Advances in Steel Structures - part 39 pptx

The current design strength Pn predicted by the standard and specification are unconservative, except that they closely predicted the web crippling strengths for the EOF loading conditio

360 B Young and G.J Hancock

the measured material properties as detailed in Table 1 A value of 203,000 MPa specified in the AISI Specification was used for the Young's modulus of elasticity (E) in calculating the design strength The current design strength (Pn) predicted by the standard and specification are unconservative, except that they closely predicted the web crippling strengths for the EOF loading condition in most of the cases On average, the web crippling strength of a specimen subjected to either IOF or ETF loading condition was reached in the test at 67% and 66% of the value predicted by the specifications respectively, as shown in Table 2 For a specimen subjected to the ITF loading condition, the corresponding value is 56% It is noteworthy that a test strength as low as 43% of the current design strength was obtained in the test for a certain specimen subjected to the ITF loading condition

Figure 2: Mechanism model

PROPOSED DESIGN EQUATIONS

The nominal web crippling strength (P,,) of unlipped channels calculated according to the AS/NZS

4600 and AISI design rules are unconservative, as shown in Table 2, probably because they were calibrated for sections with more slender webs (h/t > 60) Hence, design equations for unlipped channels with stockier webs are proposed in this paper It is assumed that the bearing load is applied eccentrically to the web due to the presence of the comer radii, which produces bending of the web out

of its plane causing a plastic mechanism as shown in Fig 2 A plastic mechanism model is used to establish design equations, which account for the eccentric loading of the web This approach is similar to that used for square and rectangular hollow sections (SHS and RHS) by Zhao and Hancock (1992 and 1995) to determine the web crippling strengths for both interior and end bearing loads The SHS and RHS tested by Zhao and Hancock (1992 and 1995) also had stockier webs than was intended for the AS/NZS 4600 and AISI web crippling equations

The proposed equations for channel sections are summarised as:

where

Web Crippling Tests of High Strength Cold-Formed Channels

f yt 2

m p = 4

t

r = r / + - -

2 t;

N,,, = ed

+

2

for Interior loading for End loading

361

(2)

(3)

(4)

in which, Ppm is the web crippling strength predicted by using the plastic mechanism model, Mp is the plastic moment per unit length, r and r~ are the centreline and inside comer radii respectively, h is the depth of the flat portion of the web measured along the plane of the web, t is the thickness of the web,

fy is the yield stress, d is the overall depth of the web and N is the length of the bearing In Eqn 4, Nm

is the assumed mechanism length, as shown in Figs 3a and 3b for interior and end loading respectively

It is based on an assumption that the dispersion slope of the load through the corner and the web is 1:1 with correction factors i and e for interior and end loading respectively The correction factors for interior loading are i = 1.3 and 1.4 for IOF and ITF respectively, and the correction factors for end loading are e = 1.0 and 0.6 for EOF and ETF respectively Equation 1 also accounted for the web slenderness (h/t) of the channel sections, and the equation is calibrated with the test results

Figure 3: Assumed plastic hinge position and mechanism length, Nm

COMPARISON OF TEST STRENGTHS WITH PROPOSED DESIGN STRENGTHS

The experimental ultimate web crippling loads per web (PExp) obtained from the tests are compared in Table 3 with the proposed design strengths (Ppm) using the plastic mechanism model The proposed design strengths were calculated using the average measured cross-section dimensions and the measured material properties as detailed in Table 1

TABLE 2

COMPARISON OF WEB CRIPPLING TEST STRENGTHS WITH CURRENT DESIGN STRENGTHS

tc'

7

B

a

r,

*

%

c:

E

a

3

0

0

Note: 1 in, 25.4 mm; 1 ksi 6.89 MPa; 1 kip 4.45 kN

TABLE 3

COMPARISON OF WEB CRIPPLING TEST STRENGTHS WITH PROPOSED DESIGN STRENGTHS

3

g

G%

3

s

%

3

""s

%

9

%

"rl

2

z

9

z

z

2

3

a

a

r,

6

Note: 1 in 25.4 mrn; 1 ksi 6.89 MPa; 1 kip 4.45 kN

364 B Young and G.J Hancock

The proposed design strengths (Ppm) are generally conservative The plastic mechanism model approach therefore appears to be suitable for unlipped channels with a web slenderness (h/t) value of less than or equal to 45

