‘108 515 THS .l .nl‘VQ.u'l'I‘V‘OU—"UWI"'“ul'l-q-P‘ valuv‘T AN ANALYSIS Of THE ROOF FKAMING Of BERKEY HALL Thank for m Dog-u of B. i. MCI-“GA“ STATE COLLEGE George W. Fox 1949 An Analysis of the Roof Framing cf Berkey Hall A Thesis Submitted to The Faculty of MICHIGAN SLATE COLLEGE of AGRICULTURE aEL AEPLILD SCIENCE bv J George W. Fox Candidate for the Degree of Bachelor of Science June 194 9 fl‘HESr? C./ PRBFACE Wishing to continue my study of steel construction, I decided to analyze the roof structure of Berkey hall to determine if it were adequate enough to carry the roof loads. I wish at this time to express my gratitude to the Building and Utilities Department of "ichigan State College for the use of their plans and ssecifications, and to Mr. Shermer for his advice and suggestions on this work. 216983 TABLE OF CONTENTS SECTION Introduction Purlins Dormer Beams Rafters Ridges Trusses Conclusion Bibliography A ppendix PAGE 01 20 22 27 29 INTRODUCTION The roof of Berkey hall is supported by a system of steel rafters and trusses. The roof is composed of re—inforced gypsum slabs covered with roofing felt and slate. The gypsum slabs weigh 20 pounds per square foot, the roofing felt, according to specifi- cations, weighs 50 pounds per square, and the slate weighs 15 pounds per square foot. The total weight per square foot of the roofing materials is 55.3 pounds, There are four types of purlins used in the roof framing. They are a 7"9.8 channel, a 8"11.5 channel, a 9"15.4 channel, each with a 1%xl%x% angle welded to the back, and a 8B10 section. As the purlins are fastened to the rafters with standard connections, there was no need to determine the type qfaoonnections to be used. The average weight per square foot of roof surface of these purlins is 2.9 pounds, so I used an average roof load of 58 pounds per square foot. Using the value of 58 pounds per square of roof as the dead weight Ifigured the reactions for each length of purlin. For purlins framing into valley rafters, I figured the loaded roof area as a trapezoid with the purlin length as the average of the sum of the bases. In analyzing the members of the roof structure, I used the Lansing Building and Safety code, which.was used in designiwg the structure. It specifies a maximum fiber stress in bending of 18,000 pounds pe r square inch, a maximum shearing for steel beam webs of 12,000 pounds per square inch, amaximum tensile stress of 18,000 pounds per square inch, a shearing stressof 15,500 pounds per square inch in rivets and bolts, a bearing stress on rivets in single shear of 24,000 pounds pe r square inch, and a bearing stress on rivets in double shear of 50,000 pounds per square inch. It provides that when wind load is used in figuring stressed that all stresses shall be increased 551 /5%. The Lansing Building and Safety code also specifies that the live load on a roof is to be figured as 50 pounds per square foot, and that the horizontal wind load is to be 20 pounds per square foot. The live load and the wind load on the roof were figured in the same manner as the dead load. I." a b‘ omqqmmmmmm 0 SCHEDULE OF PUBLIN ELACTIONS Area 8.56 