A hollow shaft of diameter ratio 3/5 is required to transmit 400 kW at 140 r.p.m with a uniform twisting moment. The shear stress in the shaft must not exceed 60 MPa and the twist in a length 2.5 m must not exceed 1°. Calculate the minimum external diameter of the shaft. Take C = 8 * 10 ^ 4

A hollow shaft of diameter ratio 3/5 is required to transmit 400 kW at 140 r.p.m with a uniform twisting moment. The shear stress in the shaft must not exceed 60 MPa and the twist in a length 2.5 m must not exceed 1°. Calculate the minimum external diameter of the shaft. Take C = 8 * 10 ^ 4

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.12.5P: A stepped shaft (see figure) has diameter D2= 1.5 in, and a full quarter-circular fillet. The...

See similar textbooks

Related questions

Q: A hollow steel shaft transmits 600 kW at 500 r.p.m. The maximum shear stress is 62.4 MPa. Find the…

A: Find the outside and inside diameter .

Q: A propeller shaft for a small yacht is made ofa solid steel bar 104 mm in diameter. The…

A: (a) Write the given data. d=104 mmθL=2.083.5G=80 GPa

Q: A shaft supported on bearings, 200 mm apart transmits 187 kW and 200 rpm. The maximum bending moment…

A: Given: l=200mmP=187 kWN=200 rpmMmax=2712 N.mτmax=53.3 MPaσmax=46.7 MPa

Q: Problem 16.11. A hollow shaft is to transmit 300 kW power at 80 r.p.m. If the shear stress is not to…

A: GIven data P=300KW n=80rpm To find out the mean torque P=2πnT60300000=2π(80)T60Tmean=35.81Nm…

Q: A solid circular shaft is subjected to combined bending and torsion and and made of steel having…

Q: Q3 A hollow shaft with an external diameter of 160 mm transmits a maximum torque of 16 kN.m. If…

Q: A certain circular shaft is subjected to a maximum equivalent bending moment of 36,000 in-lb and a…

Q: A 5 ft long solid SAE4340 OQT1000 steel shaft is required to transmit a power of 180 HP. The shaft…

A: Given: Length of the shaft (L)=5ft Power (P)=180HP Shaft speed (N)=3000rpm or 2π×300060=314.159rad/s…

Q: A hollow shaft for marine applications has outer and inner diameters of 400 mm and 200 mm…

Q: What is the maximum power P (kW) that can be transmitted by a shaft hollow (do = 50 mm, di = 40 mm)…

A: Outer diameter of shaft= 50mm Inner diameter of shaft= 40mm Rotational Speed of shaft= 600 rpm…

Q: B) A wind turbine with an electrical generator rated at 200 k W output. The low speed shaft rotates…

Q: A solid steel shaft ABCDE turns freely in bearings at points A and E. The shaft is driven by the…

Q: A hollow circular shaft transmits 25 horsepower while operating at a rate of 180 rev/min. If the…

Q: Determine the minimum diameter that can be used for a solid circular steel shaft which is limited…

Q: A hollow shaft has to transmit 6MW at 150rev / min. The maximum allowable stress is not to exceed 60…

Q: (a) A steel transmission shaft is 510 mm long and 50 mm external diameter. For part of its length it…

A: We can consider this case as shafts in series Both parts are subjected to the same torque We know…

Q: pplied torque of 1.5 Nm is found to produce an angular twist of 0.4°, measured on a length of 0.2 m…

A: Given data,hollow shaftD=50mm=0.05m so, R=0.025d=30mm=0.03mTa=1.5 Nmθ=0.4°⇒0.4×π180=0.006981…

Q: Problem 10.2. A stepped steel shaft with diameters d, = 56 mm and d = 52 mm is twisted by torques T1…

A: d1 = 56 mm d2 = 52 mm T1 = 2.5 kN.m T2 = 1.5 kN.m

Q: 3.30 A solid steel shaft transmits 20 hp while running at 120 rev/min. Find the smallest safe…

Q: Obtain a preliminary design of the shaft by performing the following tasks. Note that forces T1=2880…

Q: Q6. A hollow circular shaft has an external diameter of 120 mm and the internal diameter is…

A: The inside diagram can be determined as shown below.

