Inﬂuence of nonstructural components on roof...

Journal of Constructional Steel Research 64 (2008) 214–227www.elsevier.com/locate/jcsr

Influence of nonstructural components on roof diaphragm stiffness andfundamental periods of single-storey steel buildings

S. Mastrogiuseppea, C.A. Rogersa,∗, R. Tremblayb, C.D. Nedisanb

a Department of Civil Engineering and Applied Mechanics, McGill University, Montreal QC, H3A 2K6, Canadab Group for Research in Structural Engineering, Ecole Polytechnique, Montreal, QC, H3C 3A7, Canada

Received 10 November 2006; accepted 22 June 2007

Abstract

The stiffening effect of nonstructural roofing components on the in-plane shear stiffness of metal roof deck diaphragms was studied. Tests wereperformed to determine the properties of the non-structural roofing materials and the typical diaphragm connectors. A linear elastic FE modelwas used to establish stiffness values for common diaphragm configurations, and the results were applied to evaluate the impact of nonstructuralroofing elements on the fundamental period of vibration of single-storey steel buildings. The shear stiffness increase due to the nonstructuralcomponents was found to be more pronounced for the flexible steel deck diaphragms. The influence on the period of vibration was negligible formost of the buildings studied.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Buildings; Diaphragm; Fibreboard; Gypsum; Period; Roof metal deck; Shear; Steel

1. Introduction

A large proportion of the single-storey steel buildings inCanada are located in regions of active and moderate seismicitylevels, such as on the Pacific coast and in the St-Lawrenceand Ottawa River Valleys. The seismic force resisting system(SFRS) in these structures typically includes a cold-formedsteel roof deck diaphragm that transfers horizontal loads tothe vertical steel bracing bents. Steel deck roof diaphragmsare relatively flexible compared with the vertical bracing, andhence, in-plane roof deformations due to lateral loads canexceed the horizontal deformation of a building’s walls [1].The seismic loads at a given site, calculated using the 2005National Building Code of Canada (NBCC) [2], depend onthe fundamental period of vibration of the structure, which canbe estimated using empirical expressions. These formulae, forthe most part, were derived for multi-storey structures withrigid floor and roof diaphragms [3,4], and therefore, do notnecessarily reflect the behaviour of low-rise steel buildings

∗ Corresponding address: Department of Civil Engineering and AppliedMechanics, McGill University, 817 Sherbrooke St. W. Montreal, QC, H3A 2K6,Canada. Tel.: +1 514 398 6449; fax: +1 514 398 7361.

E-mail address: [email protected] (C.A. Rogers).

0143-974X/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2007.06.003

with flexible roof diaphragms. Past studies have shown thatthe dynamic response of such structures can be affected bythe flexibility of the roof diaphragm [5–9]. In particular, thefundamental period of vibration is generally lengthened whencompared to similar structures with rigid diaphragms. Anexpression to predict the period of a building that accountsfor the flexibility of the roof diaphragm was proposed byMedhekar [8] and validated by shake table testing by Tremblayand Berair [10] and Tremblay et al. [11]. Furthermore, FEMA-356 [12] allows for the introduction of the in-plane flexibility ofthe roof diaphragm when estimating the fundamental period ofvibration. Tremblay et al. [13] and Tremblay and Rogers [14]have described the possible impact of building period on thedesign and cost of the seismic force resisting system.

Although it is possible to incorporate the diaphragmflexibility in the calculation of the period of vibration,it has been observed that building periods from ambientvibration field tests do not match those obtained fromnumerical simulations [8,15–17]. Medhekar [8] suggested thatnonstructural roofing components may contribute to an increasein the shear stiffness of roof diaphragms, resulting in ashorter building period; although, at the time this suggestioncould not be verified due to a lack of test data on themechanical properties of roofing material. Recent diaphragm

http://www.elsevier.com/locate/jcsr

mailto:[email protected]

http://dx.doi.org/10.1016/j.jcsr.2007.06.003

S. Mastrogiuseppe et al. / Journal of Constructional Steel Research 64 (2008) 214–227 215

shear tests confirmed the stiffening effect of nonstructuralroofing components on metal deck diaphragm properties [18,19].

In view of this background information, there existeda need to examine further and to assess the possibleinfluence of nonstructural roofing components on diaphragmshear stiffness and on the performance of single-storey steelbuildings subjected to seismic loading. The scope of studyinvolved the determination by testing of material propertiesfor the nonstructural roofing materials, including: 12.7 mmType X gypsum board; 25.4 mm fibreboard and 63.5 mmpolyisocyanurate (ISO) insulation; all of which are used inthe Association des Maıtres Couvreurs du Quebec (AMCQ)SBS-34 roof configuration. This common and conventionalroof configuration was chosen after consulting with the AMCQand the Ontario Industrial Roofing Contractors Association(OIRCA). It was also necessary to complete testing of thetypical mechanical connectors found in the roof diaphragm. Alinear elastic finite element model of a roof deck diaphragmthat accounts for the steel panels, the nonstructural componentsand the various mechanical connections was developed. Theanalytical results obtained from the model were compared withthe test based findings of Yang [18] and Essa et al. [20].Since only a limited number of tests have been carried outon diaphragm specimens with nonstructural components, themodel was then relied upon to establish stiffness valuesfor additional diaphragm configurations, in which the deckthickness and connector pattern were varied. These resultswere then used to assess the impact of the nonstructural roofcomponents on the fundamental periods of vibration of typicalsingle-storey steel buildings.

2. Nonstructural roofing components

The choice of a roof system was based on a literature reviewand on advice received from AMCQ and OIRCA, as wellas from various roofing contractors. The roof configurationknown as SBS-34, commonly found in Canada, was previouslyselected by Yang [18] for two large-scale cantilever diaphragmtests; thus there existed test results to aid in the validation ofthe finite element model. It was anticipated that this particularroof configuration would have adequate stiffness to augmentthe in-plane stiffness, G ′, of the overall diaphragm. The large-scale diaphragm static and dynamic tests by Yang showedan increase in G ′ of respectively 62% and 49% due to theadditional in-plane shear stiffness of the nonstructural roofingcomponents. Reduced warping of the steel deck cross-sectionwas also observed in these tests [19]. As shown in Fig. 1, thishot bitumen adhered roof system is composed of the followinglayers (from bottom to top): (i) one layer of 12.7 mm thickType X gypsum board mechanically fastened to steel roof deckusing 12 screws per 2.4 m × 1.2 m panel; (ii) two layers ofKraft paper vapour retarder (perforated No. 15 asphalt felt),hot bitumen adhered to the gypsum boards; (iii) one layer of63.5 mm thick poly-isocyanurate (ISO) insulation, hot bitumenadhered to the vapour retardant; (iv) one layer of 25.4 mm thickflame resistant Materiaux Cascades Securpan wood fibreboard,

Fig. 1. SBS-34 roofing cross-section as tested by Yang [18].

