Larry D. Luttrell

Shear DiaphragmStrength

AuthorDr. Larry D. Luttrell is a professorof civil engineering at West VirginiaUniversity and the senior professorin the structural engineering pro-grams. One of his particular areasof interest is in the evaluation anduse of light gage cold-formed metalstructures and specifically dia-phragm bracing systems. For thepast 25 years he has been involvedin diaphragm test programs for vari-ous institutes and sponsoring agen-cies. These efforts have led tomany reports and publicationsincluding the Steel Deck InstituteDiaphragm Design Manual (DDM)published in January 1981 and its1987 Second Edition.

His focus in the Steel Deck Insti-tute DDM has been toward identify-ing the more important parameters,assessing their individual contribu-tions and combining such influ-ences to allow rather simpleassessments of both strength and

stiffness for typical diaphragms.Luttrell, a practicing structural

engineer, has been involved inmany design projects and theassessment of structural failures.He serves on several ASCE, AISI,Steel Deck Institute and other com-mittees, holds four outstandingteacher awards and is keenly inter-ested in education as it focuses onengineering practice.

SummaryAn overview of shear diaphragmstrength is presented as it relates tobuilding design. This paper focusesmainly on system shear strengthand shear strengths for variousconnector types used in dia-phragms. Weld-washer strengthsare included, as well as an examplebuilding design problem.

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SHEAR DIAPHRAGM STRENGTHL.D. Luttrell

Professor of Civil EngineeringWest Virginia University

Introduction.

This presentation deals with an overview of the problems associated withshear diaphragm design using commonly manufactured steel deck units. Suchshear diaphragms are assembled from panel elements in such a manner thatthey both enclose a building space and brace it against shape changes duringloading. The assemblies of panels must be sufficient to the primary purposeof sustaining gravity loading; diaphragm behavior from the assembly may besecondary and virtually free of cost. The design of a diaphragm addresses asimple question, "can the elements be assembled such that they possesssufficient in-plane strength to maintain shape under loads imposed?"

A simple view of a diaphragm system is shown in Figure 1, taken from theSteel Deck Institute Diaphragm Design Manual, Second Edition (SDI DDM).Forces on the windward and leeward walls are transferred to the roofdiaphragm as line loads q as shown for both walls. The roof diaphragm canbe isolated as the "short and deep beam" illustrated. The design then simplyinvolves the selecting of panel elements and proper methods of attaching suchthat the R-forces can be transferred off the system as to the end walls inthis case. It is worth note that the average shears across the B-dimensiondecrease toward the middle of the span L and it may not be necessary tomaintain the same shear strength over all of the building length L.

The purpose here is to review the more important parameters affectingshear strength of floor and roof deck diaphragms. Toward that end, certainformulas are taken from the DDM and these are identified here by the sameequation numbers as in the DDM. Further, a final design example is presentedalong with a typical load table developed for the diaphragm type used.

Shear Strength.

The in-plane shear strength principally is related to the panel thickness,panel widths, the types of connections used, and the placement of thoseconnections. In Figure 2, for example, a simple model shows a three-paneldiaphragm with four cross supports or purlins. If each of these supportscontained several connections through each panel, a resistance to sheardisplacements would be developed by couples within the panels and at eachsupport as in Figure 3. Such panels also may be connected to each other byQs fasteners at the panel sidelaps, away from the supports, further enhancingthe shear strength.

The SDI diaphragm studies have involved a wide range of fastener types,the layout of fasteners, panel shapes and thicknesses, and reliability of thesystems. Once a particular layout has been selected, the shear strengthlimitations may fall into three major categories: a) edge-most panels, b)interior panels, and c) panel ends.

