Equivalent Slenderness Ratio Research Articles

Trussed concrete-filled steel tubular hybrid structures subjected to axial compression: Performance and design calculation

This paper presents a study on the axial compression performance of trussed concrete-filled steel tubular (CFST) hybrid structures. A total of 26 specimens were tested, including 15 circular and 11 square cross-sectional specimens. The effects of cross-sectional types, yield strength of steel of CFST chord, web types, number of chords, and equivalent slenderness ratio were investigated to clarify the mechanical behavior of trussed structure. The analyses of the full-range response, the typical failure mode, and the distribution of the transverse deflection and strain of the structures were carried out. A finite element analysis (FEA) modelling of trussed CFST structure was established and validated against the experimental results. Through the numerical simulation, the analysis of the internal force and stress was conducted, and the hybrid effect between the web and CFST chord was revealed. Based on parameter analysis, the design calculation was proposed, and the trussed CFST hybrid structure was equivalent to a single CFST to calculate its load-bearing capacity by introducing equivalent slenderness ratio proposed.

Trussed square concrete-filled steel tubular hybrid structures subjected to axial compression

This paper introduced the mechanical performance of trussed square concrete-filled steel tubular (CFST) hybrid structure subjected to axial compression. A refined finite element analysis (FEA) modelling was established and verified against the experimental results. Based on the FEA modelling, the hybrid effect and the working mechanism of the structure were revealed through the comprehensive analysis of the internal force distribution, the axial compression force (N) versus average longitudinal strain (ε) relation, the typical failure modes, and the stress distribution. The N-ε relation was classified into five types according to the failure modes and critical factors elucidated. The criterion for determining the ultimate limit state of the trussed square CFST hybrid structure was established by investigating its load-bearing capacity and peak strain. An interface contact stress model was proposed to describe the hybrid effect of the structure. Based on parametric analysis, critical parameters used to characterize the hybrid effect were identified, thereby the equivalent slenderness ratio for straight trussed CFST hybrid structure and that for a curved one considering the influence of the initial curvature ratio were proposed. The quantitative relationships between the stability factor and equivalent slenderness ratio were established and validated so as to facilitate the calculation of the load-bearing capacity for both straight and curved trussed square CFST hybrid structures.

Performance of concrete-filled double-skin shallow-corrugated steel plate composite walls under axial compression

This research introduces a steel-concrete composite wall, namely the concrete-filled double-skin shallow-corrugated steel plate composite wall (CDSCW). It is composed of one concrete-filled double-skin shallow-corrugated steel plate wall (CDSW) and rectangular concrete-filled steel tubular (CFST) columns arranged on the sides of the wall, where the shallow-corrugated steel plates in the CDSW are featured with low energy consumption in production. Full-scale tests are conducted on the compressive behaviour of CDSCWs. Numerical models are also established for further investigation. Based on the extensive parametric study, formulas for the resistance of cross-section to compression, equivalent slenderness ratio, stability coefficient, as well as the resistance of composite wall in axial compression are proposed. It verifies that the proposed formulas are safe and reliable for the resistance prediction of CDSCWs.

Compressive behavior of bolted built-up H-section column using high-strength steel

This study presents a bolted built-up H-section column using high-strength steel with a yield stress higher than 770 MPa. Ten specimens were tested under axial compression loading to study the failure modes, load–deformation behavior, strength and stiffness, and strain characteristics. Test variables included bolt pitch (200, 400, 600, 800, and 1200 mm) and column slenderness ratio (17.8, 39.7, 63.4, and 87.1). When the slenderness ratio is small, the specimens show a local buckling dominated failure; when the slenderness ratio becomes larger, the specimens show an overall buckling dominated failure. The ultimate strength and axial stiffness increase with the decrease in slenderness ratio and bolt pitch, and the calculated axial stiffness is consistent with the test results. The axial compressive strengths were calculated according to AIJ 2002, ANSI/AISC 360-16 and GB 50017-2017 design codes; in addition, the equivalent slenderness ratio parameters were also compared and discussed. The results show that the design method suggested by AIJ 2002 provides good predictions for the ultimate strength of tested bolted built-up H-section columns.

