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Journal of Constructional Steel Research 54 (2000) 135160

www.elsevier.com/locate/jcsr

The effect of the non-linear stressstrainbehaviour of stainless steels on member

capacity

G.J. van den Berg *

Department of Civil and Urban Engineering, Rand Afrikaans University, Johannesburg 2006

South Africa

Abstract

In recent years several countries have developed specifications for the design of stainlesssteel structural members. Research work over the past 15 years by the Chromium SteelsResearch Group at the Rand Afrikaans University in Johannesburg, South Africa was used

extensively by the American Society of Civil Engineers to update their stainless steel cold-formed design specification which was published in 1991 and will be revised again soon. InEurope a design specification for stainless steel structural members was published recently aspart of Eurocode 3. This specification also refers to research results of the Chromium SteelsResearch Group. The South African Code of Practice for the design of stainless steel structuralmembers will be published soon. This design specification is based on the Canadian designspecification for carbon steel cold-formed structural members.

This paper will give an overview of some of the research that was carried out at the RandAfrikaans University to publish the two above mentioned new stainless steel design specifi-cations. It will highlight the different approaches to determine the strength of members and

sections and will make recommendations on which methods are best to use in design. Experi-mental results and conclusions will be discussed. 2000 Elsevier Science Ltd. All rightsreserved.

Keywords: Stainless steel; Stressstrain behaviour; Member capacity

* Tel.: +27-11-489-2540; fax: +27-11-489-2343. E-mail address: [email protected] (G.J. van den Berg).

0143-974X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 1 4 3 - 9 7 4 X ( 9 9 ) 0 0 0 5 3 - X


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136 G.J. van den Berg / Journal of Constructional Steel Research 54 (2000) 135160

1. General remarks

During the early 1980s a need was identified at the Rand Afrikaans University in

South Africa to update the then existing AISI Stainless Steel Design Specification[1]. Research work over the first 10 years, jointly undertaken by the Rand AfrikaansUniversity and the University of Missouri-Rolla in the USA, resulted during 1991in the publication by the American Society of Civil Engineers of a specification forthe design of cold-formed stainless steel structural members and connections [3].This specification covers the stainless steels given in Table 1. During 1994 EUROINOX published as part of Eurocode 3 a design manual for structural stainless steelfor Europe [14]. This design manual covers Type 304L and 316L austinitic stainlesssteels and a Type 2205 duplex stainless steel.

During 1997 a specification for the design of cold-formed stainless steel structuralmembers was prepared for South Africa and will be published by the South AfricanBureau of Standards [21]. This specification is based on the South African [20] andCanadian [11] cold-formed carbon steel design specification and modified to take intoaccount the differences in the behaviour between carbon steels and stainless steels.

Because stainless steels show gradual yielding stressstrain behaviour it is neces-sary to be familiar with the material properties before designing structural members.

Table 1

Design mechanical properties for longitudinal tension

Type of steel

Types 201, 301, 304, 316 409 430, 439

Annealed a 1/16 hard b 1/4 1/2

Elastic modulus Eo 193 193 193 193 186 186 186 186

(GPa)

Yield strength fy 207 310 276 310 517 759 207c 276c

(MPa)

Proportional limit 139 208 185 208 259 342 157 193

fp (MPa)Ultimate strength fu(MPa)

201 621 655 571 621 861 1034 379 448

301 621 621 861 1034

304 571 621 552 861 1034

316 571 621 586 861 1034

Shear yield strength 117 172 159 172 290 386 131 166

fyv (MPa)

Shear modulus Go 75 75 75 75 72 72 72 72

(GPa)

a Right column: for Type 201-2 (class 2).b Left column: for bars, for Type 201 only.c Adjusted yield strengths: ASTM yield strength is 207 MPa for Types 409, 430 and 439.


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137G.J. van den Berg / Journal of Constructional Steel Research 54 (2000) 135160

Not only the difference in mechanical properties in tension and compression shouldbe taken into account, but aspects like the low proportional limit, which could beconsiderable lower than the yield strength, the different moduli like the initial elastic

modulus, the tangent modulus and the secant modulus should be considered. Themechanical properties of different stainless steels are discussed and the effect of thedifference in mechanical properties with regard to carbon steels on the behaviour ofstructural members and elements are given in this paper.

2. Mechanical properties

2.1. Theoretical model for stressstrain curves

The stressstrain relationships for annealed and cold-rolled stainless steels are non-linear and anisotropic. This leads to a relatively difficult design because the stressstrain curves cannot be represented by a linear function. It is thus desirable to havean analytical expression for the study and design of stainless steel structural elementsand members. Stainless steels yield gradually under load and a typical stressstraincurve is shown in Fig. 1.

