Article

Guide to Stability Design Criteria for Metal Structures: Sixth Edition

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The definitive guide to stability design criteria, fully updated and incorporating current research Representing nearly fifty years of cooperation between Wiley and the Structural Stability Research Council, the Guide to Stability Design Criteria for Metal Structures is often described as an invaluable reference for practicing structural engineers and researchers. For generations of engineers and architects, the Guide has served as the definitive work on designing steel and aluminum structures for stability. Under the editorship of Ronald Ziemian and written by SSRC task group members who are leading experts in structural stability theory and research, this Sixth Edition brings this foundational work in line with current practice and research. The Sixth Edition incorporates a decade of progress in the field since the previous edition, with new features including: Updated chapters on beams, beam-columns, bracing, plates, box girders, and curved girders. Significantly revised chapters on columns, plates, composite columns and structural systems, frame stability, and arches Fully rewritten chapters on thin-walled (cold-formed) metal structural members, stability under seismic loading, and stability analysis by finite element methods State-of-the-art coverage of many topics such as shear walls, concrete filled tubes, direct strength member design method, behavior of arches, direct analysis method, structural integrity and disproportionate collapse resistance, and inelastic seismic performance and design recommendations for various moment-resistant and braced steel frames Complete with over 350 illustrations, plus references and technical memoranda, the Guide to Stability Design Criteria for Metal Structures, Sixth Edition offers detailed guidance and background on design specifications, codes, and standards worldwide.

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... Finite element models of fix-ended stub columns with the cross-section shown in Figure 1 were developed; α is the outer web depth, b is the outer flange width and t α and t b are the corresponding thicknesses. The models' height H was set equal to three times the maximum cross-sectional dimension enabling for local buckling failure without any coupled instability phenomena, i.e., combination of flexural or flexural-torsional and local buckling modes [10]. Columns of low member slenderness (short columns) present pure local buckling failure modes, while members of higher member slenderness (long columns) present failure modes dominated by flexural or interactive flexural-torsional buckling. ...
... Focus of this study was the investigation of pure local buckling. According to the "Guide to stability design criteria for metal structures" [10] and in line with past studies [11][12][13][14], a stub column with length three times the maximum cross-sectional dimension can be considered sufficiently long to allow for the development of the lowest buckling wavelength, leading to pure local buckling failure. ...
... Moreover, an initial imperfection sensitivity study was performed considering three fractions of the plate thickness, t: t/10, t/15 and t/50 [31][32][33]. In line with past studies [23,30], the local geometric imperfection amplitudes were taken as a function of the plate thickness, because the local buckling mode has a half-wavelength of the same order of magnitude as the thickness of the constituent plate elements [10]. ...
Article
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Research studies have been reported on aluminium alloy tubular and doubly symmetric open cross-sections, whilst studies on angle cross-sections remain limited. This paper presents a comprehensive numerical study on the response of aluminium alloy angle stub columns. Finite element models are developed following a series of modelling assumptions. Geometrically and materially nonlinear analyses with imperfections included are executed, and the obtained results are validated against experimental data available in the literature. Subsequently, a parametric study is carried out to investigate the local buckling behaviour of aluminium alloy angles. For this purpose, a broad range of cross-sectional aspect ratios, slenderness and two types of structural aluminium alloys are considered. Their effect on the cross-sectional behaviour and strength is discussed. Moreover, the numerically obtained ultimate strengths together with literature test data are utilised to assess the applicability of the European design standards, the American Aluminium Design Manual and the Continuous Strength Method to aluminium alloy angles. The suitability of the Direct Strength Method is also evaluated and a modified method is proposed to improve the accuracy of the strength predictions.
... The inelastic second order analysis can properly describe the actual behavior of a structure, since it includes the plastic behavior of materials [15]. However, the relatively complex formulation of this refined approach is a complicating factor. ...
... As stated by Ziemian [15], approximate methods must be used with caution since they may be inadequate for amplifying bending moments in regions connecting beams and columns. It is worth noting that these methodologies are only recommended for framed structures with uniform loads [18]. ...
... These coefficients may be used for the analysis of reticulated structures consisting of structural elements with uniform geometry and stiffness, provided 2 1.4 B ≤ [21]. The 2 B coefficient must be determined for each pavement, and it is not adequate for analyzing structures with split story levels [15]. ...
Article
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Current practices in structural engineering demand ever-increasing knowledge and expertise concerning stability of structures from professionals in this field. This paper implements standardized procedures for geometrically nonlinear analysis of steel and reinforced concrete structures, with the objective of comparing methodologies with one another and with a geometrically exact finite element analysis performed with Ansys 14.0. The following methods are presented in this research: Load Amplification Method, from NBR 8800:2008; the coefficient method, from NBR 6118:2014; the P-Delta iterative method and the coefficient method, prescribed in EN 1993-1-1:2005. A bibliographic review focused on standardized approximate methods and models for consideration of material and geometric nonlinearities is presented. Numerical examples are included, from which information is gathered to ensure a valid comparison between methodologies. In summary, the presented methods show a good correlation of results when applied within their respective recommended applicability limits, of which, Eurocode 3 seems to present the major applicability range. The treated approximate methods show to be more suitable for regular framed structures subjected to regular load distributions.
... Although not a conclusive observation, the ductility of the tested austenitic box sections seems to be higher than that of the studied duplex and lean duplex box sections. The stiffer plate edges in corners of box sections allow for the redistribution of stresses after local buckling, enabling the section to retain a portion of its strength and stiffness and to benefit more efficiently from the characteristics of its material type [178]. Consequently, the ductility and residual strength were found to be rather high for the studied austenitic box CFSST. ...
... L-I200 is a lean duplex I-section with an outstand width of 200 mm). The specimen lengths were selected as three times their flange width so that they would exhibit sectional response while not failing by overall flexural buckling [112,178]. with timber battens, and then, concrete was cast inside the formwork and compacted in accordance with AS/NZS 2327 [126] and AS 3600 [179]. After sufficient curing and prior to testing, the formwork was removed. ...
... In most cases, the instant of failure corresponded to the reduction of axial resistance below the 0.8Pu limit. and to benefit more efficiently from the characteristics of its material type [178]. ...
Thesis
The present thesis starts by investigating the local and post-local buckling behaviour of fabricated box and circular concrete-filled stainless steel tubes (CFSSTs) as well as stainless steel partially-encased I-sections. A comprehensive set of experiments considering austenitic, duplex, and lean duplex stainless steel grades is carried out followed by an extensive numerical parametric study. The results are then summarised to propose, for the first time, axial slenderness limits and effective width/diameter formulae for the studied section types. The investigation on the local stability is extended in the next part of the thesis where a comprehensive numerical study is conducted to clarify the role of concrete infill in the local buckling behaviour of circular tubes. The results strongly suggest that the concrete infill has limited effect on enhancing the local buckling strength of circular tubes. The enhancement is found to be much lower than that implied in international design standards. The roots for this discrepancy are identified and it is suggested that the axial slenderness limit for hollow circular tubes can be significantly relaxed to bring it closer to that of filled circular tubes. The final part of the thesis focuses on the response of compact and slender box CFSSTs under axial and flexural actions. An experimental programme is first carried out comprising compact and slender CFSSTs fabricated from austenitic and lean duplex plates. Stub columns under axial compression as well as combined compression and bending, CFSST beams under pure bending, and long CFSST columns under axial compression are all included in the experiments. The tests are followed by an extensive numerical study. Outcomes of the investigations are then synthesised to develop comprehensive procedures for the design of compact and slender box CFSSTs under compression, bending, and combined loading. Such procedures have not yet been established for CFSSTs in international design standards.
... Both of the two adopted I-sections were classified as slender cross-sections according to the slenderness limits in EN 1993-1-12 [11], ANSI/AISC 360-16 [12] and AS 4100 [13]. For each I-section, five stub column specimens with the same nominal length L were prepared and planned to be tested under eccentric compression loads at different initial loading eccentricities; it is worth noting that the nominal specimen length was set to be equal to three times the mean outer cross-section dimensions [16], which is deemed short enough to avoid flexural buckling, but still long enough to contain a representative pattern of local geometric imperfections and membrane residual stresses. Table 2 reports the key measured geometric dimensions of the stub column specimens. ...
... Specimen ID Table 3, including the Young's modulus E, the yield stress f y , the ultimate stress f u , the strain at the ultimate stress ε u , the fracture strain ε f and the ultimate-to-yield stress ratio f u /f y . The membrane residual stresses in S960 ultra-high strength steel welded I-sections were also measured by means of the sectioning method, with the setup and procedures being in compliance with those recommended by Ziemian [16]. Fig. 3(a) and 3(b) depict the distribution patterns and amplitudes of the measured membrane residual stresses for two S960 ultra-high strength steel welded I-sections I-200 × 150 × 6 and I-150 × 150 × 6, as reported in detail in Su et al. [2]. ...
... Note that all the modelled I-sections were classified as slender sections, according to the slenderness limits given in EN 1993-1- 12 [11], ANSI/AISC 360-16 [12] and AS 4100 [13]. The length of each FE model was set to be equal to three times its mean outer cross-section dimensions [16]. Moreover, the initial loading eccentricities were varied from 1 mm to 800 mm, resulting in a wide spectrum of loading combinations being accounted for. ...
Article
The present paper reports comprehensive experimental and numerical investigations into the cross-section behaviour and resistances of S960 ultra-high strength steel welded I-sections under combined compression and minor-axis bending moment. An experimental programme, adopting two slender welded I-sections – I-120 × 120 × 6 and I-150 × 75 × 6, was firstly conducted and included initial local geometric imperfection measurements and ten minor-axis eccentric compression tests. A numerical modelling programme was then performed, where finite element models were firstly developed and validated against the test results and then employed to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and loading combinations. On the basis of the test and numerical data, the applicability of the design interaction curves for S700 (or S690) high strength steel welded I-sections under minor-axis combined loading, as set out in the European code, American specification and Australian standard, to their S960 ultra-high strength steel counterparts was evaluated. The evaluation results generally revealed that all the codified design interaction curves lead to unduly conservative and scattered cross-section resistance predictions, mainly owing to the adoption of conservative bending end points (i.e. cross-section bending capacities).
