Case Study in Steel adapted from Structural Design Guide, Hoffman, Gouwens, Gustafson & Rice., 2 nd ed.

Transcription

1 Case Std i Steel adapted from Strctral Desig Gide, Hoffma, Gowes, Gstafso & Rice., d ed. Bildig descriptio The bildig is a oe-stor steel strctre, tpical of a office bildig. The figre shows that it has three 3 ft. bas i the short directio ad a large mber of bas i the log directio. Some optios for the strctral sstem iclde fll restraied with rigid coectios ad fixed colm bases, simple framig with pied coectios ad colm bases reqirig bracig agaist sidewa, ad simple framig with cotios beams ad shear coectios, pied colm bases ad bracig agaist sideswa. This last sitatio is the oe we ll evalate as show i Figre.5(c) Loads Live Loads: Sow o Roof: 3 lb/ft (1. kpa) Wid: lb/ft (96 kpa) Dead Loads: Roofig: 8 lb/ft (38 kpa) Estimated deckig: 3 lb/ft (1 kpa) Ceilig: 7 lb/ft (3 kpa) Total: 18 lb/ft (86 kpa) Materials 36 steel for the coectio agles ad plates (F = 36 ksi, F = 58 ksi) ad 99 or Grade 5 steel for the beams ad colms (F = 5 ksi, F = 65 ksi), K series ope web joists ad roof deckig. Deckig: Deckig selectio is tpicall allowable stress desig. Tables will give allowable total iform load (takig self weight ito accot) based o stresses ad deflectio criteria for tpical spas ad how ma spas are spported. The table (ad descriptio) for a Vlcraft 1. E deck is provided

2 reas i gra are govered b live load roof deflectio. The total load with sow ad roofig = 3 psf + 8 psf = 38 psf. Ope Web Joists: Ope web joist selectio is either based o allowable stress desig or LRFD resistace for flexre (ot for deflectio). The total factored distribted load for joists at 6 ft o ceter will be: w total = (1.18lb/ft lb/ft )(6 ft) + 1.(8 lb/ft estimated) = 7. lb/ft (with 1.D + 1.6(L,or L r, or S, or R) b cataloge) w live = 3 lb/ft (6 ft) = 18 lb/ft

3 Deflectio will limit the selectio, ad the most lightweight choice is the K which weighs approximatel 8 lb/ft. Special provisios for bridgig are reqired for the shaded area legths ad sectios. Cotios Beams: LRFD desig is reqired for the remaiig strctral steel for the combiatios of load ivolvig Dead, Sow ad Wid. The bracig mst be desiged to resist the lateral wid load. The load vales are: for D: w D = 18 lb/ft 3 ft + (8 lb/ft3 ft)/ 6 ft = 58 lb/ft for S: w S = 3 lb/ft 3 ft = 9 lb/ft for W: w W = lb/ft 3 ft = 6 lb/ft (p or dow) ad laterall V = 6 lb/ft(15ft/) = 5 lb These DO NOT cosider self weight of the beam. The applicable combiatios for the tribtar width of 3 ft. are: 1.D w = 1.(58 lb/ft) = 81 lb/ft 1.D + 1.6L + 5(L r or S or R) w = 1.(58 lb/ft) + 5(9 lb/ft) = 116 lb/ft 1.D + 1.6(L r or S or R) + (L or 5W) w = 1.(58 lb/ft) + 1.6(9 lb/ft) + 5(6 lb/ft) = 36 lb/ft 1.D + 1.W + L + 5(L r or S or R) w = 1.(58 lb/ft) + 1.(6 lb/ft) + 5(9 lb/ft) = 176 lb/ft 1.D + 1.E + L + 5S w = 1.(58 lb/ft) + 5(9 lb/ft) = 91 lb/ft 9D + 1.W w = 9(58 lb/ft) + 1.(-6 lb/ft) [plift] = -78 lb/ft (p) L, R, L r, & E & do t exist for or case. For the largest load case, the shear & bedig momet diagrams are: x x