Fig. 2. Installation of gypsum board panels in tests by Yang [18]: (a) panellay-out; (b) gypsum-to-deck fastener.

hot bitumen adhered to the ISO panels; and (v) two layers ofsynthetic rubber SBS (Styrene-Butadiene-Styrene) waterproofmembrane (2.2 mm thick Elastophene 180 PS + 4 mm thickSopralene Flam 250 FR Granules).

The reference diaphragm test specimens by Yang measured3.658 m × 6.096 m. A Canam P3606 steel roof deck madeof 0.76 mm ASTM A653 [21] steel was used. This deckhad a trapezoidal 38 mm deep profile with flutes spaced at152 mm o/c, and the sheets were 914 mm in width. The testspecimens were constructed of three full-width steel panelsand one half-width panel along the north and south edges ofthe frame. Hilti X-ENDK223-THQ12 powder actuated deck-to-frame connectors and Hilti S-MD 12-14 × 1 HWH #1screw sidelap connectors were placed at a spacing of 305 mm.Fig. 2(a) shows the installation of the gypsum board on themetal roof deck. Self drilling/tapping screws having a diameterof 4.76 mm, a length of 41 mm, with 16 threads per inch, wereused for this operation. The screws were installed through a0.46 mm thick galvanized steel disc with a 76.2 mm (3 in.)

216 S. Mastrogiuseppe et al. / Journal of Constructional Steel Research 64 (2008) 214–227

diameter (Fig. 2(b)). Due to the specimen plan dimensions,there were six full-size (1.2 m × 2.4 m) gypsum panels andthree half-size panels (1.2 m × 1.2 m) screwed directly tothe top of the steel roof deck (Fig. 2(a)). The smaller panelswere connected with fewer fasteners (9 instead of 12). Oncethe gypsum panels were attached to the deck, hot bitumenwas applied and the felt paper was rolled onto the gypsum.Bitumen was then mopped onto the felt paper such that the ISOinsulation board could be adhered. The fibreboard was attachedto the insulation following the same procedure. Finally, the twolayers of SBS waterproof membrane were installed by meansof hot bitumen and an open flame propane torch. Fig. 3(a) to (c)illustrate the installation of the ISO panels, the fibreboard andthe waterproof membrane. The ISO and fibreboard materialswere delivered in 1.2 m × 1.2 m panels.

3. Roofing component experiments

The material properties of the nonstructural roofingcomponents were not readily available in the literature; hence,physical testing was necessary to determine representativevalues for use with the finite element model. A total of fourdifferent test setups were fabricated to measure the initialstiffness of the materials and connections in the linear elasticrange. The first test was a centre point load flexural test, whichwas necessary to determine the flexural stiffness of the gypsumand fibreboard. This test was carried out because Yang [18]observed that the warping deformations of the steel roof deckpanels, which affect the shear stiffness of the diaphragm, wererestrained by the flexural stiffness of the gypsum board inparticular (Fig. 4). The second test setup was a simple two-sidedshear assembly in which the shear stiffness of the gypsum andfibreboard was measured on a local scale. A four-sided sheartest was then used to measure the shear stiffness of the gypsumand fibreboard on a larger scale. Specimens that incorporatedcombinations of the other nonstructural roofing componentswere also tested with the four-sided shear setup. The final testsetup was of the screw connection between the gypsum andunderlying steel deck, as well as the screw sidelap connectionsbetween the steel deck panels and the nailed deck-to-frameconnections. An MTS Sintech 30/G universal testing machinewith a 150 kN load cell was used for all tests. The LVDTs andload cell were connected to a Vishay Model 5100B scanner,which was used to record the data with the Vishay System 5000StrainSmart software. A detailed account of the test programmeis provided by Mastrogiuseppe [22].

Type X gypsum board, as defined by ASTM C 1396 [27], isspecified where a fire resistance rating for the roof structure,in this case, is required. Type C gypsum board, which wasnot utilized in testing, is also available. Type C refers to aspecially formulated (proprietary) core that meets the Type Xrequirements as stated in ASTM C 1396 and which providesfor improved fire resistance. According to ASTM C1396 thephysical requirements for any gypsum wallboard, tested inaccordance with ASTM C 473 [23], must meet certain flexuralstrength, humidified deflection and nail pull resistance values;the Type X and C designations only refer to fire resistance

Fig. 3. Installation of roofing components in tests by Yang [18]: (a) ISOinsulation panels; (b) fibreboard panels; and (c) waterproof membrane.

properties. It could be anticipated that the structural propertiesof Type X and C gypsum board are similar based on theinformation provided in ASTM C1396; however, since TypeC gypsum was not tested specific comments on its structural


Fig. 4. Warping deformation of steel deck restrained by nonstructuralcomponents in test by Yang [18].

properties relative to Type X cannot be provided. Furthermore,although numerous studies on gypsum sheathed shear walls(Type X and C) are available in the literature no references tothe specific material properties of the gypsum wallboard werefound. Engineers would need to refer to the manufacturer ofa particular type of wallboard if additional structural/materialproperties were needed for design. In addition, all tests werecarried out with the gypsum in the “dry” condition. Gypsumwallboard with elevated moisture content will not exhibit thesame level of stiffness as listed in this paper. Engineers arecautioned on the reliance of gypsum board to stiffen the roofdiaphragm if “dry” conditions cannot be ensured.

3.1. Flexural tests

The flexural tests were conducted in order to obtain theflexural stiffness of the fibreboard and gypsum board panels.The flexural test setup was a simple centre-point flexure test(Fig. 5(a)), which was based on ASTM Standard C473 [23].Each test was conducted in displacement control at a crossheadspeed of 6.35 mm/min until failure of the specimen. In all,24 fibreboard specimens were tested. This included specimensthat were cut from a single panel but without a specificorientation with respect to the grain. Eight additional specimenswere cut from the same panel: Four were cut in direction‘A’ and the other four were cut perpendicular to the previousspecimens, direction ‘B’. This approach was used to investigatethe hypothesis that any existing directionality of the woodfibres would affect the flexural properties. Directions A andB have no precise meaning other than they are perpendicularto one another. A total of 44 flexural gypsum board tests,comprising two series of specimens, were performed. The firstseries contained specimens parallel to the long side of the panel,while the second series was orientated perpendicular to the longside. Gypsum board is typically fabricated with a finishing layerof paper on one side of the panel. It was felt that this layermay have an effect on the flexural stiffness and strength of thepanel depending on whether the paper was placed in tensionor compression during testing. The white finishing paper wasplaced in compression for 22 of the test specimens, and intension for the remaining flexural specimens. It is noted thatthe actual overall thickness of the specimens ranged between15.2 and 15.4 mm. Young’s modulus in flexure, E , could thenbe calculated given that all other variables were known, such asI in the flexural stiffness expression E I .

