Interaction equation values for wood truss compression chords considering the effects of partial composite action.

Transcription

1 Calhn: The NPS Instittinal Arhive Theses and Dissertatins Thesis Clletin 1991 Interatin eqatin vales fr wd trss mpressin hrds nsidering the effets f partial mpsite atin. Gibbns, Patrik Jseph Springfield, Virginia: Available frm Natinal Tehnial Infrmatin Servie

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10 INTRACTION QUATION VALUS FOR WOOD TRUSS COMPRSSION CHORDS CONSIDRING TH FFCTS OF PARTIAL COMPOSIT ACTION APPROVD:

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12 INTRACTION QUATION VALUS FOR WOOD TRUSS COMPRSSION CHORDS CONSIDRING TH FFCTS OF PARTIAL COMPOSIT ACTION By Patrik Jseph Gibbns, B.S. RPORT Presented t Dr. Dan L. Wheat and The University f Texas at Astin in Partial Flfillment f the Reqirements fr the Degree f MASTR OF SCINC IN NGINRING TH UNIVRSITY OF TXAS AT AUSTIN Deember 1991

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14 ACKNOWLDGMNTS First, I wld like t thank Dr. Dan L. Wheat fr his sggestin f this tpi, his willingness t listen t prblems and his assistane in wrking thrgh them. It was a rewarding learning experiene wrking n this stdy nder his spervisin. Mst imprtantly, I want t express my appreiatin and lve fr my wife Gina fr all her assistane in setting p the spreadsheets and inpt f the data, her help in previewing this wrk, and her lve and spprt while she ared fr r newbrn sn Clin and patiently waited while my mpletin gals kept slipping by. I an finally say that I am dne. in

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16 ABSTRACT INTRACTION QUATION VALUS FOR WOOD TRUSS COMPRSSION CHORDS CONSIDRING TH FFCTS OF PARTIAL COMPOSIT ACTION By PATRICK JOSPH GIBBONS SUPRVISING PROFSSOR: DAN L. WHAT A finite element, planar frame analysis is sed in this stdy t analyze tp hrd (mpsite) members f mmn trss whih have tw layers fastened by flexible nnetins. A parametri stdy was ndted sing the mpter prgram LTRUSS (Layered TRUSS) t determine the effets f wd sheathing n the tp hrd members f wd trsses. This stdy is direted at determining the apprpriateness f the 1986 Natinal Design Speifiatin fr Wd Cnstrtin eqatin whih allws fr beam-lmns t inrprate the effets f the attahed sheathing and t prvide infrmatin t allw fr a mre ratinal apprah t ant fr the sheathing. Reslts f this stdy shw that the rrent design prvisins d nt adeqately ant fr the redtin f stresses realized in the mpsite members. The theretially exat interatin eqatin fr the beam-lmns iv

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18 indiates that the lads allwed ld smetimes be as great as fr times what is rrently allwed. Additinally, reslts shw that trss span, nnetr spaing and stiffness, trss member dimensins, sheathing effetive area and mdls f elastiity, and trss pith all shld be inlded in any eqatin t adeqately represent the atal stiffness gained by the mpsite member.

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20 TABL OF CONTNTS INTRODUCTION Bakgrnd Objetive and Spe 1. Literatre Review 4 LAYRD BAM ANALYSIS Intrdtin Desriptin and Assmptins 6 2. Analysis Predre 8 PARAMTRIC STUDIS 12.1 Intrdtin 12.2 Reslts ffet f Trss Span n Sheathing ffetiveness fr Interatin qatin Vales ffet f Trss Pith n Sheathing ffetiveness fr Interatin qatin Vales ffet f Chrd Mdls f lastiity n Sheathing ffetiveness fr Interatin qatin Vales ffet f Sheathing Prperties n Sheathing ffetiveness fr Interatin qatin Vales 29 vi

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22 .2.5 ffet f Spaing f Sheathing Cnnetrs n Sheathing ffetiveness fr Interatin qatin Vales ffet f Trss Member Dimensins n Sheathing ffetiveness fr Interatin qatin Vales 0 SUMMARY AND CONCLUSIONS Smmary Cnlsins Remmendatins 62 BIBLIOGRAPHY 6 APPNDIX 64 vn

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24 Figre LIST OF FIGURS Page Fig. 2.1 Layered Beam lement 7 Fig. 2.2 Analysis f Trss Flw Chart 9 Fig..1 TRUSS 1 Fig..2 TRUSS 2 Fig.. TRUSS Fig..4 TRUSS 4 Fig..5 TRUSS 5 Fig..6 TRUSS Fig..7 Fig..8 Fig..9 Fig..10 Fig..11 Fig..12 FFCT OF TRUSS SPAN FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 2 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 2 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 4 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 4 viii

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26 Figre LIST OF FIGURS Pa ge Fig..1 Fig..14 Fig..15 Fig..16 Fig..17 Fig..18 Fig..19 Fig..20 Fig..21 Fig..22 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 5 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 5 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 6 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) 6 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 7 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 7 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 8 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 8 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 9 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) 9 ix

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28 Figre LIST OF FIGURS Page Fig..2 Fig..24 Fig..25 Fig..26 Fig..27 Fig..28 Fig..29 Fig..0 Fig..1 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 40 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 40 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 41 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 41 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 42 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) 42 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 4 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 4 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 44

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30 Figre LIST OF FIGURS Pa ge Fig..2 Fig.. Fig..4 Fig..5 Fig..6 Fig..7 Fig..8 Fig..9 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 44 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 45 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) 45 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 46 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 46 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 47 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 47 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 48 xi

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32 Figre LIST OF FIGURS Page Fig..40 Fig..41 Fig..42 Fig..4 Fig..44 Fig..45 Fig..46 Fig..47 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) 48 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 49 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 49 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 50 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 50 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 51 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) 51 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 52 xii

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34 Figre LIST OF FIGURS Page Fig..48 Fig..49 Fig..50 Fig..51 Fig..52 Fig..5 Fig..54 Fig. 4.1 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 52 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 5 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6) 5 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 54 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) 54 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 55 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) 55 IDNTIFICATION OF PARAMTRS WITH GRATST CONTRIBUTION TO CHANGS IN TH IV 60 Xlll

