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.