Fig. 5. Flexural test: (a) test setup; (b) typical load–deformation response.

Fig. 5(b) shows typical load–deformation curves for thegypsum and fibreboard test specimens. The Young’s modulusfor each material was determined from the slope of the initiallinear range of the test load–deformation responses and thegeometrical properties of the specimens. The average modulusof the fibreboard specimens was 250 MPa. However, when thedata from the ‘A’ and ‘B’ data sets were compared, there weretwo different values of stiffness: 298 MPa for ‘A’ and 241 MPafor ‘B’. This represents a difference of approximately 20%,which is much larger than the calculated coefficient of variation(CoV) of the entire data set (CoV = 0.054). Nonetheless, thegeneral shape of the load vs. deformation curve was the samefor the two sets of data. The gypsum panel was found to beapproximately ten times stiffer in flexure than the fibreboardpanel with mean values of E = 2850 MPa in the paralleldirection and 2410 MPa in the perpendicular direction. Theflexural stiffness results were similar for the gypsum boardspecimens, regardless of the position of the finishing paper. Inthe development of the finite element model it was decidedto use an average Young’s modulus for flexural stiffness of250 MPa for the fibreboard and 2625 MPa for the gypsumpanels.


Fig. 6. Two-sided shear test: (a) test setup; (b) typical load–deformation response.

3.2. Two-sided shear tests

The two-sided shear tests were carried out in accordancewith ASTM D1037 [24] using the test setup shown inFig. 6(a). The shear deformation of the gypsum and fibreboardspecimens was directly measured by an LVDT placed in linewith the loading plates. The displacement controlled rate ofloading was taken as 0.2% of the length of the specimenper minute, i.e. 0.508 mm/min. A total of five fibreboardspecimens and four gypsum board specimens were tested.The fibreboard and gypsum board shear specimens behavedlinearly up to approximately 40% and 50% of the ultimateload, respectively. The ASTM D1037 Standard contains amethod for the calculation of shear strength from the testresults, however, there is no recommended equation given todetermine the stiffness of the specimen for this specific testsetup. It was, therefore, necessary to rely on the equation for thethrough thickness shear from ASTM D1037 and D2719 [25].The ASTM D2719 Standard contains a factor to compensatefor the nonuniform stress distribution in small test specimens(see Mastrogiuseppe [22]). Fig. 6(b) shows typical specimenresponses. Shear stiffnesses were determined using the loadand deflection at 40% of the ultimate load; the resulting valuesfor the fibreboard and gypsum board panels were 60 and437 MPa, respectively. The average shear stiffness for thegypsum board was over seven times greater than that of thefibreboard. However, the results for both the fibreboard andthe gypsum stiffness were scattered, as can be seen in thecoefficient of variation of 37% and 17%, for the two materials,respectively. One possible cause of the scatter of results maybe the small scale and localized loading of the test setup.Furthermore, the test setup was originally not developed todetermine stiffness, but rather the shear strength properties ofa material. The four-sided shear test setup was required to

provide additional information on the shear stiffness of the non-structural components prior to the selection of representativevalues for use with the finite element model.

3.3. Four-sided shear tests

The four-sided shear tests were conducted in order to obtainthe shear stiffness of the gypsum, fibreboard and combinationsof other nonstructural roofing components. This test setup,which was based on ASTM D2719 [25], was necessary becauseof the type and size of the nonstructural roofing elements. Asshown in Fig. 7(a), a specimen having a 620 mm × 620 mmsquare shear area was loaded along all four edges by a systemof hinges and steel rails. To avoid bearing at the ends of thepanel and to provide a more uniform transfer of shear, two19 mm thick plywood rails were screw fastened to the panelalong each edge. The rails, which were secured with 10 to12 drywall screws, then transferred the applied loads in auniform fashion to the test specimen. As the cross head of theloading machine moved vertically upwards at a constant rateof 2.1 mm/min, bearing forces were applied at the reinforcedcorners of the panel, resulting in shear forces along the foursides of the panel. The diagonal elongation of the specimen wasmeasured with LVDTs placed on both faces of the specimen.Horizontal stiffeners were installed on both sides of mostspecimens to ensure that flexural deformations of the panelwere minimized. These stiffeners were built with steel anglesthat were connected using slotted holes and loosely tightenedbolts to avoid any contribution to the specimen in-plane shearstiffness.

Fig. 7(b) shows a gypsum board specimen installed inthe test frame. In all, 22 specimens were tested, comprisingfibreboard panels, gypsum panels, as well as combinationsof other nonstructural components. In addition to the single


Fig. 7. Four-sided shear test: (a) test setup and specimen; (b) gypsum board specimen; (c) “full component” specimen.

panel specimens, it was necessary to fabricate specimens thatconsisted of combinations of fibreboard, ISO insulation, feltvapour retarder and gypsum (Fig. 7(c)). These test specimenswere similar to the diaphragm specimens with nonstructuralcomponents tested by Yang [18]. A 63.5 mm thick ISO boardwas hot bitumen adhered to a fibreboard panel for three testspecimens. A total of four “full component” specimens werefabricated in an attempt to represent all of the nonstructuralelements of a roof. A sheet of felt vapour retarder was first hotbitumen adhered to the fibreboard/ISO section. As a second stepin the fabrication, a gypsum layer was then hot bitumen adheredto the vapour retarder.

The fibreboard was used as the base material in all the multi-layer specimens because it has a lower shear stiffness than thegypsum board. This facilitated the measurement of any change

in stiffness as the additional nonstructural layers were added.If gypsum had been used as the base material, the relativeincrease in stiffness due to the added layers, would have beenmuch lower than the stiffness of the gypsum itself, perhaps evennegligible. Also, note that only the fibreboard was connectedto the loading rails; the other nonstructural layers were locatedwithin the central portion of the test specimen. These specimenswere tested in the same test setup as the plain gypsum boardand fibreboard specimens. The ISO insulation board could notbe tested by itself because the test frame as fabricated could notaccommodate for its thickness and flexibility.