... For each I-section, five geometrically identical stub column specimens were prepared and planned to be tested under eccentric compression loads at different initial loading eccentricities about the cross-section major principal axis. Table 1 reports the measured cross-section dimensions and member length L for each eccentrically loaded stub column specimen; note that the nominal member length was selected according to Ziemian [13], which is deemed short enough to avoid flexural buckling, but still long enough to contain a representative pattern of local geometric imperfections and membrane residual stresses. ...
... It is worth noting that all the modelled I-sections were categorised as Class 4 (slender) cross-sections, based on the slenderness limits given in EN 1993-1-12 [10], ANSI/AISC 360-16 [11] and AS 4100 [12]. The model length was set as three times its mean outer cross-section dimension [13]. Moreover, the initial loading eccentricities were varied from 0.5 mm to 1200 mm (see Table 6), resulting in a wide spectrum of combinations of compression load and major-axis bending moment being considered. ...
... It is worth noting that both AS 4100 [12] and EN 1993-1-12 [10] adopt linear design interaction curves, but with the differences being the end points. The AS effective width approach is employed for calculating N eff, AS , with the effective plate element width c eff,AS defined by Eq. (12), while M eff,y,AS is determined by Eq. (13), where λ sy is the AS yield slenderness limit for flanges and λ s is the AS section slenderness, as specified in Clause 5.2.2 of AS 4100 [12]. ...
Article
This paper presents an in-depth experimental and numerical investigation into the local buckling behaviour of S960 ultra-high strength steel welded I-sections under combined compression and bending moment about the major principal axis. Two I-sections (I-120 × 120 × 6 and I-150 × 75 × 6) were considered in the experimental investigation, and for each I-section, five eccentrically loaded stub column tests were conducted under different initial loading eccentricities. The experimental results were then adopted in a numerical investigation for validating finite element models, by means of which parametric studies were conducted to generate additional numerical data over a wide range of cross-section dimensions and initial loading eccentricities (i.e. loading combinations). The obtained experimental and numerical results were used to evaluate the applicability of the relevant design interaction curves, as set out in the European code, American specification and Australian standard, to S960 ultra-high strength steel welded I-sections under major-axis combined loading. The evaluation results revealed that (i) the European code results in safe but slightly conservative failure load predictions, (ii) both the American specification and Australian standard lead to relatively accurate failure load predictions and (iii) all the three design codes offer a good level of design consistency.
... Symmetrical partially tapered I-beam is generally used in girders with rigid ends. Thus, for sway frames, the beam is bent in double curvature while for no sway frames the beam is bent in single curvature [31]. The variation of the moment of inertia of linearly fully tapered Ibeam, shown in Fig. 2 with respect to x-axis origin at virtual point of zero cross section is provided in [10,14,32] as follows: ...
... In sway frames both ends of the restraining beam are subjected to equal end moments in the same direction [31] as shown in Fig. 4. The slope moment-rotation equation in this case can be written as follows: ...
... For frames prevented from sway, the restraining beam is subjected to uniform and constant bending moment (M) along its span as it is bent in single curvature [31]. The moment-rotation equation in this case can be written as follows: ...
Article
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This paper presents stability analysis of steel frames composed of linearly tapered columns and partially tapered restraining beams. In the first part of the stability analysis, closed-form equations for the bending stiffness of the symmetrical and unsymmetrical partially tapered restraining beam are derived and presented in form of design charts. Subsequently, slope deflection equations of linearly tapered column subjected to axial compressive load are then assembled along with the bending stiffness equations of partially tapered beams to determine the elastic critical load and the effective buckling length factor for non-sway and sway steel frames. Numerical examples and efficient design charts are presented for several braced and unbraced steel frames. Moreover, the effect of gravity loads acting on leaning columns connected to sway frames is investigated. Based on this investigation it is concluded that correction of effective buckling length factor based on story buckling concept can be extended to cover steel frames with tapered column as well.
... [2] Whereas www.advmatinterfaces.de on geometry and how the plate is supported. [27] Here D = Et 3 [12(1−ν 2 )] -1 , where E and ν are the elastic modulus and Poisson ratio of the plate, respectively. Assuming E = 100 GPa and ν = 0.3, a rough calculation indicates that a simply-supported metallic plate (k = 4) will buckle from a compressive stress on the order of icephobic surfaces (σ c = τ ice = 100 kPa) when w/t ≈ 2000. ...
... Compared to a plate that is simply supported, plates stiffened a distance (a -ℓ gap )/2 on both sides (for BEAMS, stiffened by the tape, see insets in Figure 1f,g), exhibit an effective critical buckling stress, σ e , much higher than σ c . [27] Given the inverse square dependency of σ c on the plate's width, the effective buckling stress should scale as σ e ≈ σ c (a/ℓ gap ) 2 . Consequently, we always observed cohesive fracture (τ ice > 500 kPa) when ℓ gap << a, and only for ℓ gap /a > 1 was ultra-low ice adhesion observed. ...
Article
Ice accretion is significantly detrimental to a range of different industries worldwide. Current methods for reducing ice adhesion include the use of lubricants, hydrophobic coatings, or soft elastomers, all of which exhibit limited durability. As an alternative, here sparsely confined metallic sheets are suspended and the surface buckling instability is tailored, resulting in ice adhesion strengths on par with these prior strategies but without the use of any coatings. These Buckling Elastomer-like Anti-icing Metallic Surfaces, or BEAMS, exhibit ultra-low ice adhesion (<1 kPa) and the mechanical resilience of metals. Results from an icing wind tunnel confirmed the efficacy of BEAMS toward impact ice accreted in realistic conditions via the high-speed impingement of ≈20 µm droplets at −20 °C. The BEAMS sheet confinement, boundary conditions, and physical dimensions of both the ice and the metallic plates can be altered to minimize ice adhesion via the mechanics of plate buckling. Additionally, BEAMS that detach ice without directly contacting it are designed, the scalability of BEAMS is demonstrated, and their durability is verified using rain erosion, sandblasting, thermal extremes, and repeated icing/de-icing, both in an icing wind tunnel and on a benchtop system.
... [2] Whereas www.advmatinterfaces.de on geometry and how the plate is supported. [27] Here D = Et 3 [12(1−ν 2 )] -1 , where E and ν are the elastic modulus and Poisson ratio of the plate, respectively. Assuming E = 100 GPa and ν = 0.3, a rough calculation indicates that a simply-supported metallic plate (k = 4) will buckle from a compressive stress on the order of icephobic surfaces (σ c = τ ice = 100 kPa) when w/t ≈ 2000. ...
... Compared to a plate that is simply supported, plates stiffened a distance (a -ℓ gap )/2 on both sides (for BEAMS, stiffened by the tape, see insets in Figure 1f,g), exhibit an effective critical buckling stress, σ e , much higher than σ c . [27] Given the inverse square dependency of σ c on the plate's width, the effective buckling stress should scale as σ e ≈ σ c (a/ℓ gap ) 2 . Consequently, we always observed cohesive fracture (τ ice > 500 kPa) when ℓ gap << a, and only for ℓ gap /a > 1 was ultra-low ice adhesion observed. ...
Article
Icephobic Surface Design In article number 2101402, Kamran Alasvand Zarasvand, Kevin Golovin, and co-workers design durable icephobic surfaces by exploiting the buckling instabilities of metallic plates. These Buckling, Elastomer-like, Anti-icing Metallic Surfaces, or BEAMS, offer exceptional icephobic performance without the need for any coating.
... Imperfections are critical when geometric instabilities are expected in nonlinear analysis problems (Galambos 1998;Ziemian 2010;AISC 2016), for this reason, care is taken in describing the approach used to apply imperfections. Member out-of-straightness and out-of-plumbness imperfections are deemed critical for flexural buckling modes, and local flange and web imperfections are deemed critical for local buckling modes. ...
... The twisting imperfection in Case study 3 is based on the measured value, whereas the twisting imperfection in Case study 4 is chosen near the maximum of the measured values of Elkady and Lignos (2018a). Finally, no imperfections are included in components with stable equilibrium paths because geometric instabilities are not expected, thereby diminishing the importance of imperfections (Galambos 1998;Gantes and Fragkopoulos 2010;Ziemian 2010). ...
Article
A warping-inclusive kinematic coupling method to be used in finite-element analysis of members featuring wide-flange cross sections is proposed in this paper. This coupling method is used in mixed-dimension macromodels that combine continuum and beam-column elements to reduce the computational cost of purely continuum finite-element models. The proposed coupling method, utilizing either linear or nonlinear constraint equations, is implemented and validated in a commercial finite-element software; the source code is made publicly available. Case studies indicate that including warping in the coupling formulation is critical for components that may experience coupled local and lateral-torsional buckling. Also highlighted is the potential of macromodels to reduce the total degrees of freedom by up-to about 60%, and computational memory use by up to around 80%, while retaining solution fidelity for beam, column, and panel zone components in steel moment-resting frames. The case studies show that the linear constraint equation formulation may not be suitable for all problems; however, it may still yield acceptable results as long as the level of twisting is insignificant and lateral-torsional buckling is not critical.
... Residual stresses, considered as an initial state existing in structures prior to the externally applied loading are caused by various manufacture processes such as cold-formed process (i) press-braking; (ii) coldrolled process; (iii) coiling and uncoiling of the steel sheet etc. and welding that induces uneven cooling/heating, as thermal-type stresses. Residual stresses can adversely affect the structural behaviour since they can cause premature yielding through part of the material thickness, leading to the further loss of the stiffness of the structure due to its superimposed stresse, and reduced stability and bearing capacity of the structural members [5,19,21,22,56]. ...
... Residual stresses can distribute in different directions for structures. Longitudinal and transverse directions are the two main categories and the residual stresses in the longitudinal direction are more influential than those in the transverse direction, as illustrated by Ziemian [56] and Schafer et al. [57]. Hence, this study focused on longitudinal residual stresses which can be further de-composed into membrane residual stresses and bending residual stresses, as represented in Fig. 21. ...