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32-3

FIG 1 A DIAPHRAGM COMPONENTS

FIG 1 B ROOF DIAPHRAGM

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FIG 2.A DIAPHRAGM AND TRUSS

32-4

FIG 2. B SCHEMATIC LAYOUT FOR DIAPHRAGM

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FIG 3 A OUTER EDGE PANEL

FIG 3 B INTERIOR PANEL FORCE DISTRIBUTION

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a. Edge Panels

(2.2-2)

end distribution factor with summation across a fullwidth w.

distance from panel centerline to any fastener in a panel at theend support, in.

panel width, in.

purlin dist. factor similar to

panel length, ft.

number of purlins excluding those at ends or end laps whereconnection patterns may differ.

structural fastener strength, kips.

Note that the edge fasteners between purlins may require special details if thepurlins set above the edge member.

b. Interior Panels (Fig. 3b)

(2.2-4)

with

(2.2-4a)

where

panel depth, in.base metal thickness, in.purlin spacing, ft.

panel length, ft.

c. End Members

The fasteners at panel corners then limit to:

(2.2-5)

The strength of the diaphragm is limited to the smaller value from Eqns. 2.2-2,2.2-4, or 2.2-5.

32-6

where number of edge connectors between cross supports inFig. 3a)

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It is clear from the above formulas that a dominant term is thefastener strength. The SDI studies have led to formulas for determining suchvalues and for proper load factors to be applied to the ultimate shearstrengths Those studies have led to recommended factors of 2.75 whenwelds are used and to 2.35 for systems assembled entirely with mechanicalconnectors. These factors anticipate that no allowable stress increases arepermitted for transient loads.

Connections.

The SDI studies have involved arc-puddle welds, welds with washers,various types of screws, pneumatically driven and powder actuated nail-likefasteners, and other miscellaneous connectors. The study of any suchfastener involves its direct shear strength and its shear-slip or flexibilityvalues. In the vast majority of cases, it is not the fastener itself but thesheet material around it, in bearing, that limits its strength. The followingstrength formulas have been developed.

Arc-puddle welds: (4.2.1-1)

where average visible diameter, in.limited to a minimum of 0.5 ins.specified minimum steel strength, ksibase metal thickness, in.

For typical steel diaphragms using A446-A steels havingksi, and with d = 5/8 inches:

(4.2.1-2)

Welding machine power settings required usually are well below thoseneeded for welding in hot-rolled steels. The settings should be such thatburn-off rates are between 0.15 and 0.25 inches of rod per second in typicalE60XX or E70XX 5/32 inch rods. The time required per weld may varybetween 3 to 6 seconds or more depending on the properties of parts beingconnected. Heavier substrata require more welding time but increased powersettings may burn out the panel faster than electrode material can bedeposited.

Welded sidelap or sheet-to-sheet connections are exceedingly difficult tomake and are not recommended. However, when they can be made, theirstrength does not exceed about 75% of a similar weld at a structural support.

Sidelap welds: (4.2.2-1)

A weld washer functions as a heat sink allowing hole formation in thinnerpanels, without excessive growth of the hole, as substrate temperature isincreased. The washer subsequently is filled with the weld stem growing intothe substrate and anchored on the washer's hole perimeter. Upon cooling, thewasher is clamped down on the attached sheet. Weld washers arerecommended for panels thinner than 0.0280 inches.

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Extensive studies involving washers of various thicknesses, withdifferent hole sizes, and used on various types of sheet steel have beenconducted at West Virginia University. An efficiency study involving washersof several different thicknesses, has indicated that 0.060" thick washers arebest suited for typical operations. During welding process, the sheettemperature reaches elevated values over an area significantly larger than theweld stem. This leads to local relief of cold-work stresses locked in duringpanel forming operations. For values between 60 and 120 ksi, nosignificant influence of was found and the material near the weld behavedas if it were fully relieved. For such washers, the strength was found to be:

Welds with washers: (4.3-1)

where hole diameter, in.

electrode strength, ksisheet thickness, in.