14.7 16.6 18.4 20 28.8 25.7 56.8 41.5 47 48.5 55 59.6 57.7 60.4 60.7 65 65.5 68.5 78.8 84 89.5 102 115 Dead Lead 550 560 650 700 760 1090 956 1400 1580 1790 1840 2090 1500 2190 2500 2500 2400 2490 2600 5000 5200 5400 5880 4560 LIve Load 257 441 498 554 600 864 756 1100 1245 1420 1460 1650 1190 1750 1810 1821 1880 1965 2050 2560 2520 2680 5060 5450 Wind Load 171 294 55 568 400 576 504 756 850 844 970 1100 792 1154 1208 1214 1260 1510 1566 1575 1680 1786 2040 2500 As there are no sectixzn moduli fer channels with l—Eixlféxg angle welded on the back given the 14.1.5.0. handbook, I had to figure the section moduli of these mrlins before I could determine the stresse 8. They are as follows: Ar'ea of channels 2.85 in? Area of angle = .69 Ina. I " " = 21.1 in? I " " .—.~. .14 in2. x-x l Iy-y " " 5 .98 in? x or y 8 .47 in. x " " : .55 in. Y " " 5.5 in. --—-x y1:2 .85x5 .56 .69x .47/ 5 .54:2 . 82 in. x1: 2.85x.55+.69x.47+ 5.54: .55 in. I“: 21.162.85x(.68)29 .69x(2.55)‘- 26.5 in? - 4 Iy-y‘ .984 2.85x.04+.14 .69xl*-‘ 1.92 in. K I I I I - -- “T“"'““““ J 2x”x = 26.5/2.82 a. 9.41:5 , 5 Z'y-y” 1.92/2.05 = .94 in. Area 0" 8" channel:- 5.56 in? ~~< —_Tl|'__‘ I“: u n was 1:14. Iy-y " " z 1.5 in? x " " -=’ .58 in. y " " :— 4 in. »----X yl : 8.56x4 i 69x.47/4.05 8 5.4 in. x115.56x.58¢.69x.47/4.05 . .56 in. Ix_x= 52.5 114 5.56x.56+.69x-(2.95)2=59.57 in? 4 Iy-y: 1.565.56x.04*.69x(1.05)28 2.5 in. X I I -!r —.-.— 1.— ? 9F-4¢-—‘_“- 4 Zx-x’ 59.57/5.4a 11.6 1:15. I ‘<.' Zy_§- 2.5/ 2.06: 1.12 ins. _:‘: X I I I I -— ~—-—-——-.-- 0—7-.." I I I I I X N Area of 9" channel:5.89 in? 1x_x " " =47.5 in? 1y_y " n = 1.8 in? x " "- ' .61 in. y " " 9 4.5 in. yl' 5 .89x4 .5 4.69x.47/4.56=5.91n. xl‘5.89x.6lh 69x.47/4.58==.59 in. 1%; 47.5 a1446.89x.56&.69(6.463 956.9 in? Iy_y'1.s.5.ssx.04+.69(1.06)2.2.87 in? zqu- 56.9/6.9s14.5 in? z . 2.87/2.09=1.57 in? ny As the wind load has no component parallel to the roof, it is onl y necessary to determinethe stresses in the purlins due to the dead load plus live load. This stress is determined by finding the mements due to the loading in a normal direction and a parallel d irection to the roof. In the plane of the roof the sag rods act as supports for the purlins and the purlins act as beams between sag rods. The stress in the p>rlin is thus the sum of the stress due to the moment due to the loa d component normal to the roof a nd the greates t meme nt due to the load component parallel to the roof. Stresses in the 8" channel D.L.+L.L. 68x5.25x.707:252 fit/ft. Ml 8252x6(16-6)xl2/2:9l,001. in.1b. M2'252xl6x12/826050 in.1b. 3:91,ooo/11.6o sow/1.12 unseat/1:12, Stresses in the 8810 section. D.L.+L.I.;.£68x5.25x.7o7x12:5040# Iv11=5040x12x12/8=54,900 in. lb. M2:1010x4x12/8=6060 in.1b. 8:54,900/7.79*6060/l.01=15,0odv/ing Stresses in the 9" channel. D.L.-t 1.15252“ /ft. M =252x10x<22—1o)x12/2=161,ooo in.1b. 1 M2: 252x16x12/8=6100 in.1b . 8:181,000/14.5+6100/1.57:16,950g/inf Stresses in the 7" channel. D.L.