The average stressstrain curves can be drawn by using the RambergOsgood [18]equation as revised by Hill [15]. A detailed discussion of the RambergOsgood equ-ation is given in Refs. [2428]. The revised equation is given by Eqs. (1) and (2).

ef

Eo0.002ffy

n

(1)

where

Fig. 1. Typical stressstrain behaviour of a stainless steel.


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nlog(ey/ep)

log(fy/fp)(2)

where e is the strain, f is the stress, Eo is the initial elastic modulus, fy is the yieldstrength, fp is the proportional limit and n is a constant.

Van der Merwe [30] found in a study that by selecting the yield strength, fy, andproportional limit, fp, as the two stresses in Eq. (2), a conservative value in goodagreement with the experimental results is obtained. These two stresses and the initialmodulus are normally mechanical properties that are determined in experimentalwork of this nature.

The tangent modulus, Et, is defined as the slope of the stressstrain curve at eachvalue of stress. It is obtained as the inverse of the first derivative with respect tostrain and can be computed by using Eq. (3).

EtfyEo

fy+0.002nEoffyn1

(3)

The secant modulus, Es, is defined as the stress to strain ratio at each value ofstress and can be computed by using Eq. (4).

EsEo

1+0.002Eofn1

fny

(4)

2.2. Mechanical properties in the ASCE design specification

The mechanical properties for the stainless steels that are included in the ASCE[3] and South African [21] stainless steel design specifications are given in Tables1 and 2 for longitudinal tension and compression only. Typical stressstrain curvesfor stainless steel Type 304 in the different temper grades are given in Fig. 2. Typicalstressstrain curves for the stainless steels in the annealed condition for longitudinal

compression are given in Fig. 3.

2.3. Experimental procedure for mechanical properties

Uniaxial tensile and compression tests were carried out on specimens taken fromthe steel in the longitudinal and transverse directions. The tensile tests were carriedout in accordance with the procedures outlined by the ASTM Standard A370-77 [2].The compression test specimens were mounted in a specially manufactured test fix-ture, which prevents overall buckling of the specimen about its minor axis. Averagestrain was measured by two strain gauges mounted on either side of the test specimen

in a full bridge configuration with temperature compensation. A more detailed dis-cussion can be found in various papers in the Collected Papers of the ChromiumSteels Research Group [2428].


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Table 2

Design mechanical properties for longitudinal compression

Type of steel

Types 201, 301, 304, 316 409 430, 439

Annealed a 1/16 hard b 1/4 1/2


(GPa)

Yield strength fy 193 283 248 283 345 448 207c 276c

(MPa)

Proportional limit 89 130 114 130 173 220 151 171

fp (MPa)

Shear yield strength 117 172 159 172 290 386 131 166fyv (MPa)

Shear modulus Go 75 75 75 75 72 72 72 72

(GPa)

a Right column: for Type 201-2 (class 2).b Left column: for bars, for Type 201 only.c Adjusted yield strengths: ASTM yield strength is 207 MPa for Types 409, 430 and 439.

2.4. Experimental mechanical properties

Stainless steels yield gradually under load. The experimental mechanical propertiesfor longitudinal tension and compression given in Tables 3 and 4 have been collectedfrom experimental tests on coupons taken from stainless steel sheets for the past 15years. They are the means of all the results reported in the five volumes of theCollected Papers of the Chromium Steels Research Group [2428]. In addition tothe stainless steels given in the design specification of the American Society of CivilEngineers [3], the mechanical properties of the South African developed stainlesssteel Type 3CR12, or better known in Europe as Type 1.3004 stainless steel, arealso given in Tables 3 and 4. The experimental stressstrain curves for these steels

are given in Fig. 4.From Tables 3 and 4 it can be seen that the experimental properties for Types201, 205, 301, 304 and 316 are considerably higher than the mechanical propertiesprescribed by the ASTM [2] in the design specification of the American Society ofCivil Engineers [3]. These stainless steels are covered in one group in the designspecification.

The mechanical properties of Type 409 stainless steel are higher but comparewell with the mechanical properties in the design specification. The experimentalmechanical properties for Type 430 stainless steel are also considerably higher thanthe mechanical properties in the design specification. It is possible and recommended

to revise the prescribed mechanical properties in the design specification of theAmerican Society of Civil Engineers [3] to take into account the additional strengththat can be utilised when designing structural members.


