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prel2_f03

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Unformatted text preview: ENGRD 202 Prelim II Read and follow these instructions careﬁilly 1. Write your name on the cover of your examination booklet. November 4, 2003 2. Write your recitation section number (1-9) on the cover of your examination booklet. 3. Write today's date, November 4, 2003, on the cover of your examination booklet. . 4. Sign the academic integrity statement on the cover of your examination booklet. 5. Label and draw a IE] around all your answers. 6. Make sure you include units with your answer where appropriate. 7. Make sure you use vector notation for vector quantities. 8. Make sure your work is neat, clear, and well organized. 9. Read through all the problems before beginning to solve them. Some potentially useful formulae: P=Tco lhp = 746 watts 19 =rcc>520 P=27r—T n=mm Page 1 of 4 mm, ENGRD 202 Prelim H Problem #1 (40 pts) A triangular plate of mass m hangs by 3 rods of diameter d, Young's modulus E, Poisson's ratio of v, and varying lengths as labeled. Each rod is attached to the plate with a pin of radius r, yield shear stress ry, and yield bearing stress of 0), through a hanger as shown below. a) (5 pts) Draw and label a complete free body diagram of the plate. Label all forces. b) (5 pts) Write symbolic expressions for the axial stress in rods A, B, and C in terms of the parameters given above. 0) (5 pts) Write symbolic expressions for the elongation of rods A, B, and C in terms of the parameters given above. d) (5 pts) Write symbolic expressions for the change in diameter of rods A, B, and C in terms of the parameters given above. 6) (10 pts) Determine which rod is under the greatest stress. t) (10 pts) Based on the hanger at the end of the rod under the greatest stress, write an expression for the maximum allowable mass of the plate, providing a Factor of Safety, in terms of the parameters given below: 13, =18 ksi 0,, = 36 ksi Factor of Safety = 1.67 Page 2 of 4 W ., WWW M. mm... mm... . M... w..- Miner. i. ,W W November 4, 2003 detail of hanger at end of rod ENGRD 202 Prelim II November 4, 2003 Problem #2 (35 pts) SOONm IOOONm 750Nm 250Nm l‘lm A solid shaft with shear modulus G = 78 GPa, diameter d = 10 cm, and total length L = 6 m is subject to the torques as above. a) (5 pts) Calculate the maximum torque in the shaft and the section in which it occurs. b) (10 pts) Calculate the maximum torsional sheart r and the corresponding maximum normal stress 0‘6. 0) (5 pts) Calculate the maximum rate of twist 0 in the shaft and where it occurs. d) (5 pts) If the shaft is hollow and the maximum allowable shear stress in the shaft is 70 MPa, what is the maximum inside diameter? e) (10 pts) If the shaft is rotating at 50 rpm, what is the horse power transmitted to disk A, at the right-hand end of the shaft? Page 3 of 4 ENGRD 202 Prelim 11 November 4, 2003 Problem #3 (25 pts) A cantilever beam of length L is subject to the loads shown to the right. a) (5 pts) Draw and label a complete free body diagram for the beam. b) (5 pts) Identify all the locations where the shear force Vis zero. c) (5 pts) Identify the location where the shear force is maximum, and determine its value. d) (2 pts) Identify all the locations where the bending moment M is zero. e) (8 pts) Determine the bending moment at the ﬁxed end: B Page 4 of 4 ...
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