Concept explainers
Two solid steel shafts (G = 77.2 GPa) are connected to a coupling disk B and to fixed supports at A and C. For the loading shown, determine (a) the reaction at each support, (a) the maximum shearing stress in shaft AB, (c) the maximum shearing stress in shaft BC.
Fig. p3.55
(a)
The reaction at the supports.
Answer to Problem 55P
The reaction at the supports are
Explanation of Solution
Given information:
The modulus of rigidity of solid shafts is
Calculation:
The radius of the shaft AB is
The polar moment of inertia of shaft AB of radius
The torque carried by the shaft AB
Here,
Substitute
The radius of the shaft BC is
The polar moment of inertia of shaft BC of radius
The torque carried by the shaft BC
Here,
Substitute
The value of total torque in the shaft is
The total torque
Substitute
Substitute
Therefore, the reaction at the supports are
(b)
The maximum shearing stress in the shaft AB.
Answer to Problem 55P
The maximum shearing stress in the shaft AB is
Explanation of Solution
Given information:
The modulus of rigidity of solid shafts is
Calculation:
Refer (a).
The value of torque in the shaft AB is
The polar moment of inertia of shaft AB of radius
The maximum shearing stress in the shaft AB
Substitute
Therefore, the maximum shearing stress in the shaft AB is
(c)
The maximum shearing stress in the shaft BC.
Answer to Problem 55P
The maximum shearing stress in the shaft BC is
Explanation of Solution
Given information:
The modulus of rigidity of solid shafts is
Calculation:
Refer (a).
The value of torque in the shaft BC is
The polar moment of inertia of shaft BC of radius
The maximum shearing stress in the shaft BC
Substitute
Therefore, the maximum shearing stress in the shaft BC is
Want to see more full solutions like this?
Chapter 3 Solutions
Mechanics of Materials, 7th Edition
- 3.51 plzarrow_forward3.6 Two forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB is 20 mm. Determine the largest allowable value of P if the shear stress in the shaft is not to exceed 120 MPa and its angle of twist is limited to 7°. Use G= 80 GPa for steel. 300 mm B 500 mm FIG. P3.6arrow_forward3.11 Knowing that each of the shafts AB, BC, and CD consists of a solid circular rod, determine (a) the shaft in which the maximum shear- ing stress occurs, (b) the magnitude of that stress. 48 N. m 144 N. m A Fig. P3.11 and P3.12 dAB 60 Nm B = 15 mm dBC C = 18 mm D dcp = 21 mmarrow_forward
- 3.38 The aluminum rod AB (G = 27 GPa) is bonded to the brass rod BD (G = 39 GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A. 60 mm T = 1600 N m 36 mm TA = S00 N - mn 250 mm B 375 mm A 400 mm Fig. P3.38arrow_forward3.5 A torque T = 3 kN • m is applied to the solid bronze cylinder shown. Determine (a) the maximum shearing stress, (b) the shear- ing stress at point D, which lies on a 15-mm-radius circle drawn on the end of the cylinder, (e) the percent of the torque carried by the portion of the cylinder within the l15-mm radius. 60 mm 30 mm T=3 kN- m - 200 min Fig. P3.5arrow_forwardComplete solution.arrow_forward
- 1. The member BD is attached to a rod at B, to a hydraulic cylinder at C, and to a fixed support at D. The bolt used at D acts in double shear and is made from a steel for which the maximum allowable shearing stress is Tallow = 40 ksi. The rod AB is made of a steel for which the maximum allowable tensile stress is Oallow = 60 ksi. The upward hydraulic force applied at C is 12 kip. 1) Calculate the minimum diameter of the rod AB. 2) Calculate the minimum diameter of the bolt at D. B FAB 12 kip 8 in. FBDarrow_forward5. The torques shown are exerted on pulleys A and B. The diameter of the shaft AB is dAB = 50mm while the di- ameter of the shaft BC is dBC = 66mm. The torque at A is TA = 500Nm while the torque at B is TB = 600N . Knowing that both shafts are solid, determine the maxi- mum sharing stress in shaft AB and shaft BC. Barrow_forward5.86 The cast iron inverted T-section supports two concentrated loads of magni- tude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d = 48.75 mm and that the moment of inertia of the cross-sectional area about this axis is I = 11.918 x 106 mm“. (b) Find the maximum allowable value of P. 1.0 m 1.0 m 15 mm 3 m 150 mm NA- d 15 mm 150 mm FIG. P5.86arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY