On North American and Chinese Standards for Design of Coldformed Steel Csection Flexural Members

XU+Lei1+ZHOU+Xu�瞙ong++YUAN+Xiao�瞝i

建筑科学与工程学报2014年文章编号：16732049(2014)01001620

Received date：20131128

Biography：XU Lei（1957）， male, professor, doctoral advisor, PhD, Email:lxu@uwaterloo.ca.On North American and Chinese Standards for

Design of Coldformed Steel Csection

Abstract:Nominal flexural strengths of coldformed steel Csections evaluated by the North American standard CSA S13607 and the Chinese standard GB 50018—2002 were investigated. To quantify the differences of the nominal flexural strength between the two standards, 6 m span joists with typical Csections subjected to the uniformly distributed load and uniform bending moment were investigated. The study results show that discrepancies between the two standards are resulted from both the difference in evaluating the effective section modulus and the difference in computing the lateraltorsional buckling stress. The lateraltorsional buckling stress evaluated based on GB 50018—2002 is generally not less than that of CSA S13607 whereas the flange effective width of Csection calculated by GB 50018—2002 is much smaller than that of CSA S13607. The adequacy of flange to prevent lateraltorsional buckling and the applied load patterns are the important factors resulting the differences of the nominal flexural strength between the two standards. If the flange is inadequate to resist latertorsional buckling and local buckling does not govern, the strength associated with GB 50018—2002 is greater than that of CSA S13607 if members are subjected to the uniformly distributed load but there is no difference for case of uniform bending moment; in the case that flange is adequate to resist latertorsional buckling but local buckling governs the strength, then the nominal flexural strength obtained from GB 50018—2002 becomes less than that of CSA S13607 in both foregoing applied load patterns.

Key words:coldformed steel; Csection member; nominal flexural strength; lateraltorsional buckling; effective width; buckling coefficient

CLC number：TU375.4Document code：A

北美规范与中国规范关于冷弯薄壁型钢C形截面受弯构件设计的比较徐磊1，周绪红2，苑小丽1，刘競楠1，刘永健3

（1. 滑铁卢大学土木与环境工程学院,安大略滑铁卢N2L 3G1; 2. 重庆大学土木工程学院,

重庆400045; 3. 长安大学公路学院,陕西西安710064）摘要:对比了北美规范CSA S13607和中国规范GB 50018—2002关于冷弯薄壁型钢C形截面受弯构件的名义抗弯强度。首先介绍了2本规范计算名义抗弯强度的方法，然后分析了控制构件名义抗弯强度的2个主要参数，即弯扭屈曲应力和有效截面模量，并对2本规范进行了深入对比，最后对典型的6 m跨长的C形托梁构件进行了名义抗弯强度比较。研究结果表明：依据GB 50018—2002计算的弯扭屈曲应力不小于依据CSA S13607规范计算的结果，而根据GB 50018—2002计算的翼缘有效宽度则远远小于根据CSA S13607规范计算的结果；2本规范名义抗弯强度的不同主要由C形截面翼缘尺寸和构件所受荷载类型控制；当翼缘尺寸较小，名义抗弯强度主要由弯扭屈曲而非局部屈曲控制时，如果构件用于均布荷载，则GB 50018—2002的计算结果大于CSA S13607规范的结果，但是当构件用于抵抗均布弯矩时，则没有区别；当翼缘尺寸较大，名义抗弯强度主要由局部屈曲而非弯扭屈曲控制时，在2种工况下GB 50018—2002的计算结果均小于CSA S13607规范的计算结果。

关键词:冷弯薄壁型钢;C形截面构件;名义抗弯强度;弯扭屈曲;有效宽度;屈曲系数

0Introduction

Csection is the most widely used section shape in coldformed steel framing construction. Typical applications of Csections as flexural members are load bearing floor or roof joists and nonload bearing curtain wall studs. In North America, procedures for design of coldformed steel members are specified in CSA S13607［1］. In China, the design procedures for coldformed steel members concerning with local buckling and lateraltorsional buckling are stipulated in GB 50018—2002［2］, while the procedure for evaluating the distortional buckling is specified in the standard JGJ 227—2011［3］. Although theoretical basis for evaluating the nominal flexural strength of Csection members are similar in the North American and the Chinese standards, there are differences in the procedure of evaluating the strength. The primary objectives of this study are to identify the differences in the procedures of evaluating the nominal flexural strength between CSA S13607 and GB 50018—2002 for coldformed steel Csection members and to investigate how the nominal flexural strength is affected by the differences of the procedures.

In the paper, procedures associated with the foregoing two standards for evaluating the nominal flexural strength of coldformed steel Csection members are firstly discussed. Then, two key parameters used for determining the nominal flexural strength of coldformed steel members, the buckling stress and the associated effective width of crosssectional elements, are compared, respectively. Finally, the differences in the nominal flexural strength between the two standards are investigated for the typical Csection load bearing floor joists.1Expression of Nominal Flexural StrengthProfile of Csection members is shown in Fig.1. As seen from Fig.1, ww is the flat portion of the web; wf is flat portion of the flange; b0 is the outertoouter dimension of the flange; h0 is outertoouter depth of the Csection members; x0 is the distance from shear center to centroid along principal axis; d is flat portion of the stiffener; D is height of the stiffener; R is inside bend radius; r is centerline bend radius. Assumptions made for the comparison of the nominal flexural strength of the Csection members shown in Fig.1 are as follows: ① the load is applied through the shear center ofFig.1Profile of Csection Member

图1C形截面构件剖面 the Csection and the resulted bending is about the x axis; ② there are no holes in the Csection members; ③ distortional buckling is not considered; ④ the yield stresses of the steel are either fy=345 MPa or fy=235 MPa.

