The design of a mechanical component requires that the maxim

The design of a mechanical component requires that the maximum principal stress to be less than the material strength. For a component subjected to arbitrary loads, the principal stresses, o, are given by the solution of the equation [sigma_xx tau_xy tau_xy tau_xy sigma_yy tau_yz tau_xz tau_yz sigma_zz] {I_x I_y I_z} = sigma {I_x I_y I_z} where the sigma values represent normal stresses in the x, y, and z directions, and the t values represent shear stresses in the xy, xz, and yz planes. The I (Latin small letter L) values represent direction cosines that define the principal planes on which the principal stress occurs. [sigma_xx tau_xy tau_xy tau_xy sigma_yy tau_yz tau_xz tau_yz sigma_zz] = [10 4 -6 4 -6 8 -6 8 14] MPa Use interactive Matlab software B principal stresses and principal planes in a machine component for the following stress condition.

Solution

>> A = [ 10 4 -6; 4 -6 8; -6 8 14];
>> [V D] = eig(A)

V =

-0.2792 0.8343 -0.4754
0.8905 0.4102 0.1970
-0.3594 0.3683 0.8574

D =

-10.4828 0 0
0 9.3181 0
0 0 19.1647

D is the principal stresses and the V is the principal directions