bottom of the X-bracing is connected (Figs. 13).

Thin-Walled Structures 43 (2005) 18051817

www.elsevier.com/locate/twsE-mail address: laboube@umr.edu (R.A. LaBoube).Behavior of cold-formed steel built-up I-sections

T.A. Stone a, R.A. LaBoube b,*

a Department of Civil Engineering, University of Missouri-Rolla, Rolla, MO65409, USAb Department of Civil Engineering, Faculty of Engineering, University of Missouri-Rolla, Rolla, MO 65409, USA

Received 18 May 2005; received in revised form 25 August 2005; accepted 29 September 2005

Abstract

An experimental investigation was conducted to study the behavior of built-up cold-formed steel

studs and to assess the current design provisions of the North American Specification for the Design

of Cold-Formed Steel Structural Members. Typical applications include framing for windows,

doorways, shear walls, and multi-story cold-formed steel framed buildings in which the lower floor

utilizes built-up studs to carry the load. The built-up studs in this study consisted of two C-sections

oriented back-to-back forming an I-shaped cross-section. For each specimen, the studs were

connected to each other with two self-drilling screws spaced at a set interval. A cold-formed steel

track section was connected running perpendicular to each end of the built-up stud with a single self-

drilling screw through each flange of the C-sections. The purpose of the track section was to keep the

ends of the studs together and represents a common end attachment. As a result of the investigation,

the current design requirements were found to be conservative in predicting the ultimate capacity of

built-up studs.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Cold-formed steel; Columns; Built-up section; Axial compression

1. Introduction

The building construction industry utilizes cold-formed steel members extensively due

to the advantages offered over other construction materials. Common applications of these

members are in door jambs, support for windows, and shear walls where the top and0263-8231/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tws.2005.09.001

* Corresponding author. Tel.: C1 573 341 4481; fax: C1 573 341 4729.

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 180518171806Cold-formed steel design in North America is governed by the [1]North American

Specification for the Design of Cold-Formed Steel Structural Members. The specification

provides for the design of built-up compression members; however, no testing has been

performed to verify these design equation for cold-formed steel members.

2. Literature review

The following summarizes key research and design methodology for the axial capacity

of built-up compression members.

Based upon research conducted on bolted double-angle compression members attached

at each end to a gusset plate, [2] showed that the most important factor in developing the

strength of the built-up member was preventing shear slip in the end connection.

Lue et al. [9] focused on the axial capacity of built-up hot-rolled steel columns

consisting of double channel sections. The tests consisted of two groups of sections in

which one group utilized snug-tight bolted connections while the other group consisted of

Fig. 1. Typical door framing.

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 18051817 1807welded or fully tensioned bolted connections. The results of the study showed that the

column strength based on the modified slenderness defined by the [3], yields conservative

strength estimates.

[1]North American Specification for the Design of Cold-Formed Steel Structural

Members stipulates design guidance for fassemblies such as built-up compression

members. The specification states for compression members composed of two sections in

contact that the nominal axial strength, Pn, shall be calculated as follows:

Pn Z AeFn (1)

Where Fn is

For inelastic buckling, lc%1.5

Fn Z 0:658l2c Fy (2)

Fig. 2. Typical window framing.

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 180518171808For elastic buckling, lcO1.5

Fn Z0:877

l2c

Fy (3)

FeZp2E

KL=r2 (4)

Where lcZ(Fy/Fe)1/2

If the buckling mode produces shear forces in the connectors between the members,

KL/r should be replaced with (KL/r)m.

KL

r

m

Z

KL

r

2o

Ca

ri

2 s(5)

Where:

Fig. 3. Typical shear wall framing.

Ae Effective area at the stress Fn, with consideration given to the web perforation

(KL/r)o Overall slenderness ratio of entire section about built-up member axis

a Intermediate fastener or spot weld spacing

Fig. 4. Typical C-section parameters.

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 18051817 1809ri Minimum radius of gyration of full unreduced cross-sectional area of an

individual shape in a built-up member

Eq. (5) was adopted from [3]. However, Eq. (5) was developed based on testing

performed on double-angles by [4] and testing performed by Aslani and Goel ([5]).

3. Experimental investigation

An experimental study was performed at the University of Missouri-Rolla

concentrating on the behavior of built-up compression members, specifically I-sections

([6]). The purpose of the investigation was to assess the behavior of the built-upFe The least of the elastic flexural, torsional, and torsional-flexural buckling stress

E Modulus of Elasticity

Fy Yield strength

K Effective length factor

L Unbraced length of memberFig. 5. Typical track section parameters.

cold-formed steel compression members and to determine if the present AISI design

methodology is valid for cold-formed steel members.