TABLE 4

STATISTICAL PARAMETER FOR RELIABILITY ANALYSIS

Variables Material (Tensile Yield Stress) Fabrication (Mass)

Statistical Parameters Mean Mm COV VM Mean F m COV V F

Values

1.08

0.063 0.97 0.03i

RELIABILITY ANALYSIS

The safety index ([3) is a relative measure of the safety of the design A lower target safety index of 2.5 for structural members is recommended as a lower limit for the AISI Specification In general, if the safety index is greater than 2.5 (13 > 2.5), then the design is considered to be reliable

The existing resistance (capacity) factor (q~) of 0.75 for web crippling strength of single unreinforced webs is given by the AS/NZS 4600 and the AISI Specification This resistance (capacity) factor (q~ = 0.75) is used in the reliability analysis A load combination of 1.25DL + 1.50LL is also used in the analysis, where DL is the dead load and LL is the live load Accordingly, the safety index may be given as,

ln/MInFmPm /

0.691~

4V2M + V~ +CpV~ +0.212

The statistical parameters Mm, F m, V M and V F are mean values and coefficients of variation for material properties and fabrication variables respectively, and these values are obtained from BHP Structural and Pipeline Products (1998), as shown in Table 4 The statistical parameters Pm and Vp are mean value and coefficient of variation for design equations, as shown in Tables 2 and 3 for current design rules and proposed design equations respectively The correction factor Cp is used to account for the influence due to a small number of tests (Pek6z and Hall 1988, and Tsai 1992), and the factor

Cp is given in Eqn Fl.l-3 of the AISI Specification The safety index in Eqn (5) is detailed in Rogers and Hancock (1996)

The safety indices (13) of the current design rules to predict the web crippling strengths for the four loading conditions are lower than the target safety index, except for the EOF loading condition as shown in Table 2 Safety indices as low as 0.48 were calculated for the ITF loading condition However, this is not the case for the proposed design equations, the safety indices are higher than the target value for the four loading conditions as shown in Table 3 Therefore, the proposed design equations are much more reliable than the current design rules The proposed design equations produce good limit state design when calibrated with the existing resistance (capacity) factors (~ - 0.75)

CONCLUSIONS

Web Crippling Tests of High Strength Cold-Formed Channels 365

A series of web crippling tests has been conducted to examine the appropriateness of the current design rules stipulated in the Australian/New Zealand Standard (AS/NZS 4600, 1996) and the American Iron and Steel Institute (AISI, 1996) Specification for cold-formed steel structures Tests were performed

on high strength cold-formed unlipped channels having nominal yield stress of 450 MPa, and the web slenderness values ranged from 15.3 to 45 The specimens were tested using the four loading conditions (EOF, IOF, ETF and ITF) according to the AISI Specification

The test strengths were compared with the current design strengths obtained using AS/NZS 4600 and the AISI Specification It is demonstrated that the current design strengths predicted by the standard and specification are unconservative for unlipped channels (single unreinforced webs), except that they closely predicted the web crippling strengths for the EOF loading condition in most of the cases For a certain specimen subjected to ITF loading condition the test strength is only 43% of the current design strength predicted by the standard and specification Since the design strengths obtained using the current design rules are generally unconservative for unlipped channels, therefore, a set of equations to predict the web crippling strengths have been proposed in this paper The proposed design equations are derived based on a simple plastic mechanism model, and these equations are calibrated with the test results It has been shown that the proposed design strengths are generally conservative for unlipped channels with web slenderness values of less than or equal to 45

The reliability of the current design rules and the proposed design equations have been evaluated using reliability analysis In general, the safety indices of the current design rules are lower than the target safety index of 2.5 as specified in the AISI Specification Whereas the safety indices of the proposed design equations are higher than the target value Therefore, it has shown that the proposed design equations are much more reliable than the current design rules for the prediction of web crippling strength of the tested channels The proposed design equations are capable of producing reliable limit state designs when calibrated with the existing resistance (capacity) factors