Article
This paper presents an experimental investigation on the material properties variation and residual stress distribution within the high strength steel (HSS) hexagonal hollow sections. Three different fabrication routes encompassing welding or combinations of welding and press-braking were employed for fabricating the HSS hexagonal sections. HSS plates of grade Q690 with two thicknesses of 6 mm and 10 mm were used. A total of 76 tensile coupons extracted from the parent plates and the hexagonal hollow sections with different fabrication routes were tested to obtain the static material properties of the parent steel plates and the material properties variation for the hexagonal hollow sections. A new material model describing the material properties for the flat portion was proposed while the existing material model for cold-formed steel was modified for the materials at the press-braked corners. In addition, residual stresses measurements for five HSS hexagonal sections with different fabrication routes and varying section slenderness were subsequently performed. Sectioning method was adopted in this study with 74 strips extracted and more than 898 strain readings obtained. Results of the residual stress distributions and the magnitudes are presented and discussed. Based on the measurement results, predictive models for residual stresses were developed and can be applied to estimate residual stresses for predicting the structural behaviour of the HSS hexagonal hollow sections.
... The adopted SHS 100×100×6 was classified as Class 1 at ambient temperature, according to the slenderness limits set out in EN 1993-1-12 [11]. The nominal specimen length was selected, following the recommendations of Ziemian [14], to ensure that there would be no occurrence of global buckling and a representative pattern of initial local geometric imperfections could also be included. The geometric dimensions of each stub column specimen were measured, as reported in Table 1, where L is the member length, h is the outer section height, b is the outer section width, t is the wall thickness and is the inner corner radius -see Fig. 1. ...
... Class 1, 2, 3 and 4) of cross-section set out in EN 1993-1-12 [11]. The member length of each FE model was taken as three times the outer section height [14]. The initial loading eccentricities were varied between 4 mm and 300 mm, leading to a wide range of combinations of compression load and bending moment being considered. ...
Article
This paper reports experimental and numerical studies on the post-fire behaviour and residual resistances of S700 high strength steel tubular section stub columns under combined compression and bending. A testing programme was firstly performed, including heating and cooling of specimens as well as post-fire material testing, initial local geometric imperfection measurements and eccentric compression tests. The testing programme was followed by a numerical modelling programme, where finite element models were developed and validated against the test results and then employed to carry out parametric studies to generate further numerical data over a wide range of cross-section dimensions and loading combinations. Given that there are no design standards for high strength steel structures after exposure to fire, the design interaction curves for high strength steel tubular section stub columns under combined loading at ambient temperature, as given in the European code, American specification and Australian standard, were evaluated, using post-fire material properties, for their applicability to S700 high strength steel tubular section stub columns under combined loading after exposure to fire. The evaluation results revealed that all the three sets of codified design interaction curves yield overall accurate post-fire residual resistance predictions for S700 high strength steel tubular section stub columns under combined loading, with the highest level of design accuracy offered by the American specification.
... Premature yielding through part of the material thickness led to further loss of the stiffness of the structure due to the superimposed stresses, invariably resulting in the instability and subsequent reductions of the resistance of the structural members [84]. The residual stresses measurements in this study focused on those in the longitudinal direction, as suggested in [85][86][87][88] that residual stresses in longitudinal directions are more influential than those in the transverse direction. The residual stresses can be de-composed into membrane residual stresses and bending residual stresses. ...
... The length of specimens used in this study is 400 mm. The specimens with such length are long enough to minimize the possibility that the operation of cutting at section ends may disturb the residual stress pattern in the centre portion of the specimen [87]. Due to the symmetrical geometry dimension, half section of CF1-145 × 6-1. ...
Article
This paper presents an experimental investigation on the material properties variation and residual stress distribution within the cold-formed high strength steel (HSS) irregular hexagonal hollow sections (IHexHS) with two different fabrication methods. The test specimens were manufactured through press-braking and gas metal arc welding (GMAW). Tensile coupons tests were conducted on specimens fabricated from the critical locations within cold-formed HSS irregular hexagonal hollow sections, namely the flat portions, corner portions of either half or quarter sections. New material models to predict the material properties for the tensile coupons with both rounded responses and yield plateau followed by significant strain hardening were proposed. In conjunction with conventional tensile coupon testing, non-contact digital image correlation (DIC) measurement through which strain fields along the gauge length before and after the occurrence of diffuse necking was carried out to obtain the accurate strain field after necking. Moreover, the residual stresses measurements for HSS IHexHS were also performed, membrane and bending residual stresses distributions on the investigated sections were measured in longitudinal directions with 59 strips cut by wire-cutting method and more than 708 strain readings obtained. Results of the residual stress distributions and magnitudes are presented and discussed. Based on the measurement results, predictive models for residual stress distribution were developed and can be subsequently applied for predicting structural behaviour of the cold-formed HSS IHexHS.
... The 2016 provisions are written in a unified form for both stiffened and unstiffened elements using the effective width formulation for all but round HSS. This change is not so much the result of new research as it is a reinterpretation of the foundational work of von Kármán et al. (1932), Winter (1947), and Peköz (1987), as summarized in Ziemian (2010). The effective widths are used to determine the effective area, and that area is multiplied by the critical stress, determined without consideration of slender elements, to obtain the nominal compressive strength. ...
... The elastic local buckling stress, F el , from classic plate buckling theory (Ziemian, 2010) is ...
Article
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Compression member strength is controlled by the limit states of flexural buckling, torsional buckling, and flexural-torsional buckling, as applicable. These compression members may buckle globally or locally, depending on the overall column slenderness and the local plate element slenderness for the plates that make up the shape. If any of the plate elements will buckle at a stress lower than that which would cause the column to buckle globally, the local buckling of the plate will control the overall column strength. When this occurs, the column is said to be composed of slender elements. This paper will briefly discuss past specification provisions for slender element compression members and introduce the new provisions in the 2016 AISC Specification. It will present a simplification that reduces the number of constants that must be used and will present the specification requirements in an alternate format. Because the 2016 requirements result in different strengths than the 2010 requirements, figures are provided to illustrate the overall impact of these changes on column strength.
... Fig. 1 displays the measured material stress-strain curves, while Table 1 reports the key average measured material properties, where E is the Young's modulus, σ 0.2 is the 0.2% proof stress, σ 1.0 is the 1.0% proof stress, σ u is the ultimate stress, ε u is the strain corresponding to the ultimate stress, ε f is the strain at fracture, and n and m 1.0 are the coefficients used in the Ramberg-Osgood (R-O) material (Arrayago et al. 2015). The membrane residual stresses in the studied austenitic stainless steel welded I-sections were measured through the sectioning method (Ziemian 2010). The measured data were carefully analyzed and then used to develop a new model for predicting the membrane residual stresses in the studied austenitic stainless steel welded I-sections, with its distribution pattern depicted in Fig. 2 and the distribution parameters (a, b, c, and d) and peak magnitudes reported in Table 2 (Sun and Zhao 2019). ...
Article
The present paper reports in-depth experimental and numerical studies of the cross-sectional behavior and resistances of austenitic stainless steel welded I-sections under combined compression and major-axis bending moment. A testing program was first performed, which employed two austenitic stainless steel welded I-sections and included initial local geometric imperfection measurements and 10 major-axis eccentric compression tests. Following the testing program, a numerical modeling program was conducted, where finite-element models were developed and validated against the test results and then employed to conduct parametric studies to generate further numerical data over a wide range of cross-section dimensions and loading combinations. On the basis of the obtained test and numerical data, the accuracy of the design interaction curves given in the European code and American design guide for austenitic stainless steel welded I-sections under major-axis combined loading was evaluated. The evaluation results generally indicated that the codified design interaction curves yield excessively conservative cross-section resistance predictions, mainly due to the conservative end points, as determined without considering material strain hardening. Finally, new design interaction curves were proposed through adopting the European code design interaction curves anchored to more accurate end points, as calculated with rational exploitation of material strain hardening by the continuous strength method. The new design interaction curves were found to offer significantly improved design accuracy than their codified counterparts. The reliability of the new design interaction curves was confirmed by means of statistical analyses.
... The FHWA-CSBRP and other projects such as NCHRP project 12À52, "LRFD Specifications for Horizontally Curved Steel Girder Highway Bridges," resulted in the unification of the design equations for straight and curved steel girders into the 2004 LRFD specifications (AASHTO, 2004;White & Grubb, 2005). Additional historical details as well as additional details of the broader subject of curvature effects on bridge girder strength are also presented in Linzell, Hall, and White (2004a), Ziemian (2010), and Weiwei and Yoda (2010). ...
Chapter
This chapter presents a new design method for considering the bracing effect of sheathing boards that are attached to CFS (cold-formed steel) structural members. It also presents a detailed summary of history, development, and flaws of the available sheathing braced design guidelines of the American Iron and Steel Institute. Previous investigations have shown that the current American Iron and Steel Institute (AISI) design specification for sheathing bracing design of CFS wall panels is unconservative (design predictions>experimental strength) due to exaggerated sheathing stiffnesses calculated from ideal loading conditions rather than worst-case loading conditions. Therefore a new design method is suggested based on the performance (strength and stiffness) of the individual sheathing-fastener connections. The current test setup of the AISI is improved to simulate realistic failure modes of the sheathing-fastener connections. The test results revealed: (1) the prominent influence of tensile modulus of the sheathing board and the geometric dimensions of the CFS stud (lever arm), (2) the sudden and catastrophic failure modes and they should be considered in the form of coefficients in the design expressions to prevent an unsafe design, and (3) the sheathing thickness did not influence the performance of the sheathing board (strength, stiffness, and failure mode). Based on test results, new expressions are formulated to predict the stiffness and strength of the individual sheathing-fastener connections. Finally, the effectiveness of the proposed simplified design method is illustrated by a design example, which quantifies the benefit of adopting this method in AISI design guidelines.
... Test Procedure. The test procedure used for the centrally loaded column test is according to Ziemian [10]. Before testing the variation in cross-sectional shape and area and initial out of straightness were measured on some of the specimen, showing imperfection within EN 10217-1 [11] tolerances. ...
Article
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This paper presents the experimental and numerical results for the axial capacity of cracked tubular steel members. Experimental tests of 11 columns in compression with simulated cracks of different sizes, defined as the percentage of the circumference (12%, 23.5% and 38.5%). The crack-tips were further treated by drilling a crack arresting hole. These specimens were then modelled by finite element analysis which were verified to match the experimental test. The DNVGL-RP-C208 standard was used as basis for performing the numerical finite element analysis. In addition, the capacity of the columns was calculated according to the 2004 revision of the NORSOK N-004 standard. The experimental tests indicated that the capacity in compression did not change significantly with the presence of cracks and crack arresting holes. The results from the numerical finite element analysis show a good agreement with the experimental work. However, the compressive capacity according to NORSOK N-004 shows a significant deviation to the safe side.