Experimental investigation into flexural buckling of double-limb built-up plate members under compression

Planar steel plates have many advantages, including high precision, flexible outline shape fabrication, and convenient transportation and storage, which make them suitable for various steel structures (e.g., reticulated shell structures). However, the steel plates are not commonly used as structural members, because they have a relatively low out-of-plane flexural stiffness. To improve the flexural buckling resistance, a novel type of built-up plate member comprising two longitudinal plates is proposed in this study. Additionally, the flexural buckling behavior of the novel built-up members is investigated. A series of compression tests on 42 specimens of built-up plate members is conducted to determine the elastic and ultimate critical loads. Flexural buckling about the minor axis is observed to be the failure mode of the specimens. The equivalent slenderness ratio method is used to determine the theoretical elastic critical loads of the specimens. With consideration of the measured material properties, geometric imperfections, and residual stresses of the specimens, a refined finite-element model is developed to simulate the flexural buckling behavior. Furthermore, the applicability of two representative specifications (American and European) to the novel built-up member is discussed. The results indicate that the design strengths calculated using these specifications are generally conservative for determining the ultimate loads of the built-up plate members. Design curve “c” in Eurocode 3 is found to be the most suitable among the specifications of interest for determining the design strength. This study provides valuable guidance for the design of built-up plate members.

Behavior of three-chord concrete-filled steel tube built-up columns subjected to eccentric compression

An experimental investigation of a series of three-chord concrete-filled steel tube (CFST) built-up columns was conducted under eccentric compression. The influences of slenderness ratio, eccentricity ratio, eccentricity direction, and brace pattern (battened or laced) on the load bearing process, failure modes, and ultimate load-carrying capacities of the specimens were analyzed. The test results indicate that a CFST built-up column exhibits better performance than a corresponding plain steel built-up column. The ultimate strengths and stiffnesses of the three-chord CFST built-up specimens decreased with increasing slenderness ratio or eccentricity ratio. Battened specimens exhibited lower load-carrying capacities than laced specimens, and different load-bearing capacities were obtained for specimens under different directions of compression eccentricity. Using the proposed equivalent slenderness ratio, three existing design codes were evaluated to predict the stability coefficient, and a new correlation equation considering two failure modes is suggested for calculating the ultimate strength of three-chord CFST built-up columns subject to combined compression and flexure.

Ultimate strength of pinned-end dual-angle cross combined section columns under axial compression

Dual-angle cross combined section columns (starred angles) have been extensively utilised as transmission tower legs because of their large bearing capacity. However, combined members may fail in different modes, and the provisions on bearing capacity in the regulations of different countries are diverse. To overcome the limitations of existing research and design approaches, a three-dimensional finite element (FE) model is developed in this study and is validated against all column test data available in the literature. Using this model, parametric analyses are performed on varying grades of steel, patterns of filler plates, and the number of filler plates, and the effect of the number and pattern of filler plates is determined. The shortcomings of the current design methods are highlighted along with the necessary solutions, based on a comparison of the results of experiments and those of numerical analysis using values calculated as per various regulatory codes. It is demonstrated that the type and the number of filler plates only affect the starred angles with flexural buckling about the imagine axis, and that torsional buckling and local buckling in the combined section columns do not occur simultaneously. When considering the influence of local buckling on the reduction in the bearing capacity of members, repeatedly factoring in torsional buckling is unnecessary. Furthermore, through modification of the slenderness ratio of the sub-members in the calculation of the equivalent slenderness ratio of starred angles, the calculation results obtained using the code agree well with the results of the numerical analysis.

Finite Element Analysis of Axial Compression Steel Members Strengthened with Unbonded CFRP Laminates.

