A Rod Consisting of Two Cylindrical Portions AB and BC is Restrained at Both Ends

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

(

,

(

) ,

(

)

E2 = 105 * 109 Pa

C

)

A1 = 1.8 * 10-3 m2 ,

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

)

)

A2 = 1.5 * 10-3 m2 , E1 = 73 * 109 Pa

)

,

,

)

T = 70,1957 + 24 = 94.2 C The length of Aluminum rod = ( ) = 0.45027 m