Experiments on Cold-Formed Steel Columns With Holes

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Thin-Walled Structures 46 (2008) 1164–1182

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Experiments on cold-formed steel columns with holes

Cristopher D. Moen�, B.W. Schafer

Department of Civil Engineering, Johns Hopkins University, Latrobe Hall 210, Baltimore, MD 21209, USA

Received 3 November 2007; accepted 21 January 2008

Available online 14 March 2008

Abstract

The objective of this paper is to observe and quantify the relationship between elastic buckling and the tested response of cold-formed

steel columns with holes. Compression tests were conducted on 24 short and intermediate length cold-formed steel columns with and

without slotted web holes. For each specimen, a shell finite element eigenbuckling analysis was also conducted such that the influence of

the boundary conditions and the hole on local, distortional, and global elastic buckling response could also be captured. Slotted web

holes may modify the local and distortional elastic buckling half-wavelengths, and may also change the critical elastic buckling loads.

Experimentally, slotted web holes are shown to have a minimal influence on the tested ultimate strength in the specimens considered,

although post-peak ductility is decreased in some cases. Tangible connections are observed between elastic buckling and

load–displacement response during the tests, including mode switching between local and distortional buckling. The columns are

tested with friction-bearing boundary conditions where the columns ends are milled flat and parallel, and bear directly on steel platens.

These boundary conditions, which greatly speed specimen preparation, are determined to be viable for evaluating the tested response of

short and intermediate length columns, although the post-peak response of intermediate length specimens must be considered with care.

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Keywords: Elastic buckling; Experiments; Ultimate strength; Holes; Cold-formed steel; Perforations

1. Introduction

Cold-formed steel structural members are commonlyprovided with holes to accommodate plumbing, electrical,and heating conduits in the walls and ceilings of buildings.These holes are typically pre-punched perforations locatedin the web of Cee or Zee sections and can alter the elasticstiffness and ultimate strength of a structural member. Themajority of existing experimental data on cold-formed steelcolumns with holes has been obtained from stub columntests, where the ultimate strength is driven by localbuckling and yielding of the cross-section [1–8]. Stubcolumn tests in [1] demonstrated that ultimate strengthdecreased as circular hole diameter increased, relative toweb depth. Similar conclusions when evaluating theinfluence of circular, slotted, and rectangular web holeson stub column ultimate strength have also been reported[2–4]. The impact of the location of the hole in the stub

e front matter r 2008 Elsevier Ltd. All rights reserved.

s.2008.01.021

ing author.

ess: [email protected] (C.D. Moen).

column [5–7] as well as the length of the hole [8] have alsoall been studied. In addition to the stub column testing, 25intermediate and long column tests were completed by [1]and demonstrated that a single hole at the mid-height of apinned–pinned column did not affect ultimate strength.The motivation for this experimental program is to

expand the existing column data set with tests on short andintermediate length columns with holes. The columnlengths and cross-section dimensions are specifically chosento explore the connection between local, distortional, andglobal elastic buckling modes, ultimate strength, and theresulting failure mechanisms. The elastic buckling behavioris evaluated for each specimen with a finite elementeigenbuckling analysis, taking care to accurately simulatethe tested boundary conditions and measured specimendimensions. These elastic buckling results are used toprovide a means of understanding the varied deformationresponse under load.The columns are tested with friction-bearing boundary

conditions where the ends of each specimen are milledflat and parallel, and bear directly against steel platens.

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Table 1

FSM local and distortional buckling half-wavelengths for nominal

362S162-33 and 600S162-33 cross-sections

Cross-section Elastic buckling half-wavelength

Local (L) (mm) Distortional (D) (mm)

362S162-33 70 390

600S162-33 120 310

0 200 400 600 800 1000 1200 1400 1600 18000

2

4

6

8

10

12

14

16

18

20

column specimen length (mm)

num

ber o

f spe

cim

ens

Specimens with holes in this study

Stub column tests

Fig. 2. Tested lengths of cold-formed steel columns with holes as

summarized in [12].

C.D. Moen, B.W. Schafer / Thin-Walled Structures 46 (2008) 1164–1182 1165

The influence of holes on column elastic buckling behavior,ultimate strength, and post-peak ductility are presentedand discussed. Recommendations are made to advise otherresearchers on the viability of the friction-bearing bound-ary conditions when testing short and intermediate lengthcolumns. This study is one component of a multi-levelresearch program where the Direct Strength Method(DSM) [9] is being extended as a general strengthprediction approach for columns (and beams) with holes.

2. Testing program

Twenty-four cold-formed steel lipped Cee channelcolumns with and without pre-punched slotted web holeswere tested to failure. The primary experimental para-meters are column cross-section, column length, and thepresence or absence of slotted web holes. The specimennaming convention, as it relates to the testing parameters,is defined in Fig. 1. The rationale for selecting theseexperimental parameters is discussed in Section 2.1.

2.1. Rationale for selecting specimen dimensions

2.1.1. Cross-section types

Two industry standard cross-sections from the Steel StudManufacturers Association (SSMA) [10], 362S162-33 and600S162-33, were evaluated in this study. The 362S162-33cross-section has a nominal web width of 92mm (3.62 in),while the 600S162-33 web is wider at 152mm (6.00 in).Both sections have a 41mm (1.62 in) flange and nominalsheet thickness of 0.88mm (0.0346 in). Specific measureddimensions are provided in Section 2.4.

The buckling half-wavelengths that form along thelength of the specimens are cross-section dependent, andcan be calculated with the semi-analytical finite stripmethod (FSM) [11]. FSM assumes simply supportedboundary conditions, and therefore the local and distor-tional half-wavelengths for the cross-sections studied here,as provided in Table 1, are only a guide as to the expectedhalf-wavelength in the fixed–fixed tests. The FSM half-wavelengths are still a useful reference when deciding onspecimen lengths (Section 2.1.2) and identifying buckling

Cro

No Holes Holes362-1-24-NH362-2-24-NH362-3-24-NH362-1-48-NH362-2-48-NH362-3-48-NH600-1-24-NH600-2-24-NH600-3-24-NH600-1-48-NH600-2-48-NH600-3-48-NH

SSMA 362S162-33

SSMA 600S162-33

Short Column

IntermediateColumn

Short Column

IntermediateColumn

362-1-24-H362-2-24-H362-3-24-H362-1-48-H362-2-48-H362-3-48-H600-1-24-H600-2-24-H600-3-24-H600-1-48-H600-2-48-H600-3-48-H

Fig. 1. Column testing paramet

modes (Section 3.2.4), especially as specimen lengthincreases and local and distortional buckling half-wave-lengths converge to the fundamental (simply supported)half-wavelengths reported in Table 1.

