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.
Probs. R10-1/2
Find the required minimum diameter of the shaft and 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 angular velocity of the shaft
Here, f is the frequency of shaft’s rotation.
Substitute
The expression for the power transmitted
Here, T is the applied torque and
Rearrange Equation to find the torque at A.
Here,
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 outer radius of the shaft is r.
The polar moment of inertia for a solid shaft of radius
The torsion formula for allowable maximum shear stress in the solid shaft
Here,
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
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
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.
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 for angle of twist of gear A relative to gear C
Substitute
Substitute
Therefore, the angle of twist of gear A relative to gear C is
Want to see more full solutions like this?
Chapter 10 Solutions
Statics and Mechanics of Materials (5th Edition)
- The shaft is made of A992 steel with the allowable shear stress of tallow = 75 MPa. If gear B supplies 15 kW of power, while gears A, C and D withdraw 6 kW, 4 kW and 5 kW, respectively, determine the required minimum diameterd of the shaft to the nearest millimeter. Also, find the corresponding angle of twist of gear A relative to gear D. The shaft is rotating at 600 rpm.arrow_forwardThe shaft is made of A992 steel and has an allowable shear stress of 95 MPa. When the shaft is rotating at 420 rpm, the motor supplies 11 kW of power, while gears A and B withdraw 7 kW and 4 kW, respectively. Determine the required minimum diameter of the shaft to the nearest millimeter. Also, find the rotation of gear A relative to C. (G=75 GPa) a. D=50.9589mm; 0.000004 rad b. D=50.9589mm; 0.0369 rad c. D=26mm; 0.000004 rad 300 mm d. D=26mm; 0.0369rad e. None of the above 300 mm Barrow_forwardGear B supplies 15 kW of power, while gears A, C and D withdraw 6 kW, 4 kW and 5 kW, respectively. If the shaft is made of steel with the allowable shear stress of Tmax = 75 MPa, and the relative angle of twist between any two gears cannot exceed 0.05 rad, determine the required minimum diameter d of the shaft to the nearest millimeter. The shaft is rotating at 600 rpm. Shear modulus of steel G = 75 MPa| 600 mm 600 mm 600 mmarrow_forward
- RIO-1. The shaft is made af A992 steel and has an allowable shear stress of Tak - 75 MPa. when the shaft is rotating at 300 rpm, the motor supplies 8 kW af 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. Alka, find the rotation of gear A relative to C. 300 mm S00arrow_forwardThe motor delivers 65 hp to the A36 steel shaft while it rotates at 1500 RPM. The shaft is supported on smooth bearings at B and E, which allow free rotation of the shaft. The gears C and D fixed to the shaft remove 70% and 30% of the power delivered by the motor, respectively. Determine the diameter of the shaft to the nearest 1/8 in. if the allowable shear stress is ττallow = 12 ksi and the allowable angle of twist of D with respect to A is 0.25 degrees.arrow_forwardThe two 3-ft-long shafts are made of 2014-16 aluminum. Each has a diameter of 1.5 in. and they are connected using the gears fixed to their ends. Their other ends are attached to fixed supports at A and B. They are also supported by bearings at C and D, which allow free rotation of the shafts along their axes. If a torque of 600 lb # ft is applied to the top gear as shown, determine the maximum shear stress in each shaft.arrow_forward
- FI0-12. Aseriesofgearsare mountedonthe 40-mm-diameter steel shaft. Determine the angle of twist of gear E relative to gear A. Take G = 75 GPa. G00 N-m 900 N-m SO0 Nm zio mm 300 N-m 200 mm S00 N-m 200 mm 200 mmarrow_forwardPI0-3. The solid and hollow shafts are cach subjected to the torque T.In cach case,sketch the shear stress distribution along the two radial linesarrow_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_forward
- The shaft is made from a solid steel section AB and a tubular portion made of steel and having a brass core. If it is fixed to a rigid support at A, and a torque of T = 50 lb.ft is applied to it at C, determine the rotation angle that occurs at C relative to A and compute the maximum shear stress and maximum shear strain in the brass and steel. Take Gst = 11500 ksi, Gbr = 5600 Ksi. 3 ft 0.5 in. B 1 in. T = 50 lb•ftarrow_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_forward10-57. The tubular drive shaft for the propeller of a hovereraft is 6 m long. If the motor delivers 4 MW of power to the shaft when the propellers rotate at 25 rad's, determine the required inner diameter of the shaft if the outer diameter is 250 mm. What is the angle of twist of the shaft when it is operating? Take Ta-90 MPa and G = 75 GPa.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