4 For the beams, we kow that the maximm braced legth is 6 ft. For the middle 6 feet of the ed spa, the momet is earl iform, so C b = 1 is acceptable (C b = 1.8 for costat momet). For the iterior spa, C b is earl 1 as well. Choosig a W18x35 (M = 9 k-ft) for the ed beams, ad a W16x6 (M = 17.5 k-ft) for the iterior beam, the self weight ca be iclded i the total weight. The diagrams chage to: x x Check beam shear: V vv 1. ( 6F w w ) Exterior V = 31.1 k 1.(6)(5 ksi)(17.1 i.)(3 i.) = k OK W18x35: d = 17.7 i., t w = 3 i., I x = 51 i. Iterior V = 1.76 k 1.(6)(5 ksi)(15.7 i.)(5 i.) = k OK W16x6: d = 15.7 i., t w = 5 i., I x = 31 i.

5 Check deflectio (NO LOD FCTORS) for total ad live load (gravit ad sow). Exterior Beams ad Iterior Beam: worst deflectio is from o live load o the ceter spa: x Maximm total = 3. i. i ed spas ad 1.87 i. at midspa Is total L/ = 36 i./ = 1.5 i.? NO GOOD We eed a I abot (3.i./1.5i.)(51 i. ) = 188 i. for the eds, ad similarl, abot 375. i for the mid sectio. Maximm live =.55 i. i ed spas ad.8 i. at midspa Is live L/36 = 36 i./36 = 1. i.? NO GOOD We eed a I abot (.55i./1.i.)(51 i. ) = 135 i. eds, ad similarl abot 76.5 i for the mid sectio. for the Live load govers. The Wx55 is the most ecoomical ot of the sectios for the eds, show with bold tpe i the grop, with I x = 133 i. The W1x is the most ecoomical ot of the sectios for the eds, show with bold tpe i the grop, with I x = 83 i. Now, live = 7 i., which is less tha allowable (b a bit). We cold probabl go with the ext most ecoomical (becase we have software to do the aalsis) with a W1x55 ad W18x which reslts i live = 96 i.! 5

6 Colms: The load i the iterior colms: P = 79 k (sm of the shears). This colm will see miimal eccetricit from the differece i shear ad half the colm depth as the momet arm. The load i the exterior colms: P = 33 k. These colms will see some eccetricit from the beam shear coectios. We ca determie this b sig half the colm depth as the eccetricit distace. The effective legth of the colms is 15 ft (o itermediate bracig). Table -1 shows desig stregth i kips for W8 shapes (the smallest). The lightest sectio at 15 feet has a capacit of 3 k; mch greater tha what we eed eve with eccetricit. The exterior colm coectio momet (magified) whe the W8x31 depth = 8.i. i 1ft ( 33 k )( 8 )( ) = 11. k-ft. 1i The capacit of a W8x31 with a braced legth of 15 ft (from aother beam chart) = 11 k-ft. Pr P For : M M x 1. Pc cp bm x bm 3k k ft : k ft ( 3k ) 11 so OK for eccetric loadig of the beam-colm (bt we kew that). Beam Shear Splice Coectio: For this all-bolted sigle-plate shear splice, R = 33 k W1x55: d = 8 i., t w = 375 i. W18x: d = 17.9 i., t w = 315 i. The plate material is 36 with F = 36 ksi ad F = 58 ksi. We eed to check that we ca fit a plate withi the fillets ad provide eogh distace from the last holes to the edge. s For the W18x, T = 15.5 i., which limits the plate height. For a plate, s (hole spacig) = 3 ad miimm edge distace is 1¼. 6

7 For ¾ i. diameter 35-N bolts ad stadard holes withot a cocer for deformatio of the holes, the capacit per bolt is: shear: : R v R 75, R F b, where F = 5 ksi ( 75i ) ( 75 )( 5ksi)[ ] so 1.8. Use bolts (1@3 i. 5.5 i. < 15.5 i.) bearig for rows of bolts: depeds o thickess of thiest web (t=315 i.) ad the coected material R R 75, R 1.5LctF 3. dtf L c = 1.75 i. from the vertical edge of the beam to the edge of a hole bolts [ 75( 1. 5)( 1. 75i )( 315i )( 65ksi) = 86 k bolts [ 75( 3)( 75i )( 315i )( 65ksi) = 69.1 k OK If the spacig betwee the holes across the splice is i., the eccetricit, e x,is iches. We eed to fid C, which represets the mber of bolts that are effective i resistig the eccetric shear force. r is the omial shear per bolt: C mi 75( 5ksi) ( 75i ) 1 8. (which we fod as ) C off the table is.5 bolts which is more tha the miimm of 1.8 (which is wh we have ). OK. (The available stregth with r fod i Table 7-1 is.5x17.9k = 5.5k) If the plate is 3/8 i. thick x 8 i. wide x 5.5 i. tall, check bolt bearig o plate: R. dtf (per bolt) bolts[.(75 i.)(375 i.)(58 ksi) = 78.3 k > 33 k OK 7