Using a 16 gage washer with inches and for two electrode types,

E60XX: , kips (4.3-2)

E70XX: , kips (4.3-3)

Nominal 5/8" diameter arc welds of good quality are more efficientlyobtained in metals thicker than 0.0280" than are welds through washers. Thuswashers are not recommended for panels having thicknesses of 0.0280" orgreater. In no cases should washers be used at interior sidelaps.

Screw connections, such as Buildex TEKS screws, may be eitherself-drilling types or the self-tapping types that require a drilled hole forinstallation. The most commonly used screws are No. 12 and No. 14 sizesthough smaller No. 8's and 10's may sometimes be used for sidelap connections.The screw shear strength is dependent on both the screw diameter and theyield strength of the connected sheets.

In connecting thin elements to heavier structural units such as bar joistsor beam flanges, little difference exists in the shear strength for No. 12 andNo. 14 screws. This is because the failure mode is one in which the sheetmaterial tends to "roll up" on the bearing side of the screw and one or twotearing lines develop in the sheet. This result is obtained for both screwsizes and, for sheet-to-structural steel connections:

No. 12 or No. 14: kips (4.5-1)

For stitch connections between sheets at the sidelaps, a differentperformance ensues. The screw, not being anchored into a thicker more rigidelement, tips over more easily and, thus, is more flexible. Its strength may belimited by bearing-tearing in the sheets or, with sufficient tipping, atearing-pull out combination.

The SDI screw studies indicate that stitch screw shear strength isvirtually independent of in all steel panels commonly used as deckdiaphragms.

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Sheet-to-structural connections can be made using nail-like pins, driveneither with pneumetic devices or using powder actuated tools. Such fastenersare made from hardened steel and usually have heat treated knurled shafts toenhance anchorage. The shaft may have a slight taper and can be fitted withwashers, concave to the driving direction, to absorb the final driving energyand thus clamp the sheet in position.

The performance studies involved tests wherein the back-up plates were3/16", 1/4", 5/16" cold rolled A36 straps or thicker wide flange beams. Thebacking element thickness has virtually no effect on shear strength since thethinner sheet material will control performance through its bearing on the pindiameter. Within sheet thicknesses between 0.024" and 0.1006", bearingcontrolled - shear failures did not develop across the fastener diameter.

Ramset 26SD: (4.6-1)

HiltiENP2 & ENP3: (4.6-3)

Hilti ENKK: (4.6-5)

These formulas apply for sheet thicknesses between 0.024" and 0.060". Whenthese fasteners are used through full-hard steels, such as ASTM A611E,somewhat higher shear values may result.

Button punched sidelaps do stabilize panel edges but, otherwise, maycontribute little to diaphragm strength. They can vary greatly in shape andeffectiveness. Typical values from well controlled diaphragm tests at WestVirginia University have led to strength and stiffness values of:

(4.7-1)

In a typical 0.0295" thickness, Eq. 4.7-1 yields a 0.209 kips strength which isabout 30% of the strength with a No. 12 stitch screw. The flexibility or sliptendency is much greater than that for a No. 12 screw.

The key in selecting any one of the above fastener types rests totally inits cost versus reliability. Quality installation is easier to evaluate with

32-9

Stitch Screws: (4.5-2)

where d = major diameter, in.

For the stitch screws studied, the following data were obtained:

Size

8101214

d (in.)

0.16350.18670.21110.2477

Qs (kips)

18.8t21.5t24.3t28.5t

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(a) PANEL LAYOUT AND FASTENER ARRANGEMENT

(b) CONCRETE FILLED DIAPHRAGM SHOWINGCOVER DEPTH OVER CORRUGATION CRESTS.

FIG 4

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mechanical connections than with welds though the latter almost always yieldhigher theoretical values. But can weld quality be maintained on the job?

Diaphragms are a part of the structural system and theirfabrication mist be treated with the same view to qualityas any other part of the structure.

Concrete Filled Diaphragms.

