a rod consisting of two cylindrical portions ab and bc is restrained at both ends

8/10/2019 A Rod Consisting of Two Cylindrical Portions AB and BC is Restrained at Both Ends

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1.

A rod consisting of two cylindrical portions AB and BC is restrained at both ends.

Portion AB is made of steel (Es = 200 GPa, αs = 11.7 * 10-6

/oC) and portion BC is made

of brass (Eb = 105 GPa, αb = 20.9 * 10-6

/oC). Knowing that the rod is initially

unstressed, determine the compressive force induced in ABC when there is a

temperature rise of 50oC.

Solution:

By dividing the rod to two parts 1) BC and 2) AB

Then, F = 142.55 KN

2. Knowing that a 0.5 mm gap exists when the temperature is 24oC, determine (a) the

temperature at which the normal stress in the aluminum bar will be equal to -75

MPa, (b) the corresponding exact length of the aluminum bar.

Solution:

In the first case:



In the second case:

( ) ( )

L1 = 0.45 m , L2 = 0.35 m , A1 = 1.8 * 10-3 m2 ,

A2 = 1.5 * 10-3

m2 , ,

E1 = 73 * 109 Pa , E2 = 105 * 10

9 Pa ,

F = 75 * 106 * 1.8 * 10-3 = 135 * 103 N

Then, C



T = 70,1957 + 24 = 94.2 C

The length of Aluminum rod =

= 0.45027 m

a rod consisting of two cylindrical portions ab and bc is restrained at both ends

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