This paper presented a non-linear finite element (FE) analysis to investigate the potential of unbonded carbon fiber-reinforced polymers (CFRP) strengthening in improving the axial compression performance of steel members. The FE model was firstly developed and validated against experimental works. Four parameters considered in the parametric study were the number of CFRP layers, CFRP length, slenderness ratio, and elastic modulus of CFRP. It was confirmed that the unbonded CFRP strengthening method is effective at enhancing the load-carrying capacity as well as delaying the overall buckling of the axial steel members. The strength increase is highly affected by the first three parameters. In addition, the method of an equivalent slenderness ratio can be used for strength design.

In-Plane Stability of Concrete-Filled Steel Tubular Parabolic Truss Arches

For determining the in-plane buckling resistance of a concrete-filled steel tubular (CFST) arch, the current technical code GB50923-2013 specifies the use of an equivalent beam-column method which ignores the effect of rise-to-span ratio. This may induce a gap between the calculated result and actual stability capacity. In this study, a FE model is used to predict the buckling behavior of CFST truss arches subjected to uniformly distributed loads. The influence of rise-to-span ratio on the capacity of truss arches is investigated, and it is found that the stability capacity reduces as rise-to-span ratio declines. Besides, the calculations of equivalent slenderness ratio for different truss sections are made to consider the effect of shear deformation. Moreover, based on FE results, a new design equation is proposed to predict the in-plane strength of CFST parabolic truss arches under uniformly distributed loads.

Studies on T-Shaped composite columns consist of multi separate concrete-filled square tubular steel sections under eccentric axial load

In order to investigate mechanical properties and load-bearing capacity of T-shaped Concrete-Filled Square Steel Tubular (TCFST) composite columns under eccentric axial load, three T-shaped composite columns were tested under eccentric compression. Experimental results show that failure mode of the columns under eccentric compression was bending buckling of the whole specimen, and mono column performs flexural buckling. Specimens behaved good ductility and load-bearing capacity. Nonlinear finite element analysis was also employed in this investigation. The failure mode, the load-displacement curve and the ultimate bearing capacity of the finite element analysis are in good agreement with the experimental ones. Based on eccentric compression test and parametric finite element analysis, the calculation formula for the equivalent slenderness ratio was proposed and the bearing capacity of TCFST composite columns under eccentric compression was calculated. Results of theoretical calculation, parametric finite element analysis and eccentric compression experiment accord well with each other, which indicates that the theoretical calculation method of the bearing capacity is advisable.

Practical formulas towards distortional buckling failure analysis for steel–concrete composite beams

SummaryAs the most predominant type of failure for steel–concrete composite beams (SCCBs) in negative moment area, distortional buckling is significantly impacted by the interaction effect between the applied loading and the torsional–lateral restraint stiffness of the bottom flange, which is termed as loading–restraint interaction here for short. Recently, a modified elastic foundation beam method capable of considering the interaction effect properly was proposed to calculate critical buckling moment for SCCBs under negative uniform moment. As a sequel to such development, a functional relationship between two dimensionless auxiliary parameters (i.e. equivalent slenderness ratio and equivalent moment coefficient) is discovered in this study. On the basis of the close association between the pair of dimensionless parameters, empirical formulas are derived in a remarkably simply explicit form to evaluate the critical buckling moment for SCCBs under negative uniform moment or moment gradient. These formulas are simple, user‐friendly and of practical use. Compared with conventional approaches without considering the loading–restraint interaction effect, the practical approach developed in this paper can achieve higher accuracy and is more easy‐implemented. The study lays a foundation for determining the ultimate bearing capacity of SCCBs considering moment gradient effect rapidly. Copyright © 2016 John Wiley & Sons, Ltd.

Simplified Model to Predict Load-Bearing Capacity of Concrete-Filled Steel Tubular Laced Column

A simplified method using an equivalent slenderness ratio was suggested to calculate load-bearing capacity of concrete-filled steel tubular laced column in this paper. The significant differences between compressive and tensile strengths of concrete-filled steel tube were considered. The comparisons between the predicted Nuc and the tested Nue showed that the predicted method gives generally good predictions of the test results.

