Canadian Structural Engineering Conference ·1976 Conference Canadienne d'ingenierie des Structures·1976

Behaviour and Design of Girts and Purlins for Negative Pressure

By Peter C. Birkemoe

Author

Peter Birkemoe obtained his B.Sc. in Civil Engineering at Purdue University, Lafayette, Indiana in 1961 and his Masters degree a year later from the same university. In 1966 he obtained his Ph.D. from the University of Illinois.

After a brief period in the Research and Development Division of the Port­land Cement Association Dr. Birkemoe returned to the University of Illinois, first as Research Assistant and later as Assistant Professor in the Department of Civil Engineering. From 1972 to the present time he has been with the University of Toronto as Assistant and Associate Professor supervising graduate research on the behaviour of bolted structural con­nections, design of light gauge steel wall and roof assemblies, and the be­haviour of hollow structural sections.

Dr. Birkemoe is a member of several technical societies including the ASCE, ASTM and SESA. He is also a member of the Research Council on Riveted and Bolted Structural Joints and the ASCE Research Council on Performance of Structures, the ASCE Committee on Tubular Structures and is Chairman of the ASCE Committee on Structural Connections.

SUMMARY

pressure due to wind) requirements of the National Bui Code have brought n£,f-p"'~"'n attention to the particularly severe loading limitations for compression flanges

of girts and in industrial building roofs and walls. Intuitively, role sag rod and tension as direct bracing or constraining elements seems obvious, but the analytical

",1"1"e>f'-t" has been tedious and Iy unverified.

This paper a brief review of the state of the art strength of gauge open cross-sections. Particularly the case of a is emphasized. A

of analytical investigations have been reviewed and have been made in an attempt to simplify analytical techniques. Experimental data on stiffness and strength from tests which incorporate realistic boundary conditions (particularly with respect to bracing) have been limited. A full scale test structure was therefore constructed to load full wall panels with suction. The wall panels were simply supported and spanned 16 feet with three 6 inch cold formed channels spaced at seven feet; two edges parallel to the channels were free. A significant variable incorporated in the test specimens was the position of the sag rod support with respect to the depth of the channel to evaluate the bracing effect on girts. Eleven tests have been conducted on two typical wall panels. Other test variables included partial versus full attachment to the web by the supporting clip angles. The experimentally obtained stiffness and strength data from the full scale tests correlated reasonably well with the analytical predictions.

The two test panels which were taken to their ultimate strength showed no significant effect of the position of the sag rod (mid-depth position versus a position in the web near the compression flange). Bracing was sufficient to develop the full strong axis yield moment of the channels.

Finally, recommendations for taking advantage of the presence of sag rods are made and some potential alternative bracing techniques are discussed.

SOMMAIRE

Les exigences du Code national du Batiment relativement a la pression negative (succion due au vent) accordent beaucoup plus d'importance concernant les limites de chargement particulierement strictes pour les semelles en compression non supportees, des entremises et des pannes pour murs et plafonds de biitiments industriels. Intuitivement, Ie role joue par les liens et les raccords de semelles en tension comme elements de contreventement ou de contrainte semble evident mais I'evaluation analytique des effets a ete fastidieuse et Ie comportement n'a pas ete verifie experimentalement.

Le memoire comporte un rapide tour d'horizon de I'etat des connaissances concernant la prevision de la resistance a la flexion des profiles legers. II souligne plus particulierement Ie cas d'une semelle tendue supportee. II revoit une certaine quantite d'etudes analytiques et fait certaines derivations pour tenter de simplifier les techniques analytiques. II limite egalement les donnees experimentales sur la rigidite et la resistance tirees d'essais comportant des conditions limites realistes, plus par­ticulierement en ce qui concerne Ie contreventement. On a donc construit une portion de mur en vraie afin d'appliquer sur des panneaux de mur, une charge negative . Les pan­neaux muraux etaient supportes simplement, avaient une portee de 16 pieds avec 3 fers en U de 6 pouces, lamines a froid, a 7 pieds d'entraxe; les deux bords paralleles aux fers en U etaient libres. Les specimens d'essai comportaient une variable significative, a savoir la position du support du lien en regard de la hauteur du fer en U afin d'evaluer I'effet du contreventement sur les entremises. Onze essais furent effectues sur deux panneaux muraux types. Les raccordements, partiel et total, des cornieres de support a I'ame representaient d'autres variables. Les donnees experimentales de rigid­ite et de resistance obtenues des essais en vraie grandeur correspondaient raisonnablement bien aux previsions de I'analyse.

Les deux panneaux d'essai qui furent portes a leur resistance a la rupture ne montrerent aucun effet sensible de la position du lien (position ami-hauteur et position sur I'ame pres de la semelle en com­pression). Le contreventement suffisait a deveiopper Ie plein moment a I'ecoulement autour de I'axe majeur des en

Enfin, Ie memoire presente certaines recommandations pour tirer Ie meilleur parti de la presence des liens et presente certaines techniques de contreventement possibles.

