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| Failure mode | Design standard |
| ASCE 10-15 | AISI S100-16 and AS/NZS: 4600-2018 | EN 1993-1-3: 2006 |
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| Flexure | SSRC (1966) equation is used for columns in inelastic and Euler’s equation for columns in elastic range of buckling. | (i) The elastic critical buckling load for a long column is determined by the Euler’s equations.
(ii) For locally stable columns, the AISC LRFD specification (1993) equation is adopted for elastic and inelastic ranges of buckling. | The resistance of compressed members is based on the “European design buckling curves” (ECCS, 1978) that relate the reduction factor to the nondimensional slenderness. These (five) curves were the result of an extensive experimental and numerical research programme (ECCS, 1976), conducted on HR and welded sections, that accounted for all imperfections in real compressed members (initial out-of-straightness, eccentricity of the applied loads, residual stresses). The analytical formulation of the buckling curves was derived by Maquoi & Rondal [33], and is based on the Ayrton-Perry formula, considering an initial sinusoidal deformed configuration corresponding to an “equivalent initial deformed configuration” where the amplitude was calibrated in order to reproduce the effect of all imperfections. |
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| Torsion | As per this code the local buckling strength is not equal to torsional buckling strength. Hence, torsional-flexural buckling strength is determined. | The torsional buckling in the elastic range is computed based on the equation provided by Winter [53] for elastic critical stress. | For members with “point-symmetric” open cross sections (e.g. Z-purlin with equal flanges), the possibility that the resistance of the member to torsional buckling might be less than its resistance on flexural buckling is considered in this code. |
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| Torsion-Flexure | The design compressive stress for torsional-flexural buckling strength is determined using an equivalent radius of gyration. | The governing elastic flexural-torsional buckling load of a column can be found from the equation suggested by Chajes and Winter [54]; Chajes et al. [55]; Yu and LaBoube [56]. | For members with mono-symmetric open cross-sections, the possibility of the resistance of the member to torsional-flexural buckling might be less than its resistance to flexural buckling is considered in this code. |
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| Local buckling | If element slenderness ratio is not small enough to develop uniform design stress distributed over full cross section, then the post buckling strength of element which buckles prematurely is taken into account by using an effective width of an element in determining the area of the member cross section. The effective width of an element is the width, which gives the same resultant force of a uniformly distributed design stress, as the nonuniform stress develops in the entire element in the post-buckled state. | In this code, the effective width Method’s approach to local buckling is adopted. It conceptualizes the member as a collection of “elements” and investigates local buckling of each element separately.
The effective width method determines a plate buckling coefficient, k, for each element, then buckling stress, and finally the effective width. | An effective width approach is adopted, whereby ‘ineffective’ portions of a cross section are removed and section properties may be determined based on the remaining effective portions.
In this standard, the local and distortional buckling modes for cross sections with edge stiffeners are considered together while estimating the resistance. |
| Distortional buckling | Not considered | Distortional buckling is an instability that may occur in members with edge-stiffened flanges, such as lipped C and Z-sections. This buckling mode is characterized by instability of the entire flange, as the flange along with the edge stiffener rotates about the junction of the compression flange and the web. The expressions in this specification are derived by Schafer [57] and verified for complex stiffeners by Yu and Schafer [58]. | EN1993-1-3 does not provide explicit provisions for distortional buckling. However, a calculation procedure is obtained from the interpretation of the rules given in the code for plane elements with edge or intermediate stiffeners in compression. The design of compression elements with either edge or intermediate stiffeners is based on the assumption that the stiffener behaves as a compression member with continuous partial restraint. This restraint has a spring stiffness that depends on the boundary conditions and the flexural stiffness of the adjacent plane elements of the cross section. The spring stiffness of the stiffener may be determined by applying a unit load per unit length to the cross section at the location of the stiffener. The rotational spring stiffness characterizes the bending stiffness of the web part of the section. |
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| Yielding | Not indicated | Very short, compact column under an axial load may fail by yielding. Hence, the yield load determined by multiplying the gross area with yield strength. | The design resistance is computed by multiplying the gross area with increased basic yield stress for the contribution from difference of average and basic yield stress reduced by a factor based on the ratio of relative slenderness for elements. |
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| Maximum element slenderness ratio (w/t) | (i) For elements supported on both the longitudinal edges, w/t ≤ 60 and (ii) for elements supported on one longitudinal edge, w/t ≤ 25
w/t = flat width to thickness ratio. | (i) For stiffened element in compression, w/t ≤ 500,
(ii) for edge stiffened element in compression w/t ≤ 90 for Is ≥ /Ia and w/t ≤ 60 for Is < Ia, and (iii) for unstiffened element in compression w/t ≤ 60
w/t = flat width to thickness ratio. | (i) For stiffened element in compression, w/t ≤ 500,
(ii) for edge stiffened element in compression a) for element w/t ≤ 60 for stiffener w/t ≤ 50, and (iii) for unstiffened element in compression w/t ≤ 50
w/t = out to out width to thickness ratio. |
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| Other Considerations |
| Material strength | As per ASTM standards with yield strength up to 448 MPa | As per ASTM standards with yield strength up to 380 MPa | As per EN standards with basic yield strength up to 460 MPa |
| Increase in yield strength of material due to cold-working | Not considered. | At Cornell University, the influence of cold work on mechanical properties was investigated by Chajes et al. [2], Karren, [3], and Karren and Winter [4]. It was found that the changes of mechanical properties due to cold-stretching are caused mainly by strain-hardening and strain-aging, Chajes et al. [2]. Cornell research also revealed that the effects of cold work on the mechanical properties of corners usually depend on (1) the type of steel, (2) the type of stress (compression or tension), (3) the direction of stress with respect to the direction of cold work (transverse or longitudinal), (4) the Fu/Fy ratio, (5) the inside radius-to-thickness ratio (R/t), and (6) the amount of cold work.
Investigating the influence of cold work, Karren derived the equations for the ratio of corner yield stress-to-virgin yield stress [3]. With regard to the full-section properties, the tensile yield stress of the full section approximated by using a weighted average is used in this specification. Good agreements between the computed and the tested stress-strain characteristics for a channel section and a joist chord section were demonstrated by Karren and Winter [4] | The increased yield strength due to cold forming may be taken into account if in axially loaded members in which the effective cross-sectional area equals the gross area, and in determining the effective area, the yield strength should be taken as basic yield strength. |
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