Fig. 8 shows typical load–deformation responses as obtainedfrom the two LVDTs placed on a gypsum or fibreboardspecimen. The average LVDT reading was used in thecalculation of the shear stiffness. For the gypsum board


Fig. 8. Typical four-sided shear test load–deformation response (gypsum boardshown).

material, the average shear stiffness was found to be 1284 MPa,which is 5.5 times higher than that obtained for the fibreboard(G = 235 MPa). An increase in shear stiffness of 30%,compared with the fibreboard alone, was measured when theISO board was added to the fibreboard. A total shear stiffnessincrease of almost 70% compared to the fibreboard alone wasrealized when the gypsum board and vapour retarder layerswere added to the fibreboard and ISO board. These resultsprovide the shear stiffness of the roofing section with theload applied to the fibreboard. However, in the actual roofthe shear load-shear deformation would first be applied to thegypsum board from the steel roof deck panels. Screw fastenersare typically used to connect the gypsum board to the deckpanels. Hence, it was necessary to identify the increase instiffness to the gypsum board because of the addition of thevapour retarder, ISO and fibreboard panels. The stiffness ofthe fibreboard and gypsum board panels was known, as wellas the “full component” and the fibreboard/ISO section. Theonly individual nonstructural component for which the shearstiffness was not known was the ISO board, excluding thevapour retarder which was assumed to have negligible in-planeshear stiffness.

Significant out-of-plane bending response developed duringthe “full component” tests, which made it difficult to rely onthe direct displacement measurements to determine the soughtafter shear stiffness values. To overcome this shortcomingMastrogiuseppe [22] developed a finite element model of the“full component” test setup in which the unknown propertiesof the ISO boards were iteratively modified until a perfectmatch between the test and numerical results was achieved.The gypsum and fibreboard materials were given the previouslymeasured properties. Fig. 9(a) shows the 1728 solid elementSAP2000 v.8.2.3 [26] analytical model used in this process.A shear stiffness of 4 MPa was found for the ISO insulationmaterial. With this value, a second FE model that includedthe three nonstructural roofing components was constructed; in

Fig. 9. Finite element model simulating a four-sided shear test on a roofassembly: (a) deformed “full component” specimen; (b) deformed three layerroof section.

which the gypsum board was placed as the base element wherethe shear force was applied (Fig. 9(b)). The shear stiffness ofthe all-combined nonstructural components was found to be1353 MPa, an increase of only 5.4% over the bare gypsumpanel (1284 MPa), which indicates that the shear stiffness ofthe fibreboard (235 MPa) would only be partially exploited in aroofing assembly due to the flexibility of the intermediate layerof ISO material. The values from the four-sided tests were usedto define the shear properties of the nonstructural componentsfor use in the finite element model.

3.4. Connection tests

The connection tests were carried out to determine the shearstiffness of the typical screw and nail (powder actuated fastener)connections that are present in roof deck diaphragms: frame-to-deck connections; steel deck sidelap connections; and gypsumboard to steel deck. A single overlap/single shear setup wasused for the testing of all individual connections (Figs. 10and 11). Each specimen was composed of two pieces (steeldeck, steel plate or gypsum) that were attached by a singlefastener. The free ends of the two pieces were then installed ina gripping device that was fastened to the testing frame. Eachtest was conducted in displacement control at a crosshead speedof 1 mm/min. Detailed information on the sidelap and deck-to-frame connection tests can be found in Nedisan et al. [28].

Test specimens were constructed of 0.76, 0.91, 1.21 and1.51 mm ASTM A-653 [21] Grade 230 MPa sheet steel. Thegypsum board was 12.7 mm Type X, and the steel plates were4.8 mm Grade 300W CSA G40.20/G40.21 [29] material. Thesteel plates were used to represent the supporting flange of aframe member beneath the steel roof deck. Hilti X-ENDK22-THQ12 powder actuated (nail) fasteners were used to connectthe deck elements to the frame. Sidelap connections were made


Fig. 10. Connection test setups: (a) deck-to-frame connection; (b) sidelap connection; and (c) gypsum-to-deck connection.

Fig. 11. Connection test specimens: (a) deck-to-frame connection; (b) sidelapconnection; and (c) gypsum-to-deck connection.

of two deck panels fastened with a Hilti S-MD 12-14 X 1 HWH#1 screw. The gypsum-to-deck screw connectors were #12 Hex

with Round Galvalume Plate DekfastTM products, made by SFSIntec.

Initial shear stiffness of the deck-to-frame fasteners wasmeasured as 32.3 kN/mm, 31.7 kN/mm, 46.6 kN/mm and50.3 kN/mm for the 0.76 mm, 0.91 mm, 1.22 mm and 1.51 mmsheet steel specimens, respectively. The sidelap connectionstiffness was 11.9, 14.7, 18.6 and 21.2 kN/mm for the samesheet steels. Stiffness parameters for various sidelap and deck-to-frame connections have also been provided by Rogers andTremblay [30,31] and the Steel Deck Institute (SDI) [32].These supplementary connection stiffness values were alsoincorporated in the finite element model for comparisonpurposes. The stiffness of the gypsum-to-deck connectionsfor the first three steel thicknesses were all very similar,hence, an average value of 3.14 kN/mm was determinedfor these specimens as a group. The connection stiffness forthese specimens was mainly dependent on the tightness of thescrew/washer combination. It was clear that if the connectorwas not well installed, or if a washer was not used, theconnection stiffness would be much lower than this averagevalue. The thickness of the sheet steel did not seem to have animpact on the stiffness of the connection; rather the placementof the washer was critical. However, the 1.52 mm thick sheetsteel specimens possessed a much higher stiffness than theothers, with an average value of 6.30 kN/mm. The thickerdeck prevented the screw from rotating, thus reducing thedependence of the connection performance on the washertightness.


4. Contribution of roofing components to roof diaphragmshear stiffness

As indicated earlier, Yang [18] carried out twelve large-scale roof diaphragm tests (3.658 m × 6.096 m in plan), twoof which were constructed with the AMCQ SBS-34 roofingnonstructural components. The Group 3 tests, characterized bya 0.76 mm thick Canam P3606 type steel deck, as well as naileddeck-to-frame and screwed sidelap connections, are relevantto this paper. Two tests were performed under monotonicallyincreasing load: Test No. 43 was composed of a bare sheet steeldeck diaphragm, while Test No. 45 included the nonstructuralroofing components. An in-plane initial shear stiffness of G ′

=

2.58 kN/mm was measured for the bare test diaphragm,whereas the clad specimen developed a stiffness of 4.17 kN/m,an increase of 62%. If the results of the cyclically loadedTests No. 44 (bare steel) and 46 (clad deck) were includedin the comparison, an average increase in shear stiffness of49% would be attained. During the loading process it wasobserved that the flexural stiffness and strength exhibited bythe gypsum board also greatly restrained the warping of thepanels (Fig. 4). In addition to the added shear stiffness ofthe gypsum, the warping restraint directly increased the shearstiffness of the complete diaphragm. Based on the observationsmade during the diaphragm and material tests, it was concludedthat the gypsum layer added to the stiffness of the steel deck,while the other non-structural layers contributed very little.This conclusion was also confirmed by the fact that significantdamage occurred in the gypsum layer (Fig. 4), whereas theother non-structural components exhibited almost no visibledistortion.

