Answered: "4₂ A two celled tube with wall…

"4₂ A two celled tube with wall thickness 0.5 mm is subjected to a torque of 10 N.m as shown in Fig.(4). The resulting shear flows in two shells are shown below

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The steel alloy shaft having a diameter of 38 mm is used to transmit torque, T as shown in Figure Q2(c). If the allowable shear stress of the shaft is 88kPa (i) Determine the maximum torque T that can be transmitted by the shaft. (ii) What would be the maximum torque T' if a 25 mm diameter hole is bored through the shaft? (iii) Sketch the shear-stress distribution along a radial line in each case. T Figure Q2(c)
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6. A 2.5 in.-diameter steel propeller shaft of a boat transmits 2800 hp @ 1800 rpm. Bending and axial loads are negligible. Clearly draw and label necessary schematic diagrams and list necessary assumptions. (a) What is the shear stress at the surface of shaft? (b) If a hollow shaft of inside diameter 0.88 times outside diameter is used, what outside diameter would be required to give the same outer surface stress? (c) Compare weights of the solid and hollow shafts. What is % saving in weight of shaft material if hollow shaft is used? (d) As a design engineer, what important lesson have you learned from solving this this? (e) What is Polar Moment of Inertia?
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(30%) A circular aluminum tube subjected to T pure torsion by torques T has an outer radius r2 equal to 2 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 500x10-6 rad, what is the shear strain y1 at the inner surface? (b) If the maximum allowable rate of twist (0) is 0.15°/m and the maximum shear strain is to be kept at 500x10-6 rad by adjusting the torque T, what is the minimum required outer radius (r2 )min?
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A hellcal spring Ils made by wrapplng steel wire 20 mm diameter around a forming cyllnder 160 mm in diameter. Calculate the elongatilon of the spring wlthout exceeding a shearing stress of 150 MPa If It ls composed of 20 turns. Let G=80,000 MPa. (Ans. 127.4 mm)
Q2(c) The steel alloy shaft having a diameter of 38 mm is used to transmit torque, T as shown in Figure Q2(c). If the allowable shear stress of the shaft is 80kPa, i)Determine the maximum torque T that can be transmitted by the shaft. ii)What would be the maximum torque T' if a 25 mm diameter hole is bored through the shaft? Figure Q2(c.) |Q2 c) (i) T c The torsion formula :7 = J Т (0.019) T (0.019)^4 ; Therefore, the max torque T = x10 Nm 80 2 Q2 c) (ii) For point lying on the outside suurface of the shaft: x10 ="(0.019) * (0.019*-0.0125 ) ; Therefore the max torque T' Nm 80 2 Q2 c) (iii) The shear stress at point located at inner surface of shaft, T'c T = -= J ) (0.0125) = 7 (0.019*-0.01254) T'c kPa 4. 2 2.
1) A stepped steel shaft, shown below, is used in a spur gear reducer. The shaft is subjected to a constant axial stress (A=40 MPa), a constant bending moment that results in a variable stress (M=60 MPa) due to loads by bearings and gears, and a steady torque (T-80 MPa). However, these stress values do not take into account stress concentration factors. The shaft has a D=45 mm, d=30 mm, and r=6 mm, resulting in kr,bend=1.34, Kr,axial=1.48, and kf,tor 1.2. The shaft is made of steel with S₁=1006 MPa, S,=648 MPa, and H₂=229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 90% reliability is required. Verify the stress concentration factors are correct for this shaft geometry. Calculate the safety factor relative to infinite life (105 cycles). If the safety factor is less than one (i.e., shaft fails), find the number of cycles to failure. (60) M