Flexural Buckling Strength Research Articles

Flexural Buckling Strength of Steel Angle with Reinforcement in Electric Transmission Towers

In Japan, mid-sized electric transmission towers are made of steel angle members connected by high-strength bolts and are mainly designed to withstand wind loads. However, recent collapses due to the increasing wind intensity caused by climate change have led to a high demand for the reinforcement of conventional towers currently in operation. This paper reports the flexural buckling strength evaluation method for reinforced steel angle members under eccentric load. The study utilizes a theoretical approach to derive the evaluation formula, considering the effect of the eccentric load and the amount of reinforcement. Finally, small-scale experiments validate the proposed design formula, which can reasonably evaluate the strength of reinforced steel angle members.

Elastic and inelastic major-axis flexural buckling of cellular steel columns

This study investigates the elastic and inelastic major-axis flexural buckling of cellular steel columns. Based on the stationary principle of potential energy, the existing elastic buckling load equation is refined to incorporate the local bending deformations at web posts. The column strength curve for determining the critical loads is then derived. For the elastic buckling, the refinement provides a significant improvement. For the inelastic buckling, the effects of residual stresses and initial geometric imperfections on the column strength are examined by the validated nonlinear finite element (FE) models. The initial geometric imperfection amplitudes of L/300 and L/500, where L is the column length, are recommended for global buckling of cellular steel columns fabricated from the parent steel shapes with h/b ≤ 1.2 and h/b > 1.2, respectively, where h/b is the depth-to-width ratio of the parent steel shapes. The developed column strength curve conservatively predicts the major-axis flexural buckling strength of practical cellular steel shapes, with an average prediction-to-FE buckling stress ratio of 0.97. A comparison also shows that the current EC3 and AISC360 equations are applicable for predicting the strength of practical cellular columns, provided that the refined elastic buckling load is adopted.

Bending and flexural-buckling strength of steel members considering strain-rate-effects at elevated temperatures

PurposeIn this study, the bending strength, flexural buckling strength and collapse temperature of small steel specimens with rectangular cross-sections were examined by steady and transient state tests with various heating and deformation rates.Design/methodology/approachThe engineering stress and strain relationships for Japan industrial standard (JIS) SN400 B mild steels at elevated temperatures were obtained by coupon tests under three strain rates. A bending test using a simple supported small beam specimen was conducted to examine the effects of the deformation rates on the centre deflection under steady-state conditions and the heating rates under transient state conditions. Flexural buckling tests using the same cross-section specimen as that used in the bending test were conducted under steady-state and transient-state conditions.FindingsIt was clarified that the bending strength and collapse temperature are evaluated by the full plastic moment using the effective strength when the strain is equal to 0.01 or 0.02 under fast strain rates (0.03 and 0.07 min–1). In contrast, the flexural buckling strength and collapse temperature are approximately evaluated by the buckling strength using the 0.002 offset yield strength under a slow strain rate (0.003 min–1).Originality/valueRegarding both bending and flexural buckling strengths and collapse temperatures of steel members subjected to fire, the relationships among effects of steel strain rate for coupon test results, heating and deformation rates for the heated steel members were minutely investigated by the steady and transient-state tests at elevated temperatures.

Out-of-plane buckling strength of free standing singly symmetric hollow pinned circular arches

This study deals with the out-of-plane flexural torsional buckling strength of singly symmetric free-standing circular arches with a hollow cross-section. The behavior of such arches is investigated numerically in terms of the out of plane critical elastic buckling load and ultimate load carrying capacity when such arches are subject to a radial pressure that creates uniform axial compression. Prediction methodologies proposed by other researchers for flexural torsional buckling of arches with an I-shaped cross-section, as well as American, European, and Australian code provisions for flexural buckling of compression members are slightly modified and compared with numerically obtained critical elastic buckling loads and ultimate load carrying capacities. All investigations are conducted using validated shell finite element simulations. A parametric study is conducted to evaluate the influence of arch depth, wall thickness, subtended angle, arch radius, yield strength, initial imperfections, and residual stresses on the 3D elastic-plastic behavior of such arches. It is concluded that it is not necessary to use eigenvalue buckling analysis to obtain critical elastic buckling loads for improving capacity predictions and that such loads may be obtained using existing formulations with slight modifications. Additionally, existing code provisions for flexural buckling of compression members may be used with minor modifications to predict the out-of-plane flexural torsional buckling capacity of such arches. Also, prediction methodologies proposed by other researchers for flexural torsional buckling of I-shaped arches may also be used with slight modifications and resulted in the most accurate, consistent, and design appropriate capacity predictions.