This diaphragm type has either a structural concrete overlayment, as infloors, or one of the lightweight insulating fills. In either case, theoverlayment provides an extra pathway through which shear forces may betransferred. Typically, the shear strength can be expressed in the form,

(5.1-1)

where See Eq. 2.2-4 definitions

concrete cover depth

concrete compressive strength, psi

test constant.

Usually such diaphragms are quite strong and stiff relative to the baredeck diaphragm over which the fill is placed. Indeed, for ones withstructural concrete, the shear strength is similar to that for similar flat slabs.The limiting condition usually is at the edge where the concrete must transferits forces off to the perimeter. This may be accomplished either throughshear studs or frequent spacing of perimeter connections spaced at e as inFigure 4a. For example, with an ultimate shear strength at = 2.0 klf andwith structural fasteners with 2.0 kips each, e could be no greater than12 inches.

Stiffness and Deflection

The diaphragm stiffness G is needed for determining the displacementsunder load. Mr. Heagler's paper, earlier in this session, has addressed thatissue. Several example illustrations are in the DDM.

A Design Problem.

The SDI DDM includes some sixteen design examples for illustrating themore common problems encountered. Further, it contains a series of "designshear tables" for the commonly used connection types such as that illustratedon the final page here. Problem 7 from the DDM and its illustrations arereproduced below as well as one table from the section on design shears.

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FIG 7.1 GENERAL DIMENSIONS AND WINDPRESSURES ON WINDWARD WALL

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32-13

Example 7. Roof Design. Make a preliminary design for the roof deck neededfor a 200'x 400'x 30' warehouse to be located in open terrain in a rural inlandarea. The construction involves tilt-up wall panels which rely on the roofdiaphragm for stability. Follow ANSI A58.1-1982 for wind loads.

Consider the structure both with and without an expansion joint at B/2where B and L follow ANSI notation and are as shown in Fig. 7-1. The wallsmay have openings up to 10% of their surface area.

a. The building is a warehouse, with:Importance Factor I = 1 (ANSI, Table 1 = T.1)Exposure C (open terrain) (ANSI, T.6)

Surface

Windward

Leeward

Sides

Roof

ANSI T.4

Surface

Windward

Leeward

Sidewall

*Positive sign means net force toward interior.

c. GUST FACTORS: AT h = 30' (ANSI T.8)

d. PRESSURE COEFFICIENTS (ANSI Fig.2 & T.9)

h/L = 30/200 = 0.120 (parallel to wind)L/B = 200/400 = 0.500 (note ANSI symbols L&B)

The pressures indicated for the windward wall in Fig. 7.1 are 1.01 wherethe values are from the first table above and reflect coefficient changeswith different elevations.

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(a) UNIFORM EXTERIOR PRESSURE (b) UNIFORM INTERIOR PRESSURE

FIG 7.2

(a) FORCES DELIVERED TO THEROOF WITH INTERNAL SUCTION

(R - 398 B/2)

(b) FORCES DELIVERED TO THEROOF WITH INTERNAL PRESSURE

(R - 398 B/2)

FIG 7.3 ROOF DIAPHRAGM FORCES

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7e. ROOF BRACING FORCES (Assumes tilt-up wall which relies on roofdiaphragm for stability.)

WINDWARD WALL (Exterior Loads. See Fig. 7-1.)

I

UNIFORM EXTERIOR LOADS (See Fig. 7-2.)

INTERNAL PRESSURES (See Fig. 7-2.)

The net forces per foot delivered to the roof are shown in Fig. 7-3.

Note that the "down wind" loads: 398 = 288 + 110 = 186 + 212. Theinternal pressure effects lead to no net diaphragm shears; those pressureeffects simply move through the diaphragm support structure to theopposite wall. Wall-to-roof connections must be designed accordingly.

The total diaphragm shear force delivered to the end walls:

R = (400')(0.5)(398 lbs/ft.) = 79,600 lbs.