The Structural Stability Research Council Technical Memorandum No. 4: Procedure

for testing centrally loaded columns ([7]) provided basic guidance for the development of

the experimental study.

Table 1

C-section geometry

T (mm) D (mm) h (mm) bf (mm) df (mm) R (mm) Fy (Mpa) Fu (MPa) % Elongation

1.372 152.40 139.70 41.28 9.53 4.98 388.04 510.98 22.38

1.155 92.08 90.09 41.28 9.53 3.97 297.06 439.35 27.44

0.880 92.08 89.69 40.64 9.53 4.76 205.30 297.03 20.47

0.841 149.23 136.53 39.70 9.53 4.76 266.52 357.47 19.02

Table 2

Test specimen length and screw spacing

Measured thickness

(mm)

Length (m) Depth (mm) Screw spacing, a (mm)

1.372 2.1 152.4 304.8

1.372 2.1 152.4 609.6

1.372 2.1 152.4 609.6

1.372 2.1 152.4 609.6

1.372 2.1 152.4 762.0

1.372 2.1 152.4 762.0

1.372 2.1 152.4 762.0

1.372 2.1 152.4 914.4

1.372 2.1 152.4 914.4

1.372 2.1 152.4 1016.0

1.372 2.1 152.4 1066.8

1.372 2.1 152.4 1066.8

1.155 2.1 92.1 304.8

1.155 2.1 92.1 304.8

1.155 2.1 92.1 609.6

1.155 2.1 92.1 609.6

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 1805181718101.155 2.1 92.1 914.4

1.155 2.1 92.1 914.4

0.880 2.1 92.1 304.8

0.880 2.1 92.1 304.8

0.880 2.1 92.1 304.8

0.880 2.1 92.1 304.80.880 2.1 92.1 609.6

0.880 2.1 92.1 609.6

0.880 2.1 92.1 914.4

0.880 2.1 92.1 914.4

0.841 2.1 152.4 304.8

0.841 2.1 152.4 304.8

0.841 2.1 152.4 609.6

0.841 2.1 152.4 609.6

0.841 2.1 152.4 914.4

0.841 2.1 152.4 914.4

3.1. Section parameters

Specimens tested in this investigation were constructed of C-shaped sections oriented

back-to-back with edge stiffened flanges and track sections. Figs. 4 and 5 illustrate typical

C- and track sections used in this study. All column specimens were 178 mm long and the

cross-section parameters of the C-sections used in this study varied as follows:

Thickness, t 0.841.37 mm

Depth, D 92152 mm

Flange, bf 41.3 mm

Edge Stiffener, df 9.53 mm

Screw Spacing, a 305914 mm

Table 1 summarizes the C-section geometries while Table 2 lists the screw spacing for

each test specimen.

3.2. Test setup

The built-up compression members were tested in a universal testing machine as shown

in Fig. 6.

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 18051817 1811Simulated pin-pin connections were used in an attempt to achieve an effective length

factor of unity (Figs. 7 and 8). The pin connection at the top of the stud was similar to

the bottom connection in that the two plates had the same half-hemisphere. However, the

upper plate in the top connection was connected to a load cell (Fig. 8).

The two C-sections were fastened together with screws through the web starting 50 mm

from one end and 19 mm from the inside of the flange. The screw spacing, a, was variedFig. 6. Test setup.

Fig. 7. Bottom pin connection.

Fig. 8. Schematic of test setup.

a = 305, 610, 914 mm

19

50 50102

38

Fig. 9. Schematic of screw spacing and layout.

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 180518171812

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 18051817 1813for the test specimen, using spacing values of 305, 610, and 914 mm. The screw layout is

illustrated in Figs. 911.

A 305 mm long track section was screw attached to each end of the built-up I-section to

simulate a typical industry application (Fig. 8).

Fig. 10. Representative screw spacing.

Fig. 11. Typical screw spacing and layout.

(mm)

1.372 152 305 80.60

1.372 152 610 82.96

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 1805181718141.372 152 610 77.00

1.372 152 610 81.22

1.372 152 762 74.06

1.372 152 762 78.38

1.372 152 762 86.74

1.372 152 914 73.53

1.372 152 914 64.32Table 3

Built-up compression member test results

Measured thickness Depth (mm) Screw spacing, a (mm) Ptest (kN)3.3. Test procedure

The load application consisted of centering the stud in the test fixture and applying a

compression load through the center of gravity of the built-up member. The ultimate

failure load for each stud was defined as when the test specimen was no longer capable of

sustaining additional load.