Column Buckling of Corroded Steel Angles and Channels: Experiments and Failure Mode Analyses

Corrosion affects the sustainability of steel structures, especially those with improper maintenance and those exposed directly to the atmosphere and seashore environments. Corrosion-related accidents have been reported frequently recently; therefore, periodically assessing the structural health condition of steel structures is crucial. Clarifying the residual strengths of corroded steel structures with moderate to severe degrees of corrosion is important. Here, the uniaxial compressive strength of corroded steel angles and channels was investigated through experiments and nonlinear finite-element analyses. The behavior of these corroded specimens was found to depend strongly on the degree of corrosion, and had combined failure modes of global flexural buckling, local buckling, and cross-sectional yielding. The failure mode of the corroded steel specimens that largely behaved in a complex manner was examined. The relationship between the ultimate strength and degree of corrosion, and the applicability of a traditional global flexural buckling strength equation using the cross-sectional properties, were analyzed for strength evaluation. The strength equation provided relatively good strength estimates for lightly to moderately corroded specimens; however, it became less applicable for severely corroded specimens, possibly owing to the local buckling interaction. An empirical strength equation that reflects the trend of the experimental results was developed by modifying the traditional equation.

Design of cold-formed steel built-up columns subjected to local-global interactive buckling using direct strength method

This paper presents the structural behavior of doubly-symmetric built-up cold-formed steel (CFS) columns that fail in local-global (flexural-torsional) interactive buckling modes. The built-up column investigated in this study is formed (back-to-back) by connecting two identical unlipped channel sections with the use of self-drilling screws. A total of 45 column tests were carried out, with various parameters such as slenderness of the section, length and intermediate spacing between self-drilling screws. The test results indicate that the axial ultimate strengths of the built-up columns are governed by buckling of the individual channel section and an unstiffened flange element due to higher local buckling stress (λl > 1.5) resulting in an interactive buckling. The test results also indicate that the effect of intermediate spacing depends on the failure mode of the CFS built-up cross-sections. The various options available to predict the elastic critical buckling stress for global flexural buckling and design strength is presented. The design strengths predicted by the current direct strength method (DSM) is unconservative when compared with the axial compressive strength of the CFS built-up column with local-global interactive buckling. Therefore, suggestions to prevent the incorrect application of the DSM method are elucidated.

Flexural buckling behavior of corroded hot-rolled H-section steel beams

This paper mainly investigates the flexural buckling behavior of corroded hot-rolled H-section steel beams under four-point bending. A total 43 observations comprising of five experiments and thirty-eight numerical analysis results were reported to investigate the corrosion types, degrees and locations on the initial imperfections, failure modes and the flexural buckling behavior of steel beam. Based on the analysis, a recommended formula of the flexural buckling strength of corroded steel beams is derived using the direct strength method. The results show that the tested specimens fail with the local buckling of upper flange and web near the mid-span, but the failure positions and the buckling half-wavelength are different with corrosion degrees. The results also show that the yield load, buckling load and ultimate load of tested specimens decrease with the corrosion degrees increasing. When the corrosion ratio reaches 16.88%, the yield load decreases at a ratio of 21.4%, the critical buckling load decreases by 33.2%, the ultimate load after buckling decreases at a ratio of 28.3%, and the ductility coefficient decreases by 59.4%. Finally, the comparison between predicted and actual flexural strength indicates that the proposed formula can calculate the flexural buckling capacity of corroded H-section steel beams with varying degrees of corrosion.