I

ions steel

di inctly un exure and buckling calcu ations for the case of compres-

(i.e. negative wind (suction) sure). This loading does -axis exure but a combination of biaxial bending and tor­

low torsion and weak-axis flexural stiffnesses of these members erally results in large lateral and torsional deflections at modest loads. Real­

zation of strong-axis bending strength occurs only if the section is sufficiently braced to restrict the lateral and torsional movements.

National Building Code requires that industrial buildings in the Toronto area be designed for negative wind pressures exceeding 40 pounds per square foot. The cur­rent CSA 5-136 ( 1) Standard considers the behaviour of girts or purl ins with unsup­ported compression flanges to be that of completely unsupported beams; the resulting design based on lateral-torsional buckling would thus seem to be rather conservative since the s of rotational a lateral support of the tension flange and dis-

anc attachments to the web (sag rods) are not included.

A major research activity on the subject of the effect and evaluation of panel at­tachment on the bracing of flexural members has been underway at Cornell University for many years. Recent reports by Pekoz ( 5, 6, 7 ) have included significant ex­perimental results of tests on continuous roof purl ins which were loaded to simulate n ive pressure (uplift) on roofs. The theoretical analyses presented were in satisfactory agreement with the results but were somewhat unwieldy for design.

ificant recent theoretical and experimental work on diaphragm-braced beams has carr out by Nethercot and Rockey (11) in England and by P. kstrom (12)

ica consi

full-scale wall assemblies 1 be made th theoretical

lation total

present­current des;

ial of

2

such tical s were The assessment of t Two full size walls the elastic (servic

i i s the verification recent phase ex attached sag s was

and sted; ten load

theory of mini­and nominal the dis-

of the on a stress

on. A com­lowable pressure

in t design a analysis some si lified analy-

1 study reported here. of particular interest.

and both walls were tested to were conducted in

ultimate load.

The choice of the wall panel construction was guided primarily to avoid partial scale models and to maintain a feasible test specimen size. A 6 x 2-3/4 x 0.09 channel with flanges stiffened by 90 degree lips was chosen with a span and spacing to develop yielding at a factored positive pressure of approximately 50 p.s.f.; properties are tabulated in Table 1. Three channels spanned 16 feet spaced at 7 feet and were supported by web attached clip angles. Several single-skin wall panels were considered, but the final choice was based on proportions which guaranteed beam failure. Fastening to the beam was by self tapping screws at one foot centres, the panels being stitched at 2 foot centres.

The section was to be tested under negative pressure loading. For this section and span the maximum allowable flexural compressive stress was calculated by CSA S-136-1974 to be 8 ksi, which corresponds to a pressure of 6 psf. This suction pressure is small compared to the allowable positive pressure of 31 psf for the same assembly and thus an opportunity to demonstrate the effects of tension flange and sag-rod re­straints was provided. Ideally, the desired loading was supposed to maintain real­istic restraint conditions (i.e., no interference by loading device) and to be uni­form over the surface of the panel. Construction of a vacuum chamber, one side of which was the test wall, provided the answer and, in addition, allowed free access to the girt during testing. A fully assembled wall section in place on the test chamber is pictured in Figure 1. Note that upper and lower girts theoretically re-

one lf the total load and are attached along free edges. are y su channel ends shown in

les were we to allow ion of avoid devel of membrane forces. Loading was accomplished

using al vacuum c eaners and controlled leakage for ntenance of reo

sting in positions and without oot when su on similar mid-web in

astic rang~ ~as performed to study the effects of various sag rod condltlons on the beam deformations and strain distributions

ilure. The first wall panel is shown duri one such test with-3. cOd rees at idspan

square 1 ilure sts were conducted , the position of the sag rod at centre span was at the unsupported flange in the other. The progressive

loading to failure for second wall panel is shown in Figure 4 (sag rod at mid-web of channel). To in a more quantitative value for the deformations, recall that cha depth is 6 inches. The failure, Fig. 4(d), by buckling of the com-

fl dspan, is shown close-up in Fi 5 for comparison with the 11 . 1. Failure were similar except that mid-web

1 (downward) of the flange while the at-sion ion of the web resulted in greater

that region was strained near yield.

1 of t wall ilure, Figure 6, shows the permanent deformation of the central The lower beam was not supported by a sag rod and retained permanent torsional and flexural deformations. (It experienced loading approximately one lf that of the centre critical beam). The similar upper beam was sag rod sup­ported and experienced no permanent strain or deformation.