+ L.L.:252#/£t . M13 252x5.4x(11.5—s.4)x12/2=45,600 in.lb. Mg: 252x16x12/8=6100in.1b. 25 6 f 2 8345,600/9.4i6lOO/.94=11,550 /in. The sections are adequate. The sag rods must take the component of the dead load and live load which is parallel to the roof. They must be des igned to carry the largest possible load to come on any one of them, consequently I used the sag rod at the peakin the wides t bay to determine the size of sag rod necessary in this build ing. DQLO" LOLO: 403(4XBOX. 707377001138 0 P:18,000A-7700 4:.426 in? To get an adequate cross-section at one inch diameter rod should be used. A‘5.l4d2/4 _2L d:(4A/5 .14 )2 _:_ d=(1.712/5.14)?’ d:.74 in. the root of the threads, a The d ormer not being an integral part of _ 8 a . ‘ 9‘ ‘1 the roof I did not attempt to determine the I“ I 1 £3 . ‘ “f stress in its' members, but did determine 23d) T the effect of the dormer Weight on the roof 355% members. For this purpose I assumed the weight I" ' 7Z?3 (f the dormer roof to be 58 pounds per square foot and the masonry walls to weigh 20 pound 5 per square foot. The wind load acts normalto the roof sunface, but due to the fact that the design load is given as a horizontal force it has to be transposed into a force normal to the roof. Grinter in Design of Modern Stgel Structures page281 suggests the use of the formula Rn PQ/45 where P is the load in pounds per 5 quare foot on a verticalsurface PD is the load normal to the roof surfacein pounds per square foot, and B is the angle of inclination in degrees. As the angle of inclination of this roof is 45degrees, Bn 5 20 pound 8 per square foot of roof surface. The dormer walls are made of masonry covered with slate so the dead load is 40 pounds per square foot. Dead load on dormer 6.5x6.5/2x40 6.5x5.52x5.8 1716 L.L. 6.5x5.52x50 690 D.L. L.L. 2400 D.L. L.L. 288 at valley ends. Wind load on the dormer front is 540 pounds, as this load is horizontal it has a component normal to the beam, this componentis :240# W.L. on roof is 455# As the dead load of the dormer acting through its ' center of mass is roughly equivalent to the actual load on the beam, I used this load in determining the bending moment in the beam, which is an 8"11.5 channel. D .LJ’ L.L. 11Rb=2400x5+680x5.75*968x7.55+288x9.75*19,650 Rb21790 Ra=:4556-179032545 M:2546x50146x.65‘7755 ft.1b. W37755x12/18 ,000=5.15 In? 6 Dormer beam continued : D.L.r%L.L.tW.L. 11 Rb = 2686x5 I‘BZOx5.651-1110x7.55l 500x9.75=22.282 Rb:2020 Ras4900—202032880 M:2880x50200x.65:8770 ft.lb. 2-8770x12/24,000=4.57 in? The be ams that support the wail and roof of the dormer fra mes into purlins that act as beams carrying the end reactionsof the dormer beams. D.L.’L.L. upper beam Roof load:54.6x68a.7o7/15=262#/rt. Ml=(1250x5.89202x169/8)12:108,000 in.1b. M28 202x16x12/624848 in.1b. 8:108,000/ll.6+4848/1.12315,600#/in€ Rhasz=12501202x15/2=2565 15 ft.span. Rasab=12504202x11/2.2565 11 ft. D.L.OinL.L.4W.L. upper beam D.L.I‘%L.L.=156#/ft. D.L.+%L.L.+W.L.:240#/ft. M1:1425x5.8o24ox169/8s10475 ft.1b. 112a 156x16 x12/885740 in.1b S810,745x12/11.60-5750/1.12t14,0907?/in2. Ra=Rb=1425+24ox15/2=2995# 15ft. Span.aa=Rb=1425+240x11/2:27505 llIt.s pan. D.Lt L.L. lower beam. Roof 1oad=55.55x68x.7o7/15s125#/rt; “ll-(1800x253 125x.69/8) x12:115,000 in.1b. 1124 l25x27.6/8)x12=5100 in.1b. s:115,ooor51oo 215,550 win? 11.6 1.12 R3311 b=1800f125x15/2226OOII" 15 ft. span. hathbilBOOOlfox11/2'2475 11ft. D.L.