Along the 200 end wall, the average shear is:

S = R/L = R/200 = 398 lbs/ft. maximum.

Note that the maximum shears vary with the shear diagram as in Figure 7.4.

32-15

Windward:

Leeward:

Ends:

With Int. Suction

237 + 51 = 288

-161 + 51 = -110

-225 + 51 = -174

With Int. Pressure

237 - 51 = 186

-116 - 51 = -212

-225 - 51 = -276

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FIG 7.4 DEFLECTION SOLUTIONS

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7f. PRELIMINARY DESIGN

Zone 1. S = 398 lbs/ft. Try a 0.0295" WR deck with a 36/7 pattern of 5/8"welds and No. 10 stitch screws. The span is 5'-0".

Prom SDI Appendix V, (see last page) with 4 stitch screws per span:

allowable S = 420 lbs/ft. O.K.

Using the Table formula with Kl = 0.226 and 129

Following Mr. Heagler's earlier example and using shear diagram areas,

Zone 2. 47760/200 = 239 lbs/ft. Try an 0.0295" WR with a 36/5pattern. (SDI App. V 10.) Use 1 No. 10 stitch screw per span.

allowable S = 275 lbs/ft.

Zone 3. Try a lighter 36/4 pattern without stitch screws. S = 170 > 80 O.K.

Notes: 1. From a strength viewpoint, these diaphragms are adequate but notethe strong influence of fastener patterns in Zone 2 on the stiffness. This hasled to a fairly large deflection, which may be excessive, and a new design forthis zone may be necessary.

2. Examine wind uplift at say 1.5 1.5(16.1) = 24 psf. In the 36/7 patternwith each weld has a tributary area of 2.5 The "hold down"required per weld is 24(2.5) = 60 lbs., a small value.

3. Examine wind load effects from other directions. Usually it will be mostsevere when loads are received from the long walls and delivered to the shortwalls.

4. Note the potential economic advantage of selecting a particular fastenerpattern and then using different panel thicknesses for various roof zones.

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(a) OPEN ENDED STRUCTUREWITH NINE ROOF ZONES.

(c) END WALL LOADS ANDSHEAR VARIATIONS

(b) SHEAR DIAGRAM FORLATERAL LOADS

FIG 7.5

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7g. EXPANSION JOINTS

Consider the building to have an expansion joint at B/2 such that eitherend is substantially independent. The "chord" forces, formerly developed inspandrel beams along the B dimension, must now be developed in thewindward and leeward sidewalls; these walls now act as diaphragms.

Consider the loading case from Figure 7.3b applied to the "open-ended"structure of Figure 7.5a. The problem is divided into two parts; first, thewindward and leeward forces are considered; and secondly, the sidewallforces. The results will be superimposed.

Windward and Leeward Forces, Fig. 7.5b:

The total reaction: R = (212 + 186)(B/2) = 79,600 lbs.

The average shear along L at the end walls is:

S = R/L = 398 lbs/ft. as before for the full structure.

At some distance x, such as x = B/4, the total shear force is:

V = R - (212 + 186)(100) = 39,800 lbs.

The average shear is V/L = 199 lbs/ft. The average unit shear changes withthe shear diagram.

The side-wall reaction forces as shown in Fig. 7.5c, formerlychord forces, are:

= 39,800 lbs.

RW and RL vary from zero at the expansion joint to a maximum at the endwall. If the wall stiffness is consistent along B, the variation is virtuallylinear. The maximum shear then is

At any point in a diaphragm, the average shears in the system, parallel tothe deck span, exactly equal those perpendicular to the span. The perimeterbeams have axial forces and are an integral part of the system eliminatingaccordion-like collapse of the deck.

Endwall Forces, Fig. 7.5c:

The total reaction 276(L) = 55,200 lbs. The maximum total shearforce on any one line parallel to B is:

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27600 lbs. and the average maximum shear is

138 lbs/ft.

