Concept explainers
The shaft is made of A992 steel and has an allowable shear stress of τallow = 75 MPa. When the shaft is rotating at 300 rpm, the motor supplies 8 kW of power, while gears A and B withdraw 5 kW and 3 kW, respectively. Determine the required minimum diameter of the shaft to the nearest millimeter. Also, find the rotation of gear A relative to C.
The required minimum diameter of the shaft.
The angle of twist of gear A relative to gear C.
Answer to Problem 1RP
The required minimum diameter of the shaft is
The angle of twist of gear A relative to gear C is
Explanation of Solution
Given information:
The allowable shear stress in the shaft is 75 MPa.
The motor supplies power of 8 kW.
Gear A and B withdraws power of 5 kW and 3 kW.
Shaft rotates at 300 rpm.
Calculation:
The expression for the power transmitted
Here, T is the applied torque and
Rearrange Equation (1) to find the torque at A.
Here,
The expression for angular velocity of the shaft
Here, f is the frequency of shaft’s rotation.
Substitute
Substitute 5 kW for
Find the torque at C.
Here,
Substitute 8 kW for
Sketch the internal torque in the segment BC of the shaft as shown in Figure 1.
Sketch the internal torque in the segment AB of the shaft as shown in Figure 2.
Refer Figure 1 and Figure 2.
Segment BC of the shat is subjected to a greater internal torque of
The torsion formula for allowable maximum shear stress in the solid shaft
Here,
The outer radius of the shaft is r.
The polar moment of inertia for a solid shaft of radius
Substitute r for c and
Substitute 75 MPa for
The diameter of the shaft is twice the radius of the shaft. So the value of diameter is 26 mm.
Therefore, the required minimum diameter of the shaft is
Determine the angle of twist
Here, L is the length of the shaft and G is the shear modulus of elasticity of the material.
Rearrange Equation (7) for angle of twist of gear A relative to gear C
Refer the properties of A992 steel.
The value of shear modulus of elasticity of A992 steel is 75 GPa.
The value of radius of the solid shaft is 13 mm.
Substitute
Refer Figure 2.
The torque in the region AB of the shaft is
Refer Figure 1.
The torque in the region BC of the shaft is
Substitute
Therefore, the angle of twist of gear A relative to gear C is
Want to see more full solutions like this?
Chapter 5 Solutions
Mechanics of Materials
- The hollow shaft has an outside diameter of 22mm and an inside diameter of 15mm. A torque of 1000N-m is applied in the end of the shift in the shown direction. Calculate the shear stress at point C .arrow_forwardIf the gears are subjected to the torques shown, determine the required diameter of the A-36 steel shaft to the nearest mm if tallow = 60 MPa.arrow_forwardThe motor produces a torque of T = 20 N # m on gear A. If gear C is suddenly locked so it does not turn, yet B can freely turn, determine the angle of twist of F with respect to E and F with respect to D of the L2-steel shaft, which hasan inner diameter of 30 mm and an outer diameter of 50 mm. Also, calculate the absolute maximum shear stress in the shaft. The shaft is supported on journal bearings at G at H.arrow_forward
- The solid 30-mm-diameter shaft is used to transmit the torques applied to the gears. Determine the absolute maximum shear stress in the shaftarrow_forwardThe gear motor can develop 1 10 hp when it turns at 300 rev>min. If the shaft has a diameter of 1 2 in., determine the maximum shear stress in the shaft.arrow_forwardThe solid 50-mm-diameter shaft is subjected to the torques applied to the gears. Determine the absolute maximum shear stress in the shaft.arrow_forward
- The drive shaft of the motor is made of a material having an allowable shear stress of τallow= 72 MPa. the shaft is operating at an angular velocity of 1700 rev/min. Take ci= 0.75 co. A) If the motor is to deliver a power of 25 kW, determine the required minimum outer diameter of the tubular shaft to the nearest mm. Express your answer in millimeters. B)Determine the required corresponding inner diameter of the tubular shaft to the nearest mm. Express your answer in millimetersarrow_forwardThe solid steel shaft is supported by frictionless bearings in D and E. This system is connected to a motor that provides 5 kW of power to the shaft while rotating at w = 75 rpm. If A and B gears get 2 kW and 3 kW respectively, determine the minimum shaft diameter. w rotation speed and safety shear stress τem = 35MPa are known and given in the table with your names below.arrow_forwardThe solid 35-mm-diameter shaft is used to transmit the torques applied to the gears. The shaft is made of steel A-36 with E = 200 GPa and G = 75 GPa a. Determine the absolute maximum shear stress on the shaft. b. Determine the angle of twist of the end B with respect to end A. c. The shaft is now change d to a hollowed shaft with an outside diameter of 40 mm. What inner diameter is required to resist the same torque with the same maximum shear stress?arrow_forward
- The shaft shown below consists of three segments AB, BC and CD is subjected to the three torques T1=114 N.m, T2=245 N.m and T3=441 N N.m. The length of each segment is L1=0.71 m, L2=0.31 m and L3=0.43 m . The diameter of each segment is d1=46 mm, d2=97 mm and d3=131 mm . The material have modulus of rigidity G = 143 Gpa. Answer the following questionsarrow_forwardThe shaft below is made of A992 steel and has an allowable shear stress of tadm = 75 MPa. When the shaft is rotating at 300 rpm, the motor provides 8 kW of power, while gears A and B draw 5 kW and 3 kW, respectively. Determine the minimum diameter required for shaft. Also, find the angle of twist of the gear A with respect to C.arrow_forwardA flange bolt coupling consists of 12-14mm diameter steel bolts on a bolt circle 320mm in diameter and 8-12mm diameter on a concentric bolt circle 260mm in diameter. What torque can be applied without exceeding a shearing stress of 60MPa in the bolts? B) Determine the number of 10mm steel bolts that must be used on the 320mm bolt circle of the coupling to increase the torque capacity by 6KN-m.arrow_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