‘I-f,o..-...J 5.3.. loser been D.L.OiL.L.=96§/ft. 0.5.5L.L..H.1..=1.47;§-'/st. M1=(2040x5.8+147x163/8)x12=J'G,500 15.15. 142’. 9611161112/8321‘ 3 in.1b. .5=1.50,5oe/11.6=2 (go/1.122155001381153 Ba?- Ezbt£0404147x15/2= 2:11:53 15 ft. 5 pan Pu=I~Zb 2040+147xll/13 11 ft. 5 pan In this roof structure there are several rafters which act as beams Spanning the distanc e from the eave to the ridge, supporting the roofing material. In the north end on the north side there are two rafters supporting a section of the foof and half of one dormer lead, and two supporting one dormer load, these are designated by me as N-2.and N-2 respectively. In the northend there are a ls 0 two rafters supporting the south side of the roof, these are designated by me as N—5. The valley rafters where the main north and south roof frames into the east and rest roof on the north end are des igna te d by me as N—4. Where the main east-and west roof frames into the main north and south roof there are two rafters at the north side each carrying a section of roof and one half of one dormer load, which a re desigr1ted by me as M—l. 0n the south side of this interesction there arefour rafters, two of which carry a section of roof and one half of a dormer load, and two of which carry a section of roof plus the res ction from the load carried by the valley rafter on the couth.side, these are designated by me ash-2 and 2-5 respectively. The valley rafter on the north is designated as Mel M-4, and the valley rafter on the south is designated as M—S. This structure is supported nea r tte peak by two trusses, truss T-l supports the valley on the north and truss T—2 supports the valley on the north. The valley rafter at the east end where the ma in eas t and west roof frames into the north and south roof on the east end I have des ignatedas E-l. 0n the east side of this roof are four rafters, two of which carry a section of roof and one half a dormer load and two of which carry one dormer load . Ihave designated these rafters 5-2 and E-5 respectively. The rafters N-l, N-Z, M—l, M—2, and M—5 are all the same length and cross-section. N-l is the most heavily loaded of these rafters and has the greatest moment, so I analyzed N-l and figured the reactions for N—2, M-1, M—2, and M—5 and noted these reactizns with the analysis of N—4, as Ineed these reactions to analyze the ridges and trusses supporting the several rafts rs . The rafters E-2 and E-S are of the same length and cross-section but E—2 is more heavily loaded, 8 o I analyzed E—2 and figured the reaction of E—S and noted it with analysis of E—E, as I need this reaction to analyze the ridge. Rafter N~E D.L. 78.75Rh:1510x5.2s+1560x1c.5oisoox15.75=57,7oo Rb=2760# Vert.=seoe# a=2760 x5+960x5.25=15,550 ft.lb. L.L. 18.75Rb=1050x5.25¢1225x10.5+a120115.7szse,oao Rb:1920# Vert.:2710# 2:192oxsr790x5.25=9010 ft.lb. W.L. 1a.75fib=977x5.25+1146x10.5+13?ax15.75: 53,540 Hb:2t40# Vert.=1440# M=2040r3r702x5.25=9820 ft.lb. D.L.fL.L. I'u::25,2eo ft.1b. z :23,260x12/18,cco=-15.5 in? D.L.d‘LJad-WJ. . M:28,120 ft.lb. z::s,120x12/24,ooo-14 in? Rafter N-l D.L.