Problem # p006

### Thermal stress, statically indeterminate

 In the figure to the left a rod is installed in between two walls the distance between which will remain at L for good. The rod is made out of two sections which both have the same cross-section, A, and initially the same length, L/2. They are made out of different material, i.e. Young's modulus E1 and E2 and coefficients of thermal expansion &alpha1 and &alpha2, respectively. The two sections are intially installed in a stress-free manner but then the temperature changes by an amount ΔT.

#### Questions

1. Sketch the free body diagrams for both sections individually and label the forces. What can you say about the relationship between the forces in terms of an equation ?
2. Define a label for the change in length of the left section (index 1 ) and one for the right section (index 2). What can you say about their relationship in form of an equation.
3. Write down the constitutive laws ( including the correct sign +/- ) for each of the two sections.
4. From the above find the equation for the force acting at the intersection of the two sections.