Restraint of purlins for various roof systems

Transcription

1 NS009 Restrint of purlins for vrious roof systems T. Vrny, M. Brhm & A. Beli ulty of ivil Engineering, zeh Tehnil University, Prh, zehi Astron Buildings S.A., Diekirh, Luxemourg, A memer of the Lind Group ABSTRAT: In the nlysis of the old formed purlins the stilising effet of the onneted old formed sheeting must e inevitly onsidered. This effet is represented y the sher nd rottionl restrints. Extensive experimentl nd theoretil reserh ws rried out to determine the rottionl nd lterl restrints of the purlins in Astron roof systems. In ddition to the typil roofs with the sheeting srewed down diretly to the purlins, the sper systems with rkets nd rils nd the stnding sem pnels with the frition free therml expnsion joints were nlysed. Doule skin roofs were studied s well. Due to the presene of the sper elements in those systems nd due to the disrete onnetions etween the purlin nd the sheeting, their ehviour is more omplited thn the ehviour of the trditionl roofs. The methodology of the nlysis is presented. The method of omponents is pplied, the pproprite stiffness of individul roof omponents is determined using either experiments or nlytil solution. Generl method nlysing the effet of the purlin lod on the rottionl restrints is presented. It is sed on the study of the ontt fores etween the purlins nd roof elements nd is verified y experiments. INTRODUTION This pper refers to the extensive reserh projet foused on the determintion of the rottionl nd sher restrints for Astron roofs nd wlls with purlins. Projet hs een rried out in severl wves. The roof systems were tested in 007 nd 008, the wll system tests re ongoing. This pper presents results of the roof systems nd is foussed on the most interesting nd so fr not pulished topis. Two stiffness prmeters, nmely the rottionl stiffness D nd the sher stiffness of the roof diphrgm S were investigted for the eh roof type. Rottionl stiffness D is defined s torsion moment relted to the top flnge of the purlin developing the unit rottion of flnge. Its unit is Nm/m/rd. Sher stiffness S is defined s lterl fore developing the unit lterl displement of purlin unit length. Its unit is N/m/m. EXAMINED ROO TYPES Lrge vriety of the exmined roof systems were grouped ording to similrity of their ehviour into four tegories: RT: Roof type is the si roof with the orrugted sheeting srewed down to the purlin diretly or through the insultion from minerl wool nd/or the polyurethne isolok, see igure ). RT: Roof type is the roof with the stnding sem sheeting hving therml expnsion lips srewed down to the purlin, see igure ). 4

2 RT3: Roof type 3 is the doule skin roof with the sper system, omeg shped spers nd rils. Inner skin is done from the orrugted sheeting nd outer skin either from the orrugted sheeting (RT3, see igure e), or from the stnding sem sheeting with therml expnsion lips (RT3). RT4: Roof type 4 is the single skin roof, with the sper system ontining ridge rkets nd ridge rils, hving the outside skin either from the orrugted sheeting (RT4), or from the stnding sem sheeting with the therml expnsion lips (RT4), see igure ), d). ) Isolok ) Ril Bridge rket ) Isolok d) Pnel lip Pnel lip Bridge rket Used sheeting: e) or LPR Omeg ril Omeg rket ousti, or LMR600 LINER igure. Anlysed roof types. 3 ROTATIONAL RESTRAINT 3. Sope of work, tests In order to determine the rottionl restrints of the vrious roof systems 9 tests using 74 different speimens were done. Severl speimens were used times to investigte the rottionl restrints in two opposite diretions of the lterl loding. Testing proedure omplied with the EN provisions. Lods were introdued y the loding jk or y the weights. Exmples of test speimens re shown in igure nd igure 3. In ddition to the stndrd tests, 9 tests were done to simulte the influene of the diret loding on the purlin. These tests re desried in prgrph