2.1.2. Column lengths

More than 80% of the tested specimens with holesavailable in the literature (see full summary in [12]) arestub columns, as depicted in the specimen length histo-gram of tested specimens provided in Fig. 2. Stub columns

362-1-24-NH

ss-section type Specimen number within common group (1,2,3)

Nominal specimen length, 610 mm (24 in.) or 1219 mm (48 in.)

Specimen with holes (H) or without holes (NH)

ers and naming convention.

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Fig. 4. A specimen with bismuth diaphragm is end-milled to a flatness

tolerance of 70.025mm.

C.D. Moen, B.W. Schafer / Thin-Walled Structures 46 (2008) 1164–11821166

accommodate local buckling half-waves, but due to theirshort length, distortional buckling is typically restrainedfrom forming at relevant stress levels. The specimen lengthsselected in this study, a 610mm (24 in) short column anda 1219mm (48 in) intermediate length column, ensurethat at least one distortional half-wave and multiple localhalf-waves can form along the length of the column (seeTable 1). Further, at least for North American practice, theselected lengths are more typical of the unbraced length ofactual cold-formed steel columns in an ‘‘all-steel’’ designwith bridging in place to brace the studs.

2.1.3. Hole type and locations

One slotted web hole (see Section 2.4 for specificdimensions of the hole shape and size) is located at themid-height of the short column to evaluate its influence atthe mid-length of one distortional buckling half-wave. Twoslotted web holes are oriented in the intermediate lengthcolumns with an industry standard spacing of 610mm [10].The holes also coincide with the locations where distor-tional buckling half-waves are expected to have theirmaximum displacement under load.

2.2. Test setup

The column compression tests are performed with the445 kN capacity two-post MTS machine shown in Fig. 3.Flat and parallel chrome-moly 4140 steel platens are rigidlyfixed to the upper cross-head and lower actuator. Thecolumn specimens bear directly on the steel platens as theyare compressed. Friction between the column ends and thesteel platens are the only lateral forces that restrain thecolumn cross-section under load. Position transducers with

Fixed Crosshead

Position transducers (with magnet tips)

Fig. 3. Column test setup

magnetic tips are used to measure the mid-height lateralflange displacement of specimens under load.

2.3. Specimen preparation

Each specimen was rough cut to length with a metalband saw before milling the specimen ends to a flatnesstolerance of 70.025mm as recommended by Galambos[13]. Each end was encased in a bismuth diaphragm, see

Load Cell

Friction-bearing boundary conditions (specimen bears directly on steel platen)

and instrumentation.

ARTICLE IN PRESSC.D. Moen, B.W. Schafer / Thin-Walled Structures 46 (2008) 1164–1182 1167

Fig. 4, to preserve the undeformed shape of the specimensand dampen vibration during milling. (Bismuth is achemical element that is relatively soft compared with steelat room temperature and which melts at 70 1C.) Thebismuth diaphragms were removed before testing.

2.4. Measured specimen dimensions

The dimension reference system and nomenclature foreach specimen is presented in Fig. 5, and measured

West B

F1

Orientation in testing machine(front view)

EastWest

South

North

L

a a

R

RT1

West

Fig. 5. Specimen measur

Table 2

Summary of measured specimen cross-section dimensions and yield stress

Specimen fy t L H B1 B2 D1 D

(MPa) (mm) (mm) (mm) (mm) (mm) (mm) (

362-1-24-NH 380 0.98 612 92.8 39.4 41.2 10.4 1

362-2-24-NH 380 0.98 612 94.3 40.3 40.3 10.6 1

362-3-24-NH 380 0.98 612 92.0 42.6 42.6 10.8 1

362-1-24-H 400 0.99 612 91.0 41.9 40.5 10.9 1

362-2-24-H 394 0.97 612 92.6 41.3 40.5 11.2

362-3-24-H 386 1.00 612 93.3 42.5 43.1 10.6 1

362-1-48-NH 412 1.00 1225 92.0 40.9 40.8 10.5 1

362-2-48-NH 409 1.00 1227 92.0 40.9 40.3 10.3 1

362-3-48-NH 407 0.99 1224 91.8 40.7 40.6 10.8 1

362-1-48-H 404 1.00 1225 92.0 40.7 40.5 10.7 1

362-2-48-H 412 0.99 1225 92.0 40.5 40.9 10.8 1

362-3-48-H 402 1.01 1224 92.3 40.7 40.9 10.0 1

600-1-24-NH 405 1.11 612 153.3 40.6 41.4 12.4

600-2-24-NH 405 1.11 612 154.2 40.2 41.0 12.0

600-3-24-NH 405 1.11 612 153.2 40.7 40.4 9.4 1

600-1-24-H 427 1.07 612 153.4 40.5 40.8 12.3

600-2-24-H 403 1.05 612 152.7 40.9 40.7 9.4 1

600-3-24-H 415 1.09 612 153.2 40.8 40.0 9.1 1

600-1-48-NH 415 1.10 1226 152.9 41.2 40.9 12.3

600-2-48-NH 437 1.10 1226 152.8 40.5 40.7 12.2

600-3-48-NH 422 1.10 1227 153.1 40.3 41.3 12.4

600-1-48-H 423 1.09 1221 152.6 40.6 41.3 12.2

600-2-48-H 428 1.09 1226 152.8 40.4 40.8 12.1

600-3-48-H 424 1.10 1221 154.0 41.5 40.3 9.3 1

specimen dimensions are summarized in Table 2. Theout-to-out cross-section dimensions and web-flange andflange-lip angles were measured at the mid-length of eachspecimen and are an average of three measurements. Notethat although web-flange angles are commonly assumed tobe 901, measured values were �61 to +41 off of 90,similarly the lip-flange angles were �21 to +131 off of 90.The slotted hole dimension notation is described in

Fig. 6. The measured dimensions and locations of the holesin Table 3 are an average of three measurements. Note that

East

D1

1

H

B2

D2

F2

S1 S2

Section a-aB1

RT2

RB2t

East

ement nomenclature.

