Section Modulus calculation and optimization

SECTION MODULUS OF AN HOOD

• Section modulus is a direct measure of strength of any sectional area of an object about an reference axis(neutral axis).
• Strength is nothing but, capable of supporting greater loads, so higher the strength it has a high capable of supporting greater loads.
• This strength can measured directly from Section modulus formula, and defined by 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 end of an 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, higher the value of moment of inertia , have higher resistance to deform under certain load, hence we can say that moment of inertia 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 positive or negative side the overall strength of the body will decrease , because when nuetral axis line lies on the middle of the section only have higher strength at particular point, so, here 'Y' value was inversely proportional to section modulus.

In thisreport By Sahil Parab , With Section Modulus of normal section of hood, after intersecting we got

We had to join the missing geometry and then find the Section Inertia.

We have

Imax = 9.26x10^7mm^4

Imin= 2.824x10^5mm^4

total length of the hood is 883.80mm.

so y= 441.9mm

Section modulus (Max): Imax/y = 209.5x10^3mm^3

section Modulus (Min) : Imin/y = 0.639x10^3mm^3

so the strength varies from 0.639x10^3mm^3 to 209.5x10^3mm^3.

Offset of 3mm was made and strength was checked again.

Imax = 9.24x10^7 mm^4

Imin = 3.17x10^5 mm^4

y= 441.9mm

SectionModulus (max) = Imax/y = 209.09x10^3mm^3

Sectionmodulus(min) = Imin/y = 0.717x10^3mm^3

The strength varies from 0.717x10^3mm^3 to 209.09x10^3mm^3 .

Conclusion

When we increased the cross section area by offsetting the inner panel sectioin by 3mm, we saw the difference of minimum strength vary from 0.639x10^3mm^3 to 0.717x10^3mm^3 .

while max strength from 209.5x10^3mm^3. to 209.09x10^3mm^3.

We here are trying to prove that if we increase the cross section area the strength of the body part also increases.

However the material used and thickness and other factors also plays a vital role.

Hence

Strength of a material is directly proportional to the Moment of inertia and moment of inertia is directly porportional to cross sectional area. As we increase cross sectional area its mass wil increase and I.