Exam 1 Solution (1)

# Exam 1 Solution (1) - CEE 372 Mechanics of Solids...

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Unformatted text preview: CEE 372: Mechanics of Solids University of Nevada, Reno Spring 2017 NAME; SOLUTION DISCUSSION SECTION (CIRCLE ONE): 8:00 9:00 10:00 11:00 12:00 1:00 Exam 1: Topics 1-8 March 6, 2017 Instructions: Exam is closed book. You may use the provided formula sheet and a calculator. Cell phones are not permitted to be used as calculators. You will have 50 minutes to complete the exam. GOOD LUCK! Do your best! ' | Problems Maximum Points Points Scored Problem 1 6 Problem 2 Problem 3 Problem 4 Problem 5 Current Course Grade: CEE 372 — Exam 1A Pg 2 of6 Problem 1 (6 pts) Answer the following multiple—choice questions. Each problem is worth one point. No partial credit will be given. 1) 2) 3) 4) 5) 6) Concrete is a(n) material a)*Bucti1e ., ,, Via/Brittle 0) Elastic (1) Plastic Normal stress acts to the surface of a member a) At an angle t,l9)/ Perpendicular c) Parallel d) In opposition Which of the following are units of normal strain? a) N/mm2 b) MPa 0) radians lAﬁ/mm/mm What is the deformation of an unrestrained steel bar that undergoes a temperature decrease of 25°C. The length of the bar is 2m, the area is 20 mmz, and 0t : 17X10'6/0C. a) 0.00085 mm shortening b) 0.00085 mm elongating c) 0.425 mm elongating W085 mm shortening A 4”x4”x4” concrete cube is under plane stress. The strain in the X, y, and 2 directions were measured to be ex = 700u8, 5y = 300u8, and El = -3428u8. What is the change in volume? a) No change in volume b) 0.283 in3 l9/0155 in3 d) Not enough information The concrete cube from problem 5 is under plane stress. What is true about the stress in the z-direction? There is no stress in the z-direction b) The stress is in compression c) The stress is in tension d) None of the above CEE 372 — Exam 1A Pg 3 of6 Problem 2 (8 pts) A stress—strain diagram is shown below. Answer the following questions about the diagram: at) Brieﬂy explain how to ﬁnd the yield strength and Show this process on the graph. (3 pts) b) Identify the ultimate strength and fracture point. (2 pts) 0) B11efl§ explain how to ﬁnd the modulus of elasticity and Show this on the graph (3 pts) wermal Stress {a} 4’4”“ Nefmal Strain (5} (’ﬂ_____ 0-00 2 1:)Dfa1u a M M (AM-fl) ltj’ mlerseéls gray!” it) RQOJ+10JJ Q ’HAM Point 0M can“ b) ULTCMQIECQ “Naif? +1 Frmclure Q and +1 (1) E : gloat: of ﬂue ﬂZMT pat/7L «2% 7A}; gray/7k (The 114130.!“ poél’m) E : 25— r-w on 'l‘m \M +1 8 ﬂ <21 P CEE 372 — Exam 1A Pg 4 of6 Problem 3 (18 pts) The rigid beam below has a point load applied at A and a moment applied at C. There is a cable connected to the beam with a pin. The cable has a cross-sectional area A = 1,500 mm2 and a modulus of elasticity of E = 75 GPa. a) Using statics, determine the force in member ( 1) (in kN). Clearly identify if it is in tension -"W**—or compressionﬂB’esurertodrawran’appropriate'FreedBody*Diagramrﬂdmts) ,_ "* ¥7ﬁi b) Compute the deformation (in mm) of member (1). Clearly identify if it is elongating or shortening. (4 pts) 0) Calculate the shear stress in the pin at B (in MPa). The cross-sectional detail of the pin is shown below. (3 pts) _ ((30 “a" d {hid W . 9‘3“ 6"“ A ‘l . a; QACb v-2 . mozlk error "/7, each . N0 M on @lnd QMW “17.. each m . i Pin atB . wrong meme-rd 01"" 4/7}ka Epm=10mm . wrong gov-ea orﬁfgo—l- l0 RU Mae v\[1’ 6 RUM F‘ M 390 p T/ ' <— —-—» , C); F, c9? 3S * A1 +1 rm \-/—“""-\ [—- Cmversiom +1 %‘ e. 20 KM 021'“) (loogﬂ) m ’ .— 2. ‘ p590 MM'L (TE 6470‘) I6 (CiOﬂaﬂgﬁ) +1 [“3“ +1 fConvcrslovx .41 c: ”ti—,i, _ 2mm N) ) QR ’ a 000 AW = ”31-3 MPa 4°w6leshw 2 (7:0)? +1 CEE 372 — Exam 1A Pg 5 of6 Problem 4 (12 pts) For each system Shown below, draw an appropriate Free Body Diagram, write the equilibrium equation, and write the GENERAL form of the compatibility equation (in terms of 5). Piug in an expression for each 5 value to express the equation in terms ofinternal force (F1, F2, etc). DO NOT SOLVE. W ,7 ‘QKWW , a) \$1 , ,_ A F BO (1} a +2 13%;. x i. 20“ ‘20 Q: *r B 27 ~!‘ 301:123 231%: £ng W0 1 (5,41% + 20k Jr 510k _. 3:1 9 'Fz.+30—.o CEE 372 ~ Exam 1A Pg 6 of6 Problem 5 (16 pts) V Consider the gear assembly shown below, with the speciﬁed torques applied to the gears. The length of each section of shaft is L1 = L2 = L3 = 3 ft. Each shaft is a hollow tube with an inner diameter of 1 in and an outer diameter of 2 in. The shear modulus for all three segments is G = 3,900 ksi. a) Sketch and properly label an internal torque diagram (include points A, B, C, and D on the WWW421iagramiepfullicredit)rwrhatrmustibeithervalueoﬁthe torque in rgearWAierWthe—awstemto , W ,_ ,7 ,, , 7 be in equilibrium? (7 pts) b) Determine the maximum shear stress (in ksi) that will occur in the system. (5 pts) 0) Calculate the angle of twist (in rad) of gear C relative to gear B. (4 pts) y; Ta ‘ 0M51~M 39 lb—ft 7; g at m :25»{+ 11 LA; for wr‘cmﬁ Sign) As *1 I; {a (05" 105.1) (El {+1 [3%, [‘17: 3 /, 141?};“1: 413?le TM. : (v 2.9 Lb.?'r)tm)(:2;n/m) (i ,%£‘i9£li).. : “0'36”???” J g): {33%; \th w “z jiw ”magi?” (bay/1+1 C; (be/ﬂ : 431 ~:. Tlef *‘l‘i— at; 6'2 WW’CWlieiV/Lii 4» 2a 6 KW (Wamtwﬁl LL11? an“) (3900 KM) 0-000 53mg. ,1 ‘iéf M M MW ’02”on H Ci]; ...
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