Press-braked stainless steel channel section columns failing by flexural buckling: Testing, numerical simulation and design

The minor-axis flexural buckling behaviour and strengths of pin-ended press-braked stainless steel channel section columns have been investigated in the present paper through laboratory testing and numerical modelling. An experimental programme was firstly conducted, and included initial global and local geometric imperfection measurements and twelve pin-ended column tests about the minor principal axis. The key obtained test results, including the failure loads, the mid-height lateral deflections at the failure loads, the load–mid-height lateral deflection curves and the failure modes, were reported and discussed in detail. The experimental programme was followed by a numerical modelling programme; finite element models were developed to simulate the test responses and then adopted to perform parametric studies to generate further numerical data on press-braked stainless steel channel section columns over a wide range of cross-section dimensions and member effective lengths. The obtained experimental and numerical data were employed to assess the accuracy of the relevant design rules for press-braked stainless steel channel section columns failing by flexural buckling about the minor principal axis, as given in the European code, American specification, Australian/New Zealand standard and SCI design manual. The results of the assessment indicated that (i) the European code yields unsafe flexural buckling strength predictions for those relatively short and intermediate press-braked stainless steel channel section columns with member non-dimensional slendernesses less than around 1.0, (ii) the American specification leads to unsafe predictions of flexural buckling strength for press-braked stainless steel channel section columns over the whole considered range of member non-dimensional slendernesses up to 3.0, and (iii) the Australian/New Zealand standard and the SCI design manual result in lower levels of design accuracy than the European code and American specification, but with significantly reduced number of unsafe flexural buckling strength predictions.

Experimental and numerical investigations of pin-ended hot-rolled stainless steel angle section columns failing by flexural buckling

A thorough testing and numerical modelling programme has been conducted to investigate the flexural buckling behaviour and strengths of pin-ended hot-rolled stainless steel angle section columns. The testing programme adopted three hot-rolled stainless steel equal-leg angle sections, and included 12 pin-ended column tests about the minor principal axis as well as supplementary initial geometric imperfection measurements on the column specimens. The testing programme was accompanied by a parallel numerical modelling programme, including a validation study, where finite element models were developed and validated against the test results, and a parametric study, where the validated finite element models were employed to generate additional numerical data over a broad spectrum of cross-section dimensions and member effective lengths. The test and numerical data were then adopted to evaluate the accuracy of the relevant design rules, as given in the European code and American design guide, for pin-ended hot-rolled stainless steel angle section columns prone to flexural buckling about the minor principal axis. On the basis of the evaluation results, it can be concluded that (i) the European code results in overall accurate and consistent flexural buckling strength predictions, but many of the predictions for short and intermediate columns with member non-dimensional slendernesses less than around 1.0 are unsafe, and (ii) the American design guide leads to unduly conservative and scattered flexural buckling strength predictions. Finally, a new design approach was developed through modifications to the Eurocode design rules, and shown to offer accurate, consistent and safe-sided flexural buckling strength predictions for pin-ended hot-rolled stainless steel angle section columns over the whole considered range of member non-dimensional slendernesses up to 4.0. The reliability of the new design approach was confirmed by means of statistical analyses according to EN 1990.

Flexural Buckling Strength of Tapered-I-Section Steel Columns Based on ANSI/AISC-360-16

Steel tapered-I-columns are popular in modern buildings due to its material efficiency and the convenience in construction. For evaluating the flexural buckling strength of these columns, the current design methods with empirical and idealized assumptions are sometimes unreliable, especially for slender columns with significant tapering ratios. To accurately calculate the flexural buckling resistance, this paper proposes a numerical framework for tapered-I-sections. The direct analysis method (DM) with the non-prismatic high-order beam-column elements considering the factors, including the second-order effects, the geometric imperfections, and the residual stresses is developed. A new shape-function representing the most critical initial out-of-straightness curve of a tapered member is adopted. An advanced non-prismatic beam-column element incorporating this imperfection shape-function named the curved tapered-three-hinges (TTH) element is derived. With the availability of the internal degree-of-freedoms, the one-element-per-member (OEPM) modeling method is permitted. Sequentially, a series of parametric studies using the proposed numerical method are conducted for generating the buckling curves for the non-prismatic columns with various tapered-stiffness ratios. The sophisticated finite-element method is adopted to verify the proposed numerical framework. Based on the proposed numerical approach, the design method in ANSI/AISC-360-16 is modified for tapered-I-section columns.