+L.L. 51.25 sz4495x2+2655x7.25+2655x12.5+4398x17.75:520,560 Rb=10,250# vert.=14,50o# Mzio,2soxs+6710x5.2515170x5.25:82,7oc ft.lb. 2:32,700x12/18,000=551n§ 10 . B.L.{-%L.L.¥-W.L. 51.25sz42oox2r5118x7.25'4015x17.75 B +4251x2564251x28.253559,700 Rb:11500# Vs rt.:16,2505 M:11,500x5¥7269x5.eases-82:5.25:88,500 ft.lb. 2:83,500x12/24,ooo=44 1:11.5 Rafter N—4 D.L. Rb=762x2.8+1550x9.li5,000x15.491280x21.7f5,000x28 {-11le54.53295,250 ' 'Rb:7880# Vern-798509; L.L. 58Rb=600x2.3+1070 x9.lr5680xl5.4r1000x21.7i5980x28§880x34.35 r251,430 Rb=61006 Vert.=7650# W.L. Ianbzsocmz .80892x9.1+2470x15 .4r859x21.7o-237ex2 .8 seem .5:147,4oo ~Rb25890# Vert.=5100# D.L.+L.L. M=15,980x3.6>12,000x6.sosozoxs.su49,2so £40.11». :149,2503:12/18,000-991n§ D.L. r %L.LJ-W.L. 14214820155+12540x6.5t-5170x6.5+550x6.5c155,OOO ft.1b. 2:155,000x12/24,ooo-.I77.71n5. D.L.;L.L. s 8 .15,980/2.98:4,700#/1n2. D.L.'%L.L.+W.L. 83 c 14,820/2.98a4,960#/1n2. Reactions of N—2,M-1,M-",M-2 at point where the frame into ridge or truss. , N-2:D.L.*L.L. :12,500# D.L.+%L.L. HILL. =15,000# M-l: D.L.eL.L.-s15,ooo# D.L.} %L. L.o-W.L.!15,500 M-S: Wit-WLWW D.L.-34750 L.L.85750 w.L.-2160 M—2 D.L.».Laseoo D.L.€.-L.L.+W.L.=1s,soo# D.L. 38.9 Rb:264x2.8+873x9.1fl450x15.4f1990x21.7 § 2560x28‘5100154. 5'251 ,444 . Rb .6450# M86450x4 .5 REESOXS .50-790x6 .5355 ,OOOft.lb. L.L. 58.9R'b=205x2 .8§690x9.1f~1155x15 .4 #15le21 .7 {"202 0x28+2450x34 . 5 =19? , 655 Rbsazeo# 81,05" M=5200x4.5+2650x6.5+650x6.5.~45,000 ft.1b. W.L. 58.9szl7h2.84676x9.1+944x15.4+1510x21.7fl680x28+2040x54.5:165,620 sz4250# M24250x4.5r2210x6.50650x6.5=56,580 ft.1b. D.LtL.L.: Ma82,440 2882,440x12/18,000'56 in? D.L.J-iL.L.+w. L. M=87,025 ft.lb. Z¢87,025x12/24,000'45.5 inf.) The reactions at 2 being necessary to determine the 1"! load on trus s T-2 I found them as follows: 13.1.5L L.L.(M1358.9 32—469x2.8 - 1565x9.1 - 2685x15.4 - 5500x2l.7- 8580x128 - 5550::54.5 — 82,45030 58.9 R2c551,544 R2-15,650# z M5=8.1R2-1116x4-82,450=0 8.1 R2=86,9l4 32:1o,750 Tota1=24,4oo# Vert.‘I-50,56O# D.L.J-~:%;L.L.+W.L.1M1&58.9R2-757x2.8- l794x9.l— 2941x15.4- 4055x21.7- 5250:28-6565x54.5—94,145=0 38.9 R22610,064 =15,650# z M3=8.1R2-1264x4-94,445:O 8.132z99,550 32:12,500# Total:27,950# vert.=5o,900# 12 Rafter 511-5 is situated the same as rafter I‘d-4,?it is of a different section so I hsd to analyze it. I us ed the same method of analysis as in M—4, and found the reactions on trussT-l and tafter-M-‘é in the same manner. D.L. 25.41fibfi15x6.50-1270x12.6f'1850x18.9355,000 Rbs2550# M:2ESOx4.5+520x6 .5 315,880 ft .lb. L.L. 23.4Rb:48.6x6.5+lOOOx12.6013~25x18.9=41,400 =1765# 2.4.1765x4.5¢400x6.5=16;470aft‘.1b. W.L. 25.4sz472x6.54840x12.6rl200x18.9:56,EOO Rb=1550# M:1550x4.50650x6.3‘9200 ft.1b. D.L.+L.L. iii-18,650 ft.1b. 2:18,650x12/18,000c12.4in‘72 D.LJ-irLJJ-WJ. M221,655 ft.1b. Z=21,655x12/24,000=10.8 in? Reaction of M—5 on M-5 D.LI’L.L.=1750# Vert.=12507}‘ D.L.+%L.L.o-W.L.=2045# Vert.=2260# Reaction of “ll-6 on truss T-l D.L.*L.L.=fl760#;{ Vert.‘-9'?OO# D.L.O’§L.L.t-W.L.=9000# Vert.:10,240# 15 7/7 2124 3257 48m MOM" Rafter E—l D.L. 28Rb:550x2.8+1055x9.1+1590x15.4+2245x21.7 285,620 Rb=2990# Vert..5750# L.L. 28Rb=276x2.84815x9.1+1260x15.4+1885x21.7 864,574 Rb:25ou# Vert.’2880# w.L. 28Rb:229x2.8+682x9.1+1049x15.4ri415x21.7 355,690 Rb=1950# V'ert .