... Finally, the employed shield gas was 98% AR and 2% CO 2 , at a flow rate of 10-20 L=min. Printing of typical specimens is illustrated in Fig. 5. Following their fabrication, the stub columns were detached from their substrate plate using a plasma arc cutter and then cut to specified lengths of approximately four times the outer crosssection dimensions; this was chosen to be long enough to include a representative distribution of residual stresses and geometric imperfections, yet short enough to prevent overall flexural buckling (Ziemian 2010). Both ends of the stub columns were machined to be flat and parallel, and the exterior surfaces were sandblasted with glass beads to remove any welding soot from the WAAM process. ...
Article
Wire arc additive manufacturing (WAAM) is a method of metal three-dimensional (3D) printing that has the potential for a significant impact on the construction industry due to its ability to produce large parts with reasonable printing times and costs. However, there is currently a lack of fundamental data on the performance of structural elements produced using this method of manufacturing. Seeking to bridge this gap, the compressive behavior and resistance of WAAM square hollow sections (SHS) are investigated in this paper. In a previous study by the authors, testing reported of sheet material produced in the same manner as the studied SHS is first summarized. The production, measurement, and testing of a series of stainless steel SHS stub columns are then described. Regular cross-section profiles were chosen to isolate the influence of 3D printing and enable direct comparisons to be made against equivalent sections produced using traditional methods of manufacturing. A range of cross-section sizes and thicknesses were considered to achieve variations in the local cross-sectional slenderness of the tested specimens, allowing the influence of local buckling to be assessed. Repeat tests enabled the variability in response between specimens to be evaluated; a total of 14 SHS stub columns of seven different local slendernesses was tested, covering all cross-section classes of AISC 370 and Eurocode 3. Advanced noncontact measurement techniques were employed to determine the as-built geometric properties, while digital image correlation measurements were used to provide detailed insight into the deformation characteristics of the test specimens. Owing to the higher geometric variability of WAAM relative to conventional forming processes, the tested 3D printed stub columns were found to exhibit more variable capacities between repeat specimens than is generally displayed by stainless steel SHS. Comparisons of the stub column test results with existing structural design rules highlight the need to allow for the weakening effect of the geometric undulations that are inherent to the WAAM process in order to achieve safe-sided strength predictions.
... In order to develop a lightweight floor system based on sandwich panel the structural, thermal, acoustic and fire resistance requirements were identified. The structural requirements are established in the Eurocodes [11,12], the relative transposed Portuguese norms [13], the European Recommendations for Sandwich Panels [14], and the literature regarding the design of CFS members [15], fiber-reinforced polymers and sandwich panels [16,17]. ...
Chapter
A new lightweight floor system was developed to tackle the sustainability issue in the construction sector. The proposed flooring system is suited for rehabilitation of degraded timber floors in existing building. Despite the great potential that sandwich construction shows as load bearing elements their use has been hindered by the high initial cost. Three alternative architectures, all including cold-formed steel (CFS) face sheets, were envisaged, namely i) CFS webs and polyurethane (PUR) foam core system, ii) glass fiber-reinforced polymer (GFRP) webs and PUR foam system and iii) outer CFS webs and balsa wood core. The structural, thermal, acoustic and fire resistance requirements were identified in the Portuguese national codes. Particular attention is given to the description of the materials adopted for the different components with respect to the driving factors of the design of the panel, namely weight, cost, environmental impact, load bearing capacity, rigidity, thermal and acoustic properties and fire resistance. The preliminary design of the three sandwich panels is carried out considering the value of the actions established in the Eurocode standards. The final layout and cost estimate are the results of a parametric study aimed at retrieving the lightest and most economical solutions.
... Residual stresses can have a significant impact on the global buckling capacity of the compressed steel members [1]. In advanced design and analysis methods, such as in Geometrically and Materially Nonlinear Imperfection Analysis (GMNIA) of EN 1993 [2], residual stress models are needed for two purposes: (1) To incorporate residual stresses into the calculation model when designing with such a method. ...
Article
This study revisits residual stress models of cold-formed rectangular hollow sections (CFRHS). Residual stresses of CFRHS have a complex distribution that varies along the cross-sectional perimeter and through the material thickness. The distribution depends on the manufacturing methods and steel grades, which constantly evolve. Existing residual stress models are based on old measurements and for normal strength steel specimens (nominal yield strength fy,nom ≤ 460 MPa). This study evaluates the suitability of these models for modern CFRHS made of normal- and high-strength (fy,nom > 460 MPa) steels. Evaluation is carried out as an extensive analysis for a data set, which is collected from the literature, and supplemented with new measurements made for grade S700 specimens. As a result of the evaluation, an updated residual stress model is proposed, which combines the best suitable features of the existing models with slight modifications. The proposed model is valid for CFRHS made of steel grades up to S960. The model can be used in the advanced analyses of CFRHS structures. Additionally, statistical information is provided for the residual stress components such that the model can be used in probabilistic modelling and reliability studies.
... The failure load TEST is the ultimate load of each built-up column obtained from the tests and the corresponding failure modes are observed at ultimate loads. Though the columns are designed to be long (L > 20r) according to Ziemian[72], Yang and Hancock[73] and Yang et al.[74], all the columns failed in local buckling as can be observed in Failure modeFigures ...
Article
Structural behavior of Cold-formed Steel (CFS) face-to-face connected built-up closed cross-section columns is investigated in the present study. The CFS built-up columns are designed as long (L > 20r) and locally slender (λl > 1) to verify the influence of intermediate longitudinal connection spacing and check the appropriateness of the current AISI’s Direct Strength Method (DSM) design. A total of 31 axial compression tests were carried out with fixed–fixed end conditions, the design parameters such as local slenderness (λl), global slenderness (λc), intermediate longitudinal fastener spacing (a), and length of the column (L) are varied. The failure modes of the column are summarized and the reason for them is elucidated. The influence of intermediate longitudinal connection spacing was observed in the failure modes and ultimate loading capacity. The test results including ultimate load and failure modes were compared with the current direct strength method design predictions. As a preliminary work towards improving the current AISI design approach, a modified local slenderness (λlm) expression is suggested to consider the influence of intermediate longitudinal fastener spacing in the design strength of cold-formed steel built-up closed cross-section columns.
... (1) where (i) fcrG and G are the column global critical buckling stress and slenderness, and (ii) y is the material (steel) yield stress. This design curve, combining an exponential expression [6] with the (lowered) Euler curve, was first included in the CFS design manual in 1996 [7], due to the work of Peköz & Sümer [8], who showed that the above design curve, already codified in the context of hot-rolled steel members used in buildings (AISC [9]), provided better quality estimates than that adopted at that time by the CFS community [7]. These authors based their findings on 214 test results concerning concentrically loaded CFS columns with various cross-sections (lipped channels, hat-sections, box-sections and I-sections formed by back-to-back plain channels), all exhibiting low-to-moderate global slenderness values (G  1.75). ...
Article
The purpose of this work is to extend the scope of the previous studies, by considering fixed-ended columns under elevated temperatures (up to 800° C) with three cross-section shapes (lipped channels, racks and stiffened lipped channels), various cross-section dimensions (five per shape) and different lengths. The results presented and discussed consist of column FT post-buckling equilibrium paths and failure loads, which are obtained through geometrically and materially non-linear Ansys SFEA. In order to cover a wide FT slenderness range, several room-temperature yield stresses are considered. The model prescribed in EC3-1.2, for cold-formed steel, is adopted to describe the temperature-dependence of the steel material properties. Finally, the numerical failure loads obtained by the authors, together with numerical and experimental ones collected from the literature are used to propose a modification of the DSM-based FT strength curves developed previously by authors and assess the merits of the new design curves. It is shown that the proposed modification improves visibly the failure load prediction quality, thus providing encouragement to continue the search for an efficient and reliable DSM-based design approach for columns failing in FT modes at elevated temperatures.
... In the United States, laced built-up columns are preferred over battened columns and are thus more widely adopted (as shown in Fig. 1). Compared to battened columns, laced columns ensure greater shear stiffness (Ziemian 2010;Subramanian 2016) and better lateral connectivity over the column height. This results in enhanced integrity and stability of the columns. ...
Article
A test program on cold-formed steel (CFS) laced columns fabricated using plain channels has been presented in this study. Twelve specimens with single and N-type lacing configurations were fabricated. The lacing plates and the end-plates were connected to the chords by using self-drilling screws. The effect of critical parameters, like lacing slenderness and transverse chord spacing, on the performance of laced columns under concentric axial loading was investigated. The aspect ratio of the built-up section of the specimens varied from 0.75 to 1.25. The relative slenderness of the unsupported chord (with respect to the global slenderness of the column) ranged from 0.31 to 0.87 in single laced columns, and 0.15-0.44 in N-type laced columns. The performance of the specimens was assessed in terms of their failure modes, peak strengths, and load-displacement trends. Lastly, the strength estimations from both the current American (AISI S100-16) and European (EN1993-1-3) standards were evaluated, by comparison against the test strengths. It was noted that both these codes overpredicted the strength of the laced column specimens by up to about 25%. The modified design rules catering to both American (AISI S100-16) and European (EN1993-1-3) standards, previously proposed by the authors for CFS battened columns, were assessed and their strength predictions were found satisfactory for both types of lacing configurations. The reliability index determined using the modified design rules was approximately equal to three indicating high reliability.
... However, they are weaker in shear resistance. The shear deficiency of built-up columns reduces their buckling capacity and can cause a local or compound buckling [1,2]. The shear connections' important role was first recognized from the failure of the Quebec Bridge over the St. Lawrence River in 1907. ...
