Two circular rods, both of length L and having the same diameter, are placed end

Question

Two circular rods, both of length L and having the same diameter, are placed end to end between rigid supports with no initial stress in the rods.

The coefficient of linear expansion and Young's modulus for rod A are A and YA respectively; those for rod B are B and YB respectively. Both rods are "normal" materials with >0.

The temperature of the rods is now raised by T.

Part A

After the rods have been heated, which of the following statements is true?

( )The length of each rod is still L.
( )The length of each rod changes but the combined length of the rods is still 2L.

Explanation / Answer

After the rods have been heated, the length of each rod changes but the combined length of the rods is still 2L.

Total expansion of 1st rod = thermal expansion - contraction due to stress

                                            = A*t*L - F*L/(A*YA).

Total expansion of 2nd rod = thermal expansion - contraction due to stress

                                            = B*t*L - F*L/(B*YB).

Since the rods are fitted in rigid gap you need compressive strain to keep the total length constant.

Although the total length of the composite rod keeps constant, these strains differ from the thermal strain due to the different Young's modules
So, The length of the each rods change but the total combined length 2L does not.

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