2 RT1 RT2 RB1 RB2 S1 S2 F1 F2

mm) (mm) (mm) (mm) (mm) (deg) (deg) (deg) (deg)

0.9 4.8 4.8 4.4 4.8 12.8 8.4 86.0 86.8

0.7 4.4 5.2 6.7 7.1 11.4 11.6 87.6 85.5

0.1 4.8 4.4 7.1 7.1 9.6 9.4 86.3 85.4

1.1 4.8 5.2 7.1 7.1 11.1 10.9 87.6 85.6

9.9 4.8 4.8 7.1 7.1 4.4 10.3 86.3 85.2

0.8 4.8 4.8 6.7 6.7 10.5 10.8 87.7 86.1

0.8 4.4 4.4 7.1 7.1 7.8 10.1 85.0 85.6

0.7 4.8 4.4 7.5 7.1 8.0 10.8 84.2 84.6

0.2 4.8 4.8 6.7 6.7 9.1 12.2 85.3 84.1

0.5 4.4 4.4 7.1 7.1 8.5 9.8 85.6 84.2

0.2 4.4 4.4 7.1 7.1 8.3 11.2 85.6 83.8

1.0 4.4 4.4 7.1 6.4 9.7 7.3 84.1 85.3

9.3 4.4 4.0 6.4 5.2 1.6 2.1 91.4 93.8

9.7 5.2 5.2 6.7 6.7 1.7 2.3 91.5 93.3

2.3 4.0 4.4 6.7 5.6 �2.2 3.5 92.7 89.7

9.1 4.4 4.4 6.4 5.6 1.0 2.0 91.2 92.6

2.7 4.4 4.4 5.2 6.0 1.8 1.1 92.0 89.0

2.1 4.4 4.4 6.4 5.2 0.1 4.1 90.1 86.3

9.5 4.4 4.4 6.0 5.6 0.2 1.4 90.6 92.8

9.1 4.4 4.4 6.0 6.0 2.0 2.4 89.9 91.9

8.6 4.4 4.4 6.7 5.6 2.6 2.3 90.0 92.1

9.9 4.8 4.0 6.4 5.6 2.5 2.1 90.0 92.6

9.0 4.4 4.4 6.0 6.0 2.4 1.0 88.9 91.2

2.2 4.4 4.4 5.6 6.4 0.7 3.6 92.3 89.4

ARTICLE IN PRESSC.D. Moen, B.W. Schafer / Thin-Walled Structures 46 (2008) 1164–11821168

the hole was typically punched slightly off center in the362S162-33 columns. The column length L is reported inTable 2 as the average of the lengths measured at the fourcorners of the cross-section.

Base metal thickness was measured from tensile couponscut from both flange flats and the web of each structuralstud used as a source for specimens. All studs weredelivered by the manufacturer with a zinc outer coating forgalvanic corrosion protection. The zinc coating wasremoved by immersing the tensile coupons in a ferricchloride bath for 100min. See [14] for a detailed descrip-tion of the coating removal process. The thickness t

provided in Table 2 is the base sheet metal thicknesscalculated as the average of the two flanges and the webmeasurements. The average zinc coating thickness for allspecimens was 0.066mm.

North

aa

W1 W2

X

Section a-a

Lhole

hhole

Front view

2

hholerhole =

Hole detail

Fig. 6. Hole dimension and location nomenclature.

Table 3

Measured slotted hole dimensions and locations

Specimen X W1 W2 Lhole hhole(mm) (mm) (mm) (mm) (mm)

362-1-24-H L/2 24.0 29.0 101.7 37.9

362-2-24-H L/2 29.1 24.6 101.6 38.2

362-3-24-H L/2 23.7 28.3 101.7 37.9

362-1-48-H (L�610)/2 31.8 24.7 101.6 38.1

362-2-48-H (L�610)/2 28.6 25.8 101.6 38.0

362-3-48-H (L�610)/2 24.9 28.2 101.6 37.9

600-1-24-H L/2 54.5 60.0 101.7 38.0

600-2-24-H L/2 60.1 54.7 101.6 37.9

600-3-24-H L/2 59.6 55.0 101.6 37.9

600-1-48-H (L�610)/2 54.9 60.3 101.7 37.9

600-2-48-H (L�610)/2 55.0 59.7 101.6 38.1

600-3-48-H (L�610)/2 60.2 54.9 101.6 38.0

See Table 2 for measured values of column length L.

2.5. Material properties

The steel stress–strain curve and yield stress aredetermined for the flanges and the web in accordance withASTM E8 [15]. Tensile coupons taken from the 362S162-33structural studs demonstrated gradual yielding behavior,while the tensile coupons from the 600S162-33 studsdemonstrate a sharp yielding plateau. The steel modulusof elasticity, E, is assumed as 203.4GPa when determiningthe yield stress. The specimen yield stress, fy, reported inTable 2 is the average of the yield stresses from the web andtwo flanges.

2.6. Testing procedure

When placing each specimen in the testing machine,the southern end of the specimen (see Fig. 7) is oriented atthe bottom platen such that the center of the compressiveforce is applied through the gross centroid of the Ceechannel. (Since rigid platens are used this step is not strictlynecessary. Refer to Moen and Schafer [14, Section 2.3.5.2],for a detailed discussion on platen rigidity and the influenceof load eccentricities in column tests.) Fig. 6 demonstratesthat the centerline of the web is aligned with the centerlineof the bottom platen and offset towards the back of thetesting machine. All column specimens are loaded indisplacement control at a constant rate of 0.10mm/min.This rate was chosen to be consistent with the 21MPa axialstress per minute recommendation in the AISI Specifica-tion for stub column testing [13].

3. Elastic buckling calculations

Elastic buckling provides a means to categorize andpotentially better understand the load–deformation re-sponse and ultimate strength of the thin-walled columns inthis study. The local, distortional, and global elasticbuckling modes and their associated critical elastic buck-ling loads (Pcr‘, Pcrd, Pcre) are presented here for each

X W1 W2 Lhole hhole(mm) (mm) (mm) (mm) (mm)

(L+610)/2 30.4 24.2 101.6 37.9

(L+610)/2 29.7 24.7 101.7 38.0

(L+610)/2 24.6 28.8 101.7 37.9

(L+610)/2 54.9 60.5 101.5 38.0

(L+610)/2 55.3 59.9 101.7 38.0

(L+610)/2 60.1 54.8 101.7 38.0

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Plan View(Bottom Platen)

CL Platen and Column Web

9.67 mm (600S162-33)12.75 mm (362S162-33)

CL Platen

Location of interior web edge

Center of platen, center of load, centroid of Ceechannel

FRONT OF MTS MACHINE

Column specimen

Fig. 7. Specimen alignment on steel platen.