8 Check flexre of the plate: Re i desig momet: M = = 66. k-i ieldig capacit: M F S 9 (5.5 i. tall sectio, 3/8 i. thick) x 375i( 5. 5i ) 9( 36ksi) = 61.5 k-i > 66. k-i NOT OK 6 with 6 i. tall, M 7.9 k-i rptre M F S 75 et I S et et ad ca be looked p or calclated = 1.7 i c ( 58ksi)( 1. 7i ) = 75.7 k-i > 66. k-i OK Check shear ieldig of the plate: R R 1. R 6F (1.)[6(36 ksi)(6 i.)(375 i.)] = 8.6 k > 33 k OK g Check shear rptre of the plate: R R 75 R 6F for ¾ diameter bolts, the effective hole width is (75 + 1/8) = 875 i.: (75)[6(58 ksi)(6 i. x 875 i.)(375 i.)] = 1.6 k > 33 k OK v Check block shear rptre of the plate: R R 75 R. 6F U F 6F v bs t gv U bs F t with U bs = 5 whe the tesile stress is o-iform. (The tesile stress switches directio across the splice.) (ad assmig i. of width to the ceter of the bolt hole) R =. 6( 58ksi)( 375i )[ 1. 5i 3i 1. 5 ( 875)] 5( 58ksi)( 375i )( i 875i ) k 6( 36ksi)( 375i )( 1. 5i 3i ) 5( 36ksi)( 375i )( i 875i ) 7. k 33 k < 75(7. k) = 35. k OK holes Colm Base Plate: Colm base plates are desiged for bearig o the cocrete (cocrete capacit) ad plastic hige developmet from flexre becase the colm pches dow the plate ad it cold bed pward ear the edges of the colm (show as 8b f ad 95d). The plate dimesios are B ad N. The cocrete has a compressive stregth, f c = 3 ksi. 8

9 For W8 x 31: d = 8. i., b f = 8. i., ad if we provide width to pt i bolt holes, we cold se a 1 i. b1 i. plate (allowig abot iches each side). We will look at the iterior colm load of 79 k. miimm thickess: t mi l P 9F BN where l is the larger of m, ad m = (N 95d)/ = (1 i. 95 x 8. i.)/ =. i. = (B 8b f )/ = (1 i. 8 x 8. i.)/ =.8 i. db f 8.i 8.i. i. is derived from a term X which takes the bodig area of the colm, the perimeter, the axial force, ad the cocrete compressive stregth ito accot: X db ( d b f f ) P P db ( d b P 8. i 8. i ( 85 f )BN ( 8. i 8. i ) 79k 6( 853ksi) 1i 1i f c p f ) c c = 359 X so =(666)(. i.) = 1.33 i. ( 1 1 X ) ( ) therefor: l =.8 i.: t p P 79k l (. 8i ) = 515 i. 9F BN 9( 36ksi)( 1i )( 1i ) Use a 9/16 i. thick plate. The achor bolts mst also be able to resist lateral shear. There also is frictio betwee the steel ad cocrete to help. The Iteratioal Bildig Code provided specificatios for miimm edge distaces ad achorage. Cotios Beam Over Iterior Colm: The desig for this coectio will ivolve a bearig plate at the top of the colm, with a miimm mber of bolts throgh the beam flages to the plate. Becase there will be high local compressio, stiffeer plates for the web will eed to be added (refer to a plate girder desig). Flexre with a redced cross sectio area of the flages shold be checked. 9