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.


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.


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


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


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


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.


(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
i have three civil engineering fluid mechanics. 1 manometer problem 2 estimate the discharge for a channel 3 pipe system - direction of flow in line and what the value of flow in l

Question In designig of watermains, how to decide usage of double air valves and single air valves ? Answer Single air control device let squeezing air out of p

Surface Drainage: Surface drainage deals with arrangement for quickly leading the water from rainfall away from the surface of pavements, shoulders, slopes of embankments and

Hi I am looking for someone who can help to solve my assignment questions in a subject called project costing and I need him to continue with me until I complete this subject. I a

ratio of moorum and aggregate

What is the rate of application of Prime coat over WBM

Basic Considerations Governing Selection of Road Alignment: The following considerations shall be kept in view in selecting the road alignment: Roads in Plain Areas (a)

Design of Flexible Pavements: The design of flexible pavements is done by the CBR method. The CBR test, described further, gives an indication of the supporting power of the

how many programmes in road survey by level matichine and ts?