Article
Built-up columns have been widely used in buildings and bridges. However, despite wide application in steel construction, the seismic design of these columns has not been covered in either the design codes or the literature. On the other hand, past earthquakes have shown that built-up battened columns have been vulnerable to seismic actions. Therefore, it is crucial to investigate the seismic response of these columns and determine their governing failure mode, deformation, and bending moment capacity. This study investigated the effect of battens’ spacing on the cyclic response of built-up columns through experimental works and numerical simulations. Four columns with different batten spacing and chord distances were constructed and subjected to quasi-static cyclic loading. Besides, 24 built-up battened columns with different batten spacing, chord distances, and axial forces were simulated in ABAQUS software and subjected to similar cyclic loading. The obtained results indicated that the bulging of chord webs and the local buckling of chord flanges were the main reason for the failure of columns. Besides, the batten spacing significantly affected the bending moment capacity of built-up columns. Moreover, because of local buckling in flanges, built-up columns did not reach their plastic moment capacity. It was also observed that design codes’ limitations for batten spacing were not conservative and did not result in a similar safety margin for the bending moment capacity of built-up columns.
... The initial residual stress distribution pattern of the steel equal-leg angles was related to the produced method and steel grade. This study did not measure the residual stress distribution pattern of the angle section but adopted the results of the previous study ( Fig. 6) [34][35][36]. ...
Article
Structural performances and compression resistances of S460 high-strength steel equal-leg-angle section columns eccentrically connected by one leg at one end were analysed based on experiments and numerical simulations, and the results are reported in this study. It was first conducted as a testing program, which comprised material tensile coupon tests, initial global and torsional geometric imperfection measurements, and forty–eight column tests. Experimental setup and procedures have been presented in detail. Key test results, which include failure patterns, load–mid–height lateral displacement curves, and load–strain curves, are reported and discussed. Columns with slenderness ratios of 30 and 45 failed primarily owing to local buckling, and those with slenderness ratios of 60 and 80 failed primarily owing to flexural–torsional buckling. A numerical modelling program was implemented. Finite element models were developed and verified based on test results. Numerical data based on various cross-sectional dimensions and member lengths were obtained. Then, the accuracy of the codified design methods based on the Chinese, American, and European standards and direct strength method (DSM) design approach was evaluated based on the obtained test and numerical data. The evaluation results revealed that the predicted load–carrying capacities of columns with eccentric connections using GB50017 and AISC360 well agreed with the corresponding experimental and finite element analysis results. The prediction results of columns based on the other codified methods were relatively unsatisfactory. Based on the application of the revised GB50017 and DSM–based approaches, improved resistance predictions were achieved.
... The residual stresses in steel structures can be considered in both longitudinal and transverse directions. Ziemian [46] and Schafer et al. [47] demonstrate that the residual stresses in the longitudinal direction have the most significant effect on the structures, therefore, longitudinal residual stresses were investigated in this study. Moreover, residual stresses can be further decomposed into membrane and bending residual stresses based on the distribution through the thickness of the hollow section [48]. ...
Article
A systematic investigation into the variation of the material properties and residual stress distribution across cold-formed high strength steel (HSS) irregular octagonal hollow sections (IOctHS) is presented in this paper. The specimens were fabricated through welding the two cold-formed half-sections by gas metal arc welding (GMAW). Non-destructive inspection was executed to detect any cracks in the welding internally and externally. Tensile tests on coupon specimens taken from the critical locations within the cross sections were carried out to measure the material properties variation within the HSS IOctHS. The material strength variations within different cross sections exhibit an anticipated similar pattern that strength enhancement at corner regions was more obvious than flat coupons counterpart. The largest strength enhancement is 8.4% at corner region compared with the average yield strength of parent plates, whereas the yield strength and ultimate strength of flat coupon specimens generally fluctuate at a certain level. Based on the obtained material properties, the existing material models for predicting the stress-strain curves were assessed and new material models are proposed to generate the stress-strain relationship for materials within the HSS IOctHS. Moreover, the residual stress measurement for cold-formed HSS IOctHS was performed using the sectioning method. A total of 55 strip specimens were extracted from the cross sections of HSS IOctHS with more than 660 strain readings. Based on the residual stress measurement results, the magnitude and distribution pattern of the residual stresses are presented and discussed. A predictive model for residual stress distribution of the cold-formed HSS IOctHS was developed.
... The initial imperfection was introduced in order to initiate lateral-torsional buckling. The distribution of residual stress, as shown in Fig. 11(c), was used based on typical residual stress patterns (Ziemian 2010). ...
... Several experimental studies reported that flange buckling can occur at very early stages without causing loss of bending strength (e.g. see Zieman [21] p.832). In such cases, it is very difficult to identify the initiation of local buckling from moment rotation hysteresis curves. ...
Article
This paper focuses on the characterization of the rotation capacity of steel deep and shallow members made with European profiles subjected to cyclic flexural loading by considering several influencing parameters such as geometrical imperfections, material ductility, lateral unbraced length, and member length. For this purpose, an advanced finite element model, validated with past experimental data, was developed and an extensive para-metric study was conducted. The numerical simulations revealed that shallow and deep members have different buckling behaviours and rotation capacity trends. Based on the numerical results and the experimental data collected from the literature, empirical equations are derived to quantify plastic rotation capacity limits. Compared with existing estimations, the proposed empirical equations show a more reasonable estimate. These rotation limits can be useful as modelling parameters for nonlinear static and response-history analysis and for the identification of the damage states in the context of Part 3 of Eurocode 8.
... Due to the bottom end being closed, very thin wall thickness, and poor formability of the material at room temperature, end press types of forming process are mostly used for the necking process. However, a local buckling failure associated with the necking is the main problem due to the higher ratio of the tube diameter to tube thickness [2]. When designing the necking process, the effect of material damage and strain path on the initiation of local buckling should be properly predicted. ...
Article
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Because of thin wall thicknesses and closed bottom ends of the extruded aerosol can, the necking limit analysis needs intensive investigation. The numerical analysis of the necking process of 0.45 mm thickness pure aluminum aerosol can was carried out. The result indicated that the length of the aerosol can wall, which is not fixed by the bottom die and the angle of inclination of necking tools are important factors that affect the development of deformation boundary limits due to plastic instability of local buckling. The fraction of taper angle of tool becomes more series parameter while necking at larger free length and it needs more concentration. Instead, the ratio of necking tool displacement to the total free length to initiate buckling was increased while increasing free length.
... A similar approach can be found in the studies of He et al. [58] and Ban et al. [70]. It should be noted that, for comparison of the results with codified column curves, global imperfection magnitudes of L/1000 were used in the parametric studies [58,70,71]. ...
Article
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An extensive investigation on the behaviour of compact and slender box concrete-filled stainless steel tubular (CFSST) members is carried out studying their response under compression, bending, and combined compression and bending, with the main aim of developing comprehensive design procedures. Under this objective, an experimental programme is first conducted comprising compact and slender CFSSTs fabricated from austenitic and lean duplex stainless steel plates. Stub columns under axial compression as well as combined compression and bending, CFSST beams under pure bending, and long CFSST columns under axial force are all included in the experiments in order to investigate both the section and member responses. Specimens with high width-to-thickness ratios, high length-to-width ratios, and those under combined compression and bending are particularly considered in the experiments as test data is very scarce for such CFSSTs in the literature. A special technique is used to estimate the loads carried individually by the stainless steel section and concrete infill to assist with the development of design recommendations. The experiments are followed by an extensive numerical study comprising over two hundred three-dimensional nonlinear finite element simulations. Outcomes of the experimental and numerical programmes are presented, analysed, and discussed thoroughly. Comprehensive procedures are then developed for the design of compact and slender CFSSTs under compression, bending, and combined loading, which incorporate the effects of local and global buckling in strength predictions. Such procedures have not yet been established for CFSSTs in international design standards. The validity of the recommendations is demonstrated through comparison with the results of the present study as well as the test data available in the literature.
... Membrane residual stress measurements were conducted by means of the sectioning method, with the test setup and procedures being in compliance with those recommended in Ziemian [28]. Based on the measured results, a new predictive model [2] was proposed for predicting the membrane residual stress amplitudes and distributions in S690 high strength steel welded I-sections, with the distribution pattern shown in Fig. 2 and the distribution parameters and peak magnitudes reported in Table 2. ...
Article
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The present paper reports a thorough experimental and numerical investigation into the local–flexural interactive buckling behaviour and resistances of S690 high strength steel slender welded I-section columns. A testing programme, adopting two S690 high strength steel slender welded I-sections, was firstly conducted and included initial geometric imperfection measurements and ten pin-ended column tests. The testing programme was accompanied by a numerical modelling programme, where finite element models were developed and validated against the test results and then employed to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and member effective lengths. On the basis of the test and numerical results, the interaction of local and flexural buckling of S690 high strength steel slender welded I-section columns was carefully analysed. Regarding the design of S690 high strength steel slender welded I-section columns failing by local–flexural interactive buckling, the existing European code, Australian standard and American specification adopt the same design concept of using effective width method to consider local buckling and buckling curves to consider flexural buckling. Evaluation of the three existing design standards generally indicated that both the European code and Australian standard yield conservative interactive buckling resistance predictions for S690 high strength steel slender welded I-section columns, owing mainly to the adoption of conservative design flexural buckling curves, while the American specification results in an overall good level of design accuracy, but with many over-predicted resistances. An improved approach was then developed through the use of a new design flexural buckling curve combined with the effective width method given in the European code, and shown to yield accurate, consistent and safe interactive buckling resistance predictions for S690 high strength steel slender welded I-section columns.
Article
Design provisions for axially compressed rectangular hollow section (RHS) members with slender elements were evaluated using an approximate first-order reliability method analysis. A total of 342 nonlinear finite-element models, covering a range of width-to-thickness, height-to-thickness, and nondimensional slenderness ratios, were developed and analyzed. Calculated ranges of reliability indexes (β+) were computed and compared with β+ values obtained from the expanded separation factor approach and with target values in codes. The results showed that the Canadian Standards Association (CSA S16:19) design provisions for locally slender RHS compression members are imprecise, resulting in underpredictions of column strength by as much as 22%. AISC 360-16 design provisions, and a recently proposed modified CSA approach were shown to be better predictors. Considering all 342 columns together, the current resistance factor of ϕ=0.9 was shown to be acceptable in both codes.
