Section Modulus calculation and optimization

Aim: Doing an analysis of the hood to get the section module and modifying the cross-section area of the hood to increases the section modules of the hood.

Objectives:

• Study of the moment of inertia of the hollow parts.
• Study about section modulus and on which parameters it depends Learn how to do get a moment of inertia in NX software.

Theory:

Section properties involve the mathematical properties of structural shapes. They are of great use in structural analysis and design. Note that these properties have nothing to do with the strength of the material, but are based solely on the shape of the section. It explains why some shapes are more efficient at supporting loads than others.

These properties are looked at in more detail following:

• Centre of the area (or centroid)
• The second moment of area or moment of inertia (I)
• Section modulus (Z)

Centre of area (centroid)

The centroid of a section is important in structural design and is like the center of gravity of the shape. Most structural shapes have their centroid tabulated by the manufacturer. Many other simple shapes are symmetrical about the x-x and y-y axes and the centroid can easily be seen. Occasionally a structural shape is made up of more than one structural section. In these cases, a calculation is needed to work e the position of the centroid so that further structural design and analysis can be carried out.

Second moment of area (I):

The second moment of area is also known as the moment of inertia of a shape. It is directly related to the area of material in the cross-section and the displacement of that area from the centroid. Once the centroid is located, the more important structural properties of the shape can be calculated. The axis that determines the centroid is also known as the neutral axis (N/A).The second moment of area is a measure of the efficiency of a shape to resist bending caused by loading. A beam tends to change its shape when loaded. The second moment of area is a measure of a shape's resistance to change.

Formula:

S = Section Modulus

I = Moment of Inertia

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

S = I/y.

Now we calculate the section inertia for the hood model that we have designed along the 0 y axis:

To calculate the Moment of inertia we require a closed section, so what we do is take the section and join the open embossed part with spline tool and this is the section that we get after joining the outer part of the hood and the lower most surface of the inner pannel

This is the section of the hood and we have calculated the section inertia for it along the 0y axis and the calculation are shown in the below images.

Here we can see that the maximum MOI is 4.90 and the minimum MOI is 1.46

We have to improve the MOI of the section, to improve the section inertia we increase the distance between the emboss and the outer panel of the hood surface from 23.04 mm to 30.00 mm and the resulting section and the MOI has been shown below:

The maximum MOI is 5.77 and the minimum MOI is 2.65