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36 CHAPTR 1 INTRODUCTION 1.1 Bakgrnd Light frame wd trsses are ne f the mst mmn strtral elements in the light frame market. A reasnable estimate wld say that ver 80 perent f all new residential nstrtin ses metal plate-nneted rf trsses[l]. Typially, these trsses are spaed either 16 in. r 24 in. n enter and they have spans whih are generally less than 50 feet. Attahed t the tp f the tp hrd f the trss, generally, is a sheathing layer whih is sed t transfer the lads t the trsses and t share in arrying sme f the lad. This sheathing is sally nailed t the tp hrd f the trss, whih prvides fr sme mpsite atin f the tw materials. Hwever, de t the fat that the sheathing and the tp hrd are nt rigidly nneted-bease f the finite stiffness f the nail in single shearthe sheathing and lmber annt be nsidered t be a mplete mpsite member. This inreases the diffilty in qantifying the inreased stiffness f the hrd member, and therefre the entire trss, de t the presene f the sheathing. One methd f anting fr the additinal stiffness prvided is the se f a bkling stiffness fatr, Cj-, whih is explained by the Natinal Design Speifiatin fr Wd Cnstrtin [5]. This fatr is applied t the mdls 1

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38 f elastiity,, in the allatin f the vale "K" (sed t determine whether a lmn is shrt, intermediate r lng) and the design mpressin stress parallel t the grain (F' ). One f the ritiisms f this fatr is its limited range f appliatin. It may nly be applied t visally graded 2x4 hrds whih have / 8 - in. thik r thiker plywd nailed diretly t the narrw fae f the hrd. Additinally, the member mst be sbjet t bth flexre and mpressin and dry nditins are essential. This fatr, ltimately, is sed t inrease the maximm allwable mpressive stress f the member, whih in trn, redes the vale fr the interatin eqatin sed t hek members that are in flexre and mpressin. Anther limitatin f the bkling stiffness fatr is its failre t ant fr the inflene f the sheathing n the flexral stresses felt by the member and what fatrs inrease r derease the effet that the sheathing has n the mpressive and flexral stresses. Thrgh the se f the planar frame mpter analysis prgram LTRUSS, whih inrprates a stiffness relatinship fr layered members with partial mpsite atin, an imprved nderstanding f the mpsite effets in the layered members may be realized. With a better nderstanding f the mpsite effets f layered members, a mre ratinal apprah t designing trsses may be fnd. This wld be a benefit nsidering the tremends se f light-frame wd trsses in the residential market as well as ther markets.

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40 1.2 Objetive and Spe The bjetive f this researh is t qantify the inflene f sheathing n the 1986 NDS design interatin eqatin vales fr tp hrd members f mmn wd trsses and t determine the apprpriateness f the rrent design prvisins. Stresses in wd trss members with sheathing attahed are determined thrgh se f an eight degree-f-freedm, ne dimensinal finite element. The element stiffness matrix fr these mpsite members was inrprated int the planar frame analysis prgram LTRUSS [4]. LTRUSS allated stresses fr eah trss stdied by way f tw separate analyses. The first analysis inlded the effet f the partial mpsite atin between the slid wd member and the sheathing, and the send analysis was a nventinal analysis nsidering the wd members nly. Frm the stresses allated by LTRUSS, the interatin eqatin fr beam-lmns was allated. This stdy shws the relatinship f the stresses present in the members and its relatinship t hw the design interatin eqatin vale is hanged. A ttal f six mmnly sed light-frame wd trss nfigratins were stdied while varying the span length, pith, material prperties, material sizes and nnetr spaing.

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42 1. Literatre Review A signifiant amnt f researh has been ndertaken in the past regarding the behavir f strtral systems inlding the effets f sheathing. Tw f these wrks dealt diretly with the linear analysis f wd trsses whih had sheathing attahed. These are Seif, Vanderbilt, and Gdman [7] and Warner and Wheat [8]. A brief verview f these tw wrks fllws. Seif, et al. attempted t develp an analytial predre fr analyzing planar metal plate-nneted trsses inlding the effets f the mpsite behavir f the layered members and the flexible behavir f the metal jints where the web members interset with the hrds. Fr the tw-layered mpsite members, an eight degree-f-freedm finite element was develped. Of these eight degrees f freedm, six were fr the slid wd: axial, transverse, and rtatinal displaements at eah end. Tw degrees f freedm were fr the axial displaement at eah end f the sheathing. This analysis predre divided eah member int between 12 and 21 elements and then sed stati ndensatin t btain a 6 x 6 member stiffness matrix. Frm Seif, et al. it was nlded that mpsite behavir had a ntieable effet n the maximm stresses and defletins fr several trss types. These reslts appeared t rrespnd in a favrable manner with previs experimental reslts, inlding that f Gdman [] and Newmark, et al. [6].

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44 The apprah by Warner and Wheat relied n the derivatin f the gverning differential eqatins fr tw-layered beams by Newmark, Siess, and Viest [6] by sing the methd f nsistent defrmatins t derive member stiffness matries as well as fixed-end atins fr tw-layered members. In this apprah there was n need t sbdivide the members int smaller elements, thereby eliminating the need fr stati ndensatin. Bilding pn these stdies, Jerrett [4] develped a mpter prgram LTRUSS (Layered TRUSS ) in rder t better nderstand the effets f sheathing n trss member stresses. These reslts nfirmed that plywd sheathing attahed t wd trss members reded the maximm axial and bending stresses in trss slid hrd members.