1

2

3

ABAQUS “pinned “rigid body reference node constrained in 2 to 6 directions, ensures that all nodes on loaded surface move together in 1 direction

Nodes bearing on top platen constrained in 1, 2 and 3

45

6

Fig. 8. Boundary and loading conditions implemented in the ABAQUS

eigenbuckling analyses.

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Pn/

Pyg

Local DSMDistortional DSM

D

D

L

L

362S162-33 short columns

600S162-33 short columns

Local (L)-Distortional (D) interaction is expected since predicted strengths (Pn)are of similar magnitudes

slenderness, λ or λd

Fig. 9. Local (L) and distortional (D) DSM strength predictions are

similar in magnitude for both 362S162-33 and 600S162-33 cross-sections,

indicating that L–D modal interaction will occur during the tested

response of the columns.


specimen. Calculations are performed with a shell finiteelement eigenbuckling analysis as opposed to an analysisusing FSM [11] to capture the influence of the slotted webholes and the tested (fixed–fixed) boundary conditions.

3.1. Finite element modeling assumptions

Eigenbuckling analysis in ABAQUS [16] is performedfor the 24 column specimens. All columns are modeled withS9R5 reduced integration nine-node thin shell elements.Cold-formed steel material properties are assumed asE ¼ 203.4GPa and n ¼ 0.3. The centerline Cee channel


cross-section dimensions input into ABAQUS are calcu-lated using the out-to-out dimensions and flange and lipangles at the mid-height of each column specimen asprovided in Table 2.

The loading and boundary conditions used in theeigenbuckling analyses are summarized in Fig. 8. Eachcolumn specimen is loaded with a set of consistent nodalloads in ABAQUS to simulate a constant pressure acrossthe bearing edge of the specimen. The nodes on the loadedcolumn face are coupled together in the direction ofloading (one direction) with an ABAQUS ‘‘pinned’’ rigid-body constraint. This constraint ensures that all nodes on

Local Buckling (L) Distortional Buckling

Hole terminatesweb localbuckling

Fig. 10. Local and distortional elastic buckled mode shapes for short

(L ¼ 610mm) 362S162-33 specimens.

DLocal Buckling (L)

Hole terminates web local buckling

Fig. 11. Local and distortional elastic buckled mode shapes for

the loaded face of the column translate together, while therotational degrees of freedom remain independent (as inthe case of platen bearing).

3.2. Elastic buckling results

3.2.1. Buckled shapes/eigenmodes

The first (lowest buckling load) local (L) and distortional(D) buckled shapes for specimens with and without slottedholes are compared in Figs. 9–12. The L and D modes foreach specimen were identified visually by manuallysearching through the elastic buckling modes produced inthe eigenbucking analysis. The nominal cross-section half-wavelengths in Table 1 were compared to the half-wavelengths in the finite element model to assist in the

istortional Buckling (D)

Holes cause mixed distortional - local mode

D+LD

intermediate length (L ¼ 1219mm) 362S162-33 specimens.

Local Buckling (L) Distortional Buckling (D)

Hole changes numberof half-waves from5 (NH) to 6 (H)

Fig. 12. Local and distortional elastic buckled mode shapes for short

(L ¼ 610mm) 600S162-33 specimens.


categorization. The local and distortional modes that mostresembled the FSM result for L and D modes were selected.This method of modal identification is neither exact norideal, especially when both local and distortional bucklingare present in the same eigenmode. Formal modalidentification has recently been developed in the contextof the FSM [17] and future work is ongoing to extend thismethod to finite element analyses and to problems such asthe ones encountered here.

3.2.2. Buckling loads/eigenvalues

The primary goal of this research program is to extendthe DSM to cold-formed steel structural members withholes. The DSM [9], a design method for cold-formed steelstructural members, predicts column ultimate strength bypredicting the column failure mode and ultimate strengththrough knowledge of the local (L), distortional (D), orglobal (G) elastic buckling modes. This connection is madeusing the critical elastic buckling load, Pcr, and theslenderness, defined with the ratio of column squash loadPyg to Pcr for the L, D, and G modes. Table 4 summarizesPcr and Pyg for the specimens evaluated in this study. Thesquash load Pyg is calculated with the gross cross-sectionalarea, and Pcr includes the effects of the holes and the tested(fixed–fixed) boundary conditions. (Note that the use ofPyg as opposed to Pynet is a matter of ongoing research, see

Table 4

Critical elastic buckling loads and the influence of holes on elastic buckling

Specimen name Elastic buckling

Pyg (kN) Pcre (kN) Pcr‘ (kN)

362-1-24-NH 68.8 486.8 21.6

362-2-24-NH 69.2 500.2 21.1

362-3-24-NH 69.9 498.9 22.1

362-1-24-H 72.7 530.5 26.0

362-2-24-H 69.9 501.6 24.1

362-3-24-H 73.0 580.7 25.4

362-1-48-NH 75.3 135.5 22.9

362-2-48-NH 74.5 131.1 23.0

362-3-48-NH 73.8 131.5 22.7

362-1-48-H 73.7 133.2 23.5

362-2-48-H 74.9 132.2 23.2

362-3-48-H 74.9 160.9 25.3

600-1-24-NH 109.7 1087.5 15.3

600-2-24-NH 109.1 1044.9 15.3

600-3-24-NH 108.8 971.5 15.3

600-1-24-H 111.3 1064.6 14.5

600-2-24-H 102.8 1060.6 14.3

600-3-24-H 110.0 1079.2 15.4

600-1-48-NH 111.8 274.9 15.4

600-2-48-NH 116.5 265.3 15.0

600-3-48-NH 112.9 267.6 15.2

600-1-48-H 112.3 250.3 15.1

600-2-48-H 113.2 235.9 15.1

600-3-48-H 113.7 248.0 15.3

aFor specimens with holes (H), the holes are removed and elastic buckling ca

otherwise identical, isolating the influence of the holes.