In CSA S13607, the equation to evaluate the nominal flexural strength (nominal moment) Mn of the flexural member is

Mn=min{fySe,fcSc}(1)

where fc is the nominal stress computed based on lateraltorsional buckling［46］; Se and Sc are the effective section moduli associated with the yield stress fy and nominal stress fc, respectively.

On the other hand, in GB 50018—2002, although the nominal flexural strength Mn is not explicitly expressed, the standard provides the following equation to check the strength and stability

σ=MmaxSe≤f(2)

σ=MmaxφbxSc≤f(3)

where Mmax is the maximum factored load; f is the design strength; φbx is the stability coefficient; Se and Sc are the effective section moduli concerning with the design strength f and stress φbxf, respectively.

To obtain the equivalent nominal moment Mn based on GB 50018—2002, Eq.(2) and Eq.(3) can be rewritten as

Mn=min{fySe,φbxfySc}(4)

Because the stability coefficient φbx is a stress reduction coefficient to account for the lateraltorsional buckling of the flexural member, the products of φbx and fy in Eq.(4) can be considered as the equivalent to the nominal stress fc shown in Eq.(1) as both of them are calculated based on lateraltorsional buckling.

Comparing Eq.(1) to Eq.(4), it can be seen that the two standards are similar to each other by specifying the minimum value of the section (local buckling) strength fySe and the lateraltorsional buckling strength fcSc (or φbxfySc) being the nominal flexural strength Mn. The stress fc (or φbxfy) is evaluated based on the lateraltorsional buckling, and the effective section moduli Se and Sc are obtained with the consideration of the local buckling at the stress levels fy (or f) and fc (or φbxf), respectively. In order to compare the nominal flexural strength Mn between the two standards, the procedures of evaluating the lateraltorsional buckling stress fc (or φbxfy) and the effective section moduli Se and Sc are needed to be investigated.2Lateraltorsional Buckling Stress

In CSA S13607, the nominal stress fc is calculated as follows

fc=fyfe≥2.78fy

109fy(1-1036fyfe)2.78fy＞fe＞0.56fy

fefe≤0.56fy(5)

where fe is the elastic lateraltorsional buckling stress.

fe is evaluated as

fe=Cbr0ASfσeyσt(6)

where Sf is the elastic section modulus of fully unreduced section relative to extreme compressive fibre; r0 is the polar radius of gyration; σey is the elastic flexural buckling stress about the y axis; σt is the elastic torsional buckling stress; Cb is introduced to account for the increasing moment resistant capacity if the applied bending moment is not uniform along the span of the beam.

r0, σey, σt and Cb are calculated as follows

r0=r2x+r2y+x20(7)

σey=π2E/(KyLy/ry)2(8)

σt=1Ar20［GJ+π2ECw(KtLt)2］(9)

Cb=12.5M′max2.5M′max+3MA+4MB+3MC(10)

where Ky, Ly and ry are effective length factor, laterally unbraced length, and radius of gyration of fully unreduced cross section about the y axis; rx is the radius of gyration of fully unreduced cross section about the x axis; Kt and Lt are the effective length factor and the unbraced length for twisting; A is the gross area; E and G are the elastic modulus and shear modulus, respectively, with E=203 GPa and G=78 GPa in CSA S13607; Cw is the warping constant; J is the torsional constant; MA, MB and MC are absolute values of moments at the quarter point, centerline and threequarter point of the unbraced segment; M′max is the absolute value of the maximum moment in the unbraced segment.

In GB 50018—2002, the stability coefficient φbx, which is the equivalent to the ratio fc/fy, is evaluated as

φbx=φ′bxφ′bx≤0.7

1.091-0.274/φ′bxφ′bx＞0.7(11)

φ′bx=4 320Ah0(KyLy/ry)2Sfζ1·

4Cwh20Iy+0.156JIy(Lyh0)2235fy(12)

where Iy is the moment of inertia about the y axis; and ζ1 is the equivalent to Cb in Eq.(6).

Substitute elastic modulus E=206 GPa (specified in GB 50018—2002) and E/G=2.6 into Eqs.(8) and (9), the resulted elastic lateraltorsional buckling stress fe in Eq. (6) will be the same as the product of φ′bx and the yield stress fy if the bending coefficient ζ1 in Eq. (12) is identical to the coefficient Cb in Eq.(5). If Cb is not identical to ζ1, however, fe in Eq. (6) would be different from the product of φ′bx and the yield stress fy.

Bending coefficients Cb in CSA S13607 and ζ1 in GB 50018—2002 are both introduced to account for the increasing moment resistant capacity when the applied bending moment is not uniformly distributed along the span of the flexural member. However, procedures of the evaluation of Cb and ζ1 in the two standards are different. In CSA S13607, Cb is evaluated based on the actual applied moment distribution through Eq.(10), whereas in GB 50018—2002, tabulated values of ζ1 provided in Appendix A.2 are listed for only seven load patterns. Values of Cb calculated based on CSA S13607 and the tabulated ζ1 in GB 50018—2002 for the seven load patterns are presented in Tab.1. It can be seen from Tab.1 that differences between Cb and ζ1 are not greater than 10% except: ① ζ1 are 18.0%, 41.6%, 49.1%, 13.4% greater than Cb for load patterns 4, 5, 6, 7, respectively, if the weak axis of the member is braced at the midpoint; ② except load pattern 3, ζ1 is 22.3% to 62.4% greater than Cb if the weak axis of the member is braced at 1/3 point and 2/3 point. For these cases, since Cb is considerably different from ζ1, the resulted difference between φ′bx of GB 50018—2002 and the ratio fe/fy of CSA S13607 cannot be neglected.