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46 CHAPTR 2 LAYRD BAM ANALYSIS 2.1 Intrdtin The analysis sed t determine the stresses in the member inlding the effets f sheathing was develped by Jerrett [4]. His prgram, LTRUSS, was develped t establish the differenes between the tensile, mpressive, and bending stresses fr bth nn-layered and layered analysis. The prgram was slightly mdified t prvide the tpt neessary fr this stdy. The mplete details f the stiffness matrix f the mpsite member whih is sed in this stdy is beynd the spe f this reprt. Hwever, the basi nderlying apprah as develped by Calixt and Wheat [2] has nt been hanged. 2.2 Desriptin and Assmptins If a tw-layered member f linear elasti material, in whih there is n mpsite atin, is sbjeted t bending, then the lwer fibers will lengthen and the tp fibers will shrten in eah layer. This lengthening and shrtening is linear within eah f the layers relative t its distane frm its respetive netral axis. If the same tw members fastened in sme manner, then interatin rs at the layer interfae whih inflenes the strains in the layers. The amnt f lengthening and shrtening in the tp and bttm layers then depends n the

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48 degree f mpsite atin, r the nnetr stiffness ating alng the layer interfae. As the nnetr stiffness inreases, slip f the fibers at the nnetin dereases and the hrizntal shear stresses inrease. If a nnetr stiffness f sffiient strength were determined t allw n slip at the interfae, then the member wld at as a mpsite member. Similarly, this interfae inflenes the atal stresses felt de t an axial lad. If partial mpsite atin is present between tw members, and nly ne member is nder an axial lad, the ther member will als nderg sme axial strain. The element whih is sed t mdel the trss members f this stdy is shwn in Fig This element has eight degrees f freedm (DOF), where DOF 1 and 5 are the axial DOF fr the sheathing; DOF 2,, and 4 are the axial, transverse, and rtatin DOF's fr the left end f the trss member, respetively; and DOF 6, 7, and 8 are the respetive axial, transverse and rtatin fr the right end f the trss member. Figre 2.1 shws all the degrees f freedm in the psitive diretin. C^.t a 6 "> Fig. 2.1 Layered Beam lement

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50 A mplete desriptin f the develpment f the stiffness matrix sed in this analysis is ntained in Calixt and Wheat [2] and will nt be detailed in this reprt. Hwever, the fllwing is a smmary f the assmptins made: (1) The lad defrmatin relatinship (r lad-slip relatinship) fr the nnetr was assmed t be linear. (2) The shear nnetin between the sheathing and the trss member is nsidered t be ntins alng the length f the member. () Plane setins remain plane within layers. (4) Bth layers are assmed t deflet eqally in the transverse diretin and defletins were finite. (5) Shear defrmatins are negleted. (6) Member jints are either mpletely rigid r pinned. (7) The fritin between the layers is disregarded. 2. Analysis Predre Cndting the analyses fr this stdy was a tw-step press. The first step sed the mpter prgram LTRUSS [4]. The send step tk the data reeived frm the LTRUSS analysis and thrgh the se f many spreadsheets allated the fr interatin eqatin vales fr eah analysis. A brief flw hart f the analysis is ntained n the fllwing tw pages.

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52 ANALYSIS OF TRUSS AND DTRMINATION OF INTRACTION QUATION VALUS Read Trss Cnfigratin Inpt Read Member Infrmatin Callate Member Lengths Divide Layered Members int 10 Segments and Re-nmber Ndes Start Analysis fr Given Trss Cnfigratin Are ffets f Sheathing t be Inlded? N Yes Set Sheathing Prperties t Cmpte Trss Stiffness Matrix Slve fr Ndal Displaements Callate Member Stresses Figre 2.2

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54 10 ANALYSIS OF TRUSS AND DTRMINATION OF INTRACTION QUATION VALUS(nt.) Cmpte Maximm Stresses in Original Trss Members Print Stresses in Original Members Print Stresses in ah Segment f Layered Members Callate the Length f Tp-Chrd Members Between Zer Mments Callate Allwable Stresses Callate Fr Vales fr Interatin qatin Cmpare Vales and Analyze Figre 2.2 (nt.)

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56 II The majrity f the steps shwn were part f the prgram LTRUSS. A detailed explanatin f LTRUSS is available elsewhere [4] and therefre will nt be made here. The majr item t nte fr this stdy frm LTRUSS is the divisin f all layered members int segments. Thrght this researh, layered members were sbdivided int ten segments (the nmber f segments may vary depending n the apability f the mpter y are wrking with). The prpse f this divisin was t allw the prgram t allate stresses at intermediate pints within the layered member. Then, the stresses within eah segment that made p a layered member were mpared, and the maximm axial and bending stresses were determined. These were the stresses sed t determine all f the interatin eqatin vales, with the exeptin f the "xat Maximm IV." T determine this vale, the stresses in eah segment f the layered member were tpt and these stresses were sed t allate an interatin eqatin vale at the eleven new ndes f the riginal layered member. The maximm vale frm these eleven ndes beame the "xat Maximm IV."

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58 CHAPTR PARAMTRIC STUDIS.1 Intrdtin The reslts f the entire stdy investigating the impat f nine variables n the effetiveness f the plywd sheathing n the trss members are set frth in this hapter. This effetiveness is presented in bth graphial and tablar frm and is shwn as a fatr f hw interatin eqatin vales are reded. The variables whih were investigated were: trss nfigratin, trss span, trss pith, trss member mdls f elastiity, sheathing dimensins, nnetr spaing, sheathing mdls f elastiity, and trss member dimensins. very attempt was made t selet a range fr eah variable s as t arately reflet trss prperties mmnly sed in the indstry. Trss nfigratin was nsidered by sing six separate mmnly-sed trsses and nsidering the effet n eah tp hrd member. The six different trss nfigratins are shwn in Fig..1 thrgh Fig..6. These figres shw nly half f the trss sine they are symmetri abt the vertial axis at the ridge. Member and nde nmbers are shwn. Panel pints were set eqally spaed alng the bttm and tp hrds. The span parameter nsidered the trss length and eah trss was analyzed fr lengths sh that the nmber f tp hrd members divided by the span was 5.0, 7.5, and Pith f the trss was 12

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60 1 DISPLACMNT FIXD IN TH VRTICAL DIRCTION ROTATIONS FIXD AND DISPLACMNTS FIXD IN TH HORIZONTAL DIRCTION Fig..1 TRUSS 1

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62 14 Fig..2 TRUSS 2 Fig.. TRUSS

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64 15 Fig..4 TRUSS 4 Fig..5 TRUSS 5

