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FinalKeyS06 - ENGR 213 Spring 2006 Final Exam Name l< EY...

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Unformatted text preview: ENGR 213 Spring 2006 Final Exam Name: l< EY Instructions: 1. Do not open the exam until you are told to do so 2. Fill in your name above 3. There are 4 problems on this exam 4. This is a partial credit exam. All work must be shown in the space provided and must be legible for credit to be awarded. 5. The exam is 1 hour and 50 minutes long, so budget your time accordingly 6. You are permitted three 8.5 x 11 equation/note sheets 7. No worked problems are permitted on equation/note sheet 8. Write your name on your equation/note sheets and hand them in with your exam Do not write in this space Useful formulae fSinede = -C036 iSinB = C059 dx Semicircle Rectangle H l! “ijgbh 3 11gb 5h fibh 3 é—b 3]: fibhfl)? + h?) I) Shear and moment diagrams. a) For the given free-body diagram i) Draw shear diagram. (28 pts) ii) Label the diagram with values at cross-sections A through H. (32 pts) 75[0.5 (14-x)] lb/in 1558.7 in-lb ‘ l t . A _- ‘- 19 C0110. ‘FM'CGJ 0%CA' 120 U) Iii/FD x = h) _0 ‘ AV- - = av _ ___ BIC) fig: ’lu: '35'0) canS'JL. MC; .SiVPQ. 4/0 £525.” “-83 fig flip-5p 4 I'D L5H '9 1.3m —l?.a +v+ngoak=o 1‘ . v' THU V v: "‘3 30 120 “('iF" 0 9 #9 $- 5‘60 =- 0 ‘IZD +V+ izSpdx *S/Jflsjrzéhgyrzx-‘wal ’4’ ’- D/E) git—:11) flaps: aarflvras—v Esra ., + 5’37g-[pf5-64WDA ‘9 2.51 M 421130 4- g ' ' _ ___ _3273 E) ¢C£LWQ§ —\7_a +v+§ 2§0Jx *S‘wasm (”';WL*"J)>JX= 0 ma. V=";1'§;’a7 b) For the given free-body diagram and shear diagram i) Draw the moment diagram (8 pts) ii) Label the diagram with values at cross-sections AB, and C. (12 pts) 200 lb/ft 2) An aluminum (Young’s modulus equals 70 GPa) rod with a semicircular cross section of radius 0.012-m (as shown) is bent into the shape of a circular arc of radius p =‘2.5-m. The moment of inertia about the neutral axis is equal to 2.276*10'9-m4. Knowing that the flat face of the rod is turned toward the center of curvature of the arc, answer the following. a) What is the distance between the flat face and the neutral axis? (10 pts.) b) What is the magnitude of the applied moment? (20 pts.) 0) Will the stress at point P be tensile or compressive? (10 pts) d) If the answer to part (b) is 100 N—m, what is the normal stress (perpendicular to the page) at point Q? (20 pts.) e) If the answer to part (b) is 150 N—m, what is the magnitude of the maximum normal stress acting on the cross-section? (20 pts) Eat-70 X109 ”ma ‘4?: Q‘s—m EQIU— +6 F:- Oiflll m 94- —-— unsun- If m wast.— +2? Eli» MW? sung". 719 lee ~ g;- 970 Fife/1‘ “f '- Awsri—l - - 5" :12: 1094539091 p.00 a9>=ln 3 lama JULQMPAJ EQm,+|o Sum-r9 0" -= , 9. RM.+{ J: allWIX/fl EQM-Ho a I: NC- : (/5’fl>LJ.flJ’Q—~ prays—J99 suesz—r—g 1:” 3: ’10.?)«10—9 A15, *7 2-. 4,g§—42< lg? Pa» @ 3) A beam is built by applying adhesive to two semi-circular and one rectangular cross section bars. A transverse shear force, V, of magnitude 5100 lb. is applied to the cross-section shown below. The centroidal moment of inertia is 12.77 in4. The equation to calculate the stress caused by a transverse shear force is _ VQ 1b Assuming it is desired to calculate this stress at the upper adhesive joint, answer the following: a) What is the correct value of Q? (40 pts) b) What is the correct value of I? (20 pts) 0) What is the correct value of b? (20 pts) 27 adhesive 1.5" I fa. 3. :'_7.i.+"l n-ns- 4) In the unloaded state, the steel block shown has dimensions AB = 0.080-m BC = 0.040-m BD = 0.060-In In the loaded state, the steel block shown is subjected to a uniform pressure on all its faces (each face is subjected to the saute pressure, p). determine the following a) Knowing that the change in length of edge AB is -24.0"‘10'6 meters (i.e. AB decreases in length), what is 8;; ? (10 pts.) b) What are the stresses, 0x, 03,, and Oz in terms of the pressure p?(21 pts.) c) What are the strains, 83,, and 32 in terms of p, E, and v ?(34 pts.) d) If sx= 8y = £z= 250*10'9, what is volume of the block in the loaded state? (15 pts.) ...
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