The left-hand segment has diameter 80 mm and length 1.2 m; the right-hand segment has diameter 60 mm and length 0.9 m. Shown in the second part of the figure is a hollow shaft made of the same material and having the same length. The thickness t of the hollow shaft is d/10, where d is the outer diameter. Both shafts are subjected to the same 313 Maximum Torque That Can be Applied to a Hollow Steel Shaft313 Maximum Torque That Can be Applied to a Hollow Steel Shaft Problem 313 Determine the maximum torque that can be applied to a hollow circular steel shaft of 100-mm outside diameter and an 80-mm inside diameter without exceeding a shearing stress of 60 MPa or a twist of 0.5 deg/m.

L/2 1/4 M 0.80 Fig. 2 A stepped shaft is fixed to rigid walls as shown in Fig. 1. The length and diameter of the left portion of the shaft are li and d, respectively, and those of the right portion are 12 and d2, respectively. The modulus of transverse elasticity (shear modulus) of the shat is G. A twisting moment M is applied at the step Chapter 7. Torsional Loading:Shaftsto the shaft length. L T Shaft BC is hollow with inner and outer diameters of 90 mm and 120 mm, respectively. Shafts AB and CD are solid of diameter d. For 4 4 4 4 1 4 2 13.92 10 m 0.060 0.045 Common Exam 1, Phys 106, Summer 2010, Name:The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The cord is then pulled from below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is a. 8.0 b. 4.0 c. 12 d. 2.0 e. 6.0 12.____A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as

The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The cord is then pulled from below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is a. 8.0 b. 4.0 c. 12 d. 2.0 e. 6.0 12.____A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as DEPARTMENT OF CIVIL ENGINEERING, IIT BOMBAYsteel shaft having the same weight per unit length and limiting shear stress. Take G = 80 GPa. 2. A steel shaft consists of a hollow shaft 2m long, with an outside diameter of 100 mm and an inside diameter of 70 mm, rigidly attached to a solid shaft of 1.5 m length and 70 mm diameter. Determine the maximum power that can be transmitted by the Example - Department of PhysicsPendulums The pendulum consists of a uniform disk with radius r=10.0cm and mass M=500g attached to a uniform rod with length L=0.5m and mass m=270g.

0.015 m r 2 = 0. 025 m What is most nearly the l argest torque that can be applied? (A) 1700 N-m (B) 1900 N-m (C) 2300 N-m (D) 3400 N-m 6. An aluminum (shear modulus= 2.8 x 10 10 Pa) rod is 25 mm in diameter and 50 cm long. One end is rigidly fixed to a support. Most nearly, what torque must be applied at the free end to twist the rod 4.5 FE ReviewMechanics of Materials0.015 m r 2 = 0. 025 m What is most nearly the l argest torque that can be applied? (A) 1700 N-m (B) 1900 N-m (C) 2300 N-m (D) 3400 N-m 6. An aluminum (shear modulus= 2.8 x 10 10 Pa) rod is 25 mm in diameter and 50 cm long. One end is rigidly fixed to a support. Most nearly, what torque must be applied at the free end to twist the rod 4.5 MECHANICS OF MATERIALS Pages 101 - 150 - Flip PDF P3.16 3.16 The shaft carries a total torque T0 that is uniformly distributed over its length L. Determine the angle of twist of the shaft in terms of T0, L, G, and J. 3.17 The steel shaft of length L ¼ 1:5 m and diameter d ¼ 25 mm is attached to rigid walls at both ends.

Mechanics of Structures, 2nd year, Mechanical Engineering, Cairo University t )a = t )b = constant = q and 2tA0 T = Fig. 6 (a) Tubular bar of variable thin-walled cross section. The shear flow q = t is constant. Where, A0 is the enclosed area by the median line. The shear stress varies inversely with t. PART 3 INTRODUCTION TO ENGINEERING HEAT HT-7 () = = f TT kA L 2 AB TA TB 0. (2.5) In equation (2.5), k is a proportionality factor that is a function of the material and the temperature, A is the cross-sectional area and L is the length of the bar. In the limit for any temperature difference T across a length x as both L, T A - T B 0, we can say dx dT kA L Physics 2210 Homework 18 Spring 2015L = 4 7 mg T L = 0:813N 4) Using conservation of energy 1 2 I!2 = mg L 4 Solving for the angular speed7! = mgL 2I = 6g 7L! = 5:800rad=s 5) Acceleration of the center of mass is completely centripetal8 ac =!2 = 6g 7L L 4 and hence ac = 3 14 g ac = 8:409m=s2 7Using the moment of inertia about the pivot - see above. 8The radius of

Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle = 30 .The sphere has mass M = 8 kg and radius R = 0.19 m . Solved:A shaft of solid, circular cross section The left-hand segment has a diameter of 80 mm and length of 1.2 m; the right-hand segment has a diameter of 60 mm and length of 0.9 m. Shown in the second part of the figure is a hollow shaft made of the same material and having the same length. The thickness t of the hollow shaft is d/10, where d is the outer diameter. Both shafts are UNIT-3 PART-A 2. Write down the eion for the A hollow shaft of 55 mm external diameter and 35 mm internal diameter is subjected to a torque of 2.5 kN-m to produce and angular twist of 0.6o measured over a length of 0.3 m of shaft. Calculate the value of modulus of rigidity. Calculate also the maximum power which could be transmitted by the shaft at

This preview shows page 3 - 7 out of 33 pages. (a) If the wire has length L 4.0 m and the shear modulus of elasticity for the wire is G 15 GPa, Pure Shear Problem 3.5-1 A hollow aluminum shaft (see figure) has outside diameter d 2 4.0 in. and inside diameter d 1 2.0 in. Solved:Figure 2 Shows A Solid Cylindrical Rod With A Diam Figure 2 shows a solid cylindrical rod with a diameter of 76 mm and 1.2 m in length. If the shaft is given 5 kN-m torque (T), determine:(i) the maximum shearing stress, T. 15 Marks (ii) if the solid cylindrical shaft was replaced with a hollow cylinder of the same outer diameter (76 mm) and inner diameter of 30 mm, calculate the maximum shearing stress, T. 15 Marks] 1.2 m 76 mm T Figure 2