Compute depth of yielding in the hollow shaft, Mechanical Engineering

Compute depth of yielding in the hollow shaft:

A solid shaft 80 mm diameter is solid for a certain length from one end but hollow for the remaining length along inner diameter of 40 mm. If a pure torsion is applied such that yielding occur at the surface of the solid part of the shaft. Compute:

 (1) the depth of yielding in the hollow shaft, and

 (2) the ratio of the angles of twist per unit length.

Solution

τ = Shear stress at yield point.

Torsion in the solid shaft =τ × ( π× 803 /16)

T1 =τ × (π× 803 /16)            ------------- (1)

 For Hollow Shaft

Torsion in the unyielded part

T2 =τ × (π/16 D) (D 4 - 404)                    ----------- (2)

where D = diameter of the hollow section at which yielding begins.

Torsion in yielded part

= (πτ /12 )(803  - D3 ) --------------  (3)

         T1  = T2  + T3

⇒ 803/16 = D4  - 404/16 D +  (803 - D3/12)

⇒         12 × 803 D = ( D4  - 404 ) 12 + 16 D (803  - D3 )

⇒         6144 × 103 D = 12D4  - 3072 × 104  + 8192 × 103 D - 16 D4

⇒         4D4  - 2048 × 103 D + 3072 × 104  = 0

⇒         D 4  - 512 × 103 D + 768 × 104  = 0           ----------- (4)

2411_Compute depth of yielding in the hollow shaft.png

By trial and error, D = 74.8 mm

T / J =  τ/ R = G θ/ l

⇒         θ=  τl /GR                                 ---------- (5)

θS  =2τl / (G × 80)            ------ (6)

θH  = 2τl / (G × D)           --------- (7)

θH/ θS  = 80/ D =   80/74.5 = 1.07

Posted Date: 1/21/2013 5:23:16 AM | Location : United States







Related Discussions:- Compute depth of yielding in the hollow shaft, Assignment Help, Ask Question on Compute depth of yielding in the hollow shaft, Get Answer, Expert's Help, Compute depth of yielding in the hollow shaft Discussions

Write discussion on Compute depth of yielding in the hollow shaft
Your posts are moderated
Related Questions
Base Circle: this is the smallest circle tangent to the cam profile. Trace Point: this is theoretical point on the follower whose motion explained the movement of the foll

Q. What do you mean by Dilution method? Dilution methods are more suited especially in hilly streams and torrents where current meter measurements are not feasible on account o

The background for the oil storage tank failure is as follows: the tank involved was a four million gallon circular tank that was built in 1940 for Ashland Oil Company in Cleveland

Variables used in WPS Depending on their influence on obtaining a desired weldment, the welding variables are then classified and listed. Some of them are listed as "Essential

Roller Spot Welding In this process, a series of intermittent spot welds are made using wheels or rollers as electrodes. The rollers are power driven and are stopped while ind

Q. Explain Coating Repairs? Any coatings found to be damaged or that do not pass the inspection stage shall be recoated or repaired at the expense of the Applicator. The entire

Concurrent force system: It state that if force acting at a point on a rigid body, it can be considered to act at any other point on its line of action, given this point is ri

What is Two Way Punching Shear? Two Way Punching Shear In columns, generally the tendency of the column is to punch through the footing.  This also is to be considered in de

Explain the concept of time dilation. Describe experimental verification of time dilation. Explain: (i) Length contraction (ii) Time Dilation in STR What are proper length an

What are the different theories of failure under static load, explain briefly? The major theories of failure of a member subjected to bi-axial stress are as below: > Maximu