=1560m9’ D.L.} L.L. M!5290x6.5+1745x6.5:44,550 ft.1b. Z144,550x12/18 ,ooo:29.5 in. 5 D.LJ%L.LJ~W.L. M65 M=6580x6.51~2265x6.5=55,840 ft.1b. éfiaa 49w” 2.:55,840x12/24,ooo:27.9 in§ Rafter qu 3 D.L.”..L. 24 24Rb=5180x2+1950x7.25i1950x12.5F4085xl7.75&116,860 Rb:4875# Vert.:6900# M=4875x6.25}792x5.25 34,450 ft.1b. £4,45ox12/1’8moo- 25 in? D.L¢6%L.L.+W.L. 24Rb36685x2+2590x7.2502590x12.5‘4625xl7.753156,170 Rb=5660# Vert.-8,000# H:5660x6.25+1055x5.25940,850 ft.1b. z=4o,850x12/24,000:20.4 ins. The vertical reaction of rafter E—S at the ridge is 6700# D.L.‘L.L. and 790% D.L. *%LOLO*WOLO 3 The main east and west roof ends in a gable on the eas t end. The roof at this end is supported by an 8WF17 section. This section is used because A N a '3 N3 * a there is an air duct at this end, and the section ”,0." gives clearanceto the duct and adequate support to the roof. D.L.?L.L. 19.2Ra=2150x5.54e150x8.55+2150x15.8-55,2oo REL-2860154 M:2880x5.29710x5.25-18,85o ft.1b. Zs18,650112/18,ooo=12.4 in? D.L.*~§'5L.L.fW.L. 19.2 Ra=2566x5.502568x8.5502568x15.8365,890 Ra-=2850# Ma2850x5.25+855x5.25s22,540 ft.1b. Z:22.540le/24,060:ll.l in? Shear inrafter: D.L.+ L.L. S 85590/l.6902150#/in‘€ D.L.+%L.L.+W.L. s=4284/1$9=254o¥/1n? Ridge on east end. no - “mi D.L.+L.L.:557#/£t. D .L.§%L.L.+W.L.'550#/ft. Mas onry load '144#/ft. ° 3 A D.L.O-L.L. 25Rb:6900112§4000x18.1h557x18.1x 9 +144x6.9x21.55-254,000 libs-”9400 Ra¢18555-9400=8950 z=(9400 +5100¢144/2)/18,ooo=58 ins. D.L.+%L.L.+W.L. 25Rba8,000x12+5990x18.19-55Ox18.1x9 Shear on rafter: +995x2155’ 245,150 D.L.‘LJ... . 2 s : 9400/2.7c5500#/in. Rb=9800 D§L.+%L .L.|'W.L. 2 ss .9800/2.7:564o#/1n. z:(9800+585(bc144/2)/24,ooo:47 1mg Section E-E is shown in plate 10 . I analyzed it as follows: E D.L.,LQL. Q? a 3% 17.75Rb :5180x2fl950x7.2541950x12 .5-44,500 «5 0 m _ N N Rb =2500# M32500x5.250'570x5.25 216,000 ft.1b. D.L.f'gfL.L.*W .L. 17.75 Rb=5685x2+2590x7.25r2590x12.5=54,67O Mdmw M:308015.25‘690x5.25=19,820 ft.1b. D.L.f-L.L. K/ £M3=6.25R2-11,800=0 2M2‘6.25R5-11800=0 I » . .. [4,700 I R,- 190054 R5- -1900? 2M1=17.75F2-5180x2— 195017.25-1950x12.5-ll,800=0 17 . 75112: 56 ,100 11225160 Tota1.9145# H.15,000# Value of 2 angl es 3x2§x3=59,500# in compression. D.LagL.L.:-W.L.2'M2:6.25R5'14,700=0 Ills-=6.25ng 44,700.20 ass—2550;; 82:255076‘ zM5z17.75R2—5685x2-2590x7.25-2530x12.5-14,700.-0 1221590076l Tota1310875# H:15,4002é" Value of 2 angles 4x4x2:52,750# in compression. The load on the angle in this section is 7,225#. The value of one bolt in shear is 5950# and in bearing, single shear, it is 6750#. As there are nine bolts and the load may be assumed to be applied to each equally it is obvious that no bolt is overstressed. The size a nd number of bolts was determined by the bond between the bolts and the msonryc x N ts. K V‘ 5? § a c‘: N 8: p ‘ N h a V” V" . ‘9 The main roof tr-lss I analyzed as a 3 '37” 7 4.! B span continuous beam sxmoorted at the pmel m” -9 a- , “16,54 . points. I found the reactions at the panel :w aqua points in the same manner as in rafter M-S -.?z I. j“ +.4£ and used these reactions as loads on the .. .41- 1!th if; roof. I f t .5 a 1 -.t :9 -I24 D L +L L 15 ft s- P": o o o o 0 Pan {/1245 7.5572»! - £1 M2:1160x28x17/450=ll40 ft.1b. Mt M2: 2080x7 . 