Article
This paper presents an experimental study on the flexural behaviours of new-generation direct-formed square and rectangular hollow sections (collectively referred to as RHS herein). A total of 22 beam specimens covering wide ranges of cross-sectional dimensions and nominal yield stresses (350 and 690 MPa) are tested. The results are compared to those from previously tested indirect-formed and hot-finished RHS to study the effect of different production processes. The effects of post-production hot-dip galvanizing on residual stresses and flexural behaviours are also studied. The applicability of slenderness limits and flexural design formulae in the current North American steel design standards are examined using the experimental data. The experimental results demonstrate that the existing flexural design rules are generally conservative for direct-formed RHS (ungalvanized and galvanized).
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This work aims to investigate the performance of pultruded glass fiber reinforced polymer (pGFRP) I-section columns subject to short term concentric compression. A review of existing theories is presented, including the instability concepts, global and local buckling theories, perfect columns failure modes and the behavior of real columns. An experimental program including material characterization was conducted. Twenty-nine stubs – with three different I-sections geometries, having distinct flange width-to-section depth ratios (bf/d = 0.5; 0.75 and 1.0), mechanical properties, overall lengths and matrices – were tested. In a global point of view, the columns were fixed at both ends. The constituent plates, on the other hand, were tested with different end-conditions: clamped (CC), simply supported (SS) and simply in contact with base plates of the universal machine (CB). The third analyzed boundary condition, which is the most adopted in previous studies, was concluded to be closer to a clamped end-condition. The non-linear elastic strains distribution throughout the cross-section was also investigated. Finally, guideline recommendations for successful local buckling tests were proposed.
Article
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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.
Article
Beam-columns of uniform rolled or equivalent welded sections are the member types most commonly used in steel skeletal structures. EN1993-1-1 [1] provides two design procedures of such members, one based on the interaction equations for the section resistance and the member buckling resistance, and the other one based on the so-called General Method (GM) that tends to follow that of Ayrton-Perry's procedure used for extreme cases of compression without bending and bending without compression. Above cited design procedures yield similar results when the beam-column is predominantly under bending but sometimes results being away from each other when the beam-column is predominantly under compression. Recently, a novel version of GM has been proposed [2], providing a tool of more rational design that yields the results from Eurocode 3 interaction equation procedure in both extreme cases. The proposed procedure is based on the Euclidean norm of dimensionless action effects and evaluation of Maquoi-Rondal imperfection factor interpolated between those for compression without bending and bending without compression. This analytical procedure was verified with a wide range of advanced numerical simulations incorporating geometrical and material imperfections (residual stresses). In order to validate the accuracy of the proposed procedure, an experimental study on the buckling resistance of rolled I-section beam-columns was carried out the results of which are presented in this paper. Firstly, an overview of the experimental programme carried out on subframe specimens is given and then followed by the summary of measurements of deformations as well as global load vs. displacement characteristics for selected specimens. Finally, an assessment of the beam-column buckling resistance, experimental vs. predicted by Eurocode 3 interaction equations procedure, is presented and conclusions with regard to the preliminary validation exercise are drawn.
Article
This study evaluates the seismic response of an advanced hybrid steel-timber structure using a nonlinear static and dynamic analyses. A three-story prototype building located in Vancouver, BC, Canada was designed first. The gravity load resisting system (GLRS) consists of cross-laminated timber (CLT) floor slabs, glulam beams, and glulam columns. The lateral load resisting system (LLRS) includes a chevron-type steel Concentrically Braced Frame. The numerical model of the structure was then developed in the OpenSees program. Nonlinear hysteresis response of steel braces and timber joints were explicitly simulated. The results of the analysis revealed that the hybrid structure possess an acceptable lateral stiffness while providing sufficient ductility to dissipate seismic energy. No unsatisfactory response was observed in the timber system.
Article
This paper presents the development of flexural buckling curves for austenitic and duplex stainless steel welded I-sections and structural hollow sections, which are proposed for implementation in the new AISC stainless steel specification. The proposed buckling curves were developed following the same type of reliability analysis employed to develop the flexural buckling curve included in AISC 360 Specification for Structural Steel Buildings for carbon steel, considering all the experimental data available in the literature and a large number of numerical results. In order to facilitate their implementation, the proposed curves follow a similar form as the AISC-type of curve included in AISC 360, with the only differences being the addition of a yield plateau and the values of selected coefficients used to adjust the shape of the curves. Three different buckling curves are proposed: one buckling curve for circular hollow section (CHS) columns and I-section columns buckling about the major axis; one for rectangular hollow section (RHS) columns; and one for I-section columns buckling about the minor axis. The proposed curves represent a significant improvement with respect to the currently available stainless steel flexural buckling curve included in AISC Design Guide 27, providing an increase in strength predictions of up to 55%.
Article
High strength steel has been employed in modern steel-framed building structures. It should be highlighted that these steel structures may be built-up through fabrication of hot-rolled steel sections or welded high strength steel plates. This study performed an extensive series of compression tests on high strength stub columns. These columns were made of Q620E steel plates through welded steel plates. The ultimate loads and displacements were extracted from the load-displacement curves observed from the tests. The continuous strength method (CSM) was employed for analysis of the local buckling behavior of stub columns. In addition, a series of tensile strength tests were performed for standard steel coupons. A modified stress-strain constitutive model was then proposed for design purpose for high strength steels. The predicted ultimate loads were compared with the recorded ultimate loads. It can be found that a reliable predication may be achieved in application of CSM in high strength steel sections.
Article
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Wire arc additive manufacturing (WAAM) is a metal three-dimensional (3D) printing method that enables large-scale structural elements with complex geometry to be built in a relatively efficient and cost-effective manner, offering revolutionary potential to the construction industry. Fundamental experimental data on the structural performance of WAAM elements, especially at the member level, are however lacking. Hence, an experimental study into the flexural buckling response of WAAM tubular columns has been conducted and is presented in this paper. A total of 18 stainless steel square and circular hollow section (SHS and CHS) columns were tested under axial compression with pin-ended boundary conditions. Regular SHS and CHS profiles were chosen to enable direct comparisons against equivalent, conventionally manufactured sections and hence to isolate the influence of the additive manufacturing process, while the cross-section sizes and column lengths were varied to achieve a broad spectrum of member slendernesses. Owing to the geometric undulations inherent to the WAAM process, 3D laser scanning was used to determine the as-built geometry and global geometric imperfections of the specimens; digital image correlation (DIC) was employed to monitor the surface deformations of the specimens during testing. Full details of the column testing program, together with a detailed discussion of the experimental results, are presented. The applicability of the current column design provisions in EN 1993-1-4 and AISC 370 to WAAM stainless steel members was assessed by comparing the test results with the codified strength predictions. The comparisons emphasized the need to allow for the weakening effect of the inherent geometric variability of WAAM elements, in order for safe-sided strength predictions to be achieved.
Chapter
This paper proposes a method of reasonable selection of the fixation scheme, and the number of intermediates supports for straight multi-span beams in order to ensure the given values of the critical load from the compressive axial force. This axial force may be an external load or may occur, for example, as a result of a change in beam temperature. An effective way of providing the first critical force of the beam is to choose the appropriate method of fixing it: the type of the main supports and, if necessary, intermediate supports. This paper proposes a method of normalizing effective length factors, which enables to obtain convenient comparable values when choosing a fixation method and, as a result, to develop a method for a reasonable selection of a support arrangement system for a straight beam. The technique is based on the well-known theory of beam stability and uses effective length factors as a criterion for selecting the fixation scheme, which is formed after solving the corresponding differential equations of the beam state and is determined only by the fixing conditions. The obtained results can be used in calculations and design of any extended beam structures to control their stability by selecting the appropriate fixation scheme.
Article
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Current design standards for stainless steel such as ASCE 8-02 and EN 1993-1-4 prescribe provisions for the design of cross-sections and members that account for material nonlinearities and strain hardening, although these features are not considered in the global design of structures. Recent studies have highlighted the need of accounting for material nonlinearities in order to design efficient and safe stainless steel structures, and it is expected that the forthcoming versions of the standards will incorporate updated rules for the global design of these structures. To contribute to this field, this paper presents a Stiffness Reduction Method (SRM) for the in-plane design of stainless steel members and frames with stocky sections based on the prescriptions given in the next version of EN 1993-1-4. The proposed approach predicts the ultimate capacity and internal forces in stainless steel structures by performing a second-order elastic analysis in which the stiffnesses of the members are reduced by a set of factors defined in this paper to account for the effect of the spread of plasticity, residual stresses and member imperfections. The accuracy of the presented method is assessed for individual stainless steel structural members (columns, beams, and beam-columns) with different cross-sections and material properties, and for austenitic stainless steel portal frames, against numerical results obtained from nonlinear analyses conducted on finite element models. A comparison between the proposed approach and the Direct Analysis Method prescribed in the upcoming AISC 370 Specification is also provided, showing that the results are comparable in the two approaches.
Article
Tees are utilized as chord members in a number of arrangements of aluminum alloy trusses. The purpose of this study is to investigate the buckling behavior and design methods of concentrically loaded T-section aluminum alloy columns. Using column tests and finite element analysis, this study analyzed the buckling modes and ultimate strengths of high-strength aluminum alloy T-columns under axial compression and validated the numerical model against the experimental results. Comparisons with the current Eurocode 9 and Direct Strength Method (DSM) design rules were also conducted. Fixed- and pin-ended columns exhibit a quite different buckling behavior. The failure modes of flexural buckling about the two principal axes could be treated with sufficient safety and accuracy using the column design rules in Eurocode 9 and DSM. The effects of the effective centroid shift due to the local buckling of slender parts could be ignored. The Eurocode 9 and DSM leads to inaccurate and conservative results for fixed-ended columns failing by local-torsional buckling and flexural–torsional buckling. The paper recommends suggestions based on the DSM approach that improve the design strength predictions for aluminum alloy T-section columns.
Article
This paper reports an experimental and numerical investigation into the minor-axis flexural buckling behavior and capacity of press-braked S690 high-strength steel channel–section columns. The experimental investigation comprised initial geometric imperfection measurements and 10 pin-ended column tests. This was accompanied by a numerical modeling program, in which finite-element models were developed and validated against the test results and then adopted to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and member lengths. The obtained test and numerical data were adopted to assess the accuracy of the buckling curves, as given in the Eurocode, North American specification, and Australian/New Zealand standard, for press-braked S690 highstrength steel channel–section columns prone to minor-axis flexural buckling. Overall, it was found that the Eurocode buckling curve yields many conservative capacity predictions, whereas the buckling curves in the North American specification and the Australian/New Zealand standard lead to an overall good degree of design accuracy. A revised Eurocode buckling curve is proposed, and was shown to offer accurate capacity predictions for press-braked S690 high-strength steel channel–section columns prone to minor-axis flexural buckling.