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Fig. 2. Stressstrain curves for Type 304 stainless steels.

3. Structural behaviour of members

The design of cold-formed stainless steel structural members is similar to that of

cold-formed carbon steel. Because the mechanical properties of stainless steels aremore complex than those of carbon steels, the design procedures for stainless steelsare more complex. In order to account for the different response to load betweenstainless steels and carbon and low alloy steels, certain modifications to the designequations are needed.

In the following sections some of the modifications in the stainless steel designspecifications are given and the design recommendations are compared with experi-mental results that were carried out at the Rand Afrikaans University.

3.1. Local buckling of flat elements

The critical local buckling stress for a rectangular plate can be predicted by usingEq. (5) [32]:


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Fig. 3. Stressstrain curves for stainless steels in the ASCE specification for longitudinal compression.

Table 3

Mean experimental mechanical properties for longitudinal tension

Type of steel (annealed)

201 205 301 304 316 409 430 3CR12


(GPa)

Yield strength fy 360 310 276 290 275 224 323 293

(MPa)Proportional limit 197 208 185 187 180 167 241 212

fp (MPa)

Number of 1 1 1 8 2 1 9 11

different sheets

Coefficient of a a a 2.42 0.87 a 4.29 6.59

variation

Ultimate strength fu 745 704 622 389 498 461

(MPa)

a Not enough samples to determine coefficient of variation.


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Table 4

Experimental mechanical properties for longitudinal compression

Type of steel (annealed)

201 205 301 304 316 409 430 3CR12


(GPa)

Yield strength fy 296 310 276 292 267 229 331 301

(MPa)

Number of 1 1 1 8 2 1 9 11

different sheets

Coefficient of a a a 7.22 0.93 a 9.73 6.91

variation

Proportional limit 160 208 185 168 157 167 225 211fp (MPa)

a Not enough samples to determine coefficient of variation.

Fig. 4. Experimental stressstrain curves for various stainless steels for longitudinal compression.

fcrhkp2Eo

12(1v2)(w/t)2(5)

where fcr is the critical local buckling stress, h is the plasticity reduction factor, kis the buckling coefficient, Eo is the initial elastic modulus, n is the Poisson ratio,w is the flat width of the element and t is the thickness of the element. The buckling


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coefficient k depends upon the edge rotational restraint, the type of loading and theaspect ratio of the plate. When local buckling of an element occurs at a compressionstress that exceeds the proportional limit of the steel, the resulting inelastic behaviour

leads to instability of stainless steel compression elements at lower stresses thanthose of carbon steels. The reduced stiffness of the flat elements is taken into accountby the introduction of the plasticity reduction factor, h, in Eq. (5).

3.1.1. Stiffened and unstiffened compression elements

The values for k are 0.425 for unstiffened compression elements, 4 for stiffenedcompression elements and between 0.425 and 4 for partially stiffened compressionelements and are given in the design specifications [3,11,20,21]. The plasticityreduction factors suggested are h=Es/Eo for unstiffened compression elements andh=Et/Eo for stiffened compression elements.

In Fig. 5 a comparison is made between theoretical predictions and experimentalresults for Type 3CR12 steel for stiffened and unstiffened compression elementswhen the above two plasticity reduction factors are used [22].

3.2. Partially stiffened compression elements

The plasticity reduction factor for partially stiffened compression elements is notdefined and was investigated in a study by Buitendag [9,10], Reyneke [19] and Vanden Berg [29]. Different plasticity reduction factors for stainless steel Types 304,

430 and 3CR12 were investigated. The results for Type 304 stainless steel Hat and

Fig. 5. Critical buckling stress for stiffened and unstiffened compression elements.


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Zed section compression elements in columns [9,10,19] are given in Fig. 6 and theresults for compression elements in stainless steel I-section beams [29] are given inFig. 7.

It is difficult to determine the critical local buckling stress from experimentalresults accurately. The strain reversal method suggested by Johnson [16] and Wang[31] was used. It can be seen from the experimental results for partially stiffenedcompression elements in Figs. 6 and 7 that a reduction in critical stress is found inthe inelastic stress range. A secant or tangent modulus plasticity reduction approachshow good agreement with the experimental results for certain cases.