25x7 .75X 22 .25/45025880 ft .lb . M2.2525x12.5x25x27.5/450a4850 ft.1b. D.L.+%L.L.+W.L. 15 ft. Span & Km4~lfl 1‘52: 1586Ka6Xl7/450 51565 ft: 01b 0 M2: 2485x7 . 253:? .75x22 .25/550 £6850 ft . lb . M20 5012le .5x2 .5x27 .5/450 6765 ft . 1b . D.LJ- L.L. center span M2t297mc2.75x81/159 '4700 £5.15. M55 2970x7.55x9/159 21450 ft.1b. M2:5410x8xl4.4/159=2825 ft.1b. M5:5410x64x5.8/l59a5989 ft.1b. Total = 7525 ft.1b. Total .7410 D.L.i-éL.L.+W.L. centerSpan M2:5547x2 .75x81/159=5625 ft .lb . M52554 7x7 . 55x9/159 sl750 ftllb . M224077x8x14.4/159:§_5_§Q ft.1b. M5. 4077x84x5.8/159 =7l4Q ft.1b. Totalpsooo ft.1b. Total -8880 ft.1b. D.L.§L.L. and span D.L.f-é-L.L.+W.L. end span M2: 5850x15 . 2x22 .5/27834700 ft . 1b . Pig-4597x315 .2x22 .55/278 :6115 ft . 1b . M5: 4155x55.2x1705/278 egos ft.1b. M5:4965x55.2x17.06/2‘.78='.IQ,7gQ ft.1b. Total=15,660 ft.1b. Tota 1.18,855 ft.1b. D.L.O-L. L. z :10, 1108:12/18 , 000’6 . 75.0” D .L.‘ %;L.L.+7€.LZ-'12 ,090x12/24 ,000:8 .05 in? Vertical reactions used as loads on the truss. D.L. L L. R1348“! R.Ill65# W.L. normal to the roof R235500fi’ - $55051 Ill-.3833? mg: we 22:57.5 4 R5125“ Hitachi! 7 Frame "D" is made similarly to the main roof truss and I analyzed it in the same way. k \\ K} B .2: a v .12. u], w _.-“'. _ «0: :-7L" r Hvfi “:\\‘>Jk;:d:flflu' 9 D.LJL.L. M2 :1255x21x14 .5/51231200ft .lb . M2. 1880x2 . 25x5 .25xl9 . 75 /512'.45 25 ft . 1b . D.L.%L.L. W.L. M231750x21xl4.5/312 =l700 ft.1b. M281979x2.25x5.25x19.7534767 ft. lb. Reactighs used as loads D.L. 1212:1190}? Ila-20007:l 115: -900# . L.L. 12129207? 152: 1700;:l 33—“-74017‘ Shearing stresses in the beam 2:4180x12/18,000=2.771n§ D.L.+L.L. Z=4685x 12/24,000:2.54 in? D. L.+%L .L.: '-.-...L W.L. Rf 655# R2: 100819i 555-40699“ D.LJ-L.L. s=11,500/2.12=54oo¥/1n? D.L.+%L.L.+W.L. s=12884/2.1236000#/1n’§ Detail "a—A" is used as the base for the rafters and the main truss. fl \1, The loads on this section that I used in analyzzingit are the greatest that I figured 8W3! . A A... I all X % Hue Flt: 4 as coming on the section. D.L.kL.L.=24,405# D.L.+%L.L.+W.L. «25,4767? According to the Lansing Building and Safety code, if the web of a girder or beamis 60 times its' thickness or greater, the allowa ble l8 , 0002 Shearing stress is to be determinedby the formula; L; h in WhiCh 7200t 18 'hfis the distance between the flangcsand t is the thickness of the web In this section h is 7.154" , t is .288" 60t 1317.28" . The allowable shearing far stress in beams where the height does not exceed 60t is 12,000#/ln? The allowable load on this section is 12,000x7.154x.288 or 24,600 pounds. The section is not overstressed. The rafter is welded to the 8WF51 section and the section.is welded to the base plate. The necessary length of weld is24,400x.707/50c0x.25 or 15.8 inches. The welds are longer than this, so they a re not ofer- stressed. Check base plate: Bearing value of base plate=24,400/180;156#/In2 D.LcrL.L. '3156x2xls272 in.1b./in. t}(6M/bf% = (6x272/18,CLO)%=.501" Bearing value of base plate: 25,476/1802142#/in2. D.L.; fi-L. L.i-‘.