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' is 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

Thats why formula represented as above.

By using the same principle i going to calculate the strength of an hood panel.

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

I_{min, M1}:6.401x10^-7m^4

I_{MAX, M2}: 1.336x10^-4m^4

Total length of 'Y' value was 478.8978mm

So,at neutral axis we need 'Y' value:-Y/2=478.8978/2=239.4489mm

1)Section modulus(S):-I/Y=6.401x10-5mm^4/239.4489mm

=2.673X10^-3mm^4(Minimum strength).

2) Section modulus(S):-I/Y=1.336x10-2mm^4/239.4489mm

=0.5579mm^4(Maximum strength).

So the strength of an hood varies from 0.5579mm^4 to 2.673X10^-3mm^4

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

I_{min, M1}:6.751X10^-7 m^4

I_{MAX, M2}:1.388X10^-4 m^4

Total length of 'Y' value was 478.8978mm

So,at neutral axis we need 'Y' value:-Y/2=478.8978/2=239.4489mm

1)Section modulus(S):-I/Y=6.751X10^-5mm^4/239.4489mm

=2.8194X10^-3mm^4(Minimum strength).

2) Section modulus(S):-I/Y=1.388X10^-2mm^4/239.4489mm

=0.5796mm^4(Maximum strength).

So the strength of an hood varies from 0.5796mm^4 to 2.8194X10^-3mm^4.

• So, here when comparing both the hoods there is changes in both MAX and MIN strength values, what i came to know that when i increased sectional area by 0.5mm the value of minimum strength was increased from 0.5579mm^4 to 0.5796mm^4, Hence with increase in cross sectional area results in increase in strength.
• The strength of the material also depends upon the composition of material ,thickness and cross sectional area of an object.
• So above discused value of hood panel moment of inertia and optimised hood inner panel value of moment of inertia as given in the attachment. the values in the attachment is helps to calculate all the above calculation.

CONCLUSION:-

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