3 igure. Tests of rottionl restrint of srewed-down roofs ording to igure ). ) ) igure 3. Tests of rottionl restrint of sper system roofs ) Prtil test, ) Whole roof test. 3. Methodology of nlysis The rottionl restrint D for eh RT test n e determined from the eqution (0.8) of EN nd the expression KB for the purlin stiffness is modified for ses, when the defletion mesurement point or the lod pplition point is not in the plne of the free flnge: E t 3 lb KB 4 ( -ν h ) Δ ( 3 h - hδ ) mod h hδ () where: hδ is the distne etween the defletion mesurement point nd inner fe of the sheeting nd h is the distne etween the lod pplition point nd inner fe of the sheeting. 44

4 The sttistil evlution ws done for eh roof vrint. Due to the reltively lrge stter of results, the tests were grouped. ollowing proedure ws pplied for eh group hving the sme sheeting nd insultion, ut the different purlin type. The rottionl flexiility (/ D ) onsists of the lol flexiility of the top flnge of the purlin φ nd the lol flexiility of the sheeting φ s (involving lso the effet of the insultion): - φ φ D s The flex iility φ for the speifi purlin n e found using the method desried in Vrný (00). Its priniple is illustrted on igure 4. The rottionl flexiility of the onnetion is used y the mutul vertil displement δ of the ompression ontt line nd the line of srews. () sheeting K D M δ φ φ purlin igure 4. Purlin-sheeting ontt re - model of ehvior. rom the igure 4 follows: D K D (3) φ where p δ K D (4) δ p is the pith of fsteners long the purlin length nd is the lol defletion of the top flnge of the purlin in the point of fstener due to the unit fore; using Vrný (00): 4 δ 8, 8 0 [mm/kn] (5) 3 t defined in igure 4 nd t is the purlin sheet thikness. The flexiility φ s is then determined for eh test nd sttistilly evluted for the whole group. The totl stiffness of the sper roof systems RT3 nd RT4 n e determined y the omponent method. In se of RT4 (single skin roof with rkets nd rils) the prtil stiffness ws determined for different levels. Two proedures were pplied: lterl defletion ws mesured t two different depth levels of the purlin, see igure 3), to otin two test vlues for two unknown rottions, prtil tests without purlins were exeuted, see igure 3); the flexiility of the purlin-rket onnetion ws exluded from the results of these tests. Both, rket spers nd the therml expnsion lips were onsidered s rigid odies. Then the stiffness t eh level of the roof ws determined s: where: h Δ h δ D( AB) M h φ δ h Δ is the distne etween the defletion mesurement nd inner surfe of the sheeting, is the distne etween the lod pplition nd inner fe of the sheeting, is pplied fore nd is mesured lterl defletion. 45 (6)

5 Distortion of the ril, whih depends non-linerly on the mutul positions of the rket spers nd the therml expnsion lips, ws determined y the numeril nlysis. Then the finl rottionl stiffness ws lulted s: D l lip D( A ) D( B ) l rket D( B ) l rket D( ) where D(A) is the rottionl stiffness of the therml expnsion lips nd sheeting ontt, D(B) is the rottionl stiffness orresponding to the ril distortion, D(B) is the rottionl stiffness of the therml expnsion lip, ril nd the rket ontt, D() is the rottionl stiffness of the rket nd purlin ontt, l lip is the distne of the therml expnsion lips nd l rket is the distne of the ridge rkets. or the RT3, the doule skin roof ording to igure e), the totl stiffness is given s sum of the outer roof system D, stiffness (ording to eqution (7)) nd the inner skin stiffness D, : (8) D D, D, (7) 3.3 Effet of purlin lod The torsion moment relted to the purlin-sheeting onnetion is used y the externl purlin lod. The rtio of the lterl lod produing torsion nd the purlin externl lod, depends exlusively on the ross-setion of the purlin. Aording to igure 5, tg α q z /q k h. In order to determine the effet of the purlin externl lod on the rottionl stiffness D, the originl test rrngement ws proposed. The inlined lod with the given ngle α ws pplied to the free flnge, see igure 5. Both grvity nd uplift loding were simulted in this wy. The tests were exeuted on the sme speimens s the stndrd tests. In the serhed rtio k q D / D,0, D represents the stiffness due to the lterl lod omponent from test omprising the lod effet nd D,0 represents the stiffness from stndrd test. igure 5. Tests overing the effet of externl purlin lod sheme, test to simulte grvity lod. or the RT (srewed down roof) the grvity loding ws simulted in 7 tests nd the uplift loding in tests. In the 5 of 7 grvity lod tests, the rehed flexiility ws smller thn the flexiility due to purlin deformtion /K B. In suh se the D nnot e determined, euse the flexiility / D is negtive. This orresponds well with the theoretil nlysis of Vrný (005). In the remining tests the grvity lod showed the inrese of the D (k q,4 nd 5,38 respetively). Despite the generl expettion with the tests representing the uplift loding, 8 tests of showed the k q >. 46

