Internal and external diameters - solid shaft, Mechanical Engineering

Internal and external diameters - solid shaft:

Two shafts are of the similar material, length & weight. One is solid & of 100 mm diameter, the outer is hollow. If hollow shaft is to be store 25% more energy than the solid shaft while transmitting torque, what should be its internal & external diameters? Consider the similar maximum shear stress in both the shafts.

Solution

Consider A is the solid shaft of diameter Da & B is the hollow shaft with external diameter Db & internal diameter db. As both of the shafts are to be the similar material and of equal weight, their volumes must be equal.

Therefore,

2055_Internal and external diameters.png

or

798_Internal and external diameters1.png

As the maximum shear stress is the similar for both the shafts, we have,

                                 τa  = τb

                           Ta Da  /2J a = Tb Db/2J B   ( since τ = T × r/ J = T × D/2J )

Therefore,

Ta/ Tb  = Db/ Da  × J a/ Jb

But it is also given that the strain energy of B = 1.25 × strain energy of A.

Thus,

471_Internal and external diameters2.png

From the relationship, this reduces to

1379_Internal and external diameters3.png

After that,  ∴

2345_Internal and external diameters4.png

1158_Internal and external diameters5.png

Therefore, the internal & external diameters of the hollow tube are 57.74 mm & 115.47 mm, respectively.

Posted Date: 1/21/2013 6:28:12 AM | Location : United States







Related Discussions:- Internal and external diameters - solid shaft, Assignment Help, Ask Question on Internal and external diameters - solid shaft, Get Answer, Expert's Help, Internal and external diameters - solid shaft Discussions

Write discussion on Internal and external diameters - solid shaft
Your posts are moderated
Related Questions
A semi circular frame of flexural rigidity EI is built at A and caries a vertical load W at B. calculate the magnitude of the vertical and horizontal deflection at B and hence the

Question: As shown in the figure, the jet transport B is flying north with a velocity v B = 600 km/h when a smaller aircraft A passes underneath the transport headed in the 60

Simple Rules FIFO (first in first out) PN j = t aj SPT (shortest processing time) PN j = o j ODD (earliest operation due dates) PN j = t dj EDD (earliest job due

Q. Flange Assembly with Torque Measurement? Select the proper bolts and gasket for the intended service. Use only new, undamaged gaskets. Lubricate the bolt threads and nut

Railway Station: Types of Stations There are the following types of stations: (a) Terminal stations, Howrah station in Kolkata and Mumbai Central being good exampl

The joint bevels shall be prepared in accordance with the registered and approved weld procedure. Internal and external surfaces to be welded shall be clean and free from paint, o

Find out change in diameter: A cylindrical shell, 0.8 m in a diameter and 3 m long is along with 10 mm wall thickness. If the shell is subjected into an internal pressure of 2

Differentiate between porosity & blowholes in welding

CAUSES AND REMEDIES OF MOTORCYCLE PROBLEMS  If Engine Overheats Causes of Problem Remedy   Incorrect spark plug make/model

Q. Define Current for electrical resistance welding? - With other parameters kept constant, the temperature in resistance welding is regulated by controlling the magnitude a