4.1. Development and validation of a finite element diaphragmmodel

The objective of the analytical phase of this research projectwas to develop linear elastic finite element (FE) models thatwould adequately reproduce the initial stages of the roofdiaphragm in-plane shear behaviour measured in Tests No. 43(bare) and 45 (clad) by Yang [18]. The analytical models werebuilt using the SAP2000 software [26]. The 20456 node bare

Table 1Material properties of shell elements

Property Steel deck Nonstructuralcomponents

0.76 mm 0.91 mm 1.21 mm 1.52 mm

t (mm) 0.72 0.905 1.22 1.51 12.7E (GPa) 195.2 197 203 203 3.07G (GPa) 75.1 75.8 78.1 78.1 1.38µ 0.3 0.3 0.3 0.3 0.11

Table 2Stiffness properties of link (connection) elements (kN/mm)

Connection Steel deck thickness0.76 mm 0.91 mm 1.21 mm 1.52 mm

Deck-to-frame 32.0 32.0 46.6 50.3Sidelap 11.6 14.7 18.6 21.2Gypsum-to-deck 3.14 3.14 3.14 6.28

sheet steel models had three full 6.096 m long deck panelsand two half width panels which were represented with 17812four-node flat shell elements capable of developing bendingand membrane behaviour (Table 1) (Fig. 12(a)). Each steelpanel was modelled separately, which required link elementsto connect the various panels and framing members. Theunderlying pin connected frame was composed of 600 six d.o.f.beam elements that were assigned material properties such thatthe shearing deformation of the model would only take placein the sheet steel and its connections. A total of 1999 linkelements were used to represent the sidelap and deck-to-frameconnections (Table 2), as well as contact surfaces; this includedmulti-link elements that restricted movement of the steel deckinto the frame at contact locations away from connections.For Test No. 45, the nonstructural roofing component modelconsisted of the same 600 beam elements that represented theframe, as well as 35 092 shell elements for the steel deck panelsand the non-structural panels (Table 1), 1870 link elementsfor connections (Table 2) and contact areas, as well as 37 264nodes (Fig. 12(b)). There were fewer link elements than withthe bare sheet steel model in order for a converged solutionto be reached. A single layer of 12.7 mm thick material that

Fig. 12. Undeformed shape of the full-scale diaphragm model: (a) bare steel; (b) bare steel with nonstructural roofing.


Table 3Comparison of test-based and analytical shear stiffness G′

Deck thickness(mm)

Fastener pattern(mm/mm)

Cladding G′ test(kN/mm)

G′FE model (kN/mm) % Inc vs. Prev. % Inc vs. Bare Test/FE

0.76 305/305 Bare steel 2.58a 2.74 N/A N/A 0.940.91 305/305 Bare steel 4.22b 4.49 63.5% N/A 0.941.21 305/305 Bare steel N/A 8.30 85.0% N/A N/A1.52 305/305 Bare steel N/A 13.0 57.1% N/A N/A0.76 305/305 SBS-34 4.17c 4.35 N/A 58.6% 0.960.91 305/305 SBS-34 N/A 6.42 47.7% 43.2% N/A1.21 305/305 SBS-34 N/A 10.8 68.9% 30.8% N/A1.52 305/305 SBS-34 N/A 15.2 40.4% 16.9% N/A

a Test 43 by Yang [18].b Test 17 by Essa et al. [20].c Test 45 by Yang [18].

Fig. 13. Warping and shear deformation of the bare steel diaphragm model.

Fig. 14. Restrained warping and shear deformations of the model with roofingcomponents.

represented the complete nonstructural section (gypsum, ISOinsulation & fibreboard) was connected to the sheet steel shellelements through links that represented the gypsum screwfasteners.

Material properties for the shell elements were assignedbased on a combination of measured and codified values.Properties for the steel deck shell elements were taken from thetest data compiled by Yang [18] for the 0.76 and 0.91 mm thickdeck. The properties of the nonstructural components weretaken from the results of the material tests presented above. Avalue for Poisson’s ratio of µ = 0.11 was found for the gypsum

and assumed for use with the full cross-section of nonstructuralcomponents. The thickness of the gypsum, 12.7 mm, was alsoused, however the Young’s and shear moduli of the gypsumwere increased to account for the additional stiffening effectof the ISO insulation and fibreboard layers (Table 1).

In addition to the two tests by Yang, a bare steel specimenmade with four 0.91 mm thick, 6.096 m long deck panels(Test No. 17) that was tested by Essa et al. [20] was also usedfor validation purposes. The plan dimensions, deck profile andfastener systems for this specimen were identical to those of thesamples studied by Yang. Further verification of the ability tocorrectly predict the stiffening effect of non structural roofingelements with the model was performed by examining trendsobtained with five additional models of deck configurations forwhich test data was not available: two bare sheet steel roofdiaphragms with a steel thickness of 1.21 and 1.52 mm, andthree roof deck diaphragms built with 0.91, 1.21 and 1.52 mmthick steel sheets and clad with non-structural components.These models included the same 38 mm deep deck profile asin the tests by Yang and by Essa et al. Screw fasteners wereused for all sidelap connections while powder actuated nailswere modelled at all deck-to-frame connection locations. A305/305 connector pattern was considered in all cases with bothdeck-to-frame nail and sidelap screw spacings of 305 mm. Themodelling assumptions for these additional models were similarto those adopted for the tests by Yang. Since testing for thetwo thicker deck types (1.21 and 152 mm) had not been carriedout, the material properties were obtained from the CSA S136Standard [33].

The FE model was able to reproduce the elasticload–deformation behaviour of the diaphragm tests accurately.Figs. 13 and 14 illustrate the deformed bare steel deckdiaphragm and the deformed shape of the deck with the gypsumboard models, respectively. The warping of the steel deckcorresponds to that observed during testing of the diaphragmspecimens, which was much less apparent in the model andtest with the nonstructural components. Fig. 14 shows theflexural deformation in the nonstructural components, as wasobserved in the diaphragm specimens tested by Yang. Table 3lists the computed stiffness of the models, both bare steel andclad, as well as the measured in-plane shear stiffness of thecorresponding diaphragm tests by Yang and by Essa et al.