6 The nlytil method (Vrný (005)) determining the effet of the lod on D for purlins, whih is sed on the moment equilirium onditions in the purlin-sheeting re, n e pplied lso for the sper systems RT3 nd RT4, where one hs to determine the vlues of k q seprtely for the rilsheeting onnetion (the rottionl stiffness t this level is denominted s D(A) ) nd for the sperpurlin onnetion (the rottionl stiffness t this level is denominted s D() ). h h,a, rket Plne of restrint D(A) Plne of restrint D() Point of ompression ontt α H V α V H igure 6. Model of determintion of the effet of externl lod for RT4 (single skin sper system roof). In se of the RT4 (single skin roof system with the ridge spers nd rils), the moment t the point of the ompression ontt of the ril-sheeting onnetion for uplift lod is (see igure 6): H ( h h ) ( ) M (9) V Rtio of the moment M to the one due to the lterl lod only: H h h V,A tg α h h k q( A) H ( h h ) tg α h h,a ( ) ( ) ( ) (,A ) ( ) The moment to the ompression ontt of the ridge sper with the purlin for uplift lod: H V ( ), (0) M h () Rtio of this moment to the one due to lterl lod only (relevnt for the rottionl stiffness D() ): kq( ) H h V H ( ) tg α h ( ) h, tg α h In se of the RT4 (single skin sper system with orrugted sheeting, see igure ), 4 tests were done simulting the grvity loding nd 3 tests simulting the uplift loding. The grvity lod showed smller flexiility thn the flexiility due to the purlin deformtion in ll tests (similr ehviour s oserved in the most RT grvity tests). The uplift loding led to the inrese of the rottionl stiffness. The test results nd omprison with the lultion re shown in Tle. ompred vlues re: - the flexiility δ exp /K exp from the test with the uplift lod, - the flexiility δ th lulted from the stndrd test using the.m. theoretil proedure: ( h h ) ( h h ), () hδ h Δ δ th (3) K B kq( A) D( A ), 0 kq( ) D( ), 0 Lst olumn shows the good greement of the proposed theoretil proedure with the test results. It should e noted tht the result is very sensitive on the hosen rottion points. Tle. Tests to simulte uplift lod for RT4 roof system Speimen t h K exp,0 K exp K B D(A) D() k q(a) k q() δ exp δ th Experiments Rot. restrints tors Defletions Rtio δ exp /δ th No. [mm] [mm] [N/mm] [Nm/rd] [mm/kn]