4. Test results

The failure load, Ptest, was the largest load that each built-up member sustained during a

test. Table 3 summarizes the failure loads. Although each test specimen was loaded until

1.372 152 1016 79.36

1.372 152 1067 79.36

1.372 152 1067 79.80

1.155 92 305 55.29

1.155 92 305 66.90

1.155 92 610 51.24

1.155 92 610 51.15

1.155 92 914 47.55

1.155 92 914 55.96

0.880 92 305 42.75

0.880 92 305 37.63

0.880 92 305 27.40

0.880 92 305 33.85

0.880 92 610 36.65

0.880 92 610 42.48

0.880 92 914 36.65

0.880 92 914 41.06

0.841 152 305 32.69

0.841 152 305 38.21

0.841 152 610 43.81

0.841 152 610 37.05

0.841 152 914 32.03

0.841 152 914 35.32

each end, but continued to carry load until the stud formed a smooth curvature with the

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 18051817 1815flanges buckling near mid-span and eventually failed as shown in Fig. 12.

5. Data analysisfailure, the specimens experienced local buckling between the connections and also on

Fig. 12. Typical failure mode.The recorded failure load, Ptest, for the 32 tests was first compared to the

unmodified predicted failure load, Pn, as determined by Section C4 of the AISI

specification without using the (KL/r) modification (Eq. (5)). Fig. 13 illustrates the

comparison of Ptest/Pn.

Fig. 13 indicates that for the thicker materials the existing AISI design equations

without using the modified slenderness ratio (Eq. (5)) are conservative by an average of

Ptest/Pn

0.40.60.81.01.21.41.6

1.8

0.8 0.9 1 1.1 1.2 1.3 1.4Material Thickness (mm)

P tes

t/Pn

Fig. 13. Test versus computed strength using the unmodifed KL/r.

The recorded failure load, Ptest, for the 32 tests was also compared against the modified

predicted failure load, Pnm, as determined by Section C4 of the AISI specification, using

the (KL/r) modification (Eq. (5)). Fig. 14 illustrates the comparison of P /P .

0.60.8

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 180518171816test nm

Fig. 14 indicates that for the thicker materials the existing AISI design equations

including the modified slenderness ratio (Eq. (5)) are conservative by an average of 65%.

This suggests that the modification is not necessary for the thicker materials. The capacity

of the thinner material (0.89 mm) was overestimated by an average of 16%; with only two

of the Ptest/Pnm values less than unity.

6. Conclusions

A total of 32 specimens were tested for this study. An analysis of the data determined43%. This suggests that the modification is not necessary for the thicker materials. The

capacity of the thinner material (0.89 mm) was slightly overestimated by an average of

1%, with five of the 14 values being less than unity.

0.40.8 0.9 1 1.1 1.2 1.3 1.4

Material Thickness (mm)

Fig. 14. Test versus computed strength using the modifed KL/r.Ptest/Pnm

1.01.21.41.61.82.0

P tes

t/Pnmthat for thicker materials the modified slenderness ratio is not necessary when computing

axial capacity, and therefore the designer can use the actual slenderness ratio of the built-

up member. Analysis of the data also determined that the existing design specifications

pertaining to the modified slenderness ratio may be on the average conservative when

designing thinner members (0.89 mm).

References

[1] American Iron and Steel Institute, AISI. North american specification for the design of cold-formed steel

structural members. Washington, DC: American Iron and Steel Institute; 2001.

[2] Sherman DR, Yura JA. Bolted double angle compression members. J Construct Steel Res 1998;46:13 [Paper

No. 197].

[3] American Institute of Steel Construction, Inc., AISC. Manual of steel construction, load and resistance factor

design. 3rd ed. Chicago, IL: American Institute of Steel Construction, Inc., AISC; 2001.

[4] Zandonini, R., Stability of compact built-up struts: experimental investigation and numerical simulation,

construzioni metalliche, No. 4; 1985.

[5] Aslani Farhang, Goel Subhash C. An analytical criterion for buckling strength of built-up compression

members. Eng J 1991;28(4) (American Institute of Steel Construction, Inc., Chicago, IL).

[6] Stone, T.A. Behavior of built-up cold-formed steel I-section wall studs. Thesis presented to the faculty of the

University of Missouri-Rolla in partial fulfillment of the degree Master of Science; 2004.

[7] Galambos Theodore V, editor. Guide to stability design criteria for metal structures. 5th ed. New York, NY:

Wiley; 1998.

[8] Lue Dung-Myau, Yen Tsong, Liu Jui-Ling, Hsu Yao T. Experimental investigation for buckling strength of

double-channel columns Structural stability research council (2004). Proceedings of the annual stability

conference, Long Beach, CA; 2004.

T.A. Stone, R.A. LaBoube / Thin-Walled Structures 43 (2005) 18051817 1817

Behavior of cold-formed steel built-up I-sectionsIntroductionLiterature reviewExperimental investigationSection parametersTest setupTest procedure

Test resultsData analysisConclusionsReferences