Q: 4. A round steel shaft rotates at 200 rpm while delivering 5000 W to a gear producing a bending…

Q: 12 A line shaft ABCD, 9 metres long, has four pulleys A, B, C and D at equal distance apart. Power…

A: Given Data:N=630 rpmζmax=55 MpaG=85 GpaTo Find :1dAB2dBC3dCD4θD/A

Q: Problem 6.7 A steel shaft, originally 15 cm diameter is sub- jected to an uniform radial compressive…

A: Given data, Original diameter of the steel shaft, do = 15 cm Applied radial compressive stress, σr =…

Q: 2 A hollow simple supported shaft 3m made of steel with di/do of 0.6. e shaft is subjected to a…

Q: 0.6 m 1 m 1200 N.m d,= 30 mm- B A 800 N.m d, = 60 mm Figure 4 c) Consider a shaft in Figure 4 is a…

Q: A shaft supported on bearings 200mm apart transmits 187 kW at 200rpm. The maximum bending moment is…

Q: A 100 mm diameter, 10 m long shaft is used to transmit power at 150 rpm. If angle of twist produced…

Q: A solid shaft 125 mm in diameter transmits 120 KW at 160 rpm. Taking C = 8 x 104 N/mm2 and length…

A: Write the expression to determine the powerP transmitted by a shaft. P=2πNT60 Here, speed of the…

Q: A hollow shaft has to be designed for a marine engine delivering 1200 kW when running at 120 r/min.…

Q: A hollow steel shaft transmits 600 kW at 500 r.p.m. The maximum shear stress is 62.4 MPa. Find the…

Q: A solid shaft has to transmit 120 kW of power at 160 rpm. If the shear stress is not to exceed 60…

Q: Consider a simply supported steel shaft as depicted below with 4 cm in diameter and 1 m span between…

A: The critical speed of the shaft with multiple loading can be found out by using methods like…

Q: T 100 mm 70 mm 70 mm 1.5 m 2 m T

Q: 4. A solid shaft 125 mm in diameter transmits 120 KW at 160 rpm. Taking C = 8 x 10 N/mm² and length…

A: P=120 kWRPM, N=160C=G=8×104 N/mm2D=125 mmlength, L=7.5 m

Q: be designed for a marine engine delivering 1200 kW when running at 120 r/min. The maximum allowable…

A: Hi and thanks for the questions. Since you have asked multiple questions, as per our honour code, we…

Q: Design a suitable diameter for a circular shaft required to transmit 90 kW at 180 r.p.m. The shear…

A: GIVEN DATA- MAXIMUM SHEAR STRESS = 70MPa POWER P=90KW SPEED N=180 r.p.m. MAXIMUM TORQUE = 140% OF…

Q: Example 7.5: (Numerical problem of a circular shaft) A circular shaft 10 cm diameter and 1.1 m…

Q: A shaft is transmitting 100 kW at 160 r.p.m. Find a suitable diameter for the shaft, if the maximum…

A: Given, Power transmitted by shaft = P = 100 kW = 100 x 103 W Speed of shaft = N = 160 rpm Relation…

Q: A motor driving a solid circular steel shaftwith diameter d = 1.5 in. transmits 50 hp to a gear atB.…

A: Consider a shaft having radius R is subjected to a twisting moment T. Then, shear stress developed…

Q: hollow steel shafts transmits 200kW of power at

A: Given Data : Speed(N)=150 rpm Power(P)=200 KW Length(L)=5 m Angle of twist(A) =30 Permissible…