Table 4SDI stiffness properties of link (connection) elements (kN/mm)

Connection Steel deck thickness0.76 mm 0.91 mm 1.22 mm 1.51 mm

Deck-to-frame 19.4 21.2 24.6 27.4Sidelap 10.1 11.0 12.8 14.2Gypsum-to-deck 3.14 3.14 3.14 6.28

The test-to-predicted ratios of the three diaphragm specimensvary from 0.94 to 0.96, which indicates that the FE modelcan be considered as relatively accurate. As expected, theoverall stiffness of the bare sheet diaphragm increased as thethickness of the panels increased. The shear stiffness of thediaphragm with 1.52 mm thick panels was 4.5 times thatobtained for the diaphragm with 0.76 mm panels. An increase inthe elastic shear stiffness was recorded when the nonstructuralcomponents were added to the model. This result was mostevident for the diaphragm with the thinnest steel deck panels.The effect of the nonstructural components diminished as thesheet steel thickness increased, i.e. a 58.6% increase in stiffnesswas calculated for the 0.76 mm steel, whereas only a 16.9%increase was obtained for the 1.52 mm panels.

The stiffness values obtained with the FE models wereapproximately 5% higher than the values measured duringtesting, for both the bare sheet steel and clad diaphragms.This could be due to material nonuniformity or irregularitiesthat occurred during the construction of the test specimen. Itis possible that the quality of installation of the fasteners inthe tested diaphragms was not consistent, and hence in somelocations the connection stiffness may have been lower thanused in the FE models. The overall stiffness of a steel roofdeck diaphragm is highly dependent on the performance of theindividual deck-to-frame and sidelap connections. This wouldhave led to a decrease in the measured shear stiffness of thetest diaphragm. To verify whether the 5% discrepancy betweenthe test and FE derived stiffness was due to poor connectorquality an additional model was created for Test No. 43 byYang in which 10% of the connectors had their stiffness reducedby 10%. Note that this decrease in stiffness was arbitrarilyselected. The results of the analysis gave a shear stiffness of2.63 kN/mm, which resulted in a test-to-predicted ratio of0.98. This indicates that only a slight change in the connectionstiffness for a small number of fasteners can change the overalldiaphragm stiffness.

4.2. Parametric study: Influence of gypsum board on di-aphragm stiffness

A parametric study involving the FE analyses of thirty-twonail–screw diaphragm models was carried out to determinethe contribution of the nonstructural components to overallroof diaphragm in-plane shear stiffness. The scope of studycomprised four different steel deck thicknesses (0.76, 0.91,1.21 and 1.52 mm) and four structural connector configurations(305/305, 305/152, 152/305, and 152/152 — the two numbersrepresent the deck-to-frame and sidelap fastener spacings,respectively), and with and without gypsum board. The

Fig. 15. Influence of the gypsum board on diaphragm shear stiffness: (a) ratioof the clad to bare steel shear stiffness; (b) increase in shear stiffness due to thepresence of the gypsum board.

diaphragm dimensions, the deck profile and the fastener typesstudied by Yang were again considered in the study. Designerscommonly rely on the SDI [32] design method to calculateoverall shear stiffness and capacity of metal roof diaphragms.Therefore, the FE analyses were conducted using the basicmodel described previously with SDI defined frame and sidelapfastener stiffness properties instead of the test based values(Table 4). This approach was taken in an attempt to identifythe possible increase in stiffness of the bare steel diaphragm,as calculated using the SDI method, due to the presence ofnonstructural roofing components. For this study the gypsumboard alone was incorporated in the models due to the findingthat the remaining nonstructural components (ISO insulation &fibreboard) augmented the stiffness of the gypsum by only 5%.The material properties of the gypsum board were as follows:t = 12.7 mm, E = 2625 MPa, G = 1284 MPa, and µ = 0.11.

Shear stiffness values obtained from the FE analyses for thebare steel deck diaphragm models and for the diaphragm mod-els with a gypsum board layer are provided in Table 5. Notethat these values do not match those previously listed (Table 3)because SDI connection stiffness values were incorporated inthe models instead of test-based values. The ratios between theclad and bare steel diaphragm shear stiffness values are tabu-lated in Table 6 and are plotted in Fig. 15(a) (G ′

BS+GB = stiff-ness of diaphragms with the gypsum board; G ′

BS = stiffnessof bare steel diaphragms). The results clearly indicate that asthe steel diaphragm becomes stiffer due to either the use of a


Table 5Finite element analysis linear elastic diaphragm stiffness G′(kN/mm)

Deck thickness (mm) Bare steel fastener pattern Bare steel + gypsum fastener pattern305/305 305/152 152/305 152/152 305/305 305/152 152/305 152/152

0.76 3.26 4.05 9.29 11.8 4.78 5.59 10.7 13.20.91 5.17 5.40 12.4 15.5 6.46 7.06 13.7 16.91.21 8.51 8.70 17.4 23.1 10.0 10.1 18.7 24.41.52 12.6 13.1 22.3 30.0 13.8 14.4 23.8 31.5

Note: SDI connection stiffness values used in model.

Table 6Diaphragm stiffness ratio between clad and bare steel diaphragms

Deck thickness (mm) Fastener pattern305/305 305/152 152/305 152/152

0.76 1.46 1.38 1.15 1.120.91 1.25 1.31 1.11 1.0881.21 1.18 1.17 1.078 1.0561.52 1.10 1.10 1.067 1.048

Note: SDI connection stiffness values used in model.

thicker deck or more closely spaced structural connections, thecontribution of the gypsum board to overall diaphragm stiff-ness decreases on a percentage basis. For the 0.76 mm speci-men with a 305/305 connector spacing, a significant increasein G ′ (46.4%) was caused by the addition of the gypsum layer.Conversely, for the 1.52 mm specimen with a 152/152 spac-ing, the increase was less than 5%. In fact, the contribution ofthe gypsum board seems to be constrained by the stiffness ofthe gypsum-to-deck fasteners, as demonstrated by an additionalanalysis in which continuity was recreated along the joints be-tween the gypsum panels for decks made of 1.52 mm thick steelsheets and a 152/152 fastener pattern. The resulting stiffnessvalue was 34.4 kN/mm, only 9.3% higher than the correspond-ing value in Table 5 (31.5 kN/mm). When comparing G ′ val-ues for bare diaphragms versus diaphragms with the gypsumboard, it was also observed that the actual contribution of thenonstructural layer was very similar in absolute terms for allof the configurations modelled. This is illustrated in Fig. 15(b)which compares the shear stiffness obtained with and withoutthe gypsum board. The increase in shear stiffness when includ-ing the gypsum panels varied between 1.27 and 1.65 kN/mm,with an average value of 1.42 kN/mm and a CoV of 0.076.Hence, the deck thickness and structural connector layout donot substantially influence the contribution of the nonstructuralcomponents to in-plane shear stiffness of a roof diaphragm inabsolute terms. This observation is used below in the analysisof building models to address the influence of the nonstructuralgypsum layer on the fundamental period of vibration of typicalsingle-storey steel buildings.

