Assignment 1

Text Problems

Problem 1.6

Problem 1.15

Problem 1.39

Problem 1.50(a)-modified

a) Obtain the principal stresses in descending order for case (a)

b) Form the matrix [l] whose columns contain, respectively, the direction cosines of the principal axes, oriented to form a right-handed system.

c) Perform the product  [l]^T[s][l].  Is the result what you expect? Explain.

d) Let [s_p] be the stress tensor in principal axes. Perform the product   [l][s_p][l]^T.  Is the result what you expect? Explain.

Problem 1.56(a)-modified

a) Determine the maximum shear stress for case (a).

b) Determine the direction cosines of the normals to the planes of maximum shear

c) Determine the direction cosines of the maximum shear stresses

Class Notes

Exercise 4.4.1 (Analysis of Stress - Part 2 )

s_x = -12 ksi

s_y = 10

t_xy = -8

a) Determine the principal stresses and the principal axes of stress by solving Eq. (1).  Check the result using the general formulas.

b) If the principal stress in the z direction is s₃ = 0, what is the absolute maximum shear stress, and on what planes does it act?