THEORETICAL AND EXPERIMENTAL RESULTS

Experimental results consisted of strain and deformation measurements which were made at various applied pressures. Analytical results followed the same format, but were limited by the small deflection assumptions of the theory. Several of the measurements which were made on the two wall specimens are presented here. The primary difference in the two wall specimens besides sag rod configuration in the ultimate load tests was the fastener location in the tension flange. The second wall was assembled under more controlled conditions and the resulting fastener loca­tion tended to be more uniform and closer to the junction of the web and tension flange than in the first wall. This created a slightly stiffer rotational restraint as well as a load application closer to the shear centre of the section.

The restraint of the sag rod is demonstrated by the reduction in the midspan rota­tions shown in Figure 7. The theoretical solution shown here is based upon the known parameters, an estimated rotational stiffness and rigid lateral support of the tension flange. A second theoretical solution in which the rotational restraint was removed is also shown in Figure 7 to illustrate, theoretically, the effect of rota­tional restraint. The total deformation along the length of the member is shown, in Figure 8, to be influenced by the presence of the sag rod. The three components of displacement are plotted along the length of the beam.

The horizontal (strong axis) deflection of the girt in Wall 2 is shown in Figure 9 to be relatively close to the displacement of a uniformly loaded simple beam. The non-linearity of the horizontal displacement at approximately 33 p.s.f. is the first i ion of flexural yielding of Wall No.2. The non-linearity occurring at 25 p.s.f. in the plot of vertical deflection is an indication of local web yielding at the point of sag rod attachment. In Figure 10, the strains in the compression flange at midspan of Wall No.2 indicate simple flexure (uniform strains up to approximately 20 p.s.f. With increasing load yielding again is shown to initiate at approximately 33 p.s.f. (also in g. 9). At a loading of just over 40 p.s.f. the entire flange is experiencing yielding strains.

In Wall No.1 the midspan compression flange strain is higher at the junction of the lip and the flange because of the more complete rotational restraint by the sag rod. Note here that with the sag rod removed the strain at this location virtually van­ishes because of the tensile components of strong-axis (of the flange) flexural strains in the ange.

sag rod force also provides some insight into the behaviour of these wall as­semblies. As the applied pressure increases, Figure 11, the sag rod force (Wall

3

4

No.2) grows rel ve to phenomenon may be found

, particularly at ng steners.

tension fl and pl conduc th

contrary vari ion of sag rod

rod is nearer

The analysis of the resul to s rod and the panel attachment as stiffen; tions with unsupported compression flanges.

iveness of the sag ents of channel sec-

The brief summary of loads presented in Table 2 i cates a disparity between speci­fication requirements and actual behaviour. The present requirements may build in rather excessive strength in structures when they are designed for negative pressure. It would appear from observation of these results that a limit on torsional deforma­tion at service loading may be an appropriate basis for design.

Z sections would be expected to behave similarly and the results from the Cornell research indicate just that. Further analytical study is now planned on the Z and channel sections to further the progress towards more realistic design of light gauge structural wall systems.

ACKNOWLEDGEMENTS

The writer wishes to acknowledge the work of Dimos Polyzois who has recently com­pleted a thesis (13) for the M.A.Sc. degree and who conducted the tests and analy­sis described herein. The paper is a statement of progress in a continuing research effort at the University of Toronto on the design of light gauge structural steel. This research was sponsored by the Canadian Steel Industries Construction Council. Material for construction of the test wall panels was contributed by Canadian Metal Rolling Mills Ltd.

1.

2.

nad i an tural

SI,

soci ion

ia

S 136-1 , HCold Struc-

, First ition 1967.

4. Winter, G., " on the 1968 ition of the Specification for the Design of Cold-Formed Steel Structural Members

5. Pekoz, T., "Progress Report on Co ld-Formed Steel Purl in Design", Proceedi ngs of the Third International Specialty Conference on Cold-Formed Steel Structures, University of Missouri- Rolla, November 1975

6. Pekoz, T., "Evaluation of the Results of Continuous Purlin Test", Report prepared for MBMA and AISI, 1975.

7. Pekoz, T., "Conti nuous Purl in Tests", Department of Structura 1 Engi neeri ng Report, Cornell University, Ithaca, New York, 1975.

8. Pincus, G., and Fisher, G.P., "Behavior of Diaphragm Braced Columns and Beams", Proceedings ASCE Vol. 92, ST2, April, 1960.

9. Errera, S.J., "The Performance of Beams and Columns Continuously Braced with Diaphragms - I", Report No. 321, Department of Structural Engineering, Cornell University, October, 1965.

10. Celebi, N., "Diaphragm Braced Channel and Z-Section Beams", Report No. 344, Department of Structural Engineering, Cornell University, May, 1972.

11. Rockey, K.C., and Nethercott, D.A., "Stabilization of Beams Against Lateral Buckling", Proceedings of First Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, August 19-20,1971.

