Consider a three bar system shown in the figure below. the two outer bars are ma

Question

Consider a three bar system shown in the figure below. the two outer bars are made of material 1 with properties E1, v1, and alpha . the cross-sectional area of each outer bar is A1 and that of middle-bar is A2. the middle bar has a length of L whereas each of the two outer bars as an initial length of L - g. the system is subjected to a temperature change of Delta T and a downward force P at the top of the rigid cap. Determine the displacement of the rigid cap due to the force P and the temperature change Delta T. Specialize the solution for the cases (a). When Delta T = 0 and (b). When p = 0.

Explanation / Answer

1)when temperature is increase then

elongation will occur

so chnge in height = L*alpha2*delta T in the upward direction

but due to force P

downward displacement

will be there...

stress= F/A

and

E2= stress/strain

thus

P/A2 = E2*delta L/L

thus delta L= P*L/E2A2

applying principle of superposition we get net displacemnt

=L*alpha2*delta T- P*L/E2A2

2).

case a- displacement= P*L/E2A2 below

case b-displacement= L*alpha2*delta T

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