[18]. For the purposes of this paper, Pyg is used to provide areference squash load disregarding net section behavior).The influence of holes on Pcr is of interest in the context

of DSM because elastic buckling loads and slenderness areused to predict ultimate strength. To isolate the influence ofholes on Pcr, additional eigenbuckling analyses of thespecimens with holes (specimens labeled with an H) wereperformed, but with the holes removed (the boundary andloading conditions were not modified and the mesh used inthe models was identical except for the removed elementsat the hole location). The comparison of Pcr for specimenswith holes (H) and then with holes removed (noH) is alsosummarized in Table 4.

3.2.3. Modal interaction at ultimate strength

An additional reason for the selection of these specimencross-sections, at these lengths, beyond the reasonsdiscussed in Section 2, is that the specimens provide muchneeded experimental data on cross-sections with potentialmodal interaction at ultimate strength both with andwithout holes. Typically modal interaction is understood tobe a concern when the elastic buckling loads of multiplemodes are at or near the same value, and the ratio ofany two elastic bucking loads (e.g., Pcr‘/Pcrd) is con-sidered a useful parameter for study. However, for modeswith different post-buckling strength and where material

Hole influencea

Pcrd (kN) Pcre/PcrenoH Pcr‘/Pcr‘

noH Pcrd/PcrdnoH

46.9

45.3 N/A

47.6

59.9 0.98 1.03 1.12

55.1 0.98 1.02 1.13

57.5 0.99 1.02 1.12

43.0

42.9 N/A

42.4

42.0 0.94 1.03 0.98

41.5 0.94 1.03 0.98

42.6 0.95 1.03 0.98

30.1

29.6 N/A

29.5

31.2 1.01 1.02 1.09

30.0 1.01 1.01 1.08

32.7 1.02 1.01 1.08

23.0

25.3 N/A

25.2

22.5 0.87 1.02 1.02

22.1 0.87 1.02 1.02

22.4 0.86 1.02 1.02

lculated (noH). The hole (H) and no hole (noH) finite element models are


yielding is considered, a more pressing concern may be thesituation when both failure modes predict similar capa-cities. Which mode does the column fail in if the predictedcapacity in local (Pn‘) and distortional (Pnd) buckling are ator near the same level? What impact does a hole have onthe failure mode that is triggered?

In the specimens selected here, the ratio of Pcr‘/Pcrd

varies from a min of 0.44 to a max of 0.68, but is never near1.0. Therefore, by this traditional measure no meaningfulinteraction would be anticipated. However, if the DSMmethodology [9] is used to predict the capacities, asillustrated in Fig. 9, the predictions for the ratio of thetwo limit states Pn‘/Pnd ranges from a min of 0.86 to a maxof 0.90 in the 362S162-33 short columns and from a minof 1.0 to a max of 1.05 in the 600S162-33 short columns(the ratios are similar for the long column specimens).Thus, these cross-sections provide a means to examine thepotential for local–distortional modal interaction atultimate strength, and offer valuable data for determiningany necessary modification to the DSM methodology whenholes are present.

3.2.4. Discussion of elastic buckling results

3.2.4.1. Local buckling. Boundary conditions have littleinfluence on the local buckling mode shapes (comparedwith FSM L modes), but the presence of the slotted webholes can change the shape, half-wavelength, and bucklingload of the first (lowest) local buckling mode observed. Inthe 362S162-33 specimens, the web holes terminate localbuckling in the vicinity of the holes, see Figs. 10a and 11a.In the 600S162-33 specimens, the web holes causean increased number of half-waves along the lengthto occur in the lowest local mode, see Figs. 12a and 13a.The presence of holes causes a slight increase in Pcr‘ (seeTable 4), which is consistent with the increased number ofobserved local buckling half-waves. The more extensive

Local Buckling (L) D

Holes change number of half-waves from 8 (NH) to 12 (H)

Fig. 13. Local and distortional elastic buckling mode shapes for

elastic buckling studies in [19] demonstrate that a hole canincrease or decrease the number of buckled half-waves (andthe critical elastic buckling load) of rectangular plates andcold-formed steel structural studs.

3.2.4.2. Distortional buckling. Boundary conditions andthe presence of holes have an influence on the observeddistortional buckling mode shapes (compared with FSM D

modes) and buckling loads. The boundary conditions(fixed–fixed) allow a smaller number of half-waves toform than predicted using the simply supported FSM D

modes of Table 1. For example, observe the restrainedshape of the buckled distortional half-wave near themember ends in Fig. 10b. In longer specimens (seeFigs. 11b and 13b), the influence of the boundaryconditions lessens and the half-wavelength of distortionalbuckling at mid-height approaches that of the FSM D

mode of Table 1.The presence of the web holes complicates the predicted

D modes, see Figs. 11b, 12b, and 13b. Local buckling nowappears within the D mode itself. The half-wavelength ofthese interacting L modes is significantly shorter than thelowest L modes observed. Further, and rather unintui-tively, the buckling load, Pcrd, actually increases with thepresence of holes in the short column specimens (as muchas 13%). However, this increase is lost at the longerspecimen length where the maximum change in thebuckling load is 72%. This result suggests that in theshorter specimens the removal of the material mostsusceptible to out-of-plane bending, at the mid-depth ofthe web, actually serves to stiffen the column. Thisinfluence does not persist in the longer specimens suggest-ing that the increased stiffness is only relevant when the D

mode is at a restrained half-wavelength. Thus, if the D

mode is free to form (over a long enough unbraced length)the holes do not increase the elastic buckling load.

istortional Buckling (D)

Holes cause mixed distortional – local mode

D D+L

intermediate length (L ¼ 1219mm) 600S162-33 specimens.

ARTICLE IN PRESS

Table 5

Specimen ultimate strength results

Specimen Ptest (kN) Ptest statistics

Mean (kN) Std. dev. (kN)

362-1-24-NH 46.6

362-2-24-NH 46.7 46.2 0.9

362-3-24-NH 45.1

362-1-24-H 44.5

362-2-24-H 46.2 45.0 1.1

362-3-24-H 44.2

362-1-48-NH 40.4

362-2-48-NH 42.2 41.6 1.0

362-3-48-NH 42.2

362-1-48-H 39.8

362-2-48-H 40.8 40.8 0.9

362-3-48-H 41.7

600-1-24-NH 53.1

600-2-24-NH 53.2 53.6 0.8

600-3-24-NH 54.4

600-1-24-H 54.0

600-2-24-H 51.7 52.7 1.2

600-3-24-H 52.4

600-1-48-NH 49.6

600-2-48-NH 50.9 50.2 0.6

600-3-48-NH 50.2

600-1-48-H 49.6

600-2-48-H 52.0 50.4 1.4

600-3-48-H 49.6

362-1-48-NH

600-1-48-H362-1-48-H

600-1-48-NH

CUTWP predictions using classical stability theory

Finite element eigenbucklinganalyses predict global buckling interacting with local and distortional buckling

Global (Euler) Buckling

Fig. 14. Comparison of global mode shapes for intermediate length 362S162-33 and 600S162-33 specimens.


