Section Modulus calculation and optimization

Aim

To calculate section modulus of hood and optimize the design to have improved section modulus.

Section modulus:-

Section modulus is a direct measure of a strength of any cross sectional area of an object about an reference axis.

The formula of section modulus is given by,

S=I / Ymax

Where,
I = Moment of inertia (mm^4)
Y = Distance between neutral axes and outermost fiber (mm)

- Second moment of area or moment of inertia

- 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.

- This picture contains the following scene. 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 the straight beam and it is bending in the middle.

- Certain shapes are better than others at resisting bending as demonstrated in the diagram. Clearly, the orientation of the shape also influences bending.

Steps to calculate section modulus:-

• Step 1:- Find location of centroid of given cross section.
• Step 2:- Find moment of inertia about neutral axis (INAINA)
• Step 3:- Find YmaxYmax from neutral axis.
• Step 4:- Find elastic section modulus using the formula provided above.

Moment of inertia is nothing but offering resistance against the moment, bending or twisting. So higher the moment of ineria higher will be its resistance to deform is higher.

Here the sectional modulus of hood design before optimization

Momemt of inertia is calculated by NX-CAD software

I_max – 8.268922918 x 10^5 (mm^4)

I_min – 3.798770229 x 10^3 (mm^4)

Y = Total length / 2

= 486.13/2

=243.065 mm

section modulus for max. = 8.268922918 x 10^5 / 243.065

= 3.4019 x 10^3

section modulus for min. = 3.798770229 x 10^3 / 243.065

= 0.01562 x 10^3

So for this hood design section modulus range from 3.4019 x 10^3 mm^3 to 0.01562 x 10^3 mm^3

Optimized design

Inorder to increase the sectional modulus, cross sectional area has to be increased. So here the optmized design:-

I_max – 8.289608213 x 10^5 (mm^4)

I_min – 3.881908444 x 10^3 (mm^4)

Y = Total length / 2

= 486.13/2

=243.065 mm

section modulus for max. = 8.289608213 x 10^5 / 243.065

= 3.410449 x 10^3

section modulus for min. = 3.881908444 x 10^3 / 243.065

= 0.01597 x 10^3

So for this hood design section modulus range from 3.410449 x 10^3 mm^3 to 0.01597 x 10^3 mm^3

It is evident that if the section modulus is increased from 3.4019 x 10^3 mm^3 to 3.410449 x 10^3 mm^3 by increasing the sectional area.

Conclusion

Strength of material is directly proportional to the moment of interia, thus increasing the sectional area increase the increases strength of component.

Thus sectional modulus for hood design is calculated and optimized design is also done to increase the section modulus of the hood.