3.3. Post buckling of flat elements

For the theoretical calculation of the post buckling strength of partially stiffenedcompression elements the model suggested by the Canadian [11] and South African[20] carbon steel cold-formed design specifications, which is similar to the ASCE[3] stainless steel specification, will be used. The proposed South African [21] stain-less steel design specification is similar. The equations in the above specificationswill be revised to take into account the non-linear behaviour of stainless steels inthe inelastic stress range by introducing plasticity reduction factors. The proceduresdescribed in the South African [20] and Canadian [11] carbon steel cold-formeddesign specifications and the proposed South African [21] stainless steel designspecification will be followed.

When the width-to-thickness ratio (W=w/t) of a stiffened and unstiffened com-pression element exceeds the limiting width-to-thickness ratio given in Eq. (6) the

Fig. 6. Critical local buckling of partially stiffened compression elements in columns.


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Fig. 7. Critical local buckling strength of partially stiffened I-section beams.


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Fig. 7. (continued)


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width of the compression element must be reduced according to Eq. (7). In theseequations the values for the buckling coefficient k are 0.425 and 4 for unstiffenedand stiffened compression elements, respectively. The plasticity reduction factors for

stiffened and unstiffened compression elements given previously can be used.

Wlim0.644hkEof (6)The effective width ratio of a compression element is given by:

B0.95

h

kEo

f

1

0.208

W

hkEof

(7)

The design procedure to calculate the effective width of partially stiffened com-pression elements is divided into three categories. Case 1 deals with compressionflanges that are fully effective, even if it has no lip and it is an unstiffened com-pression element. For this case it is not necessary to add a stiffener lip to the oneside of the compression flange. The effective area of the compression flange is thus

equal to the full unreduced area of the compression element. Only the stiffener liphas to be checked for local buckling.

The following equations are used in all the cases.

Wlim 10.644hkEof with k0.425 (8)

Wlim 20.644hkEof with k0.4 (9)

Case 1: WWlim 1

No reduction in the width of the compression element is necessary.Case 2: Wlim 1WWlim 2Case 3: WWlim 2

For Cases 2 and 3 the value of the buckling coefficient k is calculated from theequations given in Table 1 of the Canadian [20] and South African [20] carbon steeldesign specification as revised by Schuster [13], with similar equations in the ASCE

design specification [3]. The effective width is calculated using Eq. (7), where Wlim1 is the the limit for the flat width ratio above which an unstiffened compressionelement will buckle, Wlim 2 is the limit for the flat width ratio above which a stiffened


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compression element will buckle, h is the plasticity reduction factor, kis the bucklingcoefficient for different types of compression elements, Eo is the initial elastic modu-lus, f is the maximum stress in the compression element, B is the effective width

ratio b/t for compression elements, W is the flat width ratio w/t for compressionelements, b is the effective width for compression elements, w is the flat width ofcompression elements and t is the thickness of the steel.

The results in Fig. 8 of the short axially loaded Hat and Zed section columns byBuitendag [9,10] show that by using a secant or tangent approach plasticity reductionfactor a good agreement is found between the experimental results and the theoreticalpredictions. In the beam tests by Van den Berg [29] it is shown in Fig. 9 that someof the experimental results are lower than the predicted results when no plasticityreduction factor is used. All the experimental results are, however, higher than thepredicted values when the two plasticity reduction factors are used. It can be con-cluded that, by using one of the plasticity reduction factors, conservative designestimates can be made.

3.4. Shear buckling of webs

A study on the behaviour of cold-formed stainless steel beam webs subjected toelastic and inelastic shear buckling was carried out by Carvalho [12]. The materialsunder investigation were stainless steel Types 304, 316, 430 and 3CR12. The theor-etical critical shear buckling stress of each profile was determined using Eq. (5) with

a plasticity reduction factor =Es/Eo and k=5.34. The experimental critical shearbuckling stresses are compared with the theoretical predicted values and are given

Fig. 8. Ultimate strength of partially stiffened compression members.


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Fig. 9. Ultimate strength of I-section beams.


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Fig. 9. (continued)


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in Fig. 10. It can be concluded that a good agreement is found between the experi-mental results and the theoretical predictions when the plasticity reduction factorsare used.

3.5. Web crippling

An investigation on the web crippling strength of cold-formed stainless steel chan-nel sections was done by Korvink [17]. The stainless steels that were considered inthis investigation were Types 304, 430 and 3CR12. Experimental results for stainlesssteel Type 304 were compared with the theoretical predictions that are given in theASCE [3] and South African [21] stainless steel design specifications and shown inFig. 11. In this study different bearing length to thickness ratios (N=n/t) and web

height to thickness ratios (H=h/t) were investigated.It was concluded in this study that the experimental results compare reasonablywell with the theoretical predictions except that they are conservative for larger bear-ing lengths and shorter web heights.

