Job No. Sheet 1 of 6 Rev A. Made by JG/AO Date Feb Checked by GZ Date March 2006

Transcription

1 Jo No. Sht 1 of 6 Rv A Jo Titl Sujct Clint Stainl Stl Valoriation Projct Dign xaml 11 Dign of a two-an trazoidal roof hting ad y JG/AO Dat F 006 Chckd y GZ Dat arch 006 DSIGN XAPL 11 DSIGN OF A TO-SPAN TRAPZOIDAL ROOF SHTING Thi xaml dal with a two-an trazoidal roof hting with a thickn of 0,6 mm from tainl tl grad CP500, i.. cold workd to a yild trngth of 500 N/mm. Comarion will mad to a imilar hting of grad in th annald condition, i.. fy = 40 N/mm ( alo Dign xaml 3). If th nominal yild trngth in all dirction of th ht i not guarantd y th roducr it hould rducd to 80% of it valu. In thi xaml it i aumd that th trngth wa not guarantd in ordr to dmontrat thi. Sction 3..4 Th dimnion of th roof hting ar hown low. 1,5 1,5 1,5 1, A dtaild ktch of th roof hting i givn in th figur low. Th lowr flang will in comrion ovr th mid uort and thrfor thi ca will chckd in thi xaml. u0 / h 0 r / h r r0 / id lin dimnion: h0 = 70 mm w0 = 1,5 mm u0 = 57 mm r = 0 mm hr = 6 mm r0 = 8 mm l0 = 65 mm h r r0 / r / r radiu, r = 3 mm angl, ϕ = 57,1 l0 / w 0 / 177

2 Jo No. Sht of 6 Rv A Jo Titl Sujct Clint Stainl Stl Valoriation Projct Dign xaml 11 Dign of a two-an trazoidal roof hting ad y JG/AO Dat F 006 Chckd y GZ Dat arch 006 Data San lngth L = 3,5 m Load q = 1,4 kn/m Slf wight g = 0,07 kn/m Shting thickn t = 0,6 mm idth of uort = 100 mm Yild trngth fy = 0,8 500 = 400 N/mm odulu of laticity = N/mm Partial factor γ0 = 1,1 Partial factor γ1 = 1,1 Load factor γg = 1,35 (rmannt load) Load factor γq = 1,5 (varial load) ffctiv ction rorti aximum width-to-thickn ratio max( l0 / t, u0 / t) = l0 / t = 108 < 400 h / t = 117 < Tal 3.5 Tal.1 Tal.1 Sction.3. Sction.3. Tal 4.1 Location of th cntroidal axi whn th w i fully ffctiv ffctiv width of th comrion flang Sction l0 r 35 = =,5 mm ε = = 0,75 Tal 4. fy / t Tal 4.3 k = 4 = = 0,883 q. 4. 8, 4ε k 0,77 0,15 ρ = 0,714 = = ρ = 16,1 mm q. 4.1a ff,l Tal 4.3 Rducd thickn of th flang tiffnr: Sction Th lowr comrd flang i hown in dtail low. Intrmdiat tiffnr A, I t l ff,l / 178

3 Jo No. Sht 3 of 6 Rv A Jo Titl Sujct Clint Stainl Stl Valoriation Projct Dign xaml 11 Dign of a two-an trazoidal roof hting ad y JG/AO Dat F 006 ffctiv thickn of th inclind art of th tiffnr r r0 + h r t trl = = 0,85 mm h A t ht r Chckd y GZ Dat arch 006 = ( ff,l + r0) + r rl = 4,6 mm Figur 4.3 hr ht r0 r + hr trl = =, 41 mm A Th cond momnt of ara for th tiffnr i calculatd with two tri of width 15t adjacnt to th tiffnr (mallr trm nglctd) 3 hr trlhr 4 I = 15 t + r0t( hr ) + ht r rl + = 159,1 mm 1 r r0 r r0 = h + + = 4,97 mm 4 3 l Figur 4.3 I ( + 3 ) = 3,07 = 51,0 mm q. 4.9 t w0 u0 l0 w = + h0 = 83,4 mm d = + = 70,0 mm q k + w d wo = = w + 0,5d 1, 37 q l w = 3, 01> kw = kwo = 1,37 q , k I t = = 557,5 N/mm 4 ( 3 ) 3 w cr, A + f y d = = 0,85 d d cr, q. 4.3 χ = 1, 47 0, 73 = 0,86 q trd = χdt = 0,51 mm Otionally itrat to rfin th valu of th rduction factor for uckling of th tiffnr. rn , clau (3) 179

