Section Modulus calculation and optimization

SECTION MODULUS ANALYSIS

Use the Section from your Hood design and calculate the Section Modulus using the formula

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object

Come up with a new section that has an improved Section Modulus compared to the previous one and mention what changes you made which resulted in the increased strength.

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:

The section modulus (S) is the geometry property of the cross-section used for designing beams and flexural members. It does not represent anything physically.

The formula of section Modulus: It may be defined as the ratio of total moment resisted by the section to the stress in the extreme fiber which is equal to yield stress.

Which is equal to yield stress.

Therefore

S=I/y, Where

S= Section modulus (mm^3)

I = Moment of inertia of the section to the stress in the extreme end of the object (mm^4)

Y= Distance between the neutral axis and extreme end of the object (mm).

Area Moment of Inertia:

The area moment of inertia of a beam cross-section area measures the beam's 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

Neutral Axis: When the beam is subjected to pure bending the top most fibers of the beam are subjected to maximum compression, while the bottom most fiber of the beams are subjected to maximum tension.

• This picture contains the following scene, a Diagram of a beam on its narrow edge supported at both ends. A man is walking on a straight beam. Diagram of a beam resting on its flat side supported at both ends. A man is walking on a straight beam and it's bending in the middle.

Calculation:

Case 1: Before Optimization

The hood which was already created is imported and the section inertia analysis is done.

We have to make sure that the curve obtained is a single/closed curve.

I (MAX) = 127700000 (mm^4)

I (MIN) = 397400 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) Value is considered

Y = Total distance / 2, Total distance = 477.96 mm

Y = 477.96 / 2

= 238.98 mm

Therefore, S = 397400 mm^4 /238.98 mm

S = 1662.901 mm^3

Case 2: After Optimization

The hood inner panel’s curve is offset by 0.5mm outwards and section inertia analysis is done the same as in case 1 for a closed curve.

I (MAX) = 132400000 (mm^4)

I (MIN) = 422200 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) Value is considered

Y = Total distance / 2, Total distance = 477.96 mm

Y = 477.96 / 2

= 238.98 mm

Therefore, S = 422200 mm^4 /238.98 mm

S = 1766.675 mm^3

Conclusion:

Resulting by comparing case 1 & case 2,

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

*****THANK YOU*****