Experimental study on cyclic behavior of composite beam with corrugated steel web considering different shear-span ratio

This paper proposes an innovative use of corrugated steel plates as the webs of the crossbeam in the tower of a suspension bridge to get better seismic performance. Three 1/4-scaled models of composite beam with corrugated steel webs considering different shear-span ratio were fabricated to conduct quasi-static test. The structural behaviors including failure modes, hysteretic curves, ductility, strength and stiffness degradation, energy dissipation capacity, deformation recovery ability, shear force distribution and strain responses were investigated. Test results indicate that the specimen with large shear-span ratio presents ductile flexural failure, and the hysteretic curve is stable and plump with slight pinching, which indicates good energy dissipation performance. However, the specimen with small shear-span ratio fails due to brittle shear buckling of corrugated steel web, showing remarkable pinching phenomenon and poor hysteretic behavior. With the increase of shear-span ratio, the load-carrying capacity and lateral initial stiffness are reduced, but the ductility and energy dissipation ability are improved significantly. The energy dissipation capacity of such composite beam is better than that of the RC structures, the strength degradation is slight for the specimen with a proper shear-span ratio, and the deformation recovery ability is good for all test specimens. The corrugated steel web carries about 80% of the shear force and shear stress uniformly distributed along the web height. The test results demonstrate that the composite beam with corrugated steel web of a reasonable shear-span ratio can be applied in anti-seismic structure with superior energy dissipation performance. In addition, simplified formulas were proposed to evaluate the flexural strength and shear buckling strength of a composite beam with corrugated steel webs, the calculated results agree well with the test results, verifying the accuracy of these proposed formulas.

偏心継手を有する山形鋼部材の曲げ座屈耐力

Transmission steel towers and radio communication steel towers, where the size is less than middle, are usually constructed by angle members. Angles in the towers are commonly connected by bolts and lap joint is used. Lap joint will generate an eccentricity; secondary bending moment due to this eccentricity will be subjected to the member and affect to the flexural buckling strength. Currently, structural design of the steel towers follows two Standards. Transmission steel towers follows Design Standard on Structures for Transmissions (JEC-127); radio communication steel tower follows Design Standard on Structures for Radio Communication in Power System (JEC-144). In these Standards, effect of eccentricity is categorized in three classes; flexural buckling strength of the members are evaluated. However, the categories shown in the Standards are qualitative and not evaluating the eccentricity quantitatively. To clarity the effect of eccentricity due to lap joint, firstly, full scale testing were conducted in this study. Moreover, difference of bending stiffness of connected angles will affect to the strength; therefore, this parameter is also included in the testing. Test parameters are location of the lap joint, difference of the bending stiffness of connected angles, and member length (i.e., slenderness ratio). From the testing, following results were observed. (1) Location of the lap joint affected the flexural buckling strength even if the connected angles were same sizes. The specimen where the joint was located L/4 in the member showed smaller strength than the specimen where the joint was located at the middle (L/2) of the member (L is member length). (2) Difference of bending stiffness of connected angles affected the flexural buckling strength. The strength of the member which had different size of angles decreased compared to the strength where the member was composed with same size. Difference of angle sizes will change the amount of eccentricity at the joint and also changes the equivalent bending stiffness of the member. (3) Flexural buckling deformation in elastic range showed two patterns. Specimens where the joint was in the middle of the member showed maximum deformation at the end of the lap joint. On the other hand, specimens where the joint was in L/4 of the member showed maximum deformation at the middle of the member. Observation from the testing showed that difference of bending stiffness of connected angles, location of lap joint, and eccentricity according to the lap joint shall be evaluated to estimate the flexural buckling strength. To evaluate these parameters, Rayleigh-Ritz method and energy equilibrium theory were applied. Based on Rayleigh-Ritz method, firstly, difference of bending stiffness of connected angles without eccentricity was evaluated; coefficient α that can be used to evaluate this effect was derived. Secondary, based on energy equilibrium theory, effect of eccentricity at the lap joint and location of the joint was evaluated; coefficient β that can be used to evaluate these effects was derived. Finally, coefficients α and β are incorporated to evaluate the flexural buckling strength of angle member with lap joint. Utilizing the derived flexural buckling strength, effective slenderness ratio which is useful to evaluate the flexural buckling strength is proposed. Proposed formula was validated with the test results, and reasonable results were confirmed.

