Section Modulus calculation and optimization

SECTION MODULUS OF AN HOOD

• Section modulus is a direct measure of the strength of any sectional area of an object about a reference axis (neutral axis).
• Strength is nothing but, capable of supporting greater loads, so higher the strength it has a highly capable of supporting greater loads.
• This strength can be measured directly from the Section modulus formula, and defined by the below formula.
• Section modulus represented with a symbol of 'S:

S = I/Y

Where ‘I’ moment of inertia

‘Y’ is the distance from the reference line (neutral axis) to one of the extreme ends of the object.

• Moment of inertia is nothing but offering resistance against of moment, bending or twisting, i.e., if we applied any external load on the body, how much resistance its offering to tend to deform.
• So, the higher the value of the moment of inertia, have higher the resistance to deform under a certain load, hence we can say that moment of inertia is directly proportional to the strength of the material, and strength of the material can be calculated with the help of section modulus.
• If we vary the neutral axis towards the positive or negative side the overall strength of the body will decrease, because when neutral axis line lies in the middle of the section only have higher strength at a particular point, so, here 'Y' value was inversely proportional to section modulus.

Here the moment of inertia was calculated by using CATIA V5 obtained values are

Imax = 8.147X10⁵mm⁴

Total length of Y value was 476.483mm

So.at neutral axis we need Y' value: Y/2 = 476.483/2 = 238.241mm

Section modulus(S) = I/Y-8.147X10⁵mm/238.241mm

=3.41X10³mm (Maximum strength)

Now, one more trail is that here the inner panel curve offsetting outside by 0.5mm i.e., increasing in cross-sectional area, the results shown below.

I obtained the values of

Imax = 8.561X10⁵mm⁴

The total length of Y value was 476.483mm

So.at neutral axis we need Y' value: Y/2 = 476.483/2 = 238.241mm

Section modulus(S) = I/Y-8.561X10⁵mm/238.241mm

=3.59X10³mm (Maximum strength)

• Newton’s first law also explains that, if higher the mass, the force required to move the object is also high due to offering more resistance in order to move the object. This resistance we call it as “MOMENT OF INERTIA”.
• In the case of the hood also the same principle will work, i.e., when an increase in cross-sectional area by 0.5mm the minimum load carrying or strength was increased by approximately 18% what we observed from the above discussion.
• The strength of the material also depends upon the composition of the material, thickness and cross-sectional area of an object.

Conclusion

The strength of the material is directly proportional to the moment of inertia, hence increase in the sectional area there is an increase in the overall mass of an object, hence have increase in strength.