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66 Fig..6 TRUSS 6

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68 17 stdied by varying the slpe f the tp trss hrd between fr inhes per ft and twelve inhes per ft. The sheathing dimensin parameter was nsidered by varying the sheathing rss-setinal area and the effetive mment f inertia f the sheathing. The mdls f elastiity fr the sheathing and fr the trss members were nsidered separately as was the spaing f the sheathing nnetrs. Finally, the trss member dimensins were hanged t stdy its effet n the stiffness gained by the sheathing. Typially, the wd trss members analyzed were nsidered as standard nminal 2x4 members (1.5 inhes x.5 inhes) with the narrw fae attahed t the sheathing. Hwever, fr the last parameter, trss members were nsidered as 2 x 4, 2 x 6, and 2x8 nminal members. The lading fr eah trss was seleted as 0 pnds per linear ft ating vertially alng all tp hrd members. The mplete ategrizatin f the parameters stdied is shwn in Table.1. The trsses were mdeled as having ntins tp and bttm hrds. The tp hrd was mdeled as pin-nneted at the vertial spprt and at the peak. The bttm hrd was mdeled as pin-nneted at the vertial spprt als. Sheathing was nsidered t be ntins alng the tp hrd. The web members were nsidered as pin-jinted members attahed t the hrds. The spprts were nsidered in the vertial diretin at the ter ndes and in the

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70 18 2 ~r X r i x n T.= C C S - Ci/1 'r. C/ -r -T U 2 & CI - - IL >n < - < LU S -g 2 4 «2 -f O s g -s = I s. U- _ Q ' y. s, a ' XI ^ s -C 5 5 -r z < Ql, r l ^, ^,, in * <n " H?i ^ J ~ f ^h <N <«> ^ /) /. ^ r7 ) T <n C m h?i ^ in Q IT) i r^ tt 2 in n *. "1 ^ ^ "1 v CJ r*1 f- UJ aa < a: < > e a U d 60 <; M

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72 \ ( t t x X X S-.5 C t a - S 5 g r i _ s =. -ar Pi - 5? < C < UJ _ 2 UJ V. [*«~ s. s. ^ (/ JC f. ^ S r X s /". g T "X _ 5 -. > ^ s '-/ U i - y. t - ffl z < '/"< in "/" O >/". A O 1/1 w i/-, m v. U-, - i" j' < OS < ' = bfl 2 r ^ U > - s >^.5 t.«v. 8 1 UJ _ 'J. e y. =.a

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74 20 hrizntal diretin at ndes alng the enter line f the trss. Alng the enter line f the trss, the rtatins were als fixed t zer in the bttm hrd..2 Reslts In 1986 NDS design predres fr beam lmns, the gverning interatin eqatin nsists f an axial part and a flexral part. Members sbjeted t bth flexre and axial mpressin are prprtined by the eqatin: /e + /b < l. ( q-!) f; F b ' - j/ The terms in the abve eqatin are defined as: / -- the atal nit stress in mpressin parallel t grain inded by an axial lad, in pnds per sqare inh (psi). F ' - the design vale in mpressin parallel t grain, adjsted fr the l e /d rati, psi. / ~ the atal nit stress at extreme fiber in bending, psi. F b ' «the design vale fr extreme fiber in bending, adjsted by the slenderness fatr, psi. J ~ a nitless nveniene fatr defined as shwn belw: J = (le/d) - 11 K- 11 where K = the smallest slenderness rati (l e /d) at whih the lng lmn frmla applies fr determining the design vale in mpressin parallel t grain.

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76 21 Typial design f tp hrd trss members wld se the abve interatin eqatin fr determining the safe lads whih an be arried r the size r spaing f the trsses. The stresses sed in q. 1 (I) are sally determined negleting the additinal stiffness prvided by the sheathing. Then, sing these "witht sheathing" stresses, the 1986 Natinal Design Speifiatins fr Wd Cnstrtin (NDS) [5], allws an additinal stiffness fatr t be sed t ant fr the inreased strength prvided by the sheathing. This fatr, the bkling stiffness fatr, Cy, is a fatr f the mdls f elastiity,, and the effetive bkling length sed in the design f the tp fr mpressin lading. Cj is then mltiplied int the eqatins sed t determine F \ the design vale in mpressin parallel t grain. In Jerrett's wrk [4], the effets f the sheathing n the axial and flexral stresses in the hrd members were reprted. The reslts f this researh have inrprated the reded stresses, rrespnding t the inlsin f sheathing stiffness in the analysis, int the design interatin eqatin vale. ah trss was analyzed twie fr the given lad. The first analysis nsidered the prperties f the trss members alne, assming n sheathing was present; the send analysis inlded the effets f the sheathing. Frm the analytially-predited stresses btained frm the tw separate analyses, fr vales were allated fr the "Design Interatin qatin Vale."

77

78 22 The tablar reslts f this analysis are shwn in the Appendix in Tables A.1 thrgh A.6. In these tables the first Interatin qatin Vale (IV) was allated frm the analysis negleting sheathing. This vale was sed as the base vale t whih all ther allated vales were mpared. This was nsidered as the base vale bease this is the methd f trss analysis mst ften sed in design pratie [1]. The next Interatin qatin Vale mpted is referred t as the "IV Inlding se f Cp" This vale represents the vale f the interatin eqatin whih wld be derived sing the stresses allated negleting sheathing and then sing the allwed bkling stiffness fatr, C^, frm Setin.10.5 f Natinal Design Speifiatins fr Wd Cnstrtin [5]. Ths, this is rrently the vale given by the de t ant fr the stiffness gained with the sheathing. The third lmn f vales in the tables is the perent redtin in the interatin eqatin vale whih is realized by sing the rrent design predre. It shld be nted that this vale was allated fr all tp hrd members in rder t shw a mparisn vale, althgh sme f the hrd members d nt meet the speified reqirements fr the se f Cp The next lmn f vales in the tables is that f the vales fr the "IV frm Analysis Inlding Sheathing" whih nsidered the maximm stresses mpted fr eah member inlding the effets f sheathing. In this ase, the stresses determined inlding the sheathing were sbstitted int the same eqatin whih was sed in the witht sheathing ase. Additinally, this analysis