2. Wikstrom, P., "Z-and Channel-Purlins Connected With Corrugated Steel Sheeting",

13. Po is, D., "Flexural iour of Cold Formed Channels v/ith Unsupported Compression Flanges". r~.A.Sc. Thesis, University of Toronto, 1976.

5

Section Properties ( Provided by tv1anufacturer)

Thickness (in) 0.090

Area (in2) 1. 09

Ix ( i n 4 ) 6.12

Sx (in 3) 2.04

rx (i n) 2.37

Iy (in4) 1. 10

Sy (in 3) 0.59

ry (i n) 1. 01

X (in) 0.89

0 (i n) 6.0

B (i n) 2.75

L (in) 1.0

Specified Mechanical Properties (As Tested)

Web Coupon Flange Coupon

Yield Strength 55 ksi (55.8 ksi) (59.8 ksi)

Tensile Strength 67 ksi (70.9 ksi) (73.8 ksi)

Elongation in 2" 22%

6

SON OF I BEHAVIOUR

Ex~eriment No Sag Rod

(Mid-web) (Near Flange)

First Yield 41 psf 38 psf (flanges)

Fa ilure 49 psf 48 psf

Theory (Limiting condition

Design (Allowable) Loading (5136-1974)

6 psf 6 psf

* Pressures shown are for the wall and pa

17 psf (Wall #1)

22 psf (Wall #2)

6 psf

geometry described in this report.

7

8

FIG. 1. WALL SPECIMEN NO.1 IN PREPARATION FOR LOADING WITHOUT SAG RODS

FIG. 2. v

9

FIG. 3. VIEW OF FLEXURAL AND TORSI L ON OF CHANNEL WITHOUT C SAG ( IDSPAN = 10° A

10

(a) Wall Loading 12 p.s.f. (b) Wall Loading 19 p.s.f.

(c) Wall Loading 32 p.s.f. (d) After ilure (49 p.s.f.)

FIG. 4. IVE LOADING TO FA! . 2

11

12

(a) Test No.1, Sag Rod Located Near Compression Flange

(b) Test No.2, Sag Rod Located at Mi

FIG. 5. FLANGE BUCKLING FAILURES VARIABLE SAG ROD LOCAT

FIG. 6.

13

14

30

o

25 - I o

I o

I 20 - I

o

I . 4-

Vl 0 . I c.. ........ 15 - 0

OJ S­:::s Vl Vl OJ S­

o...

I o

I o

10 - / o

I

o

D. No Sag Rod

o S.R. at Mid-web

o S.R. near Flange

o

/ Theory

(No Sag Rod)

o

I o

/ o

/ o

/ No Rota tiona 1 Su pport l- __ --- - ------ ----

-----I I I

5 10 15 20 25

Rotation (degrees)

FIG. 7. MIDSPAN ROTATION OF CHANNEL (WALL NO.1)

c: .r-

<J .

+J s-a;

::>

".-...

c: .r-

<J

N .,... s-o :c

en a; "0

c: 0 .,.... +J ro +J 0

c:::

Or

.5 ~-

0

.5

0 -

5

------ .6.

v No Sag Rod

o Sag Rod at Mid-web

o Sag Rod near Flange

Theory (no sag rod)

_____ :::1

_____ 0 _-----v ------- - ---

---~---- 6, --___ .6.

---- ---

FIG. 8. DISPLACEMENTS OF THE SHEAR CENTRE AND ROTATIONS ALONG CRITICAL BEAM (WALL NO.1, 12 p.s.f.)

15

50

40

· 4-

30 I · (/)

· 0-

(l) S-:::::l (/) 20 (/)

(l) s-

o...

10

o

16

. 4-. (/)

0-

(l) s-:::::l (/) (/) (l) S-

o...

60 r---------------------________________________ -,

50

30

20

10

o o

Failure 49 p.s.f.

2

Displacement (in.)

__ G

•

o Vertical

• Hori zonta 1

.3 4

FIG. 9. VERTICAL AND HORIZONTAL DISPLACEMENT OF BEAM (WALL NO.2)

Failure 49 p.s.f. -----------------

. ~ • --. • , ---• ~ •

/ • /

/ • 0 f

1 2 3 4 5 6 7 8 9 10 Strain x 10 3

FIG. 10. COMPRESSION FLANGE STRAINS (WALL NO.2)

4-

til

OJ S­;:, til til OJ S­

o...

50~----------------------------------------------~

40

30

20

10 0/

/J cf{ //-

0/

0/

/ o 0/

:J

~o

/0 ~O

/ o

~/ I O~/_p-;'-'--~------~----~----__ ~I------~----~I----~ o 200 400 600 800 1000 1200

Sag Rod Force (lbs)

FIG. 11. SAG ROD FnRCE DURING TESTING (WALL NO.2)

17

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