q what do you mean by section modulus z what is

Question

Q. What do you mean by section modulus (Z)? What is value of bending moment in the terms of section modulus?

Sol.: Section modulus is ratio of M.I. about neutral axis which is divided by the outer most point from the neutral axis.

Z = I/y_max  .

For the Circular Shaft (Z) = I/y = ( ? D⁴/64)/D/2   =(  D³/32)

For the Hollow Shaft (Z) = I/y = {?  (D⁴ - d⁴)/64}/D/2   =( ? /32)( D4  - d4)/D
For the Rectangular section (Z) = I/y = (bd³/12)/d/2 =bd²/6

Section modulus represents strength of the section of the beam.

As; M =  σ .I/y =   .Z

Stress at outer fiber will be highest. That is,

M =   _max.(I/y_max) =   _max.Z