ACKNOWLEDGEMENTS

The authors are grateful to the Australian Research Council and BHP Structural and Pipeline Products for their support through an ARC Collaborative Research Grant Test specimens were provided by BHP Steel

REFERENCES

American Iron and Steel Institute (1996) Specification for the Design of Cold-Formed Steel Structural Members, AISI, Washington, DC

Australian Standard (1991) Methods for Tensile Testing of Metals, AS 1391, Standards Association of

Australia, Sydney, Australia

Australian/New Zealand Standard (1996)

Standards Australia, Sydney, Australia

Cold-Formed Steel Structures, AS/NZS 4600:1996,

BHP Structural and Pipeline Products (1998) Pipe, Tube and Structural Products - Mechanical Test Data Somerton plant, NSW, Australia

366 B Young and G.J Hancock

Hetrakul N and Yu W.W (1978) Structural Behavior of Beam Webs Subjected to Web Crippling and

a Combination of Web Crippling and Bending Final Report Civil Engineering Study 78-4, University

of Missouri-Rolla, Mo, USA

Nash D and Rhodes J (1998) An Investigation of Web Crushing Behaviour in Thin-Wall Beams

Thin-Walled structures 32, 207-230

Pektsz T.B and Hall W.B (1988) Probabilistic Evaluation of Test Results Proceedings of the 9th International Specialty Conference on Cold-Formed Steel Structures, St Louis, University of Missouri-Rolla, Mo, USA

Rogers C.A and Hancock G.J (1996) Ductility of G550 Sheet Steels in Tension-Elongation Measurements and Perforated Tests Research Report R735, Department of Civil Engineering,

University of Sydney, Australia

Tsai M (1992) Reliability Models of Load Testing PhD dissertation, Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign

Winter G and Pian R.H.J (1946) Crushing Strength of Thin Steel Webs Cornell Bulletin 35, Part 1,

Comell University, Ithaca, NY, USA

Young B and Hancock G.J (1998) Web Crippling Behaviour of Cold-Formed Unlipped Channels Proceedings of the 14th International Specialty Conference on Cold-Formed Steel Structures, St Louis, University of Missouri-Rolla, Mo, USA, 127-150

Zetlin L (1955) Elastic Instability of Flat Plates Subjected to Partial Edge Loads Journal of the Structural Division, ASCE 81:795, 1-24

Zhao X.L and Hancock G.J (1992) Square and Rectangular Hollow Sections Subject to Combined Actions Journal of Structural Engineering, ASCE 118:3, 648-668

Zhao X.L and Hancock G.J (1995) Square and Rectangular Hollow Sections under Transverse End- Bearing Force Journal of Structural Engineering, ASCE 121:9, 1323-1329

LOCAL AND DISTORTIONAL BUCKLING OF

PERFORATED STEEL WALL STUDS

Jyrki Kesti 1 and J Michael Davies 2

~Laboratory of Steel Structures, Helsinki University of Technology,

P.O Box 2100, FIN-02015 HUT, Finland 2Manchester School of Engineering, University of Manchester,

Manchester, M 13 9PL, UK

ABSTRACT

This paper considers the compression capacity of web-perforated steel wall studs The web perforations decrease the local buckling strength of the web and the distortional buckling strength of the section An analytical prediction of the compression capacity is described Local and distortional buckling stresses are determined by replacing the perforated part of the web with plain plate of equivalent thickness The effective area approach is used to consider local and distortional buckling Comparison between the test results for short columns and the corresponding predictions shows that the method used gives reasonable results for web-perforated C-sections with or without web-stiffeners

KEYWORDS

Cold-formed steel, wall stud, perforation, compression, local buckling, distortional buckling

INTRODUCTION

Web-perforated steel wall studs are especially used in the Nordic countries as structural components in steel-framed housing The slotted thermal stud offers a considerable improvement in thermal performance over a solid steel stud The wall structure consists of web-perforated C-section studs with U-section tracks top and bottom and, for example, gypsum wallboards attached to the stud flanges The sections investigated in this paper are shown in Figure 1 Both types of stud had six rows of slots with dimensions as shown in the Figure

The perforations reduce the elastic local buckling stress of the web and also reduce the bending stiffness of the web which, in turn, results in decreased distortional buckling strength The aim of this paper is to analyse the local and distortional buckling strength of the perforated steel stud The local and distortional buckling modes are taken into account in design by using the effective area approach