79

80 2 nsidered the atal effetive length, l, r the length between pints f zer mment. Therefre, the stresses effeted the reded vales as well as sing a mre exat analysis than that sed in the witht sheathing ase. The next lmn, then, is the perent redtin whih is btained when sing this interatin eqatin vale mpared t the first vale. The last tw lmns f the tables represents the "xat Maximm IV" and its perent redtin frm the vale assming n sheathing is present. The "xat Maximm IV" was allated frm the analysis whih nsidered the effets f the sheathing. Hwever, it is different frm the vales fr "Analysis Inlding Sheathing" bease it allates the vale fr the interatin eqatin based n axial and flexral stresses whih rrespnd t eah ther, r whih r at the same pint in the wd. This is alled the "xat" vale bease it is mpted t be the maximm after nsidering the stresses at eleven different latins alng eah tp hrd member. One the stresses at these eleven pints were identified, the interatin eqatin vale at eah latin was allated and the maximm vale is what is shwn in the table. Ths, the send t last lmn is the theretial exat interatin eqatin vale nsidering the effets f the sheathing, and the last lmn, therefre, is the perent redtin whih ld be fatred in with the vale negleting sheathing witht verstressing the wd.

81

82 24 All vales shwn are based n the same material prperties exept where a variane is shwn. Therefre, all analyses were perfrmed assming the member mdls f elastiity,, f 1,6,0 psi; extreme fiber stress in bending, F b = 14 psi; and F = 975 psi. These are vales befre nditins f se fatrs were applied. All nditins f se fatrs were nsidered t be 1.0 t simplify the allatins. The tablar reslts f this analysis are shwn in the Appendix in Tables A.l thrgh A.7. In additin t the reslts in tablar frm, they are als presented in graphial frm at the end f this hapter. These graphs mpare the hange in the interatin eqatin vales, fr the "IV Inlding the se f C^," the TV frm Analysis Inlding Sheathing," and the "xat Maximm IV" frm the analysis in whih sheathing is ignred. Fr eah trss ne member was seleted as being representative f the entire tp hrd and is sed in the fllwing graphs. The series f graphs presents the effets f eah f the parameters stdied. The term "sheathing effetiveness," whih appears in eah figre, refers t the perent redtin in the interatin eqatin vales de t the inlsin f the sheathing in the analysis. The vales n the vertial axis f the graph are the varis interatin eqatin vales divided by the base vale (r the vale fr the ase negleting sheathing). A vale f 1. represents a ase where n redtin in the interatin eqatin vale reslted frm the indiated analysis.

83

84 Interatin 25 Figre.18, belw shws the effet f trss pith n the sheathing effetiveness fr member nmber 1 f trss type 6. This figre shws the typial reslts f this researh. The dtted line, "Cde Vale" Vales Sheathing qatin fr Cde Vale Vale Negleted > - ^_ -- -f a W/ Sheathing the > xat Vale by Design Divided i l 2 Pith/12 Fig..18 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) represents the sheathing effetiveness allwed by the NDS prvisins. As with almst all trsses and parameters, this vale was nsiderably less than the ther tw sheathing effetiveness vales with the slid line "xat Vale" representing the theretial maximm vale fr the interatin eqatin fr the given lading nditins. The spread f the "Cde Vale" line (whih ses the term Cj) frm

85

86 26 the ther tw lines indiates that the de des nt d an adeqate jb in flly regnizing the sheathing whih is atally present..2.1 ffet f Trss Span n Sheathing ffetiveness fr Interatin qatin Vales Typially, the effet f the sheathing was t derease the vale fr the interatin eqatin vale as the span inreased (Figs..7 t.12). The lne exeptin t this ase is Trss 1, whih had higher vales fr the interatin eqatin at the lngest span fr bth the "W/ Sheathing" and "xat Vale." This rare instane f the vales inreasing is attribted t tw fatrs. Primarily, it is de t the fat that the mpressive stresses in the member inreased by a fatr f fr de t inlding sheathing in the analysis and the sendary fatr is that, as there is nly ne tp hrd member and it was mdeled as pinned at bth ends, there was n redtin f the effetive length t be inlded in the "W/ Sheathing" r "xat Vale" allatins. As disssed abve, the "W/ Sheathing" and "xat Vale" eqatins have taken int ant the atal effetive length, l e, f the member. Therefre, it wld be expeted that the tw middle hrds f Trss 6, members 12 and 1, wld be affeted the mst by the sheathing. This is evident in Fig..12 whih shws a sheathing effetiveness, fr member 1, f 55 perent fr the span/panel

87

88 27 rati f 10. Similarly, frm Table A.7 it an be seen that fr member 12 the sheathing effetiveness is 58 perent. This is primarily de t the fat that these are members that have negative mment at eah end and therefre have the greatest redtin in the l e /d rati de t the shrter span between zer mments. It an als be seen frm mparing Fig..8 with Fig..10 and Fig..9 with Fig..11 that the trss type is nly a signifiant fatr based n hw it ntribtes t the span. Ths, althgh trsses 2 and 4 are different, the sheathing effetiveness f the tw is very similar. Therefre, the nly inflene that trss type has n the vales is that the larger spanning trsses have greater sheathing effetiveness and the trsses whih have members with negative mments at eah end als have greater sheathing effetiveness. In general, it an be seen frm Figs..7 thrgh.12 that inreasing the span is a signifiant ntribtr t reding the interatin eqatin vales de t the effet f sheathing. It an als be seen that the eqatin in the de has made that rrelatin; hwever, it has nt mathed the magnitde f the gain whih is atally realized.

89

90 ffet f Trss Pith n Sheathing ffetiveness fr Interatin qatin Vales Figres.1 thrgh.18 indiate that the pith f the trss des nt have a great impat n the sheathing effetiveness. Typially, the vales fr the eqatins are slightly less fr the higher pith, mstly de t the inrease in the length f the members. As the graphs are very nearly straight, there is nt mh gain de t added sheathing stiffness. Hwever, frm these figres it an be seen that there is signifiant rm fr imprvement in the de eqatin. Figres.15 and.17 (Trsses and 5) reflet very nstant relatinships between the three vales pltted with the "xat Vale" being between 1 and 15 perent less than the "Cde Vale"..2. ffet f Chrd Mdls f lastiity n Sheathing ffetiveness fr Interatin qatin Vales As with the trss pith, Figs..19 thrgh.24 als shw that variatins in the mdls f elastiity f the hrd members des nt have a signifiant effet n the vale f the interatin eqatin. The impat is very slight, hwever, it shld be nted that stiffer members, with inreased mdls f elastiity, will reslt in lwer vales fr the sheathing effetiveness. This is as wld be expeted as the effet f the sheathing wld ntribte the same stiffness gain hwever its effet is less n a stiffer member.

