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.

Come up with a new section that has improved the section modulus of the previous section and mention what change you made that has increased the strength.

Section Modulus:

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

What is Section Modulus ?

Section modulus is defined as the ratio of moment of inertia of a section about the neutral axsis to the distance of the outermost layer fromt the neutral axsis.It is defned by the symbol S.

Formula of section Modulus: It may be defined as the ratio of total moment resisted by the section to the stress in the extreme fibre 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).

What is Moment of Inertia?

The moment of inertia of an object is a determined measurement for a rigid body rotating around a fixed axis. The axis might be internal or external, and it can be fixed or not. However, the moment of inertia (I) is always described in relation to that axis.

The moment of Inertia depends on the distribution of the mass around its axis of rotation. MOI varies depending upon the position of the axis that is chosen. That is, depending on the location and direction of the axis of rotation, the same item might have various moment of inertia values.

Angular mass or rotational inertia are other names for the moment of inertia.

The SI unit of moment of inertia is kg m².

Calculation:

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.

MOI (MAX) = 4.812952890e+06 (mm^4)

MOI (MIN) = 1.619911838e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) Value is considered

Y = Total distance / 2,

Total distance = 877.3178 mm

Y = 877.3178 / 2 = 438.6589 mm

Therefore,

S = 1.619911838e+04 mm^4 /438.6589 mm

S = 36.9287 mm^3

2: After Optimization

The hood inner panel’s curve is offset by 0.5 mm Downwards and section inertia analysis is done in closed curve.

MOI (MAX) = 7.305009867 e+06 (mm^4)

MOI (MIN) = 2.633710424e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) Value is considered

Y = Total distance / 2,

Total distance = 877.3178 mm

Y = 877.3178 / 2 = 438.6589 mm

Therefore,

S = 2.633710424e+04 mm^4 /438.6589 mm

S = 60.0400 mm^3

Conclusion:

Resulting by comparing 1 & 2,

1. The section modulus value of 2 is higher than the 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.