by the non‐linear behaviour of columns, and an accurate prediction of their combined axial and bending vs rotation response is needed in order to control the seismic behaviour of the frame. In order to predict the ultimate resistance and rotational capacity of steel members subjected not only to bending but also to axial loads, two kinds of experimental testing and an analysis joint activity carried out. The monotonic behaviour of SHS subjected to bending only or combined bending and axial loads are investigated. Subsequently, numerical analysis are conducted to extend the experimental sample. At the end, the results of the experimental end FE work are used to calibrate a model able to express the ultimate resistance of SHS as a function of the main geometrical and mechanical parameters of the section.

05.29: Interaction curves for local and distortional buckling of polygonal tubes in combined torsion and axial loading

ABSTRACTThis paper investigates the interaction of uniform axial loading (compressive or tensile) and uniform torsion on the linear elastic buckling behaviour of long tubes with regular convex polygonal cross‐sections. The analyses pertain to tubes of sufficient length such that the results are independent of end boundary conditions. Using the generalised constrained finite strip method (cFSM), pure local buckling is examined for triangular through octagonal tubes. The interaction curves for pure local buckling are akin to those previously generated from the exact finite strip method and a square and octagonal tube are analysed in‐depth to assess the changes in interaction behaviour as the number of sides in the section is increased. The pure distortional buckling behaviour is examined for pentagonal through octagonal tubes using recent developments in Generalised Beam Theory (GBT) and an almost linear interaction between torsion and compression is found, as has been noted previously for circular tubes. The distortional interaction curves are essentially identical for all analysed tubes.

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.