4.3. Parametric study: Influence of gypsum board on buildingperiods

In-plane shear flexibility of metal roof deck diaphragms canimpact the building deformations achieved under lateral loads,and hence must be considered in design. This is particularlyrelevant for single-storey buildings for which diaphragminduced deformations can represent the major portion of

building drifts. Shear deformations of roof diaphragms also leadto longer fundamental periods of vibration for the building,which generally result in reduced seismic force demand.Tremblay and Rogers [14] showed that significant cost savingscould be achieved for single-storey steel structures if this forcereduction could be exploited in seismic design, but this requiresthe prediction of a reliable period of vibration that accounts forfactors such as nonstructural roofing elements. The knowledgegained in this study is applied herein to assess the impactof using the AMCQ SBS-34 roofing system for the buildingsstudied by Tremblay and Rogers [14].

The buildings included in the parametric study were regularsingle-storey steel structures with a rectangular foot printand constant height. Building areas varying between 600 and4200 m2, plan aspect ratios ranging from 1.0 to 2.5, andbuilding heights from 4.8 to 10.8 m were considered. Thestructures were designed according to the seismic relatedprovisions of the 2005 NBCC [2] and the CSA S16 Steeldesign standard [34] for firm ground conditions (Site ClassC) at two sites in Canada: Vancouver, BC, and Montreal,QC. The seismic hazard in Vancouver is moderate and isrepresentative of that of other cities in the Pacific Northwestregion, including Seattle, WA, Portland, OR, and Victoria,BC. The seismic hazard is lower in Montreal, especially inthe long period range, as is the case in many eastern citiessuch as Boston, MA, New York, NY, and Ottawa, ON. X-bracing symmetrically distributed along the four perimeterwalls was used as the vertical bracing system. Two differentbracing systems were considered: tension–compression andtension-only. Three braced frame categories were examinedfor each system, to which were assigned different valuesof the ductility-related seismic force modification factor, Rd :Type MD (Moderately ductile) with Rd = 3.0, Type LD(Limited ductility) with Rd = 2.0, and Type CC (Conventionalconstruction) with Rd = 1.5. In total, 1362 building cases werestudied for each site. Details on the design can be found inTremblay and Rogers [14]. For each building, the fundamentalperiod was computed in each of the two principal directionsfor both the bare steel and the clad conditions, assuming anincrease of 1.42 kN/mm for G ′ for the second case. The periodwas estimated using the formula proposed by Tremblay andBerair [10].

Fig. 16(a) shows the ratio of the clad diaphragm period,TBS+GB, to the bare steel diaphragm period, TBS. The ratiosvary from 0.88 to nearly 1.0, and the average values forVancouver and Montreal are 0.99 and 0.98, respectively.The decrease in building period due to the roofing material


Fig. 16. Influence of the gypsum board on building fundamental periods: (a) ratio of the periods for diaphragms with and without gypsum board; (b) reduction inbuilding period due to the presence of the gypsum board.

(Fig. 16(b)) was on average 0.01 s in Vancouver and 0.02 s inMontreal. The corresponding maximum reductions in periodsare respectively 0.09 s and 0.15 s. No definite trends could beobserved between period variations and building geometricalproperties. As expected, however, the larger period reductionsgenerally coincided with buildings having very flexible roofdiaphragms, i.e. structures for which the design force demandon the diaphragm was lower: square buildings located inMontreal and built with Type MD tension-only bracing. Thistrend can be observed in Fig. 16 where larger changes tendto occur for buildings with longer TBS values. It is noted thatthese occurrences do represent only a small fraction of thebuilding sample studied herein. For instance, the reduction inperiods exceeds 5% only for 5% of the structures in Vancouverand 13% of the buildings in Montreal. Similarly, a 0.05 speriod change is noted only in 4% of the Vancouver structuresand 12% of the structures in Montreal. Hence, the influenceof roofing material on building period would be marginal,except for a few buildings. Considering that the AMCQ SBS-34 roof design used in this study has a high content of stiffmaterial (gypsum and fibreboard) compared to other roofingsystems commonly used in the industry, it can be concludedthat non-structural roofing materials have a marginal influenceon building fundamental period for the vast majority of the low-rise steel buildings constructed in Canada.

5. Conclusions

The overall goal of this research was to provide a betterunderstanding of the effect of nonstructural roofing componentson the dynamic properties of single-storey steel buildings,specifically on roof diaphragm properties. This has beenachieved by means of materials tests, finite element analyses, a

parametric study of the effect of deck thickness and connectionconfiguration on the stiffening effect of gypsum panels ondiaphragm shear response and, lastly, a parametric studyof the effect of increased diaphragm shear stiffness on thefundamental periods of a wide range of single-storey steelbuildings. The AMCQ SBS-34 roof design with 12.7 mmthick gypsum board, 25.4 mm fibreboard and 63.5 mm poly-isocyanurate (ISO) insulation was considered in the research.The gypsum board was found to be the stiffest element of thenonstructural components, and because of this had the greatestinfluence on the in-plane force–deformation behaviour of thesteel roof deck diaphragm. The other nonstructural elements,either due to their low in-plane shear stiffness or lack of a directconnection to the steel deck, did not have as much of an effect.

A finite element model was developed to predict the linearelastic behaviour of bare sheet steel deck diaphragms and di-aphragms constructed with nonstructural roofing components.A comparison of the measured stiffness of three diaphragmspecimens provided test-to-predicted ratios in the range of0.94 to 0.96. The parametric study performed with that modelshowed that the bare steel diaphragm stiffness increases as thethickness of the steel roof deck panels is increased and whencloser connection spacing is used. The contribution of the gyp-sum board, in terms of an increase in in-plane shear stiff-ness, was apparent for all deck thicknesses and fastener pat-terns. The increase was however less on a percentage basis forthe stiffer bare steel diaphragm designs, and the contributionof the gypsum board remained relatively constant in absoluteterms regardless of deck thickness and connector spacing. Thefundamental period of vibration of buildings computed usingdiaphragm properties with and without non-structural roofingcomponents was found to be nearly identical for the vast major-


ity of single-storey steel structures likely to be constructed inCanada.

Acknowledgements

The research documented in this paper was funded by theStrategic Grants Programme of the Natural Sciences and Engi-neering Research Council of Canada. The authors would like toacknowledge the support provided by the Canada Foundationfor Innovation, the Canam Group Inc. and Hilti Limited.