Ultimate Flexural Strength of Cylindrical Steel Shell for Wind Tower

풍력발전 타워용 원형단면 강재 쉘에 대하여 재료 및 기하학적 비선형 유한요소법으로 극한휨강도 해석을 수행하였다. 쉘의 기하학적 초기변형, 반경 대 두께비, 적용 강종 등이 극한휨강도에 미치는 영향을 분석하였으며, Eurocode 3와 AISI 설계기준에 의한 설계휨강도와 유한요소해석으로 구한 극한휨강도를 비교하였다. 비선형 FE 해석에는 DNV-RP-C202에 제시된 쉘의 좌굴모드와 유로코드에 규정된 진원도 허용오차 및 용접에 의한 변형을 기하학적 초기 결함으로 고려하였다. 원통형 쉘의 반경 대 두께비는 60~210 범위를 고려하였으며 SM520과 HSB800 강재로 제작된 것으로 가정하였다. Ultimate flexural buckling strength of cylindrical steel shells for the wind turbine tower structure was investigated by applying the geometrically and materially nonlinear finite element method. The effects of initial imperfection, radius to thickness ratio, and type of steel on the ultimate flexural strength of cylindrical shell were analyzed. The flexural strengths of cylindrical shells obtained by FEA were compared with design flexural strengths specified in Eurocode 3 and AISI. The shell buckling modes recommended in DNV-RP-C202 and the out-of-roundness tolerance and welding induced imperfections specified in Eurocode 3 were used in the nonlinear FE analysis as initial geometrical imperfections. The radius to thickness ratios of cylindrical shell in the range of 60 to 210 were considered and shells are assumed to be made of SM520 or HSB800 steel.

A study on flexural buckling strength F cr of inelastic buckling for compressive members

Since Euler’s classical theory, which he proposed in 1759, many column curve formulations have been proposed. This study investigates the flexural buckling strength (Fcr) calculated using the allowable stress design specification and the load and resistance factor design (LRFD) specification of the American Institute of Steel Construction. It is noted that the exponential function of the column curve formulation using LRFD is difficult to use in practice. Therefore, a simple parabolic function is proposed for the inelastic buckling strength of a steel column loaded with uniaxial compression, and it is shown to be consistent with many design codes. The expressions for inelastic buckling strength formulation as defined previously for ASD are used here. To verify the proposed equation, 118 individual test results of steel columns are examined. The mean of the ratio of the column strength to the proposed flexural buckling strength is 1.089, indicating that the proposed strength curves are in good agreement with the test results.

Buckling of Built-Up Columns of Pultruded Fiber-Reinforced Polymer C-Sections

This paper presents the test results of an experimental investigation to evaluate the buckling behavior of built-up columns of pultruded profiles, subjected to axial compression. Specimens are assembled by using four (off the shelf) channel shaped profiles of E-glass fiber-reinforced polymer (FRP), having similar detailing to strut members in a large FRP structure that was executed in 2009 to start the restoration of the Santa Maria Paganica church in L’Aquila, Italy. This church had partially collapsed walls and no roof after the April 6, 2009, earthquake of 6.3 magnitude. A total of six columns are characterized with two different configurations for the bolted connections joining the channel sections into a built-up strut. Test results are discussed and a comparison is made with closed-form equation predictions for flexural buckling resistance, with buckling resistance values established from both eigenvalue and geometric nonlinear finite element analyses. Results show that there is a significant role played by the end loading condition, the composite action, and imperfections. Simple closed-form equations overestimate the flexural buckling strength, whereas the resistance provided by the nonlinear analysis provides a reasonably reliable numerical approach to establishing the actual buckling behavior.