With changes in y across the shear diagram, as in Fig. 7.5-c, S also changes.At y = L/3, for example, S = 0.333 46 lbs/ft.

Addition of Shears

The small element shear forces, shown near the left corners of Pigs. 7-5band 7-5c, have directions dependent on the shear diagram. As shown andfollowing the values from the prior section, the upper left block would have amaximum possible value of 398 + 138 = 536 plf and the lower block could have398 - 138 = 260 plf. However the wind direction may reverse leaving eitherblock at the maximum 536 value. This approach is used in the following table.

The addition of shears from different load conditions is direct since theorthogonal values always are equal. Therefore, it is good practice to considereither different deck thicknesses or fastener patterns to meet the actualconditions; there is little reason for the roof diaphragm to be everywhereidentical. Consider the present case with the roof subdivided into nine zonesas in Figure 7.5a.

The six different diaphragm shear values could be met using six differentdiaphragm arrangements. This could be troublesome to manage duringconstruction, but perhaps three would not. With joists at 5 ft. centers andusing 36" wide deck panels, consider:

Maximum ShearsLoading Condition

Figure 7.5bFigure 7.5cTotals

1

398138536

2

265138403

3

133138271

4

39846

444

(plf)5

26546

311

for Zone6

13346

179

7

398138536

8

265138403

9

133138271

Zones

1,7

2,4,8

3,5,6,9

Diaphragm Selection (1)

36/7 pattern, 20 gage deck with 5/8 welds and5 No. 10 stitch screws per span. S = 555 plf.

36/7 Pattern, 20 gage deck with 5/8 welds and3 No. 10 stitch screws per span. S = 460 plf.

36/7 Pattern, 22 gage deck with 5/8 welds and2 No. 10 stitch screws per span. S = 340 plf.

(1) See following page with typical load tables.

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STANDARD 1.5" DECK

StitchConnectorsper span

0123456

3.0415475535590640690730

t = design thickness = .0295"

DESIGN SHEAR, plfSpan, ft.

3.5360415470520570615655

4.0315370420465510555595

4.5275325375420460500540

5.0 5.5245 225295 265340 305380 350420 385460 420495 455

6.0205240280320355390425

6.5185220255295330365395

7.0170205240270305335370

K10.4860.3770. 3080.2610.2260.1990.178

Dwr = 129 Dir = 226 Dnr = 356 K2 = 870

Substitute these values into the equation for G' as appropriate.

Stitch

t = design thickness = .0358"

DESIGN SHEAR, plfConnectorsper span

01234567

4.0375445505560615670715765

4.5335395455505555605655695

5.0300355410460510555600640

5.5270320370420465510550590

Span, ft.6.0 6.5245 225290 270340 310385 355430 400470 440510 475550 510

7.0210250290330370410445480

7.5195230270305340380415450

8.0180215250285320355390425

K10.5350.4150.3400.2870.2490.2190.1960.178

Dwr = 97 Dir = 169 Dnr = 266 K2 = 1056

Substitute these values into the equation for G' as appropriate.

StitchConnectorsper span

012345678

t = design thickness = .0474"

DESIGN SHEAR, plf

5.0390465535600665725785840890

5.5355420485550610665720775825

6.0320385445505565615670720770

6.5295355410465525575625670715

Span, ft.7.0 7.5275 255325 305380 350430 400485 450535 500580 545630 590670 630

8.0235285330375420470515555595

8.5220265310350395440485525565

9.0210250290330375415455495535

K10.6150.4780.3910.3300.2860.2530.2260.2040.187

Dwr = 63 Dir = 111 Dnr = 175 K2 = 1398

Substitute these values into the equation for G' as appropriate.

See page V1 for notes.

32-21

FRAME FASTENING: 5 / 8 " WELDS on 36/7 Pattern.STITCH FASTENING: #10 SCREWS (BUILDEX) SAFETY FACTOR: 2.75

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