1. Review Questions: Chapter 0 Given, calculate all the possible binary products of a, a T, b and b T What are the eigenvalues of the matrix ? Is it positive definite? No positive semi-definite. For other answers check with Matlab

2. Chapter 1 – from last year’s exam The only non-zero stress components are What is the normal stress in the direction of the vector i+2j+2k? -6.67MPa What are the three principal stresses? 60, 0, -30 MPa If the yield stress of the material is 180 MPa, What is the safety factor? 2 using Tresca, 2.27 using von Mises Young modulus is 100 GPa, and Poisson’s ratio is 0.25, and the shear stress 0.0005

3. Chapter 1 strains The only non-zero strain component is Illustrate the geometric meaning of the shear strain in a drawing. If you are showing angles give their units (radians, degrees). Provide a displacement field that will generate this strain Show that [1 0 1]’ is a principal direction. What is the normal strain in that direction?

4. Chapter 2 – For the spring system shown below, if springs 1, 2, 6 are very stiff, and spring 3 is very flexible what would be the displacement vector in terms of the spring constants 4 and 5 and the forces. F2F2 F3F3 F4F4 1 2 3 4 5 6 1 2 3 4 5

5. Chapter 2 - continued For the 3-bar truss of example 2.5, the equation for solving the displacements at Node 1 was What would be the equations if we doubled the areas of all three members? 3 instead of 1.5 Given that all members are the same, and the angles between them are the same, write the stiffness matrix if we double only the area of member 2. The 1.5 multiplying v changes to 2.5 1 2 3 4 1 2 3 F 45 