Section Modulus calculation and optimization

Title : Section Modulus calculation and optimization

What is 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 and shear, ragius of gyration for compression, and moment of inertia and polar 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 and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.

Second Moment of Area (I)

The second moment of area is also known as the moment of inertia of a shape. It is directly related to the area of material in the cross-section and the displacement of that area from the centroid. Once the centroid is located, the more important structural properties of the shape can be calculated. The axis that determines the centroid is also known as the neutral axis (N/A).

The second moment of area is a measure of the 'efficiency' of a shape to resist bending caused by loading. A beam tends to change its shape when loaded. The second moment of area is a measure of a shape's resistance to change.

Section Modulus Formula :

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre.

Section Modulus of Hood Design :

Moment of inertia maximum = 8.19398 x 10^5 x mm^4

Moment of inertia minimum = 5.34031 x 10^3 x mm^4

Y = 485.75 / 2 = 242.88 mm

S = I / Y

S = 5.34031 x 10^3 / 242.88

= 21.98 mm^3

Moment of inertia maximum = 8.16698 × 10^5 mm^4

Moment of inertia minimum = 5.51216 × 10^3 mm^4

Y = 485.7599 / 2 = 242.8799 mm

S = I / Y

S = 5.51216 × 10^3 / 242.87

= 22.69 mm^3