91

92 29 Again, it an be seen that the "Cde Vale" lags nsiderably behind the theretial maximm vales and ths an be imprved..2.4 ffet f Sheathing Prperties n Sheathing ffetiveness fr Interatin qatin Vales The hange in sheathing effetiveness de t the variatin in sheathing prperties was als very lw. Hwever, it shld be nted that there were sme differenes in the hanges with variatins in the different prperties. The variatin f the area f the sheathing (Figs..25 t.0) shwed almst n effet n trss 1 bt shwed a mh greater hange in trss 6. This is de t the fat that the lnger spans develp larger strains and slips whih are neessary t develp larger fres in the sheathing. Trsses 2,, 4, and 5 shw effetiveness between thse f trss 1 and trss 6. The mment f inertia f the sheathing, hwever, shws almst n hange in sheathing effetiveness de t a variatin f the parameter (Figs..1 t.6). Of the three sheathing variables, this is the least signifiant. The last parameter f the sheathing, its mdls f elastiity, had a sheathing effetiveness smewhere between that f the sheathing area and the mment f inertia (Figs..7 t.42). ffetiveness was smallest fr trss 1 and was larger fr the lnger span trsses. This fat is mstly attribted t the fat that the stiffer sheathing (higher ) develps higher fres and mments fr a

93

94 0 given strain, and the lnger spans have larger differential displaements de t strains..2.5 ffet f Spaing f Sheathing Cnnetrs n Sheathing ffetiveness fr Interatin qatin Vales Cnnetr spaing had a large impat n the sheathing effetiveness Figs..4 t.48). Clser spaing dereased the stresses in the wd members and therefre dereased the interatin eqatin vales. This parameter is an imprtant vale t inlde sine either a derease in the nnetr spaing r an inrease in nnetin stiffness will ase the layered member t respnd mre like a mpsite member. This effet will inrease the stresses in the sheathing and the layer interfae and ase the interatin eqatin vales t derease..2.6 ffet f Trss Member Dimensins n Sheathing ffetiveness fr Interatin qatin Vales Als as expeted, the member dimensins had a signifiant impat n the sheathing effetiveness. The prpse f stdying the effets f this parameter was t investigate whether r nt an appreiable effetiveness wld be felt by the larger members, nt t shw that the inreased member dimensins wld rede the sheathing effetiveness.

95

96 1 Figres.49 thgh.54 learly shw that the effetiveness is reded in the 2 x 6 and 2x8 members. Hwever, there is still sme effetiveness felt by the members, as mh as 25 perent in a 2 x 6 and 18 perent in a 2 x 8 (vales fr trss 6). Therefre, the de prvisin, whih limits the bkling stiffness fatr t nly 2x4 members, neglets a signifiant amnt f sheathing effetiveness.

97

98 2 L.2 Jl at. r. -CZ CO > CO QJ zz x: rs CO O s ^ ^: a; _^ ar j QJ -7»- CO -il l O >1 zz JC ^ z Cde Vale W/ Sheathing xat Vale OL -a > zz Q H Span/# f Tp Panels ( ft. Fig..7 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) 1 C/2 &C CD %>- e,<-! en / fr qal e QJ 0.6 i 0) OS an 0) _> < z 0.4 ZD r CO _ =.1 t nter by r- "O /q -S CD.2 C! C 0.1 <> Cde Vale " - W/ Sheathing xat Vale Span/# f Tp Panels ( ft. ) Fig..8 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

99

100 r VI 01 G 0.9 r, > CJ B JB O OT 0.8 r -J r aj 0J =i O B aj 1)./ > m a; LJ OJ -?- r -C l_ 0! >i B - B B4U v\ > 01 C-. C 6 1)5.-<> ' Cde Vale - W/ Sheathing xat Vale Span/# f Tp Panels ( ft. Fig..9 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 0.9 B -C zn 0.8 g ««0.7 QJ ^ 0.6!^ "... -^ :*h Cde Vale W/ Sheathing xat Vale qj.2 Q Q Span/# f Tp Panels ( ft. Fig..10 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5)

101

102 Interatin! 1 4 i- Vales vo. Sheathing *». qatin fr " " Cde Vale Vale Negleted --J "» _ ~~ ~~ ~~ ~~ W/ Sheathing the by p O On ^**"*'* xat Vale Design Divided O l/i p j^ i Span/# f Tp Panels ( ft. Fig..11 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) t/i QJ CU). _ 0.9 CO _> > CO QJ G JS O rn 0.8 qati fr ^ e >. (I / O0 CI O <& T»- _C CO 1 J >, 0.6 C -Q " Cde Vale W/ Sheathing xat Vale 5. j 2 - <v.2 =i Span/# f Tp Panels ( ft. Fig..12 FFCT OF TRUSS SPAN ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1)

103

104 Interatin 5 i ^J I Vales Sheathing b > " -" "*" - #- ' ~~ qatin fr * Cde Vale Vale Negleted pp W/ Sheathing the «xat Vale by t Design Divided Pith/12 Fig..1 FFCT OF TRUSS PrTCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) in CJ. r CT > CO CJ : r/ CD CO - i_ QJ >-, C JS C CJ CUJ - / 01 > 1= Q 0.8 = rr T 0.6 J QJ CJ CJ C 5* CO QJ Q QJ CJ OJ z r -t-- " Cde Vale W/ Sheathing xat Vale Pith/ 12 Fig..14 FFCT OF TRUSS PrTCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

105

106 6 w r C CJ -: -C tr. S> CO -1= T: s- B CJ _- a CJ CO -J* a> a a; CJ CJ "T" CO 45 1 CJ >-, jj -a.^y~z Cde Vale W/ Sheathing xat Vale =l =: Pith/ 12 Fig..15 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) t/i CJ r -C CO > CO CJ C -C O r/ CO 0.8 -= r CJ CJ <-- "... -» Cde Vale -j C J > CO CJ r, a; CJ CO x: y t- CJ =>^ JO e -a CJ QJJ - CJ > C-2 O W/ Sheathing xat Vale Pith/12 Fig..16 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5)