4 Jo No. Sht 4 of 6 Rv A Jo Titl Sujct Clint Stainl Stl Valoriation Projct Dign xaml 11 Dign of a two-an trazoidal roof hting ad y JG/AO Dat F 006 Chckd y GZ Dat arch 006 Ditanc to th nutral axi from th comrd flang (fully ffctiv w) A = A i = 84,0 mm c tot A i i = = 36,3 mm A tot ffctiv cro-ction of th w Sction h0 c ψ = = 0,99 k = 7,81 6, 9ψ + 9, 78ψ =,1 Tal 4.3 c,w = w = 83,4 mm 0,77 0,15 ρ = 0, 490 = / t,w = = 1,391 q. 4. 8,4ε k 1 ψ,w ff,w = ρ = ff,1 = 0, 4ff,w = 8, 47 mm ff, ff,w 1, mm q. 4.1a, Tal 4.3 = 0,6 = 1,7 mm Tal 4.3 ffctiv cro ction rorti r half corrugation Aff,tot = Aff, i = 70,8 mm A ff, i ff, i ff,c = = Aff,tot 40,0 mm ( ) 4 Itot = Iff,i + Aff,i c ff,i = mm Bnding ritanc r unit width (1m) Sction mm I = Itot = mm 0,5w ff,l I = = 1165 mm c ff,u = I 167 mm h = 0 c 3 ff,l < ff,u ff,min = ff,l = ff,min fy γ 0 = 4, 4 knm q

5 Jo No. Sht 5 of 6 Rv A Jo Titl Sujct Clint Stainl Stl Valoriation Projct Dign xaml 11 Dign of a two-an trazoidal roof hting ad y JG/AO Dat F 006 Chckd y GZ Dat arch 006 Ritanc to local tranvr forc at intrmdiat uort Ritanc to local tranvr forc r unit width (1 m) α = 0,15 (for hting rofil) and la = 1000 mm R = αt f r t + l t + ϕ γ ( 1 0,1 / ) 0,5 0,0 / (,4 ( /90) ) y a 1 0,5w0 R = 0,9 kn rn , q. 6.0c, 6.19 and 6.18 Intraction twn nding momnt and tranvr forc Th maximum nding momnt will aar at th intrmdiat uort whr it will intract with th uort raction and thrfor th following chck mut rformd. d 1 Fd d Fd 1 + 1, 5 R R rn , q. 6.8a-c Dign load r unit width (1 m) Sction.3. qd = γ Gg+ γ Qq=,0 kn/m q..3 Th dign load, qd, giv th following nding momnt and uort raction at th intrmdiat uort. ql 5 d = = 3,37 knm Fd = ql= 9,63 kn 8 4 d 0,76 = Fd d Fd = 0, 46 + R R = 1, OK Dflction at rvicaility limit tat For vrification in th rvicaility limit tat th ffctiv width of comrion lmnt hould ad on th comriv tr in th lmnt undr rvicaility limit tat loading. Th maximum comrion tr i calculatd a follow. A conrvativ aroximation i mad ad on ff,min from ultimat limit tat. ( q+ g) L rn , clau 5.5.1(4) d,r = =, 5 knm Sction d,r com,d,r = = 186 N/mm ff,min Now, th ffctiv ction rorti ar dtrmind a for ut with fy rlacd y com,d,r. Th calculation will not hown hr ut th intrting rult ar: I = mm 4 u = mm 3 l = mm 3 181

6 Jo No. Sht 6 of 6 Rv A Jo Titl Sujct Clint Stainl Stl Valoriation Projct Dign xaml 11 Dign of a two-an trazoidal roof hting ad y JG/AO Dat F 006 Chckd y GZ Dat arch 006 Dtrmination of th dflction: Scant modulu corronding to th tr in th tnion and comrion flang rctivly. d,r 1,d,r = = 14 N/mm u,d,r = = 133 N/mm d,r l = = N/mm,1 n 1 1,d,r 1+ 0,00 f y f y = = N/mm n,d,r 1+ 0,00 f y f y, 1,1 +, = = N/mm n = 7,0 A a imlification, th variation of along th lngth of th mmr may nglctd and th minimum valu of of that mmr may conrvativly ud throughout it lngth, i.. =,1 = N/mm Th rmittd dflction i L/300 = 11,7 mm x= L= 1, 47 m (location of maximum dflction) 16 ( ) g+ q L x x x δ = ,4 mm 3 4 = 48,1I L L L OK Andix C Andix C Tal C.1 Andix C Comarion with hting in grad in th annald condition Th nding ritanc r unit width of idntical hting in grad in th annald condition (fy = 40 N/mm ) i: = 3, knm and th ritanc to local tranvr forc i: R = 16, kn ith hting mad from grad in th annald condition, th an mut rducd to,9 m comard to 3,5 m for matrial in th cold workd trngth condition. Hnc, hting mad from cold workd matrial nal th an to incrad, maning that th numr of condary am or urlin could rducd, lading to cot rduction. 18