Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMISATION

AIM:

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

S=Section Modulus.

I=Moment of inertia.

Y=distance between the neutral axis and the ectreme end of the object.

SECTION MODULUS:

The section modulus of the cross sectional shape is of significant importance in desiging of structures. It is a direct measure of the strength of the structure.

A structure that has a larger section modulus than another will be stronger and capable of supporting greater loads.

Area moment of inertia:

The area moment of inertia of a beams cross sectional 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=Youngs modulus.

R=Radius of gyration.

Neutral axis: When beam is subjected to pure bending the top most fbres of the beam are subjected to maximum compression, While the bottom most fibers of the beams are subjected to maximum tension.

Now to calculate the section modulus from the hood design:

Take the front section since we are dealing with the frontal crash. For that create a datum plane on the curve and at a halfway distance of the hood.

Find the intersection curve between the newly created datum plane and the hood.

The intersection curve obtained is 3D curve. We need to convert it into 2D curves so as to edit it.For that the curve is to be projected onto the datum plane.

The section is to be made a closed section to calculate the section modulus. Take only the outer line of the outer hood and inner panel and arc.

Using the inertia analysis command calculate the moment of inertia of the section.

Case1:

The outer line of the inner panel is 25 mm. In other words the depth of the inner panel is notice the changes in the section Modulus.

Calculatin of Section Modulus:

I(MOI) = 1.607 x 10^4 mm^4

Y=L/2

Y=895.47/2=447.5mm

S=I/Y

S=1.607 x 10^4 / 447.5

S=35.923 mm^3

Case 2:

The outer line of the inner panel is offset to 0.50 mm downwards. In other words the depth of the inner panel is increased to notice the changes in the section modulus.

Calculation of Section Modulus:

I(MOI) = 1.629 x 10^4 mm^4

Y=L/2

Y=895.47/2=447.5mm

S=I/Y

S=1.629 x 10^4 / 447.5

S=36.422 mm^3

CONCLUSION :

The section modulus of the section was calculated.

When the depth of the section is increased it is noticed that the section modulus increases and hence the load bearing capacity of the section. By evaluting the above cases, we can say that moment of inertia is directly propotional to the strength of the material.