4. Stability of columns and beams

4.1. Strength of columns

Fig. 10. Critical shear buckling stress in beam webs.


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Fig. 11. Web crippling strength of beam webs.

4.1.1. Flexural buckling

A slender axially loaded column may fail by overall flexural buckling if the cross-section of the member is a doubly symmetric shape (I-section), closed shape (squareor rectangular tube), cylindrical shape, or point symmetric shape (Z-section or cruci-form section). If a column has a cross-section other than the above shapes but isconnected to other parts of the structure, such as wall sheeting material, the membercan also fail in flexural buckling.

The elastic buckling stress can be determined by the Euler formula:

fp2Eo

(kL/r)2(10)

where f is the critical elastic buckling stress, Eo is the initial elastic modulus, k isthe effective length factor, L is the length of the column and r is the radius ofgyration. Eq. (10) is applicable to ideal columns made of sharp yielding steels with-out consideration of residual stresses or the effects of cold working. In view of thefact that many steel sheets and strips used in cold-formed structural members are ofthe gradual yielding type and that the cold-forming process tends to lower the pro-portional limit, Eq. (10) would not be suitable for columns made of gradual yieldingsteel having small and moderate slenderness ratios. Whenever the stress is above theproportional limit, the column will buckle in the inelastic stress range. The carbon

steel design specifications [1,20] make use of a parabolic fit between the proportionallimit, which is taken as half the yield strength, and the yield strength to take intoaccount the inelastic behaviour of the steel and it is given as:


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ffy1fy4fe (11)where fe is the Euler buckling stress in Eq. (10).

For stainless steels, in the inelastic stress range, the value of the elastic modulusin Eq. (10) should be replaced by the tangent modulus, Et and the critical bucklingstress is given by:

fp2Et

(kL/r)2(12)

This takes into account the effect of the low proportional limit, the effect of residualstresses and the gradual yielding behaviour of stainless steels.

4.1.2. Torsional and torsionalflexural bucklingAxially loaded thin-walled compression members that have open sections can fail

in flexure, torsion and torsionalflexural buckling. In the torsionalflexural mode,bending and twisting of the section occur simultaneously. Usually, closed sectionswill not buckle torsionally because of their large torsional rigidity. The flexural andtorsional buckling loads are given by Eqs. (13)(15). The initial elastic modulus andthe shear modulus are replaced by the tangent modulus and the tangent shear modulusto take into account the inelastic behaviour of a gradual yielding stainless steel.

Pxp2EtIx

(Lx)2

(13)

Pyp2EtIy(Ly)

2(14)

Pt1

r20p2EtCw

L2tGtJ (15)

4.1.3. Doubly symmetric shapes

Doubly symmetric sections will fail either in pure flexure or in pure torsion. I-section and cruciform sections are examples of doubly symmetric sections where theshear centre and the centroid coincide.

The critical buckling load is the lowest value of Eqs. (13)(15).

4.1.4. Singly symmetric shapes

Singly symmetric shapes are shapes such as angles, channels, hat sections, T-sections and I-sections with unequal flanges. For torsional flexural buckling the x-axis is chosen as the symmetry axis. Singly symmetric sections can fail in flexuralbuckling about the y-axis or in torsional flexural buckling and the torsionalflexuralbuckling load is given by:

Ptf1

2b[(PxPt)(Px+Pt)24bPxPt] (16)


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A singly symmetric section may buckle either in pure flexure about the y-axis orin the torsional flexural mode depending on the dimensions of the cross-section andthe effective length of the column.

Similar to flexural buckling, the inelastic torsional flexural buckling stress can beobtained by replacing the initial elastic modulus, Eo, by the tangent modulus, Et, andthe shear modulus, G, by the tangent shear modulus, Gt=GEt/Eo.

4.1.5. Discussion of experimental results

Various studies on the behaviour of cold-formed [23,29] and hot-rolled [6,8] singlyand doubly symmetric stainless steel columns were carried out to determine theflexural and torsional flexural buckling strengths.

Van der Merwe [30] studied the strength of doubly symmetric I-sections for Type3CR12 steel. The comparison of experimental results with the theoretical predictionsis given in Fig. 12.

Van den Berg [23] carried out studies on singly symmetric hat sections to studythe torsional flexural buckling strength. The experimental results are compared withtheoretical predictions by using the SSRC equation and the tangent modulusapproach. The results for Type 304 stainless steel and Type 3CR12 stainless steelare given in Figs. 13 and 14, respectively.