Drift-based and dual-parameter fragility curves for concentrically braced frames in seismic regions

This paper discusses the development of drift-based and dual-parameter fragility curves for steel braces as part of concentrically braced frames designed in seismic regions. The experimental results from 24 different research programs are compiled into a database for this effort. Drift-based fragility curves are developed for three damage states of steel braces subjected to cyclic loading associated with brace flexural buckling, local buckling and brace strength loss due to fracture. The effects of material variability, brace cross sectional shape and loading protocol on the drift-based fragility curves are investigated. The effect of global and local slenderness ratios on the fracture ductility of various shapes of steel braces is examined through dual-parameter fragility curves that relate these geometric ratios with the expected story drift ratios that each of the three pre-described damage states occur. The proposed fragility curves can be employed for rapid assessment of the seismic vulnerability of concentrically braced frames.

Effective Width Method for determining distortional buckling strength of cold-formed steel flexural C and Z sections

This paper proposes a design method, based on the Effective Width Method, for determining the nominal distortional buckling strength of typical cold-formed steel C and Z sections subjected to bending. The method can be integrated into the classic effective width design provisions specified in AISI S100, and it allows the conventional design approach to cover more comprehensive limit states. The proposed method is calibrated by the flexural distortional buckling strength predicted by the Direct Strength Method. Comparison with experimental results indicates that the proposed method yields reasonable predictions for the flexural distortional buckling strength of industrial standard C and Z sections. The method offers the same level of accuracy and reliability as the Direct Strength Method.

Imperfection sensitivity analysis of lipped channel columns at high temperatures

An imperfection sensitivity analysis is carried out on cold formed lipped channel columns integrated in wall structures. The equations given in Eurocode 3: Part 1.3 and finite element analyses are used to evaluate the flexural buckling strength and ultimate strength of the sections. The analyses are performed at both room and fire temperatures by introducing corresponding material data values obtained from high temperature transient tensile tests into the models. The purpose of the study is to evaluate the possibility of using normal temperature design formulae directly at high temperatures and to evaluate the influence of the choice of initial geometric imperfections on the modelled behaviour of the columns. The analytical estimations are compared to the results of the finite element analyses, which in turn are validated using available test results. It is shown that the magnitude of the modelled types of local imperfections has an effect on the compression stiffness of the members, whereas the magnitude of global flexural imperfections has more influence on the ultimate strength obtained in the analyses. The influence of the choice of buckling curve at high temperatures is discussed.

Development of Column Curve for Steel Angles

Structural steel angles have a wide range of applications requiring a comprehensive design methodology. One of the most important aspects of steel-angle design is the flexural buckling strength. In this paper, the test data for flexural buckling reported in a companion paper as well as in published investigations are compared with current specifications, and the need for the development of a separate column curve for hot-rolled steel angles is established. The experimental data consist of 71 compression tests from five different studies and residual stress and out-of-straightness measurements. A finite-element analysis and a maximum strength analysis have been carried out using the available test data. Nine column curves have been generated. The average curve lies between the Structural Stability Research Council (SSRC) curves 1P and 2P. Equations for the curve have been presented. This column curve can be adopted for routine design or may be used to calibrate special code clauses.

Flexural Buckling of Steel Angles: Experimental Investigation

Structural steel angles have a wide variety of applications. However, steel angles have not received the attention comparable to heavy shapes such as wide flange sections. For steel angles, flexural buckling strength is the basic design strength, while the torsional-flexural buckling strength is computed in many codes by modifying the design procedure for flexural buckling strength. This paper presents the results of an experimental investigation of 26 hot-rolled steel angles under concentric axial compression failing in flexural buckling. The width-thickness ratios of test specimens ranged from 6 to 16. The slenderness ratios varied from 68 to 188, covering almost the entire practical range. Residual stresses and yield stresses across the cross sections were determined and initial out-of-straightness was measured. These data were used in the development of a column curve reported in a companion paper.