7 4 LATERAL RESTRAINT 4. Generl methodology of nlysis Lterl restrint of the purlin upper flnge is used y the sher stiffness of the roof diphrgm. The sher stiffness ssures the mutul restrint of the two points long the purlin length in lterl diretion. The nlysis is sed on the ES Reommendtions (995) nd the sher flexiility of the fsteners ws determined y tests. There is n importnt effet of the roof slope length (roof dimension perpendiulr to the purlin spn), representing the depth of the sher diphrgm, on the sher stiffness. or the Astron typil roofs this dimension ws limited to minimum m. Dimension of the sher diphrgm n e ritil for wlls. 4. Anlysis of the sper roof systems RT3 nd RT4 or the sper roof systems RT3 nd RT4 the lterl flexiility of the spers (omeg sper for RT3 nd ridge sper for RT4) nd the therml expnsion lips (equl for oth RT3 nd RT4) hs to e determined. The proposed method is desried here elow. ) Model Ril D(A) Sper Moments MA Deformtion D() h M ϕ Top flnge of purlin ) Model Top line of pnel lip Ril Pnel lip Sper Moments M A Deformtion D(A) hlip ϕ A D(B) h D() M M B ϕ ϕ B Top flnge of purlin δ igure 7. Model for the lterl stiffness of the spers nd the therml expnsion lips: ) RT3 nd RT4 sper roof systems, ) RT3 nd RT4 sper roof systems The flexiility due to the sper rottion 3 is defined s the lterl movement of the ril with respet to the top flnge of the purlin due to unit lterl fore. It n e derived from the rottionl restrint tests. The spers nd the therml expnsion lips re onsidered s stiff odies fixed t the oth ends. These fixings re not infinite nd the stiffness t the onnetion to the sheeting is denominted s D(A) nd t the onnetion to the purlin s D(). The distriution of moments is liner. or the roof systems RT3 nd RT4 with the srewed down sheeting, the moment pttern orresponds to the rtio of the end vlues of the stiffness. The following formuls pply: M M ϕ A (4) D( A ) D( ) 48

8 M M A M h (4) K M M A D( ) D( A) D( ) 3 3 δ h h φ φ h D( A) h The sme ttitude is used for the roof systems RT3 nd RT4 (see igure d)) with the stnding sem sheeting hving the therml expnsion lips. The rottions re: D( A ) (5) M A M B M ϕ A, ϕ B, ϕ, ϕ A ϕ ϕb (6) or the moments we n write: D( B ) D( ) M M A M ( h h lip ) (7) h M B M ) (8) h ( M A M hlip The moments n e evluted y merging the equtions (6), (7) nd (8). Set of two equtions to evlute the M A nd M is otined nd onsequently the lterl stiffness K 3 is determined s: K 3 (9) δ h lip ϕ h ϕ A 5 ONLUSIONS The si priniples for the determintion of the sheeting prmeters needed for the design of the Astron old formed purlins re presented. In ddition to the rief outline of the extensive experimentl progrm whih is still ongoing in 009, some speifi theoretil pprohes were emphsized, nmely: determintion of the test proedures for the non-stndrd ses of the rottion stiffness, priniple of the grouping for the tests with the sme sheeting ut different purlins, pplition of the omponents method for the determintion of the rottionl restrint of the sper roof systems, generl method for nlysis of the effet of the purlin lod on the rottionl stiffness, method for the determintion of the lterl stiffness of spers nd therml expnsion lips used with the sper roof systems. Aknowledgment The pper ws worked out with the support of the reserh projet of the zeh Ministry of Edution No nd support of Astron Buildings, S.A. This help is grtefully knowledged. REERENES ES Pulition No Europen reommendtions for the pplition of metl sheeting ting s diphrgm. Brussels: ES EN Design of steel strutures, Prt.3: Generl rules Supplementry rules for old formed thin guge memers nd sheeting Brussels: EN Vrný, T. 00. Torsionl restrint of old-formed ems provided y orrugted sheeting for ritrry input vriles. Eurosteel - The Third Europen onferene on Steel Strutures, oimr: Vrný, T Effet of loding on the rottionl restrint of old-formed purlins. Thin-Wlled Strutures Vol. 44: Vrný, T Seondry stiliztion of purlins. Reports No to -5, No Prgue: TU in Prgue. 49