107

108 Interatin 7 C C/ r OJ x: CO > -C r /~. CT = a 0.6 OJ C J ea ^» en 09 v -C ;j >, -O "0 S at O -CT > ea ^ Cde Vale W/ Sheathing xat Vale Pith/12 Fig..17 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 1 _ Vales Sheathing > qatin fr Vale Negleted» - m~ Qxle Vale W/ Sheathing the xat Vale by Design Divided I l 2 Pith/12 Fig..18 FFCT OF TRUSS PITCH ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1)

109

110 8 1 QXD "B < 8 - < r -2 >. CJ. a-1 ~. _ z 0.4 ' * " " Cde Vale W/ Sheathing xat Vale - - > CJ CO -g n? - ii L.8 Chrd Mdls Of lastiity (thsand ksi) Fig..19 FFCT OF CHORD MODULUS OF LASTICITY ON FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) SHATHING ir. 0J r, B.fi > 0 CJ B.6 r/2 CO r OJ Cj _; 5 ' B? > QJ",,:- CJ CJ -pr -C QJ >1 B XJ * ' Cde Vale " - W/ Sheathing xat Vale e= OJ.S^- a a Chrd Mdls Of lastiity (thsand ksi) Fig..20 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

111

112 9 r J-. 0! C.J_ CO > CC CJ e _C rn O rr- a OJ B B > Qj RS _C 1- C1J :>-. -O B a x. a CO 01 > C2 a 0.8 -a 0.6 QJ z " " " Cde Vale " W/ Sheathing "xat Vale l 6 l.k Chrd Mdls Of lastiity (thsand ksi) Fig..21 FFCT OF CHORD MODULUS OF LASTICITY ON FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) SHATHING n CO 01 ~i - r > 0 CJ B -C O CO - ^ 0J QJ _J CJ B > S n ij CJ QJ T^ CO J 1 0J >, _ B ^ QJ x, T CO > CJ _: C »- - * " Cde Vale - W/ Sheathing xat Vale Chrd Mdls Of lastiity (thsand ksi) Fig..22 FFCT OF CHORD MODULUS OF LASTICITY ON FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5) SHATHING

113

114 Interatin Interatin 40 1 i Vales Sheathing 0.8, qatin fr < 0.6 ' - t < > i Cde Vale Vale Negleted W/ Sheathing the xat Vale by 0.2 Design Divided IK Chrd Mdls Of lastiity (thsand ksi) Fig..2 FFCT OF CHORD MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) Vales Sheathing p > qatin fr Cde Vale C>. 1 > Vale Negleted - W/ Sheathing the by * " xat Vale N> Design Divided O Chrd Mdls Of lastiity (thsand ksi) Fig..24 FFCT OF CHORD MODULUS OF LASTICITY ON FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1) SHATHING

115

116 1 41 < n -s «-i 0.8 >. _~~ i CO &a aqj = qj > QO -*». QJ 2 z: 0.4 i -2 >. - - _ -a 0.2 O Q» * Cde Vale - W/ Sheathing xat Vale 4 Area f Sheathing (in 2 ) Fig..25 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) Ctf) QJ xz ea > UK S> QJ -C O CO «* viz PJ QJ QJ C ).IS QJ : 0.6 C.J QJ QJ xs ===: 0.4 i_ OJ. j >^ C X> _ B - a; 0.2 q -re QJ.2 C2 Q "-.»--> " Cde Vale W/ Sheathing xat Vale 4 Area f Sheathing (in 2 ) Fig..26 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

117

118 1 42 m Cf 01 B -C r. > B x: r/-, re r i "CJ QJ QJ _ C J B C QJ >> M) O CJ Q; ^r 1 Gj JS >-l B, B CiL T >. r^ " " " Cde Vale - W/ Sheathing xat Vale 4 Area f Sheathing (in 2 ) Fig..27 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) S B r QJ B ^ CJ OX). T Q CJ s- T 09 x: ^ CJ n r < < " " " Cde Vale - - W/ Sheathing xat Vale 4 Area f Sheathing (in 2 ) Fig..28 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5)

119

120 r- " a <U JS CO UK S» «OJ B JS fr qal ^ 0.6 e! = C J QJ m a; _ 2Z 0.4 i_ OJ -J >> C -O " " " Cde Vale " W/ Sheathing xat Vale QJ.2 C2 C2 4 Area f Sheathing (in 2 ) Fig..29 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) W &0 QJ 6 > JS CO (IK > CO < 1= J= 1 -n 06 ;.11 a/i O QJ t 4>. j >-. a> CO JS z. 0.4 C -Q _ - / 'C.2: Q Q 0.2 Cde Vale W/ Sheathing xat Vale 4 Area f Sheathing (in 2 ) Fig..0 FFCT OF TRUSS SHATHING ARA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1)

121

122 44 ^ Qf G p xz CO > CO C -C rn t r a 0.6 9J CJ 5> r QJ1 q; a ^- re -C i- QJ >-, C -O aj bl) T a; > Q a )4 0.2 Cde Vale W/ Sheathing xat Vale Sheathing Mment f Inertia (in 4 ) Fig..1 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) t/5 r CJ = rn > r J -C O W re X r j r > tan CO CJ r^ 7^ r - i >1 C _ 2 -a.s-' ' >» II «* HI " * Cde Vale W/ Sheathing xat Vale Sheathing Mment f Inertia (in 4 ) Fig..2 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

123

124 ! 1 I 1 45 ClC 1)8 T=J Cde Vale - W/ Sheathing _g Z 0.4 xat Vale t aj Q >-, a -a > Sheathing Mment f Inertia (in ) Fig.. FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) 1 in x) sy.s O CO 1 -i DA i 1 QJ O QJ a QJ O QJ 5S 01 t. >> _ - _ - QJD-5 n? - QJ.5 O Q " * Cde Vale - W/ Sheathing " xat Vale Sheathing Mment f Inertia (in ) Fig..4 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5)