Buckling Strength of Single Angle Struts Part 2: Angles Connected by One Leg at Both Ends

A single angle strut connected at both ends by one leg is simple in execution, but complex in behavior. As a monosymmetric section, the angle is subjected simultaneously to compression, biaxial bending and torsion. Furthermore, there exist at the two ends rotational restraints whose rigidity depends on the member arrangement and joint detailing of the truss. So, a rigorous solution of the bearing capacity of such angle is very difficult to establish. The common practice in design work is to transform this complex problem into the buckling of an axially compressed strut, hinged at both ends, by taking an equivalent slenderness ratio. In this study, new formulas for this equivalent slenderness are suggested, where a concept of partial adjustment is introduced so that they apply to angles of high strength steel as well as to those of low carbon steel. The detrimental effect of torsion on the strut capacity is not negligible when the angle has slender leg, especially for high strength steel. Formulas of reduction factor to the member yield strength are proposed in this regard and are given as a function of the flat width-thickness ratio instead of the overall width-thickness ratio of the leg. These formulas, in conjunction with those for equivalent slenderness, correlate well with the test program of angle struts, steel grade 460 MPa. Lastly, limitations to the formulas of equivalent slenderness are discussed.

Buckling Strength of Single Angle Struts Part 1: Angles Subject to Axial Compression

Hot rolled angles are classified into two categories: equal-legged and unequal legged. They behave differently when subjected to axial compression owing to the difference in section symmetry: the equal-leg angle has one axis of symmetry while the unequal-leg one is asymmetric. This article aims at providing practical approaches for determining buckling strength of the two kinds of single angle struts subject to axial compression. For equal-leg angles, the first issue of concern is the failure mode. Although most researchers agree that equal-leg single angle buckles flexurally about the minor axis in the inelastic range as well as in the elastic range, some others got different conclusion. Through meticulous analysis based on tangent modulus concept, it is shown in this study that flexural-torsional buckling about the major axis is not the dominant failure mode. On the other hand, leg plate buckling may occur before the flexural buckling. So, a factor of effective yield strength is suggested for calculating the interactive local-flexural buckling, and the approach is verified with available test data. For unequal-leg angles, which always buckle in flexural-torsional mode, attention is focused on the simplification of the formula for calculating the critical load. Simplified formula of equivalent slenderness ratio is derived to transform the flexural-torsional buckling problem into a flexural one and is verified with available test data. The results arrived at in this study are recommended for routine design use.

Curved concrete filled steel tubular (CCFST) built-up members under axial compression: Experiments

A series of tests on curved concrete filled steel tubular (CCFST) built-up members subjected to axial compression is described in this paper. Twenty specimens, including 18 CCFST built-up members and 2 curved hollow tubular built-up columns, were tested to investigate the influence of variations in the tube shape (circular and square), initial curvature ratio (βr, from 0 to 7.4%), nominal slenderness ratio (λn, from 9.9 to 18.9), section pattern (two main components, three main components and four main components), as well as brace pattern (battened and laced) on the performance of such composite built-up members. The experimental results showed that the ultimate strength and stiffness of CCFST built-up specimens decreased with increasing βr or λn. Different load-bearing capacities and failure modes were obtained for the battened and laced built-up members. A simplified method using an equivalent slenderness ratio was suggested to calculate the strength of CCFST built-up members under axial compression.

