File Tutorial4withAnswers - ‘ Tutorial 4 Problem 6-43 A...

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Unformatted text preview: ‘ Tutorial 4 Problem 6-43 A member having the dimensions shown is to be used to resist an internal bending moment of M = 2 kNm. ‘ Determine the maximum stress in the member if the moment is applied (a) about the z axis, (b) about the y axis; 6 Sketch the stress distribution for each case. Solution 6—43 ‘ I” = L 500203) = 8640000 mnf ‘ 12 I}? = .1:— (120)(603) = 2160000 1111114 a) Maximmn stress: For 3-: axis: Mc 2(103)(103)(6) 0 z = = 13.89 MPa “m 13 8640000 b) For y—y axis: . 3 3 . _ 2‘ 0 " MC ., M = 27.78 MPa -———._. c, _ m I}, 2160000 13.89 MPO Ans 'Ans Levi? Tc: FIND 0 . REAQ'TNDQS ' . MAfl' GHQ?“ ' 'D I M.A'-..: kafim-G V ' I59 New MA,éki\\m CSAGGIQG) ' M_¢- to Mom CHOGGWGD 4 :: \QOfilDKE ——-—=.. —-——- msomoxgs é eewo “m‘m AT C" HoCCNC- MOMENT: 6 ‘__‘ \Oxle‘Oi 2190 1M 62°” — (9.6:Caauoc" CD A; 6 -—* _ - 6 écmmob Am MCMEQT M “ A“ ememe 0, 6.xloexi-Sé' / ' 1. Saw $.66“qu ~ Dado-1‘ I V - STEIN) : L —- C316 “H‘s/W1, O Aéémo _ Larflaa’r Aramafle. slw‘gsg o cams OJ: A. and 4‘er is, 1461th 42ch COMFN‘gSSlUQ s-tnresg .' OCCLH‘S' at Cg and 1"” 1'3 _ ' q, ' v: 4.90.. ELS‘ “mm ‘ 7 . 7'3 7;”? Faculty of Engineering _ I @IU I Tl SI Staff / Student use only 4 JOB M_ NAME MW DATE _¥_____ PAGE gill 2"""3‘2 Faculty of Engineering @IU ] T} S! 'Staff / Student use only JOB We NAME WW DATE ____'_____'_ PAGE 1.9—7.3 6% 4‘ /é:9 N/mmv 62 9-“ EON/min" cafe/7% Mia) JfiA/V a: J/MPL >4 JUMaD/QTJ?‘ 2; my M= ,uo kM-m‘ . , a ' .__ 11:»: 6-2 I . __ : i-MX/ogx/fl'g 160 Wax“ M; '_ A) _.._. M0 le’é’ZK/d?! 3x 49 x/fi-é _ _ ‘ :— /L kN/m . 7 ‘v 6E "‘ 1‘7 ‘ go ____ .zwx/oé'xs';-4 2W6 MW; ‘ a) 3' EMU'é wag . = 25/ ' .C- ‘ f L) ._ Faculty of Engineering '- @1U‘T‘ 8| . Staff / Student use only / 503 NAME M DATE WWW pAGE ZL-ZL’L CAJECK #7 ED \S'Ufibflzéf 5/: - W M=éwkM—m_ '6 éZAgi’Lji ‘ '_ I 6 3' x / 61... 650K534 m: e2J‘6K/gaé' . a) :- Maxi,” git/a6 5x6WX/6-é' -= M KM/m . ’ I 9 625 z [‘11 J 1‘ 5M :- 6wxmgx ”7’2”; ‘ 42/6 Km?! ._ 8492(2/‘6x/0g “- 696x; "'"‘ DZ’W/m 6-47 The beam is made {mm three boards nailed logclhcr as shown. If the moment acling on the cross scclion is M - 600 N - m. deumine lhc maximum bending slrcss .‘m the beam. Sketch a three-dimensional View of 1m: slress dislri- buliun acting over the cross semion. ”I" 200 mm M 2 MUN-m _ (0.0i25)(0.24)(0.025) + 2 (0.1)(0.]5)(0.02) _ 0.24 (0.025) + 2 (0.15)(0.02) 1 ~13 (0.24)(0.0253) + (0.24)(0.025)(0.G43752) —- 0.05625 m 1 + 2 (fi)(o.02)(o.153) + 2(0.15)(0.02)(0.043752) 34.53125 (10“) m“ M c T 600 (0.175-0.05625) 34.53125 (10“) 2.05 MPa Ans =63: My 600 (005625) T 34.53125 (106) = 0.977 MPa .643 The beam is made from lhrcc boards nailed logelhcr as shown. Ii rhe moment acting, on (hr: cross scclion is M " 611] N - m. determine the resultant [circa the bending amass . produces an the mp board. .5; 3,-Wflfljm — 0.24(0.025) + 2 (0.15)(0.02) = 035625 In l 33 (0.2000253) + (0.24)(o.025xo.o43752) 1 . + 2 (-13)(0.02)(0.155) + 2(0.15)(0.02)(0.043751) = 34.53125 (10")m‘ 03774:???“ a, 2 5112 = 600(0056255 _ 0 9774 MP ”wig ' I 34.53125(106) _ ‘ a 451(3004/9» _ My _ snowman—0.025) ‘ 0'5 — —— — —. = I 34-53125(10“‘) 0.5430 MPa 1 F = 5(0.025)(0.9774+0.5430)(10‘)(0.240) = 4.56 1m 6-49 A beam has the cross saclicm shown. [I it is mark at steel lhal has an aliowable slress of 11mm = 14 ksi‘ dclcri mine ihc largest iniamal Inomanl the beam can resist ii the moment is applied (a) abnul the z axis. (b) aboui may at?” _1_ 3 1 9 ; 3 I 12(6)(5.5 ) -’ EGJSXG ) = 33.3125 111!4 _ 1 ‘ 1y - Elam-23(6)] + Emma?) = 9,0073 m4 24(33.3125) c 3.25 - = 249.7 kip-in. = 20.8 kip-fl Ans a) (MIHOW)Z =5 Ohio“); " 1» (MM), = ”'“""I’ — “mm” c 3 =72.0625 kip-in. = 6.00kip-fl Ans 311 ...
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