Maximum stress in each material, Mechanical Engineering

The maximum stress in each material:

A copper tube of external diameter 60 mm and internal diameter 40 mm is closely fitted to a steel rod of 40 mm diameter to compose a composite shaft. If a torque of 6 kN-m is to be resisted by the shaft, discover the maximum stress in each material and the angle of twist in 2 m length.

Take  G = 80 kN/mm for steel, and

G = 40 kN/mm2 for copper.

Solution

Copper Tube

G = 40 kN/mm2  = 0.4 × 1011 N/m2 , l = 2 m

d1 = 60 mm = 0.06 m

d2 = 40 mm = 0.04 m

2451_Maximum stress in each material.png

TC = torque resisted by copper tube

θ= Tl/ GJ    =  (TC ) (2) /((0.4 × 1011 ) (1 × 10- 6 )) = 2 TC × 10- 5 radians       ---------- (1)

τmax =  (T/J )× R = (1 × 10- 6 ) × (0.03) = 0.03 TC  × 10  N/m

         = 0.03 TC N/mm2                             ------------ (2)

1689_Maximum stress in each material1.png

Figure

G = 80 kN/mm2  = 0.8 × 1011 N/m2 ,   l = 2 m

d = 40 mm

J =  (π/32) d 4 = (π /32)× 0.044  = 2.5 × 10- 7 m4

R = 20 mm = 0.02 m

θ= Tl  / GJ  = (TS ) (2) / ((0.8 × 1011 ) (2.5 × 10- 7 )) = TS × 10- 4 radians  --------- (3)

τmax =(T/ J) × R =  Ts / ((2.5 × 10- 7 ) (0.02)) = 0.008 TS  × 107  N/m

= 0.08 TS N/mm2                                    --------- (4)

In composite shafts, θC = θS

 ⇒        5 TC  × 10- 5  = TS  × 10- 4

∴          TC  = 2TS                                  -------- (5)

TS  + TC  = T

⇒         TS = 2TS  = 6

∴          TS = 2 kN-m             TC  = 4 kN-m

∴ Angle of twist, θ= (2 × 103 ) × 10- 4  = 0.2 radians

Maximum Shear Stress

For copper shaft : For steel shaft :

τmax  = 0.03 × 4 × 103  = 120 N/m2

τmax  = 0.08 × 2 × 103  = 160 N/m2

Posted Date: 1/21/2013 5:07:19 AM | Location : United States







Related Discussions:- Maximum stress in each material, Assignment Help, Ask Question on Maximum stress in each material, Get Answer, Expert's Help, Maximum stress in each material Discussions

Write discussion on Maximum stress in each material
Your posts are moderated
Related Questions
what is law of chemical combinations?

Main Features of Laser Cutting Process   1) Laser cut kerf is very narrow resulting in material saving. 2) Has very narrow heat affected zone (HAZ) and therefore gives low

Explain the Disadvantages of Automation? a) Initial cost is higher providing additional features in machine tools. b) Skilled personnel's are required for maintenance of aut

Find the speed of shaft : Find the speed of shaft driven with the belt by an engine running at 600 rotation per minute. The thickness of belt is 2cm, diameter of engine pulle

can you explain about merchant circle,cutting forces



The Cu-Sb system contains 2 eutectics, 1 eutectoid, 1 peritectic and 1 peritectoid. Mark them all on the figure, write down the temperature and composition of each point, and ident

Hello, I need some assistance in solving engineering statics problems. In the following link, I have uploaded seven questions. I need help solving these problems step-by-step. I

Calculate the weight of body and the coefficient of friction: Q: Bodies resting on rough horizontal plane required pull of 24N inclined at 30º to the plane just to move it. I