3.2.4.3. Global buckling mode shapes. The global (Euler)buckled shapes for the intermediate 362S162-33 and600S162-33 columns in Fig. 14 occur as flexural–torsionalbuckling, although local and distortional deformation areboth present in the mode shape for specimens with andwithout holes, which is an unexpected result. The interac-tion between the global, local, and distortional modesmakes the identification of the global mode difficult. TheEuler buckling load and mode shape predicted withclassical methods, which do not allow cross-sectiondistortion and ignore holes [20], were used to determinethe range of buckling loads (eigenvalues) to be visuallysearched. The reported modes (Fig. 14) are the ones closestto the expected buckling load exhibiting significant globaldeformations. Additional eigenbuckling analyses of the362S162-33 and 600S162-33 cross-sections were performedat a longer column length (2.44m, 8 ft) and these analysesshow no local or distortional interaction with the globalmodes. Therefore, the observed interaction is lengthdependent and not a fundamental feature of globalbuckling in these cross-sections.

As for the global buckling loads, the slotted holes have asmall influence on the global buckling load for theintermediate length 362S162-33 specimens, reducing Pcre

by a maximum of 6%. The magnitude of the Pcre reductionfor these fixed–fixed column elastic buckling results isslightly larger than, but still consistent with, the columnelastic buckling studies on simply supported intermediatelength 362S162-33 columns in [12]. However, Pcre for theintermediate length 600S162-33 columns decreases by amaximum of 14% with the presence of the two slottedholes, which is an unexpected result. Research work isongoing to determine under what conditions holesinfluence the global critical elastic buckling load, asidentification (i.e., Fig. 14) remains a challenge.

4. Experiment results

4.1. Ultimate strength

The peak tested compressive load for all columnspecimens and an average peak load for each test groupare provided in Table 5. The slotted holes are shown to


have only a small influence on compressive strength in thisstudy, with the largest reduction being 2.7% for the362S162-33 short columns. Complete details on eachcolumn test including the load–displacement curve, flangedisplacements, and experimental notes are provided in [14].

4.2. Failure modes and post-peak ductility

4.2.1. Short columns

The loading progression for the 362162S-33 shortcolumns is depicted in Fig. 15 (without a hole) andFig. 16 (with a hole). Both columns exhibit local bucklingof the web near the supports combined with one distor-tional half-wave along the length. This distortional

Fig. 16. Load–displacement progression for short column specimen 362-2-

Fig. 15. Load–displacement progression for short column specimen 362-2-2

(d) P ¼ 33.4 kN.

buckling pattern is consistent with that predicted by theelastic buckling mode shapes of Fig. 10b. For the columnwith the hole, localized hole deformation (Fig. 16, right-most picture) initiates at a load of approximately 0.4Ptest

and increases in magnitude as the test progresses. Thisobserved deformation behavior is visually consistent withthe ‘‘unstiffened strip’’ approach of [21] where the strip ofweb on either side of the hole is assumed to behave as anunstiffened plate.The inward flange deformation concentrates at the

hole after peak load in the short 362S162-33 specimenswith holes. It is hypothesized that the slotted hole reducesthe post-peak resistance of the web, causing the flanges andlips to carry more of the column load. This reduction in

Local buckling at hole(unstiffened strip)

24-H. (a) P ¼ 0 kN, (b) P ¼ 46.2 kN (peak load) and (d) P ¼ 31.1 kN.

Distortional buckling in one half-wave at peak load

4-NH. (a) P ¼ 0 kN, (b) P ¼ 31.3 kN, (c) P ¼ 46.7 kN (peak load) and


post-peak resistance is quantified by observing the reduc-tion in area under the load–displacement curve for thecolumn with the slotted hole, as shown in Fig. 17.

Position transducers placed at the mid-height of theshort column specimens capture the rate of lateral flangedisplacement associated with distortional buckling, dD, asshown in Fig. 18. Fig. 18 demonstrates that the initiation ofweb local buckling does not influence the axial stiffness ofspecimen 362-2-24-NH, but rather that a softening of theload–axial deformation curve coincides with the increasedrate of lateral flange movement (distortional buckling).This observation suggests that the loss in axial stiffnessassociated with distortional buckling plays a larger rolethan web local buckling in the peak load response of the

00

10

20

30

40

50

60

Col

umn

axia

l loa

d (k

N)

1 2Column axial displ

Local buckling half-waves first observed

Rate of flange distoincreases as load-displacement curve

+�wes

Fig. 18. Comparison of load–deformation response and la

0 1 2 3 4 50

10

20

30

40

50

60

Column axial displacement (mm)

Col

umn

axia

l loa

d (k

N)

362-2-24-NH362-2-24-H

Slotted hole has small influence on peak load

Slotted hole influences post-peak load path and reduces column ductility

Fig. 17. Load–displacement curve for a 362S162-33 short column with

and without a slotted hole.

362S162-33 short columns. The influence of the slotted holeon lateral flange displacement is provided in Fig. 19, wherethe post-peak flange displacement rates are significantlyhigher for the 362S162-33 short column with holes. Theresults of Fig. 19 indicate that holes potentially have asignificant impact on the collapse mechanisms triggeredfrom distortional buckling. Lateral flange displacementplots are provided for all specimens in [14].Figs. 20 and 21 depict the deformation response of the

600S162-33 short columns with and without a slotted hole.In both cases, local buckling at the loaded ends combineswith one distortional half-wave along the column length.The distortional buckling pattern for these specimens is notwholly consistent with the elastic buckling predictions of

3 4 50

10

20

30

40

50

60

acement (mm)

δ D (m

m)

rtion

softens

t

2=

+�east

�D�west + �east

teral flange displacements for specimen 362-2-24-NH.

0 1 2 3 4 50

10

20

30

40

50


δ D (m

m)

362-2-24-NH362-2-24-H

Increased rate of flange distortion is observed for column with a hole after peak load is reached

Peak load occurs here NH

H

+�west2

+�east

�west + �east�D =

Fig. 19. Influence of a slotted hole on 362S162-33 short column lateral

flange displacement.