Equivalent Slenderness Ratio Method for Design of T-Struts Subject to Compressive Force

T-struts subject to centroid compression buckle flexural-torsionally about their axis of symmetry. When the force is applied at the shear center of the section, T-struts buckle either flexurally or torsionally without coupling of flexure with twisting. Although the buckling load about the symmetry-axis of shear center loading is greater than that of centroid loading, the design capacity of T-struts with defect such as fabrication error, load eccentricity and residual stress decrease by shifting the working line of a T-section compression chord to the shear center. This feature is not well known to designer of constructional steel. This article presents the equivalent slenderness ratio method, a new method for the design of T-struts subject to compressive force, introduces another three methods including the one presented by Shaofan Chen, the one in code and the one in ANSYS, contrasts the calculation results of those four methods and recommends the implementation of equivalent slenderness ratio method in the design of T-struts subject to compressive force.

EFFECT OF LATERAL-ROTATIONAL RESTRAINT AND STRENGTH FOR CONTINUOUSLY ECCENTRIC BRACES ON BUCKLING STRESS FOR H-SHAPED COMPRESSION MEMBERS

��������������� � � � � * �� � � � ** When the non-structural members such as folded-roof plate are directly jointed to the structural members, the non-structural members may be used as the eccentric bracings. This paper clarifies the effect of lateral and rotational restraint for continuously eccentric braces on buckling stress for H-shaped compression members. The elasto-plastic buckling stress is evaluated with the buckling curve for design codes using the modified equivalent slenderness ratio. Then the elastic buckling load with energy method is applied to the slenderness ratio. Finally, the relationship between the rigidity and strength of bracings is expressed as the approximation.

EFFECT OF LATERAL AND ROTATIONAL RESTRAINT FOR ECCENTRIC BRACES ON FLEXURAL-TORSIONAL BUCKLING LOAD WITH WEB DEFORMATION FOR H-SHAPED COMPRESSION MEMBERS

When non-structural members are used as eccentric braces in real structures, flexural and torsional deformation of compression members may occur due to the eccentric joints to the braces. This paper clarifies the buckling behavior with web deformation for H-shaped compression members with laterally and rotationally eccentric braces. The elasto-plastic buckling stress is evaluated with the buckling curve for design codes using the modified equivalent slenderness ratio. Then the elastic buckling load with energy method is applied to the slenderness ratio. In addition, the relationship between the required rigidity and strength of braces is evaluated.

BUCKLING STRESS OF SLENDER PILES WITH ROTATIONAL RESTRAINT AT THE PILE HEAD IN LIQUEFIED SOIL

In our previous paper, the possibility of flexural buckling of slender piles in liquefied soil was presented, and then the boundary conditions are assumed to be ideal such as pinned or fixed end. The rotational deformation of the pile heads is, however, restrained by the footing beams in the real structures. Therefore, the boundary condition should be assumed to be arbitrary rotational spring. In this paper, flexural buckling behavior of the steel piles with rotational spring in the liquefied soil during earthquakes is clarified, and the buckling stress of piles with the soil-pile interaction is estimated by the design codes using modified equivalent slenderness ratio.

Experiments and analysis of the post-buckling behaviors of aluminum alloy double layer space grids applying ball joints

This study discusses on the experimental and analytical results of the global buckling tests, carried out on aluminum alloy double layer space grids composed of tubular members, ball joints and connecting bolts at the member ends, with the purpose of demonstrating the effectiveness of a simplified analysis method using an equivalent slenderness ratio for the members. Because very few experiments have been carried out on this type of aluminum space grids, the buckling behavior is investigated experimentally over the post buckling regions using several space grid specimen with various values for the member slenderness ratio. The observed behavior duping the experiments is compared with the analytically obtained results. The comparison is made based on two different schemes; one on the plastic hinge method considering a bending moment-axial force interaction for members and the other on a method using an equivalent slenderness ratio. It is confirmed that the equivalent slenderness method can be effectively applied, even in the post buckling regions, once the effects of the rotational rigidity at the ball joints are appropriately evaluated, because the rigidity controls the buckling behavior. The effectiveness of the equivalent slenderness method will be widely utilized for estimation of the ultimate strength, even in post buckling regions for large span aluminum space grids composed of an extreme large number of nodes and members.