Section Modulus calculation and optimization

OBJECTIVE: Use the Section from your Hood design and calculate the section modulus.

SECTION MODULUS: Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. Other geometric properties used in the design include an area for tension and shear, the radius of gyration for compression, and the 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.
S=I/Y
Here,
S = Section modulus
I= Moment of Inertia (Unit mm 4)
Y= Distance from the Neutral axis to the extreme end (unit mm)
The Unit of a “section modulus” is (mm3)

MOMENT OF INERTIA: It is also known as the second moment of area. 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.

Changing the position can show the difference in bending which is because of the centroid distance from the extreme fiber end. In Layman's terms, in this position there is more material from the axis to the specific direction, to resist the load which makes less bend and improves the strength.

SECTION MODULUS OF HOOD:

Moment of Inertia (max): 4.79041x10^6 mm^4

Moment of Inertia (max): 1.39416x10^4 mm^4

H = 879.518 mm

Y = H/2 = 879.518/2 = 439.759 mm

S = I/Y = 1.39416x10^4/439.759 = 31.70 mm^3

Section Modulus for the given section is 31.70 mm^3.

SECTION MODULUS IMPROVED SECTION:

This is the improved section of the hood after increasing the 0.5 mm thickness in some places.

Moment of Inertia (max): 4.78506x10^6 mm^4

Moment of Inertia (max): 1.41284x10^4 mm^4

H = 879.518 mm

Y = H/2 = 879.518/2 = 439.759 mm

S = I/Y = 1.41284x10^4/439.759 = 32.18 mm^3

Section Modulus for the improved section is 32.18 mm^3.

CONCLUSION: The strength of the material is directly proportional to the moment of inertia, hence increase in the sectional area of the mass of the hood also increases and results in increased strength of the hood. By increasing 0.5 mm in the thickness of the section at only some places, we have seen a 0.48 mm^3 increment in section modulus. We can further improve the section modulus by increasing thickness or other parameters if possible.