Plot the variation of Q11 as a function of the angle θ between 0 and 90° , using the material properties of given Exercise. When does Q11‾ becomes numerically equal to Q22‾?

Exercise

Consider a plane defined in parametric form as

F(x,y,z) = (x/a) + (y/b) + (z/c) - 1 = 0

where a, b, c are the intercepts on the x, y, z axes, and take a = 3, b = 4, c = 5. The stress tensor at that point, in contracted notation, is σ₁ = 100, σ₂ = 10, σ₃ = -20, σ₄ = 1, σ₅ = 2, σ₆ = -5. Compute the stress vector at x = y = z = 60/47 using Cauchy's law.