Question

In case of a circular section the section modulus is given as

Answer 1

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. ... The elastic section modulus is defined as S = I / y, where I is the second moment of area (or moment of inertia) and y is the distance from the neutral axis to any given fiber.

Answer 2

In the case of a circular section the section modulus is given as:

• S = I / y is the elastic section modulus, where I is the second moment of area (or area moment of inertia, not to be confused with a moment of inertia) and
• It's the ratio of the beam cross-moment sections of inertia (I) to the extreme fiber's distance from the neutral axis (ymax).
• The section modulus, in the case of circular sections, is Z = I/ymax

I = Moment of inertia = (πxd^4)/64

y = the distance between the neutral axis and any particular fiber = d/2

Zcircular section = I/ymax

Zcircular section = [(πxd^4)/64]/(d/2)

Zcircular section = (πxd^3)/32