2009_summary - Name MECHANICS OF MATERIALS ENGR 2070 —...

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Unformatted text preview: Name: MECHANICS OF MATERIALS: ENGR 2070 — SPRING 2009 EXAM 1 FEBRUARY 6, 2009 Instructions: 1. Write your name at the top of every page. 2. Pay attention to what the question is asking. 3. Show all your calculations; draw BRIEF pictures if you need to; state any assumptions. 1. (35 pts) A pin-connected structure made of two steel links (BC and DE) and a member ACD is subjected to a force F at point A, as w #5 __ ., shown in the figure. All pins are of the same diameter d = 15 mm. The failure strength in shear and tension of the pins and links are, respectively, Tu], = 175 MPa and quit = 425 MPa. Both links have 190mm the same cross-sectional area of A = 130 mmz. Calculate the maximum allowable load P that the assembly can withstand, using a factor of safety of 3.1. Pins B and E are in double shear, and pins C and D are in single shear. (Consider only tension failure of t the links and shear failure of the pins, i.e., don't consider bearing 130 mm failure.) ,= Piaf : 3 l . 425 MP? lg~7 MPa Livy-5‘ \ aim/0 h ganweMc-oh Lag/(Lax- F4115” \ N _, . e do _ ,Oca _ - ~> W 1.» mm...» 1 s)» _______iv4¢° P 9.943700”: (C \ E; g]? ;> SENS—(‘0' mm, 2(1T)(.OO7Sm)¢ w! I‘l\ E P 2 [Hal 7» $P14OQON/ (CF/Vic.’ -\/\ic— ‘-> SQCUL )5? ' TFSDOO'lS'n/fl?’ 9 AX ‘ , I ’JM — . "F /\/:/A e? to s (03%“ fwtoovs )1 l9 6843_ ,¢,,»,;["QD[;, "w; e far I t e Ln“ \ZFy'o P~Z4GP+H>£ o A kl 2,40? 0’ - :6: 97 W ,7. r fi—p 7):. BL AQDC ( ‘77Omw‘ (ICC)me >7 19‘ 7240” fir— 44., P _ N ’( m 1/7 Name: MECHANICS OF MATERIALS: ENGR 2070 - SPRING 2009 EXAM 1 FEBRUARY 6, 2009 2. (30 pts) A 18—ft beam that weighs W, = 200 lb supports an air conditioner that weighs Wa = 1500 lb. The beam, in turn, is supported by hanger rods (1) and (2), as shown. a) If the diameter of rod (1) is 1/2 in., what is the stress, 01, in the rod? b) If the stress in rod (2) is to be the same as the stress in rod 1, what should the w :1 500 it, diameter of rod (2) be (to the nearest 1/32 in.)? B i "J": L ~ MOO“? = goo? 9‘ w-9ft ‘ "i a) ‘ A, WWW *i’ ,,_N_.N,,,-.-sfn ,_ iq’- 5502 p; I F m» n |§Do “7 lb 2 km ‘0) (ii: 61 ; ii, I: L A; A y in» 777- M 7/” we 7-~~r~»--w—~—¥ H0 (000% (of % 9/ 5&0?» To} ’ 7‘ (radD'L ZMA=OC -{gm/3'7g£{1_zoo’bl,‘qfl)4pz(i5-§£):O lie ’9 (radfll : O 034 m1 F1’ (600 15 ii, ,, DC to 1 t7 , isoow’Zoo 4 boo°=O (ad? I 011933?“ 3 21‘ 3 (b1 ‘ l 73’ = iioo a Q ” d rad ' f M66 5z I 7 7 iiiwrii A II ‘ iL ” x ( (1 dr a i / 1‘ 5e VCCbu /€ 32/ Page 2 of 3 Name: MECHANICS OF MATERIALS: ENGR 2070 — SPRING 2009 EXAM 1 FEBRUARY 6, 2009 3. (35 pts) A circular bar of magnesium alloy is 625 mm long, and has a diameter of 25 mm. The engineering stress- strain diagram for the material is shown in the figure. a. Make a solid dot (big enough to see) to identify the proportional limit on the plot. b. What is the modulus of elasticity for this material? c. What is the ultimate stress for this material? ’ d. What load will make this bar fracture (break)? e. The bar is loaded in tension to an elongation of 5.0 mm. What stress and strain values correspond to thiselongation? What load causes this elongation? f. What is the yield stress for this material, determined using the 0.2% offset method? 4: Q/b: “.90 MPO» Plot.) Bonus (+3 pts) Answer gig of the following bonus questions: 1. In what year was burn'/s first female engineering graduate awarded a degree in electrical engineering? a. 1908 923 c. 1939 d. 1947 2. What is the bearing area for pin E in problem 1 if the width of link DE (in the plane of the page) is 10.0 mm? Page 3 of 3 ...
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