ARTICLE IN PRESS

Web localbuckling

Distortionalbuckling in onehalf-wavelengthat peak load

Fig. 20. Load–displacement progression for short column specimen 600-1-24-NH. (a) P ¼ 0 kN, (b) P ¼ 35.6 kN, (c) P ¼ 53.1 kN (peak load) and

(d) P ¼ 35.6 kN.

Web localbuckling.initiates

Similar failuremode to no holespecimens

Local buckling nearsupports combineswith distortionalbuckling (one half-wave) at peak load

Fig. 21. Load–displacement progression for short column specimen 600-1-24-H. (a) P ¼ 0 kN, (b) P ¼ 33.4 kN, (c) P ¼ 54.0 kN (peak load) and

(d) P ¼ 35.6 kN.


Fig. 12b, which shows two distortional half-waves; how-ever, specimens 600-2-24-H and 600-3-24-H did buckle intwo half-waves, see [14] for pictures. These results suggestthat geometric imperfections also have a role to play in the

details of the buckling mode initiated in the loadedresponse. The deformation response of the member withand without the hole is similar through the test progres-sion, suggesting that the hole has a small influence on


compressive strength and post-peak ductility for the holewidth to web width ratios considered here. Fig. 22 confirmsthat the slotted hole has a minimal effect on the post-peakload response of the column.

4.2.2. Intermediate length columns

Figs. 23 and 24 summarize the deformation response ofthe 362S162-33 intermediate length columns with andwithout holes. In both cases, local web buckling is first

0 1 2 3 4 50

10

20

30

40

50

60


Col

umn

axia

l loa

d (k

N)

600-1-24-NH600-1-24-H

Slotted hole has small influence on post-peak response and ductility

NH

H

Fig. 22. Comparison of load–displacement response for short 600S162-33

column specimens with and without holes.

Web local bucklingwith flange distortionin three half-waves

1

2

3

Fig. 23. Load–displacement progression for intermediate length column specim

load).

observed at approximately 0.45Ptest which is lower than,but the same order of magnitude as, the calculated localcritical elastic buckling load Pcr‘. Note in Fig. 24 that thelocal buckling half-waves are dampened in the vicinity ofthe holes, similar to the elastic buckling prediction ofFig. 11a. Further, the observed local buckling waves are athalf-wavelengths consistent with Fig. 11a, not those showninteracting with distortional buckling in Fig. 11b. (Thisobservation supports the idea that the fundamental elasticbuckling modes (L, D, and G) are representative of thephysical behavior of the column and that the mixed modesobserved in an eigenbuckling analysis only exist numeri-cally.) Three distortional buckling half-waves become wellformed at approximately 0.70Ptest, overcoming the localhalf-waves in the web except at the mid-height of thecolumn. This distortional buckling pattern is consistentwith the elastic buckling prediction in Fig. 11b. Fig. 25demonstrates that the presence of slotted holes has only aminimal influence on load–axial displacement response.All of the 362S162-33 intermediate length columns failed

soon after the peak load with a sudden loss in load-carrying capacity caused by global flexural–torsionalbuckling. Yielding of the column flanges reduces thetorsional stiffness of the section, and the friction endconditions could not restrain the twisting of the column.The twisting of specimen 362-3-48-NH is quantified inFig. 26 as the difference between the west and east mid-height flange displacements, dT, captured by the positiontransducers. The lateral displacement of the flange tips dueto distortional buckling (dD), also shown in Fig. 26, is

Pure distortional buckling dominates over local buckling in this half-wave

Local buckling mixes with distortional half-wave at peak load

en 362-3-48-NH. (a) P ¼ 0 kN, (b) P ¼ 35.6 kN and (c) P ¼ 42.2 kN (peak

ARTICLE IN PRESS

Hole dampens web local buckling bycreating two stiff web strips on either side ofhole that locally boost Pcr above Pcrd

Fig. 24. Load–displacement progression for intermediate length column

specimen 362-3-48-H. (a) P ¼ 0 kN, (b) P ¼ 35.6 kN and (c) P ¼ 41.7 kN

(peak load).

0 1 2 3 4 50

10

20

30

40

50

60


Col

umn

axia

l loa

d (k

N)

362-3-48-NH362-3-48-H

Columns fail abruptly with a global torsionalbuckling mode

NH

H

Fig. 25. Load–displacement curve for a 362S162-33 intermediate column

with and without a hole.


separated from the twisting effect by averaging the westand east mid-height flange displacements. Fig. 26 showsthat the cross-section is both ‘‘opening’’ and ‘‘twisting,’’but it is the abrupt increase in dT occurring well past peakload that leads to the collapse of the member in the test.

The load–displacement response for the intermediatelength 600S162-33 columns with and without slotted holesis depicted in Figs. 27 and 28. Local buckling is observed atapproximately 0.45Ptest for both sections. The holes do notrestrict the local buckling half-waves as was the case in the362S162-33 intermediate length columns. This local buck-ling behavior is consistent with that observed in the elasticbuckling analysis, see Fig. 13a. Three distortional half-waves form as the columns (all three of the 600S162-33intermediate length specimens) approach peak load. Twoloud sounds resonate from the columns near peak load asthe local web buckling half-waves at the two column endsabruptly snap into one distortional half-wave per end. Thechange from local-dominated to distortional-dominatedweb buckling is reflected as two drops in the load–displace-ment response near peak load for the 600S162-33 columnwithout holes, as shown in Fig. 29. The 600S162-33 columnwith slotted holes is not affected by this abrupt modeswitching, as it maintains web local buckling well beyondpeak load. The observations suggest that in this case theholes are beneficial because they maintain the localbuckling half-waves through peak load, allowing thecolumn to rely more on the post-peak strength providedby the buckled web. This mode switching is a difficultchallenge for numerical models and these results, repeatedin three tests, provides an important and challengingexperimental benchmark for future research in numericalmodeling of these members.

