Find the youngs modulus of the rod, Civil Engineering

Find the Youngs modulus of the rod:

A composite rod is made by joining a copper rod end to end with a second rod of different material but of same cross-section. At 25oC, the composite rod is 1 m in length of which the length of copper rod is 30 cm. At 125oC, the length of the composite rod increases by 1.91 mm. While the composite rod is not permitted to expand through holding it among two rigid walls, it is found that the length of constituents does not change with rise in temperature. Find the Young's modulus and coefficient of linear expansion of the second rod. For copper, α = 1.7 × 10- 5 oC-1, and Y = 1.3 × 1011 Nm- 2.

Solution

For copper rod α1 = 1.7 × 10- 5 oC- 1, and Y1 = 1.3 × 1011 Nm-2, l1 = 30 cm = 0.3 m. Let l2 be initial length of the rod of other material at 25oC, and α2 and Y2 be coefficient of linear expansion and Young's modulus for the material of this rod. Then, at initial temperature θ1 = 25oC, l1 + l2 = 1 m,

l2 = 1 - l1 = 1 - 0.3 = 0.7 m

Let the final temperature θ2 = 125oC, the increases in the length of cooper rod and that of other material be Δl1 and Δl2, respectively.

Then,

 Δl1 + Δl2 = 1.91 mm = 1.91 × 10-3  m                                                        . . . (A)

Now,

Δl1 = l1 α12 - θ1) = 0.3 × 1.7 × 10- 5 × (125 - 25) = 0.51 × 10-3 m

Also,

Δl2 = l2 α22 - θ1) = 0.7 × α2 × (125 - 25) = 70 α2

Substituting for Δl1 and Δl2 in Eq. (A), we get

0.51 × 10- 3 + 70 α2 = 1.91 × 10-3

or, α2  = 2.0 × 10- 5 oC -1

Now,

Y =   (F/A)/ (Δl/C) = FL/ A Δl ⇒ F = Y A Δl/l

Let A be the cross-section of each of the two rods, thus, tension produced in copper rod F1 = Y1AΔl1 /l1, and tension generates in the rod of other material, F2 = Y2 A Δl2/ l2. The tension developed in the two rods will be same, i.e. F1= F2.

Therefore,

(Y1 A Δl1)/l1 = (Y2 A Δl2)/l2

or        Y2  = Y1 l2Δl1/l1Δl2 ⇒ Y2  = 1.3 × 1011 × 0.7×0.51×10-3/0.3 × 1.40 × 10-3

or       Y2  = 1.105 × 1011  Nm-2

Posted Date: 1/30/2013 5:56:25 AM | Location : United States







Related Discussions:- Find the youngs modulus of the rod, Assignment Help, Ask Question on Find the youngs modulus of the rod, Get Answer, Expert's Help, Find the youngs modulus of the rod Discussions

Write discussion on Find the youngs modulus of the rod
Your posts are moderated
Related Questions
Define and discuss the various factors that help decide the number and depth of bore holes needed for subsoil exploration. What is 'N-value' of Standard Penetration Test? How do

Change the model to take into account the variation in outdoor temperature for a "typical" day in the heating season based on the heat loss by the fabric and the heating of incomin


Define the Shock Transmission Unit? Ever since engineers have started designing multi span simply supported bridges, they have been dreaming of connecting all the spans togethe

what are the uses of retaining wall?!

Determine the elastic settlement of a rectangular foundation, 6 m × 12 m, on a uniform sand with E = 20,000 kN/m 2 and Poisson's ratio,   = 0.2. The contact pressure is 200 kN/m 2

layout of harbour

#questof obstacles to both chaining and ranging. ion..

Assessing Maintenance Needs: Maintenance needs can be assessed by a careful inspection of roads at regular intervals, observing defects such as : potholes cracks

Question If contractor is likely for defective works for 12 years with pact under seal, then what is meaning of Maintenance Period? Answer Faulty works constitute a br