Section Modulus calculation and optimization

Aim:

To find the section modulus of the hood and optimization to improve the overall section modulus.

Objective:

Use the section from your Hood design and calculate the section modulus using the formula S= I/y.

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, radius 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.

S=I/Y

Here,

S = Section modulus (Unit mm^3)

I= Moment of Inertia (Unit mm^4)

Y= Distance from Neutral axis to the extreme end (Unit mm)

Area Moment of Inertia:

The area moment of inertia of a beam cross section area measures the beam ability to resist bending. The larger the moment of inertia less will be the bend.

Where,

M = Bending Moment

I = Area moment of Inertia

E = Young modulus

R = Radius of gyration

Calculation:

Case 1:

Interaction from hood design

I (MAX) = 4.863642165e+06 (mm^4)

I (MIN) = 1.556368592e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) Value is considered

Y = Total distance / 2, Total distance = 877.0999 mm

Y = 877.0999 / 2

= 438.545 mm

Therefore, S = 1.556368592e+04 mm^4 /438.545 mm

S = 35.48937 mm^3

Case 2:

By increasing the hood inner panel with 0.4mm outwards and optimise the section modulus.

I (MAX) = 4.856634818e+06 (mm^4)

I (MIN) = 1.574641543e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) Value is considered

Y = Total distance / 2, Total distance = 877.0999 mm

Y = 877.0999 / 2

= 438.545 mm

Therefore, S = 1.574641543e+04 mm^4 /438.545 mm

S = 35.90604mm^3

Conclusion:

Resulting by comparing case 1 & case 2,

1. The section modulus value of case 2 is higher than the case 1
2. As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase. Which the moment of inertia directly proportional to the strength of the material.