Conference Paper
p>The Cherry St North, Commissioners St, and Cherry St South bridges are a series of four signature steel tied arch bridges located in Toronto, Canada. The bridges are being constructed over the Keating Channel and a new extension of the Don River. The arch legs of the bridges are composed of non-prismatic open sections using curved plates. The centre domes at the tops of the arches are also composed of open steel plate sections with plates in double curvature. Steel plate hanger from the arches to the closed steel box tie girders serve to transfer the superstructure gravity loads to the arches. The in-plane and out-of-plane structural stability of the non-prismatic open section arch legs required detailed consideration during design. This paper discusses the various approaches used to analyse and design the arch legs, including the use of approximate methods.</p
Article
This paper reports a comprehensive experimental and numerical investigation of the cross-section behavior and capacity of hot-rolled stainless steel channel sections subjected to combined compression and major-axis bending. An experimental program was first carried out and comprised measurement of initial geometric imperfections and 10 eccentric compression tests. This was accompanied by a numerical modeling program, in which nonlinear finite-element models were first built to replicate the test observations and subsequently utilized to carry out parametric studies for producing more numerical data over a broader spectrum of loading combinations and cross-section dimensions. The data obtained from experiments and parametric studies were utilized to assess the accuracy of the relevant codified interaction curves as used in Europe and the US. The assessments showed that the codified interaction curves resulted in conservative capacity predictions due to the lack of proper consideration of the beneficial stress redistribution and material strain hardening. To overcome these shortcomings, new interaction curves were developed and resulted in greatly improved design accuracy in comparison with the codified interaction curves.
Article
Pada studi ini dilakukan analisis terhadap kinerja struktur bangunan baja bertingkat (5 dan 15 lantai) dengan 3 variasi tipe pengaku diagonal (Inverted V, Single Diagonal dan X-Bracing) dan gedung terbuka. Analisis dilakukang dengan bantuan software SAP 2000 v14. Hasil dari analisis ini akan dibandingkan dari 4 tipe gedung dan 2 jenis ketinggian. Melalui studi analisis ini dilakukan perbandingan perpindahan dan simpangan masing-masing gedung. Gedung dengan tambahan pengaku diagonal memiliki nilai perpindahan yang lebih kecil dibanding struktur gedung terbuka. Gedung dengan tipe pengaku diagonal X-Bracing mampu mereduksi perpindahan paling besar dengan presentase 30,78% untuk gedung 5 lantai dan 18,84% untuk gedung 15 lantai. Taraf kinerja struktur bangunan 5 lantai termasuk dalam Immediate Occupancy untuk semua variasi pengaku diagonal. Hal ini menunjukkan bahwa penggunaan tipe pengaku diagonal X-Bracing paling efektif dapat meningkatkan kekakuan, kekuatan dan stabilitas struktur.
Article
Full-text available
This paper presents an application of the AISC (2005a) Direct Analysis Method (DM) for moment and general combined framing systems. The DM accounts explicitly for nominal initial out-of-plumbness of the framing as well as the reduction in the stiffness of the structure at the maximum strength limit of its most critical member or members. As a result, this approach provides a more rational estimate of the internal forces at the maximum strength limit. Also, the column and beam-column strength checks in moment frames may be based on K = 1 by using this method. One additional modification to a conventional elastic analysis is required in general for beam-columns in moment frames, in other words, the flexural rigidity must be reduced by an additional column inelastic stiffness reduction factor, τ, for columns loaded by axial forces in excess of 0.5Py. This paper proposes two modifications to the underlying amplified first-order elastic analysis approach presented in Part 1 to extend this procedure to general rectangular framing involving any combination of moment, braced and gravity systems. These modifications are: 1. An additional term is included in the sidesway displacement amplifier, B̄lt, to account for the influence of Pδ (P-small delta) moments in moment-frame columns on the sidesway response. 2. The traditional "no-translation" (or NT) moment amplifier, B1 in AISC (2005a) based on the use of a reduced elastic stiffness, is applied to the total column moments. Suggestions are also provided for approximate handling of frames with large axial compression in the beams or rafters and/or nonrectangular geometry. The paper presents analysis and design calculations using the above combined procedures for an example from LeMessurier (1977). This example illustrates a number of important stability design considerations. The preliminary design of LeMessurier's frame starts with the calculation of a target story sidesway stiffness necessary to hold the second-order drift under service loads to a specified limit. The DM, combined with the proposed amplified first-order elastic analysis procedure for calculation of the second-order internal forces, provides a more intuitive, straightforward and accurate set of analysis and design calculations than the traditional AISC ELM and/or the AISC NT-LT analysis procedures. The combination of the AISC (2005a) DM with the proposed amplified first-order elastic analysis equations is generally applicable to all types of rectangular framing systems.
Article
Full-text available
This paper reports the results of tests on laterally unsupported angles with equal and unequal legs subjected to a uniform moment over the entire laterally unsupported span. The moment is variously applied about the loading axes. The testing program has shown that practical angle sections are governed by stress and deflection criteria rather than by buckling.
Article
Full-text available
Recent studies on connections have shown that the beam bending theory cannot predict the flow of forces near the connection regions. In this paper, a new truss analogy model has been proposed to better represent the flow of forces near the column base connections. Also, shear-moment strength envelopes, generated for different levels of axial load using the hysteretic stress-strain curves for steel, are presented. The moment and shear demand for the design of column base connection elements are calculated using the normalized P-V-M interaction curves. Appropriate strength factors applied to the moment capacity of the column section to account for the uncertainty in the estimation of yield stress, strain hardening, compactness of the section, and slenderness of the member are discussed. Finally, a generalized procedure for the capacity design of column base connections is proposed.
Article
Full-text available
Computer oriented and manual procedures are presented that enable a direct second order analysis of asymmetric building structures to be performed by means of first order formulation. This is achieved by modeling the geometric-stiffness of the structure as a fictitious column with negative lateral and torsional stiffness properties. Simplified methods are proposed for structures amenable to some form of uncoupling. The approach is also applied to elastic-plastic analysis of asymmetric structures by combining center-of-rigidity and sway-subassemblage procedures.
Article
A survey is presented which includes the buckling of shells under loads for which the shell is sensitive to initial imperfections. Results for such cases show that improvements in experiment and theory have produced previously unobtainable agreement. The necessity of the correct (and consistent) theoretical specification of boundary conditions is then demonstrated. Recent stiffened cylinder results are surveyed to expose the large effects on the buckling strength of internal or external stiffening, axial load applied eccentric to the wall neutral surface, and the addition of small meridional curvature. © 1968 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
Article
A new analytical method of determining the maximum strength of steel beam-columns is given. In-plane failure under uniaxial moment loading is investigated and full account is taken of imperfections such as residual stresses and initial curvature. A novel form of design presentation is derived which permits all four beam-column parameters to appear on a single chart. The paper is a contribution to a new design approach for biaxially loaded columns which are free to fail in a flexural-torsional mode.
Article
The variable-stiffness method, the latest available method for column design in rigid-jointed steel frames, is described in detail. Application of this method in the design of reinforced concrete columns is discussed. Various methods are progressively given covering the design of short and slender pin-ended composite steel-concrete columns when subjected to axial load only and to uniaxial and biaxial bending.
Article
Traditional design of steel columns is analyzed with a view towards actual and assumed factors of safety. It is shown that due to the variation of strength that is caused by the randomness of the column strength parameters, the real margins of safety differ from what is prescribed by the design specifications. A study of several typical column shapes shows that realistic factors of safety vary between 1. 4 and 2. 1, as compared to the assumed values of 1. 67 to 1. 92. Column design improvements are evaluated, and it is shown that an approach that involves the use of several (multiple) column curves is particularly feasible. The development of such curves in the United States is described, and it is shown that the differences between real and assumed column strength values will be significantly diminished. The traditional factor of safety concept is analyzed, and an alternative approach suggested that will lead to consistent and uniform levels of safety. This development is put in perspective by a formulation that allows its use in load and resistance factor design.
Article
An analysis is presented of the elastic buckling of infinitely wide stiffened plates. The analysis is based on a simplified model of the panel and seeks to determine the interactive behavior of the overall mode of buckling and the local buckling of the stiffener outstands. A high degree of imperfection sensitivity is predicted, particularly for geometries in which the local and overall critical loads are close. The predictions of the analysis are in good agreement with experimental test results showing that the approximations inherent in the analytical model do not lead to significant errors.
Book
The plastic analysis method has been used extensively by engineers for designing steel structures. Simpler structures can be analyzed using the basic virtual work formulation, but more complex frames are evaluated with specialist computer software. This new book sets out a method for carrying out plastic analysis of complex structures without the need for specialist tools. The book provides an introduction to the use of linear programming techniques for plastic analysis. This powerful and advanced method for plastic analysis is important in an automated computational environment, in particular for non-linear structural analysis. A detailed comparison between the design codes for the United States and Australia and the emerging European Eurocodes enables practising engineers to understand the issues involved in plastic design procedures and the limitations imposed by this design method. * Covers latest research in plastic analysis and analytical tools * Introduces new successive approximation method for calculating collapse loads * Programming guide for using spreadsheet tools for plastic analysis.
Article
A simple analysis is presented for predicting the ultimate load carrying capacity of slender plate girder webs subjected to edge loading, uniformly distributed between vertical web stiffeners, and combined bending. The analysis is based on an assumed failure mechanism which considers the formation of plastic hinges in the flange and yield lines in the web. An alternative mechanism solution is also considered for situations in which failure may be initiated by direct yielding of the web. The analysis is compared with a limited number of existing test results and is found to give satisfactory agreement.
Article
The Finite Element Method of analysis was used to determine the buckling loads of the web plate under patch loading together with simple supporting shear forces. Combinations of patch loading with shear loading or with in-plane bending moment were also studied. The results are presented in the form of interaction curves which show that the applied edge load necessary to buckle the panel is reduced by the presence of either an additional in-plane moment or shear. Tests were carried out on light gage cold formed troughs.