-'i.L. M:l42x2xl=284 in.1b./in. t3(6M/bf)%=(6x284/24,OOO)%:.508" AS/B" ba se plate is necessary for this plate. ' shock bolts: ' D.L.fL.L. on each bolt=24,400/4=6100# ('0 2 Shearssloo/.44 s15, 850#/in. Be aring=6100/.28 =21,800#/in . D.L.f-faL.L.+W.L. on each bolt:- 84009:! n r' O Shear=6400/.44=l4,6CCfi/ine Bearing 6400/.28:25,CUQ#/in§ The bolts are not overstressed. 19 70 Atthe intersection of the two main roofs there are four ridges carrying the roof between the nearest truss and the intersertion of the valley rafters. These ridges ‘4zfin0” , are the same length and cross-section and ca rry the same load. D.L. D.L.*L.L. 5.8 Rb=750x1.9 M=45,400 in.1b. Rb=250# Pa=500é 2:45 ,400/18 ,ooo=2 .4 ins. L.L. D.L.+%;L.L.+W.L. 5.8 Rb:645x1.9 M=42,7§o in.1b. Rb=215# Ra=450# q z:42,7so/24,0c-0v1.79 in'i W.L. Shear in beams: 5.8 Rb=500xl.9 D.L.‘PL.L. Rb =100# Hsezaoeé’ S:950/.655=l420#/ing D.L¢%L.L.+W.L . 9 8:915/ .655 =l4oc#/In: A 6Jr 4.4 section should be used for this ridge. 20 #3 Ridge at the north end D‘Ld L.L.s204#/£t/ Do 100+ %L0L0*EV.L.818Oi.T/FT. [3,253 D.L.+L.L. Ra=21,100x15.25/28.25+204x28.25/2sl4,eoci? Rb=26800-l4,200 =12 ,600# M=Il4,200+ll,550}2)x15x12=2,Oloooo in.1b. Z:2,0lO,DOO/18,000:112 in: mutant-mm. s hear Ra=22,950x15.25/28.25+130x:3 .25/2 :14,850# D.L.+L.L. Rb:28,050—l4,850215,250# 3:14,2oo/7e2028#/in? M=(l4,850 111,510/2) x15x1-2=2,150,000 in.1b. D.L.+%L.L.+W.L. z:2,150,000/24,000:89 in? s: 14,850/7a212M/1n2. The center ridge on the north end is the same as the center ridge on the east end. It is more heavily loaded with vertical loa ds but the sag rodfi loads are the same. I analyzedthis ridge the same as I did the purlins, using dead load plus live load and combining the stresses in the horizontaland vertical direction. D.L.-.- 114#/ft. L.L.” sown. M=114(11.58)2;(12/8 M:90(11.58)2x12/8 m:25,0001n.1b. M-l8,600 in.1b. D.L.; L.L. s :4l,ooo/234 James/inf Sag rod loads D.L.+L.L. P=2x.707x50x20£2x.707x58x20f202x3.89+125x5.89/2=1595# M=1595x5.97x12=75,000 in.1b. S=75,000/5.1=l4,500#/ln§ Total stresszls,5oo#/in§ Loads on north end column: D .L ;*Iu1u=46,l70# D. L.:§-L.L.+W.L.=47,658 Golumn va lue:l$6,500# Loads on east end column: D.L.+If.L.+-VJ.L.- 9700;? 21:01:. + ELoL.¢V€ .L.811,70(}f}' 0011151111 value :104’500f The main roof truss is sltwn in Plate 1. The analy*is of its' members is based on the loads tabulated there. Member 1-2, a 12 WF27 section, wlich acts as a column s uhrortihg the truss, is the most highly stressed. As it is the longest membe r of this cross-section in this truss, if it is not overs tressed the other, similar, members will not be overstressed. The allowable loa d 8 000A on this section is determined by the formula P21 L 2 ’ 18,000r in which P is the allowable load in pounds, L is the unsuntorted length in inches, A is the cross-sectional area of the section in square inches, and r is the least radius of gyration of the member. In this member P2 18,00€.x7.97/1+(180)2/18,000x(l.44)2 2 76,700# . The member is not overstlessed. IdemberU5L4 is made up of sanglos 533X2315xfi. Its ' value is 25,oo