Assignment 4

Text Problems 3.20, 3.23, 3.29,  3.34, 3.40, 3.41

3.20. Figure added. Statement modified.

A bar of rectangular cross-section is restrained in the x direction at the end faces, and in the y direction at the top and bottom faces, but is free in the z direction.  Use a semi-inverse approach to determine the stresses and strains in the bar for a temperature rise of T₁ degrees. Treat the problem as one of plane stress, and please follow these steps:

a) State on the figure the two boundary conditions on each of the four boundary faces of the bar.

b) Make the simplest assumptions about the solution for displacements and/or stresses that are consistent with the boundary conditions, then attempt to satisfy the governing differential equations and boundary conditions.

3.23. Modified

1. Refer to the solution of Example 3.2, case (b). Determine the axial force P_x and moment M_z that the walls in Fig. 3.6b apply to the beam, in terms of integrals involving T(y).

2. Refer to case (a) of Example 3.2.  Formulate this problem as the superposition of the problem of part 1 and another problem.  Obtain the solution to that second problem, and give the final solution for the stresses and the strains.