Section modulus:

Define the Section modulus. What do you mean by torsional section modulus or polar modulus? 

The moment of inertia of plane about the axis perpendicular to plane of area is called as polar moment of inertia of area with respect to point at which the axis intersects plane.

The polar moment of inertia of the solid body (J) = I_xx + I_yy  =   /32.D⁴

Section Modulus(Z)

Section modulus is ratio of MI about neutral axis divided by most distant point from neutral axis.

Z = I/y_max

The section modulus for the circular solid shaft (Z)    = ( ? /64.D⁴)/D/2 =   ?/32.D³

The section modulus for circular hollow shaft (Z) =[ ?/64.(D_o - D_i  )]/D_O/2 =   ?/32.(Do - D_i )/D_O

The section modulus for the rectangular section (Z)    = (bd³/12)/d/2 = bd²/6