Section Modulus calculation and optimization

SECTION MODULUS:

DEFINITION

Section Modulus is the geometric property of the given cross-section of any shaft or beam structures.

It is the direct measure of the strength of the shaft section or the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus is defined as the ratio of moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibres.

The common way of calculating Section_Modulus for a shaft requires is its diameters even if it is a solid or hollow shaft.

If it is a beam (Square/rectangle in shape) then it will require the moment of inertia and the distance of the outer fibres from its neutral axes.

S= I/Y

On the other hand, there are two types of section moduli,

• Elastic Section_Modulus, and
• Plastic Section_Modulus.

The Elastic Section Modulus has the same definition as the above-mentioned formula where it should be used for the materials which behave elastically under loading.

whereas the Plastic Section Modulus used for the materials which have plastic behaviour as a dominant character.

MOMENT OF INERTIA: The bending stiffness of a structural member’s cross-sectional shape.

Moment of inertia is specific to bending of the cross section of the member .

OBJECTIVE:

To calculate the section modulus for the hood design and to increase the strength with the modified cross section.

DESIGN

Now we have to calculate the section modulus for the hood design.

First create a centre plane and intersect it with the hood assembly.

Create a sketch on the plane and project the intersected curve and trim as per requirements.

CASE 01:

calculate the moment of inertia for the sketch.

Y - The distance between the neutral axis and the extreme end of the fibre.

Y=439 mm.

MOI (max)=4758591.461

Section Modulus (S) = 4758591.461/439=10839.616

MOI (min)=14937.58225

Section Modulus (S) = 14937.58225/439=34.02638

CASE 02:

In this we have to modify the distance between inner and the outer panel of the hood.

The curve of inner panel is offseted to about 0.5mm and the section modulus is calculated.

Moment Of Inertia

Y=439 mm.

MOI (max)=4750193.197

Section Modulus (S) = 4750193.197/439=10820.485

MOI (min)=15133.89365

Section Modulus (S) = 15133.89365/439=34.4735

CONCLUSION:

On comparing these two(as per min MOI) we know that while increasing the distance between the inner and the outer panel the Moment of inertia increases.

Moment of inertia is directly propotional to Section Modulus.

So the section modulus also increases and this indicates the increase in the strength of the hood.