4.3. Discussion of hole influence on elastic buckling and

tested response

Both local and distortional elastic buckling wereobserved in the tested response of the specimens andcontributed in different ways to the failure modes of thecolumns. Local buckling initiated plastic folding in the webat peak load, and distortional buckling was reflected aseither opening (�dD) or closing (+dD) of the cross-sectionand yielding of the flanges and lip stiffeners. All three of theshort 362S162-33 columns with holes exhibited a ‘‘closed’’distortional buckling failure (+dD), where the presence ofthe slotted hole concentrated the plastic deformation in theflanges and lips adjacent to the hole. This result wasdifferent from the short 362S162-33 columns without holeswhere mixed local–distortional failures were observed. Theslotted holes also changed the buckling influence at peakload in the intermediate length 600S162-33 specimens,where the holes prevented local web buckling fromswitching to distortional buckling in all three specimentests. The deformation at peak load for the intermediatelength 362S162-33 and short 600S162-33 specimens wasless sensitive to the presence of slotted holes, exhibitingmixed local–distortional failure modes consistent withDSM predictions (L and D of similar magnitudes) asdiscussed in Section 3.2.3.The visual observations in this study highlight the

complex relationship between elastic buckling and column

ARTICLE IN PRESS

0 1 2 3 4 5-50

-40

-30

-20

-10

0

10

20

30

40

50


δ D, δ

T (

mm

)

Peak load occurs here

Abrupt failure

2

2=

+ �west + �east

�east − �west�T

�east + �westδD =

Fig. 26. 362S162-33 long column mid-height flange displacements show the global torsional failure mode.

Multiple local half-waves change to onedistortional half-wave with loud resonantsound at peak load

Fig. 27. Load–displacement progression for intermediate length column specimen 600-1-48-NH. (a) P ¼ 26.7 kN, (b) P ¼ 49.6 kN (peak load),

(c) P ¼ 49.6 kN and (d) P ¼ 31.1 kN.


failure and the sensitivity of their interaction to the choiceof cross-section and column length. In the cases of theshort 362S162-33 and intermediate length 600S162-33

specimens, it is clearly demonstrated that holes caninfluence column deformation and ductility by changinghow elastic buckling modes, local and distortional in this

ARTICLE IN PRESS

Hole preserves web localbuckling through peak load

Fig. 28. Load–displacement progression for intermediate length column

specimen 600-1-48-NH. (a) P ¼ 0 kN, (b) P ¼ 49.6 kN (peak load) and

(c) P ¼ 44.5 kN.

0 1 2 3 4 50

10

20

30

40

50

60


Col

umn

axia

l loa

d (k

N)

600-1-48-NH600-1-48-H

Drops in load occur when multiple web local buckling half-waves change abruptly to one distortional half-wave (north end first, then south end)

Fig. 29. Load–displacement comparison of intermediate length 600S162-

33 specimens with and without holes.


case, affect the axial stiffness and plastic deformation of thecolumn under load. This result is important in the contextof the DSM, especially for the current effort to extendDSM to members with holes, since elastic buckling is usedto predict the failure mode (local, distortional, or global)and ultimate strength.

4.4. Discussion of friction-bearing boundary conditions

The friction-bearing end conditions used in this testingare advantageous because specimen alignment and pre-paration can be performed without welding or the use ofgrout or hydrostone. The specimens were aligned by handin the testing machine without special equipment. How-ever, preparing the specimen ends with a milling machinecan be time consuming. Further, small deviations inflatness may significantly impact the tested results andfailure modes; real care must be taken in the specimen endpreparation. Finally, lack of a positive connection betweenspecimen and platen makes it difficult to exactly know theboundary conditions.In this study, friction between the column ends and the

platens prevented a change in shape of the cross-section upto peak load in all specimens, but slipping of the cross-section was observed after peak load. This slipping wassignaled by loud metal-on-metal ‘‘popping’’ sounds asso-ciated with observable changes in the cross-section (�dD ofthe flanges, see Fig. 19 for definition) at the column ends.Also, uplift warping deformations like those shown inFig. 30 occurred in the post-peak range for the short600S162-33 columns experiencing distortional-type fail-ures. Distortional buckling modes are anticipated to besensitive to this uplift since they are highly sensitive towarping deformations. The intermediate length 362S162-33columns experienced a sudden global flexural–torsionalfailure shortly after reaching peak load as the twisting ofthe columns overcame the friction between the columnends and the platens. The friction-bearing end conditionsdid not allow a detailed study of the global flexural–torsional post-peak response for the intermediate length362S162-33 columns and likely decreased their ultimatestrengths.Overall, for short and intermediate length column testing

focused on local and distortional buckling modes, theadvantages of the simple friction-bearing boundary condi-tions outweighed the disadvantages. Proper care must betaken to insure the ends are milled flat and the platens arelevel and parallel. For longer column tests, where largetorsional rotations must be restrained, the bearing condi-tions employed here are not recommended for use.

5. Conclusions

An experimental study was conducted to evaluate theinfluence of industry-standard slotted holes on short andintermediate length cold-formed steel structural studs. Thepresences of slotted holes caused only a slight decrease inthe ultimate compressive strength of the tested columns,although the post-peak response and column ductility wereinfluenced by the presence of slotted holes, the cross-section type, and the length of the member. The post-peakresponse is studied in relation to the influence of holes onthe elastic local and distortional buckling behavior of thecolumns. In the case of the 362S162-33 columns, the slotted

ARTICLE IN PRESS

Flange-lip corner lifts off platen when large deformations exist past peak load

Fig. 30. Short 600S162-33 column specimen flange-lip corner lifts off platen during post-peak portion of test.


holes reduced the web local buckling capacity, causing thecolumn to rely more on the flanges and lip stiffeners tocarry load with a distortional-type failure. For the600S162-33 columns, the slotted web holes had a differentinfluence, causing the deformations to remain in the localbuckling mode through peak load. This provided a smallboost in strength and ductility when compared to a similarcolumn without a slotted hole. These results wereconsistent through the test group and will serve as a usefulbenchmark for developing nonlinear finite element model-ing techniques. Friction-bearing end conditions weresuccessfully employed to study local- and distortional-typefailures of short and intermediate length columns, althoughthey may not be satisfactory for all types of global bucklingfailures.

Acknowledgmnts

The authors wish to recognize the steadfast support ofthe American Iron and Steel Institute as the primarysponsor of this research study. The specimen preparationand testing was performed by a talented team of JohnsHopkins University students and technicians including EricHarden, Walter Krug, Michael Franckowiak, Dr. RachelSangree, Jack Spangler, Nickolay Logvinosky, MarioFasano, Rebecca Pierce, Dawneshia Sanders, and Alex-ander Pei. Clark Western Building Systems generouslydonated the structural studs tested in this study.

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