367

368 J Kesti and J.M Davies

Figure 1: Web-perforated C-section and web-stiffened C-section (Dimensions in mm)

ELASTIC BUCKLING STRESSES

Local Buckling Stress o f the Web o f a Perforated C-Section

The depth of the sections considered varied between 150 and 225 mm with a thickness between 1 and

2 mm The overall depth of the perforations was 58 mm Local buckling of the perforated region was studied using the elastic buckling analysis available in the NISA finite element software (1996) The analyses were carried out for both the isolated web element, which was assumed to be simply supported, and for the whole section, including the edge-stiffened flanges The width of the flanges was 50 mm and the width of the stiffeners was 15 mm Individual plate elements and the complete sections of 800 mm in length were modelled, including the perforations A sufficient length was chosen so that the minimum local buckling stress could be achieved

The elastic local buckling stress, l~rcr.perf, for simply supported perforated plate elements of different

widths and thicknesses was determined using the finite element method (FEM) An analytical expression for the local buckling of a perforated plate may be achieved using a buckling factor of k =

4.0 and an equivalent thickness, tr, to~, for the whole plate The equivalent thickness was determined in

a manner similar to Salmi (1998):

/ O'cr ,perf

t r ,loc " ,tl

|1| O'cr ,entire

where O'cr,pe~ is the elastic buckling stress of the perforated plate and O'cr, entire is the elastic buckling stress of the entire plate The elastic buckling stress of the equivalent plate with reduced thickness trtoc

is thus the same as that of the perforated plate The value for tr.toc was found to be in the range 0.72t- 0.75t for the plates studied Thus, for design purposes, the equivalent thickness value, tr.toc = 0.72t

could be used for the whole range of sections

Local buckling stresses for the whole of the perforated sections, including the flanges, were on average 75% higher than those of the simply supported perforated plates This indicates that assuming the web part to be simply supported leads to quite conservative results and the contribution of the flanges to the local buckling of the web should generally be considered

Distortional Buckling Stress

Because of the perforation of the web, the, transverse bending stiffness of the section is rather low and the section is sensitive to distortional buckling under compressive load In the distortional mode of buckling, the edge-stiffened flange elements of the section tend to deform by rotation of the flange about the flange-web junction The distortional buckling mode occurs at longer wavelengths than local buc.t-!ing Numerical methods, such as the finite strip method (FSM), may be used to determine

Local and Distortional Buckling of Perforated Steel Wall Studs 369 the distortional buckling stress of the section The Generalized Beam Theory (GBT) provides a particularly good tool with which to analyse distortional buckling in isolation and in combination with other modes Some approximate manual methods have also been presented, namely the Eurocode 3 (1996) method, which is based on flexural buckling of the stiffener, and a more sophisticated model developed by Lau and Hancock (1987) The most recent method has been presented by Schafer and Pektiz (1999) Schafer's method was used in this study and it was modified to cover the perforated C- sections, as shown in Figure 2

Figure 2: Notations for the perforated C-section and for the flange part alone

In the Schafer method, the closed-form prediction of the distortional buckling stress is based on the rotational restraint at the web/flange junction The rotational stiffness may be expanded as a summation of the elastic and stress-dependent geometric stiffness terms with contributions from the flange and the web,

where the subscript f indicates the flange and w the web Buckling takes place when the elastic stiffness at the web/flange junction is eroded by the geometric effect, i.e.,

Using (3) and writing the stress-dependent portion of the geometric stiffness explicitly,

ks = kcfe +kc~e fcr,d ('kofg -at- k~c~g ):0 (4) Therefore, the distortional buckling stress,f~r,a, is

k cge + k c~e

f cr ,d -'~ "~

where the stiffness terms with the notations given in Figure 2 are:

kc/e = EIx: (Xo: _hx: )2 + EIw: _Elx~ (xo: _hx: )2 + G1r (6)

lyy

k#g (L ! A: (Xo/-h~zy( I~ = [, I~ _2yo(Xoi_h~ f ~ I ~ l + [ Iy: ) h2x: +YoI 2 +Ix:+ Iyl (7)