# At what temperature will the aluminum and steel segments in Prob. 2.86 have stresses of equal magnitude after the 50-kip force is applied?

Question-AnswerCategory: Strength of MaterialsAt what temperature will the aluminum and steel segments in Prob. 2.86 have stresses of equal magnitude after the 50-kip force is applied?

At what temperature will the aluminum and steel segments in Prob. 2.86 have stresses of equal magnitude after the 50-kip force is applied?

Mazurek Gravity answered 1 year ago

Step: 1

Draw the freebody diagram of composite bar .

Step: 2

Determine the stress in each part when stress is equal.
Consider forces along horizontal direction.

Here, is force in steel segment and  is force in aluminum segment.
Substitute  forandfor.

Step: 3

Here,  is stress in steel part,  is stress in aluminum part, is cross section n area of aluminum and  is cross section n area of steel.

Step: 4

Substitute  for, for and for .

Therefore,

Step: 5

Draw the displacement diagram .

Step: 6

Calculate the at what temperature will aluminum and steel segment have stress of equal magnitude after the load  is applied by using the compatibility equation (relaxing the right support).
Compatibility equation is

Here, is length of aluminum segment,  is length of steel segment, is coefficient of thermal expansion of aluminum,  is coefficient of thermal expansion of rod , is temperature change, is cross section area of aluminum segment,  is stress in each segment, is Young’s modulus of aluminum and  is Young’s modulus of steel.
Substitute  for ,  for, for ,  for, for , for ,  for ,  for and for .

The final temperature becomes

Therefore, the at what temperature will aluminum and steel segment have stress of equal magnitude after the load  is applied is