Article
The ultimate load carrying capacity of bridge arches is investigated for the case where they fail by inelastic lateral instability associated with the flexural-torsional deformation of the arch rib. The arch bridge is composed of twin ribs connected to one another by a lateral bracing system. The ribs are subjected to a uniformly distributed vertical load. A parametric study is carried out for several representative cases by using a finite element method. The effects of the stiffness, location and type of the lateral bracing system on the inelastic behavior of twin arches are evaluated.
Article
Summary An analysis is presented of the buckling of a rectangular plate under combined biaxial compression, bending and shear. The sides of the plate to which bending is applied are simply-supported, the other two sides being supported by arbitrary edge members. The solution is expressed in a form suited to automatic computation and some sample results are given.
Article
A model is introduced for numerical simulation in verification of strength of the locally compressed web made of conventional rolled section. The model may be used also for dimensioning of beam-column connections.
Article
The Kirchhoff-Clebsch equilibrium conditions, a simultaneous system of six ordinary differential equations, are solved numerically for the case of thin-walled simply supported columns with an open cross section, where warping of the end cross sections is permitted, assuming applicability of Prandtl's bilinear material law. In this case two iterative techniques are involved, one corresponding to the ″geometrical″ nonlinearity, the other corresponding to the ″physical″ nonlinearity. A third iterative technique, governing the load-steps, makes it possible to calculate the stable branch of the load-deformation curve, in particular, the load-carrying capacity.
Article
The elastic buckling behavior of unsymmetric plate girder webs with and without a longitudinal stiffener is presented. The results of a finite element analysis were used to develop a buckling coefficient for longitudinally stiffened webs which takes into account the depth of the web in compression and the vertical location of the stiffener. The results are compared with the AASHTO Bridge Specifications and a design example is presented.
Article
A study was conducted to determine the accuracy of design method using a statistical analysis of data to evaluate effective length factors for the use in design procedures. The study found that the compact corner gusset plates is designed without consideration of buckling effects and at the effective width it provide an accurate compressive capacity. The study examined extended corner gusset plates, the single brace gusset plates, and the chevron brace gusset plates for their effective length factors and for their finite element capacities. The design procedure used in the study was semi-empirical with the empirical aspects of the design method being the 30° stress trajectory in the plate, the buckling length, and the effective length factor. The finite element models is dependent on the level of mesh refinement, the initial out-of-flatness of the plate, the material model, and boundary conditions.
Article
A numerical method is presented for predicting the post-buckling response of thin-walled continuous beams. The proposed method includes a numerical integration procedure in conjunction with the flexibility matrix method of analysis. Nonlinearities due to local buckling and nonlinear material characteristics are accounted for by the nonlinear moment-curvature relations derived with the aid of the effective width concept.
Article
A study of local buckling of wide-flange and box section beams subjected to stress gradients due to transverse loading is presented. The resulting eigen matrices are solved using a search technique. Buckling coefficients for typical cases are presented. Results are compared with those used for customary design procedure.
Article
From the point of view of the influence of cross section form upon the definition of ideal slenderness, the problem of flexural-torsional buckling of beams is analyzed. Characteristic cross-sections of steel members are classified into two groups, the first including at least monosymmetric sections loaded transversally to their plane of symmetry and centrally symmetric profiles and the second group including at least monosymmetric sections loaded in their plane of symmetry. The general equations for critical moment are expressed through the beam buckling slenderness for the possibility of direct design of the actual beam with initial imperfections.
Article
The objective of this paper is to provide designers with elastic buckling data for a range of beams with simple cable geometries so that safe lifting procedures for slender beams can be adopted. The paper begins with a definition of terms and a brief discussion of the buckling solution procedure. Buckling capacity charts are then presented in non-dimensional format. A step by step procedure for checking the stability of I-beams under self-weight lifting is presented and the paper concludes with worked examples.
Article
Revisions are proposed to Sections 10.10 and 10.11 of the ACI Building Code to simplify the design of slender columns and to recognize the use of second-order analyses. These changes are undergoing letter ballot in ACI Committee 318 and if accepted will appear in the 1995 ACI Code. Major changes include the listing of a series of EI values for use in second-order frame analyses, a test for sway and nonsway frames, a flat φ value for stability calculations, new slenderness limits, and the method of combining and magnifying the nonsway and sway moments.
Article
This paper presents analytical and experimental studies on the ultimate strength of transverse stiffeners in the horizontally curved girder bridges. Firstly, the shear buckling strength is analyzed by the theory of shallow shell. Secondly, the ultimate shear strength is also inquired through the collapse model. Based upon these analyses and some experimental data, the behaviors of the transverse stiffener are discussed. Finally, a beam-column model for evaluating the strength of the transverse stiffeners is proposed and a design recommendation to determine the rigidity of the transverse stiffeners of curved girders in the ultimate state is given by this paper.
Article
This paper presents the shear strength of the horizontally curved plate girders based upon the experimental studies on 10 model girders by alternating radii of curvature, aspect ratio and slenderness ratio of web plates as well as stiffness ratio of transverse and longitudinal stiffeners. From these tests, the buckling strength of curved girder subjected to shear is inquired in comparison with ordinary straight girders. The post-buckling strength of curved girder is, moreover, clarified and the contributions of transverse and longitudinal stiffeners are made clear. Finally, the substantial factor of safety against the allowable shear strength provided with Japanese specification for highway bridges are discussed in details.
Article
A model specification for stability design by direct analysis based on the stability provisions of the 2005 AISC Specification, written around Direct Analysis Method, is presented. This specification is organized into general stability requirements, calculation of required strengths, and calculation of available strengths. All three of the stability design methods in the 2005 AISC Specification include consideration of uncertainty in stiffness and strength. The effects of second-order effect, flexural, shear, and axial deformations, and all other deformations that contribute to displacements of the structure, geometric imperfections, stiffness reductions due to inelasticity, and uncertainty in stiffness and strength shall also be considered. The Direct Analysis Method is applicable to all structures including combinations of concrete shear walls and steel frames. Initial imperfections in the method can be modeled directly in the analysis at additional points beyond the points of intersection of members.
Article
In this paper, the bracing stiffness required for the range from continuous point bracing to a single point brace is presented. The required brace strength is also summarized. The bracing expressions are given in the form most familiar for point bracing. The expressions provide an understanding of the relationship between bracing stiffness and buckling behavior of the compression member. Furthermore, an expression for tangent modulus of elasticity is proposed as a means to apply the bracing expressions for all levels of critical load less than the yield load.
Article
After 44 years with network arches the author believes that he has come up with his most competitive design yet. Due to little bending and good utilisation of high strength steel, the structure uses very little steel. Details are simple and highly repetitive and the welds are short. Thus the cost of fabrication will be low. The methods of erection will be cheap. The network arch has many hangers. It has low maintenance costs because steel surfaces are small and above the lane. The partial prestressing also helps.
Article
Procedures are presented for the three-dimensional analysis of the overall elastic stability of multistory buildings and for the inclusion of stability effects in lateral-load analysis. The effect of axial force on the flexural stiffness of individual members is neglected. Floors are treated as diaphragms that are rigid in the horizontal plane. The suggested procedures do not require the solution of nonlinear systems of equations or nonlinear eigenvalue problems. The proposed techniques were used to study several 20-story buildings whose structural framing systems were designed in accordance with current engineering practice. The results of these analyses indicate that buildings that are designed without regard to overall elastic stability can have very low factors of safety against elastic buckling, especially in a torsional mode; second-order effects can cause substantial increases in the displacements and stresses due to wind and other horizontal loads.
Article
The main tests conducted as part of the 1966 research project at Lehigh University are described, and details given of the preparation for the tests and the testing itself. Correlation between the test results and the theory was within 12%. The introduction of a longitudinal stiffener into panels subjected to combined action of high moment and high shear resulted in an increase in strength in the range of 39 to 46% due to a more efficient distribution of internal forces.
Article
Experimental results of pure buckling on plates conducted in 49 tests are presented. An equation is presented for design of such girders.
Article
Reference is made to the Load and Resistance Factor Design (LRFD) Manual compiled by the American Institute of Steel Construction. It is shown that this manual requires some modification and amplification to be fully illustrative of correct design procedure. This article presents a revised and expanded version which attempts to accomplish this.
Article
Coupled behavior of overall and local buckling of U-shaped beams subjected to uniform bending moment is presented. A finite strip method is applied to the coupled buckling analysis and the inelastic buckling is analyzed including the residual stresses of the cross section. The buckling tests are carried out with seven welded steel U-beams. Load-deformation behavior, failure modes, the ultimate bending strength and the stiffening effects by the intermediate knee braces and diaphragms are investigated.
Article
In this paper a test program for non-slender single angle members with equal legs, utilizing a three-dimensional truss, was briefly described. The test results were given and analyzed. Comparisons were made between the actual failure loads and those predicted using methods given in the ASCE Manual 52 for Steel Transmission Towers and the AISC Specification for Steel Buildings. The test results reported in this paper indicate that current design methods for nonslender single angle members are not adequate.
Article
The paper describes a design approach for curved bridges that is extremely simple and easily understood. The V-Load Method is not only a valuable tool from the practical standpoint, but familiarity with the method should contribute to the engineer's overall 'feel' of the curved girder problem. Although curved girder analysis and design by the V-Load Method is straightforward, it is not a procedure that can be done readily by longhand. But it can be done by a variety of manageable, fast-running computer programs, starting with Program V-LOAD.
Article
The German standard under consideration deals with aluminum structures under predominantly static stress. The test program comprised stress-strain curves under compression, internal stresses of extruded sections, bending tests on the I-beams, T-shapes, tubing, U-profiles, and thin-walled sections, and others. The alloys used were AlZnMg1F36, AlMgSi1F32 and AlMgMnF20. Numerous tables.
Article
To investigate the behavior of double angle bracing members and their connections, 17 full-size, double-angle test specimens were used in this study. The bracing members were placed in a diagonal position inside a loading frame and subjected to reversed cyclic deformations similar to those expected during a severe earthquake. Emphasis of the research program was on the evaluation of current design methods and developing modified procedures in order to ensure adequate seismic performance of bracing members. This paper summarizes the most significant findings of the research program from a design perspective. Three design examples are included to illustrate step-by-step use of the recommended procedures for earthquake resistance design.