finalKeyW06 - ENGR 213 Winter 2006 Final Exam Name: K5 2...

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Unformatted text preview: ENGR 213 Winter 2006 Final Exam Name: K5 2 Instructions: 1. Do not open the exam until you are told to do so 2. Fill in your name above 3. There are 4 equally weighted 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 1) Shear and moment diagrams. a) For the given free-body diagram i) Draw shear diagram. (6 pts) ii) Label the diagram with values at cross-sections A through G. (12 pts) 25+51(x-4)2 ib/in 100 lb ‘ 100lb/in )00 j ES" CW, I W It” 7 v X Uli’: :20 - 47 IOO ~ £IOOJX+V" PW W a - Ea - r -- gkj) v i; -3: V, WZF =0 ‘ 7— . too “(0100 Jx g, 7. +[as+ 51(x-4)Jx / G 4+V=OJ DmazAM'. A—7E3 ) CaNSTAA/r Pas/T'n/E 5L 0P5 ® fiat) H0£i30NTA¢ (1471)) mm. N54. SLOPE @ 0915, thaw/imp 4‘1 Ei-ayF/ 1+d2120N779~L F767, mama/Um; @ b) For the given free-body diagram and shear diagram i) Draw the moment diagram (2 pts) ii) Label the diagram with values at cross-sections AB, and C. (5 pts) 1000 in-Ib. 2) A moment of 2500 in-lb is applied to the triangular cross-section beam as shown. The centroidal moment of inertia is 0.04688 in‘, Young’s modulus is 30 000 000 psi. a) What is maximum tensile stress in the x-direction? (5 pts) b) What is maximum compressive stress in the x-direction? (5 pts) c) What is the name given to the location of zero bending stress? (5 pts) d) If the answer to (a) was 50 000 psi, what is the minimum magnitude of axial load (a force along the x-axis) which would result in only zero or compressive stress acting on the cross-section? (5 pts) ' e) If the 2500 in—lb moment was n_ot applied, oould an axial load of 2500 lb be applied without buckling occurring? The length of the beam is 120 in. Show calculations to support your answer. (5 pts) M = 2500 in-Ib M = 2500 in-lb I A'L AX +9 55“ d) 0;)(134 c :48 -' mirth: ozx’m‘ + flail GET}. g 50 000 0 =Wm +— 500004’9/ n. >. max. *4 Pt” ‘ n‘iTfi'EI _ ~— 4/ 2 n 9) PM L1. '5» n=\) Yner \ n-pp\xc.A—H€. TT?’ L30 X/0‘>(0.0 4-é 88) +92 “94" /:Lo1 ER = 9M )2; F7: CR ER < 2500M +\ A/U/ BUdKL/A/4 WILL Uch/Z 3) A transverse shear force of 2500 lb. is applied to the triangular cross-section shown below. The centroidal moment of inertia is 0.04688 in“. The equation to calculate the stress caused by a transverse shear force is Assuming it is desired to calculate this stress at y = -0.5, answer the following: a) What is the correct value of V? (3 pts) b) What is the correct value of Q? (10 pts) c) What is the correct value of l? (3 pts) d) What is the correct value of b? (4 pts) 6) Where on the cross-section (y-coordinate) will the minimum shear stress occur? (5 PtS) _\ \4/2 X Q=jA via ‘49” *5 "I a; O ,m Q-—(m(t mimics} €1- ‘ ' ML,“ 5 = 0.0277813!“ M 4) A cantilever beam and its corresponding free-body diagram are shown below. The beam has an elastic modulus of 30 000 000 psi and a centroidal moment of inertia about the z-axis of 0.005 in“. The internal moment, M, is constant and equals 144 in- lb. a) What are the two boundary conditions needed to solve for the deflection? (4 pts) b) What is the slope of the beam at x = 6 in? (8 pts) 0) If the slope of the beam is given by the equation slope = 0.01 x what would the deflection be at x = 6 in? (8 pts) ‘ d) It’s been a fun term, have a good break! (5 pts) @ 144 in-lb y t 144 in-lb 144 in-lb () View 4" CV) v-’(o) =0 907530 M ['9 GEL/:_ M = M:‘0,0009é as? _ - a ’ (soxlo‘XmaE) W6“) if- _ 096 1“ (if 6"“ Mfldx' 0'00 'X C' J 0’“ \ {/0pé @ X26 )5 ¥\OP’-@ "0.00576, ...
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This test prep was uploaded on 04/08/2008 for the course ENGR 213 taught by Professor Keil during the Spring '06 term at Oregon State.

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finalKeyW06 - ENGR 213 Winter 2006 Final Exam Name: K5 2...

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