Section Modulus calculation and optimization

#Objective: To Calculate the Section modules of the hood design and optimize the Section to

improve the strenth.

#Theory:

Section Modulus: It is a geometric property for a given cross-section used in the design of beams

or flexural members. The section modulus is defined as S=i/y, where i is the second moment of Area (area moment of

inertia) y is the distance from the neutral axis to any given fiber.

Significance of Section Modulus:

It is a direct measure of the strength of the beam. A beam that has a larger section modulus than

another will be stronger and capable of supporting greater load.

#Obsevation:

Total Span length of hood section= 875.8367mm

y= 875.8367/2=437.9183mm.

#Initial Section Inertia Analysis:

Maximum Moment of Inertia, M1=4.76215595 X 10^6mm^4.

Minimum Moment of Inertia, M2=1.311707578 X 10^4mm^4.

We know that Section Modulus, S=i/y

Initial S(min)= M2/y= (1.311707578 X 10^4) / 437.91835= 29.9532mm^3.

#Optimizing the Section:

In order to optimize the Section, I increased the distance between the curves of the inner and outer

panels by 0.5mm by taking offset from the inner panel curve and closed the curve.

#Optimized Section Inertia Analysis:

Maximum Moment of Inertia, M1'= 4.757050478 X 10^6 mm^4.

Minimum Moment of Inertia, M2'= 1.338242506 X 10^4 mm^4.

Optimized S (min)=M2'/y=(1.338242506 X 10^4) / 437.91835=30.5591^3.

#Observation Table:

Initial Section Modulus Final Section Modulus

29.9532 mm^3. 30.5591mm^3.

#Result: Hence by increasing the gap between the panels by 0.5mm, we have obtained an

improved value of section modulus, thus strengthening the hood design.