Q: A hollow aluminum propeller shaft, 30 ft. Iong with 15 in. outer diameter and an inner diameter…

Q: Q6: The engine of a ship develops 440 kW and transmits the power by a horizontal propeller shaft…

A: The engine of a ship develops 440 kW and transmits the power by a horizontal propeller shaft which…

Q: 3. A 25-mm-diameter uniform steel shaft (E=207GPA, Y=76.5*10°N/m3) is 600 mm long between bearings.…

A: (a) Write the equation for the speed of shaft W=(π/l)2*(g*E*I/A*r)0.5 =(π/l)2*(g*E*( πd4/64)/(…

Concept explainers

Torsion

In mechanical engineering, torque, torsion, and twisting moment are three of the most important concepts which have different meanings. Torque is the consequence of a moment of a force that produces an angular acceleration in a body or induces rotational kinetic energy in a body. For instance, in an automobile, the power transmission shaft is a body that is always under rotation due to the external torque acting on it, this torque is created by the engine.

Question

Please do it properly otherwise leave to other expert.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

What is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm, inside diameter 40 mm, and shear modulus of elasticity 80 GPa) turning at 600 rpm if the allowable shear stress is 100 MPa and the allowable rate of twist is 3.0°/m?
A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?
A thin-walled steel tube having an elliptical cross section with constant thickness t (see figure) is subjected to a torque T = 18 kip-in. Determine the shear stress and the rate of twist in degrees per inch) if G = 12 × 106 psi, t = 0.2 in., a = 3 in., and b = 2 in. Note: See Appendix E, Case 16, for the properties of an ellipse.
A thin tubular shaft with a circular cross section (see figure) and with inside diameter 100 mm is subjected to a torque of 5000 N · m. If the allowable shear stress is 42 MPa, determine the required wall thickness t by using (a) the approximate theory for a thin-walled tube and (b) the exact torsion theory for a circular bar.
The stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft has a full quarter-circular fillet, and the smaller diameter D1= 100 mm. If the allowable shear stress at the stress concentration is 100 MPa, at what diameter will this stress be reached? Is this diameter an upper or a lower limit on the value of D2?
A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0 in. (see figure), A torque T = 500 lb-in. acts on the shaft. Determine the shear stress at the stress concentration for values as follows: D1= 0.7,0.8, and 0.9 in. Plot a graph showing versus D?
A long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a torque T. The tube has length L and constant wall thickness t. The diameter to the median lines of the cross sections at the ends A and B are dAand dB, respectively. Derive the following formula for the angle of twist of the tube: Hint: If the angle of taper is small, you may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube.
A stepped shaft (see figure) has diameter D2= 1.5 in, and a full quarter-circular fillet. The allowable shear stress is 15,000 psi and the load T = 4800 1b-in. What is the smallest permissible diameter D1?
A propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable stress in shear is 48 MPa, and the allowable rate of twist is 2.0° in 3.5 meters. (a) Assuming that the shear modulus of elasticity is G = 80 GPa, determine the maximum torque that can be applied to the shaft. (b) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d18. Compare values to corresponding values from part (a).
A thin-walled aluminum tube of rectangular cross section (sec fig me) has a centerline dimensions b = 6.0 in. and b = 4.0 in. The wall thickness t is constant and equal to 0.25 in. Determine the shear stress in the tube due to a torque T = 15 kip-in. Determine the angle of twist (in degrees) if the length L of the tube is 50 in. and the shear modulus G is 4.0 x 106 psi.
A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (see figure), (a) If the allowable shear stress in the shaft is 43 MPa, what is the maximum torque (T0)max that may be applied at section C? (b) Find (ï^),^ if the maximum angle of twist is limited to 1.85', Let G = 28 GPa.
A motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at B, The allowable shear stress in the steel is 6000 psi. Calculate the required speed of rotation (number of revolutions per minute) so that the shear stress in the shaft does not exceed the allowable limit.