Section Modulus calculation and optimization

Section modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension, radius of gyration for compression, and moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus (S) and the plastic section modulus (Z).

The bending equation is M / I = σ /y = E / R.

The elastic section modulus is defined as Z = 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 fibre.

Section 1

y₁

Calculations for Z₁

y₁ = 876.5483/2

y₁ = 438.27415mm

I₁ = 8.975700806 * 10⁷ mm⁴

Z₁ = I / y

Z₁ = 8.975700806 * 10⁷ / 438.27415

Z₁ = 0.0204 * 10⁷

 

Section 2

y₂

Calculations for Z₂

y₂ = 876.5483/2

y₂ = 438.27415mm

I₂ = 8.986590685 * 10⁷ mm⁴

Z₂ = I / y

Z₂ = 8.975700806 * 10⁷ / 438.27415

Z₂ = 0.0205 * 10⁷