Question 3 A steel shaft ABCD of length L = 6.5 is shown in Figure 4. Given the torque at A, B, C and D is 80 kNm, 150 kNm, 60 kNm and 10 kNm, respectively. The shaft has a diameter of 200 mm. a) Determine the angle of twist of the end A. b) Calculate the angle of twist of A relative to C. c) Plot a diagram of torque, T versus length, L of the shaft. _1.5 m7 _2 m- 3 m 10 KN•M B. 60 KN•M 150 kN·m 80 kN·m

Question 3 A steel shaft ABCD of length L = 6.5 is shown in Figure 4. Given the torque at A, B, C and D is 80 kNm, 150 kNm, 60 kNm and 10 kNm, respectively. The shaft has a diameter of 200 mm. a) Determine the angle of twist of the end A. b) Calculate the angle of twist of A relative to C. c) Plot a diagram of torque, T versus length, L of the shaft. _1.5 m7 _2 m- 3 m 10 KN•M B. 60 KN•M 150 kN·m 80 kN·m

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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A steel shaft ABCD of length L=6.5 is shown in Figure 4. Given the torque at A,B,C and D is 80 kNm, 150 kNm, 60 kNm and 10 kNm, respectively. The shaft has a diameter of 200mm. Use G=79.3 GPa a) Determine the angle of twist of the end A. b) Calculate the angle of twist of A relative to C. c) Plot a diagram of torque, T versus length, L of the shaft.
The circular shaft shown (Figure 2) has dimensions D1 = 24 cm , L1 = 6 mm, D2 = 17.5 cm, and L2 = 4 mm with applied torques T1 = 100 kN⋅m and T2 = 40 kN⋅m. The shear modulus is G1 = 60 GPa. Point B is halfway between points A and C. a) Draw the torque diagram for the shaft, using the right-hand rule to determine the correct signs. b) For the given shaft, what is the angle of twist at the free end, point D?
A B D Do F 240 N.mm 420 N.mm 300 N.mm 480 N.mm Figure 1 - Torques applied to the driveshaft 1) DERIVE the twist angle expression (mathematical) of the shaft under torque in terms of the geometric properties of the shaft and the applied torque 2) CALCULATE the diameter of the shaft if the twist angle should not exceed 1.5⁰ 3) CALCULATE the maximum shear stress due to torsion. Consider G = 70 GPa. Assume that the length between each segment is 500 mm.
The bearings at A and B exert only x and z components of force on the steel shaft. a) Draw shear, moment and torque diagrams displaying values at each section of interest (A, B and Gear points). b) Determine the shaft's diameter to the nearest integer millimeter (Roundup) so that it can resist the loadings of the gears without exceeding an allowable shear stress Tall- Fx A 75 mm 50 mm 150 mm 350 mm B F, 250 mm Fx=15KN,Fz=22.5kN,allowable shear stress=90MPA
The circular shaft shown (Figure 2) has dimensions D1 = 24 cm , L1 = 6 m, D2 = 17.5 cm, and L2 = 4 m with applied torques T1 = 100 kN⋅m and T2 = 40 kN⋅m. The shear modulus is G1 = 60 GPa. Point B is halfway between points A and C. a) Draw the torque diagram for the shaft, using the right-hand rule to determine the correct signs. b) For the given shaft, what is the angle of twist at the free end, point D?
A shaft is subjected to a torque of 28 kNm and a maximum bending moment of 25 kNm. The shaft is solid with a diameter of 125 mm. Using the Mohr circle method find the values for the principal stresses and themaximum shear stresses on the shaft i)Construct the Mohr circle on the graph paper provided. ii) Using the Mohr circle method find the values for the principal stresses and the maximum shear stresses on the shaft.iii) Show the orientations of the planes on which the principal stresses act on a rotatedelement
Question 3 A shaft ABCD is shown in Figure 3 with total length, L = 2.1 m. The shaft BC is hollow with inner and outer diameters of 90 mm and 120 mm, respectively. Shafts AB and CD are solid with diameter d. Given the torque at A, B, C and D is 6 kNm, 14 kNm, 26 kNm and 6 kNm, respectively. a) Determine the maximum and minimum shearing stress in shaft BC. b) Calculate the required diameter, d of shafts AB and CD if the allowable shearing stress in these shafts is 65 MPa. 0.9 m 0.7 m 0.5 m A 120 mm TA = 6 kN-m В TR = 14 kN-m C Tc= 26 kN·m D Tp = 6 kN-m Figure 3
The shafts of an angle drive are subjected to the action of the two torques shown in the figure. Replace both torques by a single a) equivalent torque and b) specify its magnitude and direction. S lb-ft. 6 lb-ft
The figure on the right shows a shaft (Ç1040, Sut=500MPa) housed with “A” and “B” bearings. Said shaft is driven by an electric motor. The torque of the spindle is transferred to a wheat mill (not shown!) with the help of the “C” belt pulley mechanism. According to this; a) Max. Calculate the bending stress and location? b) Calculate the maximum torsional stress and location in the shaft? c) Calculate the safety factor of the shaft against static damage according to the Tresca and von Mises criteria?
a) Figure Q5 shows a 1.4 m long steel shaft that consists of a hollow segment AB and a solid segment BC. The shaft is fixed at C and is subjected to two external torques TA and TB at points A and B, respectively. The torque developed at the fixed end C is 750 kN.m in the direction as indicated in the figure. i) Determine the values of TA and TB if the corresponding angle of twist of end A is zero. ii) Calculate the maximum shear stress developed in the shaft. Give your comment whether the shaft will fail or not if the allowable shear stress of the shaft is 75 MPa. 750 kN.m 1.4 m 0.8 m C 160 mm B Тв 200 mm- ΤΑ Section a-a Figure Q5 = [Ans: a) i) T 332 kN.m, TB=1082 kN.m, ii) TCB,max = 60 MPa, TBA,max=45 MPa]
QUESTION 2 A shaft rotates at 300 rpm. 1). If it carries a spur gear that delivers 5 hp to a mating gear and the spur gear has the diametrical pitch of 10, pressure angle of 20°, and 80 teeth, determine a). The resultant force exerted on the shaft = Ib 2). If it carries a sprocket that delivers 4 hp to a mating sprocket and the sprocket has the pitch diameter of 6", determine b). The force exerted on the shaft Ib 3). If it carries a "flat-belt pulley" (Note: NOT V-Belt Drive) that delivers 8hp to another flat-belt pulley and the pitch diameter of the pulley is 20", determine C). The force exerted on the shaft: Ib
A steel shaft can be manufactured as a circular rod with a solid body or a circular tube. The shaft is required to bear a torque of 1200 N.m. Since the shear strength for the shaft material is 40 MPa, the maximum permitted unit torsion angle of the bar is 0.750 / m and the shear modulus of the steel is G = 78 GPa;a) Find the required diameter d0 for a solid circle shaft.b) Find the required outer diameter d2 for a ring section shaft whose thickness is 1/10 of the outer diameter.c) Find the diameter ratio (d2 / d0) and the weight ratio for ring cross section and solid section shafts.