User:Eas4200c.f08.spars.lee/Homework 5

27 October
Bidirectional bending recipe

Diagram

Equation 4.26

Equation 4.27

The moment of inertia tensors, $$ \ I_y ,I_z, I_{yz}, $$ (also written as $$ \ I_y = I_{yy} , I_z = I_{zz} $$) are determined by

Equation 4.28a

Equation 4.28b

Equation 4.28c

Which is related to the bending normal stress, $$ \ \sigma_{xx} $$, according to the equation

Equation 4.29

The denominator of the above equation is also the determinant of a submatrix of the inertial tensor matrix

matrix

proof that $$ \ I_{yz} = I_{zy} $$

Along the neutral axis the bending normal stress, $$ \ \sigma_{xx} $$, is equal to zero

Equation 4.30

Diagram