Section Modulus calculation and optimization
AIM: To generate the report on finding the section modulus for the Hood design and improve its strength by optimization.
Theory:
SECTION MODULUS:
- It is the ratio of total moment resisted by the section to the stress in extreme fibre.
- It gives us an idea about how much of the load given structure can take.
- If the section modulus increases the moment of resistance increases & hence its load-bearing capacity.
Here we calculate the section modulus using the formula
`S=I/Y`
Where S= section modulus
I = Moment of inertia
Y = Distance between Neutral axis and the extreme end of the hood.
So, By using Intersect option we extract the inner hood and outer hood lines which is section of hood then we join both sections .
DISTANCE BETWEEN NA AND EXTREME END OF THE HOOD:
`Y=D/2`
Where D = extreme distance of hood
`Y=481.573/2`= 240.786mm
CASE 1: We will take the section along the length of the hood and find the moment of inertia using inertia analysis tool in CATIA.
so we take minimum value of a moment of inertia
`= 1.135e-006 m^4 `
so we convert into mm^4 by multiplying 10^12 into it.
MOI = 1135000 mm^4
so, according to formula, section modulus in case 1:
`S=1135000/240.786`
=4713.729 mm^3.
CASE 2:
In this case, we come up with the section modulus and improved the section modulus of the previous section to increase the strength of the hood.
We just offset the inner hood extracted line by 0.5 mm that we used for the previous case
After the optimization, the moment of inertia of the hood changes to
`MOI = 1.186e-006 m^4` convert it into mm^4 by multiplying it by 10^12.
`MOI= 1186000 mm^4`
Y is same for both the cases as extreame end will not change.
`Y= 240.786 mm`
Section modulus for case 2 :
S=I/Y
=`1186000/240.786`
`= 4925.53 mm^3`
Conclusion :
These calculation are necessary to know the design actual withstand capability of product. As we increase the section area the moment of inertia and section modulus increases it means capacity of material also increases.