Bosch [4] studied the strength of hot-rolled singly symmetric Type 3CR12 stain-less steel angle sections and the results are given in Fig. 15.

It was concluded in all the studies that the tangent modulus should be used to

Fig. 12. Flexural buckling strength of I-section columns.


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Fig. 13. Torsionalflexural buckling strength of Type 304 stainless steel hat sections.

Fig. 14. Torsionalflexural buckling strength of Type 3CR12 stainless steel hat sections.


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Fig. 15. Strength of Type 3CR12 hot-rolled angle compression members.

predict the flexural and torsional flexural buckling strength of axially loaded com-

pression members. The SSRC curve that is used in the carbon steel cold-formeddesign specifications cannot be used for stainless steels.

4.2. Strength of beams

When cold-formed steel flexural members are loaded in the plane of the web, thebeam may twist and deflect laterally as well as vertically if braces are not adequatelyprovided. Beams with large unbraced lengths may buckle between the braces and alower compressive stress should be used for the design of beams in order to preventfailure due to possible lateral buckling [32]. In general, the elastic lateral bucklingstrength of a beam can be calculated using Eq. (17):

McCbp

LEIyGJ+pE

L2IyCw (17)

To take into account the non-linear behaviour of cold-formed carbon steels in theinelastic stress range, Eq. (11) is used by the South African [20], Canadian [11] andAmerican [1] carbon steel design specifications. This equation is not valid for stain-less steels. To take into account the non-linear behaviour of stainless steels in the

inelastic stress range, the initial elastic modulus and shear modulus in Eq. (17) mustbe replaced by the tangent modulus and tangent shear modulus and the revised equ-ation is given as:


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McCbp

LEtIyGtJ+pEtL

2IyCw (18)where Mc is the critical lateral buckling moment, Cb is the bending coefficient forthe moment gradient, Et is the tangent modulus, Gt is the tangent shear modulus, Lis the unbraced length, Iy is the moment of inertia about the y-axis, Cw is the warpingconstant of torsion and J is the St Venant torsion constant.

4.2.1. Doubly symmetric I-sections

If it is assumed for doubly symmetric I-sections that the St Venant torsional stiff-ness in Eq. (18) is low and can be neglected, and with Iy=Iyc+Iyt, Eq. (18) results inthe following conservative equation [32]:

Mcp2EtCbdI

yc

L2 (19)where Iyc is the moment of inertia of the compression flange.

4.2.2. Singly symmetric sections

Eq. (17) also applies to singly symmetric sections and by rearranging Eq. (20)can be used to determine the ultimate moment capacity:

McCbroAfeyft (20)

where

feyp2Et

kLr2

y

(21)

ft1

Ar2oGtJp2EtCw

(kL)2t (22)

4.2.3. Point symmetric sections

The principal centroidal axes of point symmetric sections are not perpendicularto the web. When the section modulus about the axis perpendicular to the web isused in Eq. (20) the critical buckling moment should be divided by two and isgiven as:

Mc0.5CbroAfeyft (23)

4.2.4. Discussion of experimental resultsThe lateral torsional buckling strength of Type 3CR12 stainless steel singly sym-

metric lipped channel sections was investigated by Bredenkamp [7]. The experi-


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mental results were compared with the SSRC curve that is used in the carbon steelcold-formed design specifications and the tangent modulus approach that is used inthe stainless steel design specifications and is given in Fig. 16. The elastic critical

moment curve is also shown. It is concluded in this study that the experimentalresults compare well with the theoretical predictions when the tangent modulusapproach is used. Other studies on hot-rolled stainless steel sections showed similarresults [5,8].

5. Conclusions

The design mechanical properties given in the ASCE [3] stainless steel cold-for-med design specification need to be revised. The yield strengths that are obtainedthrough tensile and compression tests are considerably higher than those prescribedby the ASTM [2]. This specification should also be revised.

It is stated in the ASCE [3] stainless steel design specification that it is not neces-sary to use plasticity reduction factors when local buckling is considered. This mightbe the case for stiffened and unstiffened elements that were tested by Johnson [16]and Wang [31]. Recent results on the local buckling strength of partially stiffenedelements show that plasticity reduction factors should be considered.

Studies on the ultimate capacity of stainless steel columns and beams confirmedthat experimental results are in good agreement with theoretical predictions when

the tangent modulus is used.

Fig. 16. Lateral torsional buckling of beams.


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