125

126 VI OJ at) CO > CO 0J B - Z r/i - t rr QtZ a ' CJ > 0 CJ CO x: t_ OJ >1 B -O B T Cl6 ~ > IIS 0.6 aj OJ 5b » - ' it- «* H " Cde Vale _ W/ Sheathing xat Vale Sheathing Mment f Inertia (in ) Fig..5 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) 1 C/ QJ C =. OJ 1= J= zn 0 _C. >s 0.8 _2 ( n ID P*" 4 < Cde Vale W/ Sheathing xat Vale._ "O n? Sheathing Mment f Inertia (in 4 ) Fig..6 FFCT OF TRUSS SHATHING MOMNT OF INRTIA ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1)

127

128 47 CI (= - C 0.8 ^ - n 1 ' =. C7-' B O = CO _zi > OX) z 0.4 <i» > Cde Vale W/ Sheathing xat Vale n QJ O) > Q r Sheathing Mdls f lastiity (thsand ksi) Fig..7 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) CX G 0.8 *+^- er' Ci qj "? 0.6 Cde Vale CO, 04 W/ Sheathing xat Vale a «-> '58?2 CD > s Sheathing Mdls f lastiity (thsand ksi) Fig..8 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

129

130 ' ^ < 0 >-. CT" a t OJ re QJ " n f, - 11 Cde Vale W/ Sheathing xat Vale S OJ 5 ^ O) > n? - n 1. \ Sheathing Mdls f lastiity (thsand ksi) Fig..9 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) &0 _C > re C / m i- -> rr- *~~ - &J aj QJ Z C re >> OX) re OJ e -a ClD < en - j > r~i n 8 < ( ' U. n r - n 4 n? - - Cde Vale W/ Sheathing xat Vale Sheathing Mdls f lastiity (thsand ksi) Fig..40 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5)

131

132 Interatin 49 8 <.2 0T a «- = r.. O CO IS =* t,- CD ~^ QJ CD t». > ' Cde Vale W/ Sheathing xat Vale <= "P BUD <f> 5 72 QJ > n 7 n J i <; Sheathing Mdls f lastiity (thsand ksi) Fig..41 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) i, Vale Sheathing qatin fr Cde Vale < Vale Negleted 1 > W/ Sheathing the 0.4 xat Vale by 0.2 Design Divided Sheathing Mdls f lastiity (thsand ksi) Fig..42 FFCT OF TRUSS SHATHING MODULUS OF LASTICITY ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1

133

134 Interatin ' 50 b -: =* ^ aj C - Cf e t- r 11 W 0) n^ O aj _ >>, 1.a = T Cjf 0J TJ w > Cde Vale W/ Sheathing xat Vale 12 Nail Spaing (in.) Fig..4 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) Vale Sheathing qatin fr i Cde Vale Vale Negleted W/ Sheathing the xat Vale by Design Divided Nail Spaing (in.) Fig..44 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

135

136 ! s> 51 i -t QjO.S 0.8 CO S_ 1 O *" CT- T 0.6 U CJ O CJ CO [_ 0) ^ -Q U CJ : OJ CJ = -a r CJ T5 CJ > C^ i i Cde Vale W/ Sheathing xat Vale 12 Nail Spaing (in.) Fig..45 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) " " Cde Vale W/ Sheathing xat Vale Nail Spaing (in.) Fig..46 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5)

137

138 ' Interatin!- 52 x fl) ;_.1= > ^ QJ B C 0.8,, «-«n T 0.6 (0 S- -1 Q rr- -a W QJ Cv C R C J M a; -J* Q CJ a) CJ " -J >^ -O B - r OJ T-! CJ > O a * - " Cde Vale " - W/ Sheathing ~ f xat Vale 12 Nail Spaing (in.) Fig..47 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 10) Vale Sheathing qatin fr C* i Cde Vale Vale Negleted >- W/ Sheathing the by *. xat Vale Design Divided k) I Nail Spaing (in.) Fig..48 FFCT OF SPACING OF SHATHING CONNCTORS ON TH SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1)

139

140 5 too a> -C > CO CD B -C zn _j UK fr qal e aj.1 an j qj t- QJ < >-> QJ 0.6 JS z: 0.4 B -O _ T B QJ 0.2 OJ.2 " Cde Vale W/ Sheathing xat Vale Chrd Depth (inhes) Fig..49 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 1, MMBR ) OD QJ ;- -C CO J IIH >> CO QJ B j=. zn fr qal e CJ C I.1 OX) 0) QJ O 0.6 CO JC I- -_) QJ > ^ C -O r- B "C qj QJ " " Cde Vale W/ Sheathing xat Vale Chrd Depth (inhes) Fig..50 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 2, MMBR 6)

141

142 54 e QJ B C CO > CO B.C r/2 ~CO TUO 0.6 ' Cde Vale CO S> sa CJ aj ;=» CO - l_ 0! >s B _ B ^ QJ - 0) > Q Ci W/ Sheathing xat Vale Chrd Depth (inhes) Fig..51 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS, MMBR 11) e) QJ B ' ra -j UK > CO > B _C O CO fr qat e B.11 aj Oil QJ < 0.6 z CO JB 0.4 i- _j > J >-. C -O Cde Vale - W/ Sheathing xat Vale Q Q Chrd Depth (inhes) Fig..52 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 4, MMBR 5)

143

144 55 " n = r 5. T 0.6 * " " Cde Vale.2 > Q O QJ t X i_ QJ J >-, - - ^ QJ qjd-5 a>.5; Q Q W/ Sheathing xat Vale Chrd Depth (inhes) Fig..5 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 5, MMBR 1) QJ QJ - ZS _C CO _> UK > t QJ C X5 O GO fr qal ^ 0.6 e _J C ) QJ a/) 0) j _e z: 0.4 i _> 0) j >-^ C -O Cde Vale W/ Sheathing xat Vale t QJ =< QJ.S O Q Chrd Depth (inhes) Fig..54 FFCT OF TRUSS MMBR DIMNSIONS ON SHATHING FFCTIVNSS FOR INTRACTION QUATION VALUS (TRUSS 6, MMBR 1)