References

[1] Tremblay R, Rogers C, Martin E, Yang W. Analysis, testing and designof steel roof deck diaphragms for ductile earthquake resistance. Journalof Earthquake Engineering 2004;8(5):775–816.

[2] NRCC. National building code of Canada. 12th ed. Ottawa (ON):National Research Council of Canada; 2005.

[3] Goel RK, Chopra AK. Period formulas for moment-resisting frame build-ings. ASCE Journal of Structural Engineering 1997;123(11):1454–61.

[4] Tremblay R. Fundamental period of braced steel frames for seismicdesign. Earthquake Spectra 2005;21(3):833–60.

[5] Jain SK, Jennings PC. Analytical models for low-rise buildings with flex-ible roof diaphragms. Earthquake Engineering and Structural Dynamics1985;13:225–41.

[6] Tena-Colunga A, Abrams DP. Seismic behavior of structures withflexible diaphragms. ASCE Journal of Structural Engineering 1996;122(4):439–45.

[7] Tremblay R, Stiemer SF. Seismic behaviour of single-storey steel struc-tures with flexible diaphragm. Canadian Journal of Civil Engineering1996;23(1):49–62.

[8] Medhekar MS. Seismic evaluation of steel buildings with concentricallybraced frames. Ph.D. thesis. Edmonton (AL): Dept. of Civil and Env.Eng., University of Alberta; 1997.

[9] Adebar P, Guan Z, Elwood K. Displacement-based design of concretetilt-up frames accounting for flexible diaphragms. In: Proc. 13th worldconf. on earthquake eng. 2004. Paper No. 1054.

[10] Tremblay R, Berair T. Shake table testing of low-rise steel buildings withflexible roof diaphragms. In: Proc. 8th Canadian conf. on earthquake eng.1999. p. 585–90.

[11] Tremblay R, Berair T, Filiatrault A. Experimental behaviour of low-risesteel buildings with flexible roof diaphragms. In: Proc. 12th world conf.on earthquake eng. 2000. Paper No. 2567.

[12] FEMA. FEMA 356 Prestandard and commentary for the seismic rehabil-itation of buildings. Washington (DC): Federal Emergency ManagementAgency; 2000.

[13] Tremblay R, Rogers C, Nedisan CD. Use of uniform hazard spectrum andcomputed period in the seismic design of single-storey steel structures.In: Proc. 7th U.S. nat. conf. on earthquake eng. 2002. Paper No. 195.

[14] Tremblay R, Rogers CA. Impact of capacity design provisions and periodlimitations on the seismic design of low-rise steel buildings. InternationalJournal of Steel Structures 2005;5(1):1–22.

[15] Ventura CE. Ambient vibration test of the Safeway store. Report bythe UBC ambient vibration team. Vancouver (BC): Dept. of Civil Eng.,University of British Columbia; 1995.

[16] Paultre P, Proulx J, Ventura C, Tremblay R, Rogers CA, Lamarche C-P.et al., Experimental investigation of low-rise steel buildings for efficientseismic design. In: Proc. 13th world conf. on earthquake eng. 2004. PaperNo. 2919.

[17] Lamarche C-P. Etude experimentale du comportement dynamique desbatiments de faible hauteur en acier. M.A.Sc. thesis. Sherbrooke (QC):Department of Civil Engineering, University of Sherbrooke; 2005.

[18] Yang W. Inelastic seismic response of steel roof deck diaphragmsincluding effects of non-structural components and end laps. M.A.Sc.thesis. Montreal (QC): Dept. of Civil, Geo. and Mining Eng.; EcolePolytechnique; 2003.

[19] Rogers CA, Tremblay R, Yang W, Martin E. Ductile design of steel roofdeck diaphragms for earthquake resistance. In: Proc. 13th world conf. onearthquake eng. 2004. Paper No. 1997.

[20] Essa HS, Tremblay R, Rogers CA. Behavior of roof deck diaphragmsunder quasi-static cyclic loading. ASCE Journal of Structural Engineering2003;129(12):1658–66.

[21] ASTM. ASTM A653 Standard specification for steel sheet, zinc-coated(galvanized) or zinc–iron alloy-coated (galvannealed) by the hot-dipprocess. West Conshohocken (PA); 2005.

[22] Mastrogiuseppe S. Numerical linear elastic investigation of steel roofdeck diaphragm behaviour accounting for the contribution of non-structural components. M.Eng. thesis. Montreal (QC): Dept. of Civil Eng.& Applied Mechanics, McGill University; 2006.

[23] ASTM. ASTM C473 Standard test methods for physical testing ofgypsum panels products. West Conshohocken (PA): American Societyfor Testing and Materials; 2003.

[24] ASTM. ASTM D1037 Standard test methods for evaluating propertiesof wood-base fiber and particle panel materials — Edgewise shear. WestConshohocken (PA): American Society for Testing and Materials; 1999.

[25] ASTM. ASTM D2719 Standard test methods for structural panels inshear through-the-thickness. West Conshohocken (PA): American Societyfor Testing and Materials; 2001.

[26] CSI. SAP2000, Integrated finite element analysis and design of structures.Berkeley (CA): Computers and Structures Inc.; 2002.

[27] ASTM. ASTM C1396 Standard specification for gypsum board. WestConshohocken (PA): American Society for Testing and Materials; 2006.

[28] Nedisan CD, Mastrogiuseppe S, Tremblay R, Rogers CA. Shear tests onHILTI nailed frame and screwed side-lap fasteners for 0.76 to 1.52 mmthick cold-formed sheet steel. Research report. Montreal (QC): Dept. ofCivil, Geo. and Mining Eng., Ecole Polytechnique; 2006.

[29] CSA. CSA-G40.20/G40.21 General requirements for rolled or weldedstructural quality steel/structural quality steel. Mississauga (ON):Canadian Standards Association; 2004.

[30] Rogers CA, Tremblay R. Inelastic seismic response of sidelap fastenersfor steel roof decks. ASCE Journal of Structural Engineering 2003;129(12):1637–46.

[31] Rogers CA, Tremblay R. Inelastic seismic response of frame fasteners forsteel roof decks. ASCE Journal of Structural Engineering 2003;129(12):1647–57.

[32] Steel Deck Institute (SDI) . Diaphragm design manual, 2nd ed. Canton(FL); 1991.

[33] CSA. CSA-S136 North American specification for the design of cold-formed steel structural members with the 2004 Supplement. Mississauga(ON): Canadian Standards Association; 2004.

[34] CSA. CSA-S16 Limit states design of steel structures with 2005Supplement. Mississauga (ON): Canadian Standards Association; 2005.

Inﬂuence of nonstructural components on roof...

Documents

Transcript of Inﬂuence of nonstructural components on roof...