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 high capacity 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 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 the moment of inertia, have higher 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 the 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 the neutral axis line lies on the middle of the section only have higher strength at a particular point, so, here 'Y' value was inversely proportional to section modulus.

CALCULATIONS

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

I_min:- 7.371X10⁵mm⁴

I_max:- 1.5040x10⁸mm⁴

Total length of 'Y' value was 489.072 mm

So,at neutral axis we need `'Y' value: Y/2=489.072/2=244.536 mm`

1)Section modulus(S):-I/Y=7.371X10⁵mm⁴/244.536 mm

=1.507X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=3.18672x10⁸mm⁴/244.536mm

= 0.019x10⁸mm³(minimum strength).

So the strength of a hood varies from 0.019x10⁸mm³ to 1.507X10³mm³

Now for optimization

The max value for the inner panel curve offsetting 0.2 mm from the reference of the assemble master section.

Here the inner panel curve offsetting outside by 0.2 mm i.e increase in cross-sectional area, the results are shown below.

I_min:-7.520X10⁵mm⁴

I_max:-1.525x10⁸mm⁴

The total length of the 'Y' value was 489.072 mm

So,at neutral axis we need `'Y' value: Y/2=489.072/2=244.536 mm`

1)Section modulus(S):-I/Y=7.520X10⁵mm⁴/244.536 mm

=1.537X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=1.525x10⁸mm⁴/244.536mm

= 0.031x10⁸mm³(minimum strength).

So the strength of a hood varies from 0.031x10⁸mm³ to 1.537X10³mm³

^CONCLUSION:-

• So, here when comparing both the hoods there are changes in both MAX strength values came to know that when increased sectional area by 0.2 mm the value of minimum strength was increased from 1.504X10³mm³ to 1.537X10³mm³, Hence with the increase in the cross-sectional area resulting in an increase in strength.
• But, when we see the value of minimum strength it slightly increases from 0.019x10³mm³ to 0.031x10³mm³ , this is due to the design of the hood, here what we want to know is that when an increase in the cross-sectional area there will be an increase in minimum strength or maximum strength or increase in both.
• The strength of the material also depends upon the composition of the material, thickness, and cross-sectional area of an object.

RESULT:-

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