Two solid 1.625-in.-diameter steel shafts are connected by the gears shown in the figure. The shaft lengths are L₁ = 10 ft and L₂ = 17 ft. Assume that the shear modulus of both shafts is G = 12,900 ksi and that the bearings shown allow free rotation of the shafts. Assume Ng=51 teeth and Nc=32 teeth. If the gear at D is rotated through an angle of 7°, what is the maximum shear stress in each shaft? A Answers: T₁ = t₂ = Mi L₁ (1) Nc NB C B psi psi L2 (2) Tp D

The shear modulus of the solid steel shaft is G = 11 x 10° ksi. Motor A is directly coupled to the shaft and delivers 3 hp while rotating at 1800 rpm (revolutions per minute). Gears B, C, and D remove the powers indicated in the figure. Given the following two criteria, determine the required diameter of the shaft to the nearest 1/s in. (1) The maximum shear stress must not exceed Tallow = 9 ksi. (2) In order to prevent binding or interference in the attached machin- ery, the angle of twist of gear B with respect to gear D must not exceed 1°. 1.25 ft 1.0 ft 3 hp 1.5 ft 1 hp 0.5 hp 1.5 hp

A metal shaft ABCD with variable cross-section is subjected to three external torques (T₁=28 kip- in, T2=8 kip-in, and T3=10 kip-in) as shown in the figure below. Each torque is acting at the locations marked with circular points along the shaft. Note that a 16-inch long segment of the shaft at the free end (right) has a 1-inch diameter bore. The dimensions (lengths and diameters) of the shaft are given in the figure. Assume deformation is linear elastic and take G=12×106 psi. D [3" 16"- X C T₁ 2" -32"- T₂ 1" diam. bore B -16"- A T3 the bar has a uniform diameter d along its full length, but external torques remain the same and are applied at the same locations. If the failure shear stress for the material is equal to Tfail = 10 ksi, and the factor of safety is equal to 2, determine the required (uniform) diameter d for the bar. Assume that the bar is solid for its entire length.

The splined ends and gears attached to the steel shaft are subjected to the torques shown in Figure 4. Take G = 75 GN/m². (i) (ii) Determine the location along the 40 mm diameter shaft where the shear stress is largest and plot the variation in shear stress from the shaft centre to its outer surface. Determine the angle of twist of sections C, D, and B relative to end A by producing a graphical plot of the variation of angle of twist from end A to end B (wind-up diagram). 300 N-m 500 N-m A www. 300 mm 200 N.m MAAN 400 mm Figure 4 500 mm 400 N-m

Gear shaft ABCDE is subjected to the torques shown in the figure. Find the internal torque in each seg- ment, and then plot the torsional moment diagram. Assume that the spacing between gears is constant, i.e., 10 in. T1 = T2 = 1000 lb-in. 500 lb-in. A B T3 = 800 Ib-in. C Ta = 500 lb-in. d = 1.0 in. D T; = 800 lb-in. E

600 Nm An aluminum shaft with a constant diameter of 50 mm is loaded by torques applied to gears attached to it as shown in Figure. Using G = 28 GPa, determine the relative angle of twist of gear D relative to 900 Nm 1100 Nm 2 m 800 N-m gear A. 3m 2 m

The two solid steel shafts shown in the figure are connected together using gear wheels. The length of the CD shaft is Lcd=2 m and the length of the AB shaft is LAB= 1.5 m. The radius of gear C is rc=45 mm and the radius of gear B is rB= 90 mm. The CD and AB shafts rotate freely in the bearings on which they are supported. Also, shaft AB is fixed at point A. Each shaft has a diameter of 20 mm and a shear modulus of G=65 GPa. When a torque of T= 450 N.m is applied to the CD shaft from the D end;a) Calculate the torsion angle on shaft AB. (Write your result in radians.)b) Calculate the total rotation (torsion angle) of the D end of the CD shaft. (Write your result in radians.)

The motor shown supplies 126 hp at 1340 rpm at A. Shafts (1) and (2) are each solid 1.86-in.-diameter steel [G=11400 ksi] shafts with lengths of L₁ = 79 in. and L₂ = 105 in., respectively. Assume Ng-27 teeth and N-42 teeth. The bearings shown permit free rotation of the shafts. (a) Determine the maximum shear stresses T₁, T2 produced in shafts (1) and (2). (b) Determine the rotation angle DA of gear D with respect to flange A. Answers: (a) T₁ = (b) P DIA Nc WWAMACOM Save for Later C 9.3808 = i 2.1378 e Textbook and Media NB L₁ B D TD ksi, 1₂: = i 14.5924 ksi. Attempts: 1 of 5 used Submit Answer