Question

Mechanics of Materials.

Answer 1

Original question

Answer 2

^formulas.

Answer 3

i am here

Answer 4

The I values I have, I1, I2, and I3 need to be sub. into another equations to solve for principal?

Answer 5

so far, I have the three solutions for the cubic as \(\sigma_p\)=6,12, 19.8 (approx.), or
6.095033221071827
12.08664492527859
19.81823846971175
I'll have to work out the solutions for l,m,n (direction cosines) when I get back in town.

Answer 6

Can you please explain to me how you got sigma_P for x, y, and z. I would like to understand how to use the formulas I showed you.

Answer 7

All I did was to expand the determinant to get the cubic equation, the equivalent of the I1, I2, I3 business,thus:
f(p)=-p^3+38*p^2-434*p+1460, the solution of which are:
{6.095117269851252, 12.086,64426091995, 19.81823846971175}
The solution was obtained first by graphing to get the real roots 6,12, 19.8, then refined using Newton's method.
After that, I will have to look into RREF or eigenvalues to get the roots of l,m,n, which I believe are direction cosines.