Section Modulus calculation and optimization

SECTION MODULUS OF A 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 'l' - moment of inertia, 'Y'- it 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, that is if we apply 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 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 neutral 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.

By using the same principle I am going to calculate the strength of hood panel.

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

Imax :- 4.856942378 × 10⁶ mm⁴

Imin :- 1.33324633 × 10⁴ mm⁴

Total neutral axis length of value was 879.5674 mm

So, at neutral axis we need 'Y' value :- Y = 879.5674/2 = 439.7882 mm

1) Section modulus (S) :- Imax/Y = 4.856942378 × 10⁶ /439.7882 = 11.04382 × 10³ mm³

2) Section modulus(S):- Imin/Y = 1.33324633 × 10⁴/439.7882 = 0.03032 × 10³ mm³

So the strength of a hood varies from 0.03032×10³ mm³ to 11.0438×10³ mm³.

Now we can make one trail is that by offsetting inner panel curve to outside by 1mm that is increasing in cross sectional then the results shown below.

Imax :- 4.862506326 × 10⁶ mm⁴

Imin: - 1.387986486 × 10⁴ mm⁴

Total neutral axis length was 839.5674 mm

So, at neutral axis we need 'Y' value :- = 839.5764/2= 439.7882 mm.

1) Section modulus: - Imax/Y = 4.862506326 × 10⁶ / 439.7882 = 11.0564 × 10³ mm³

2)Section modulus :- Imin/Y = 1.387986486 × 10⁴ / 439.7882 = 0.03156 × 10³ mm³

So he strength of hood varies from 0.03156×10³ mm³ to 11.0564×10³ mm³.

• So, here when comparing both the hoods there is change in both max and min strength values, what it cane to know that when i increase sectional area by 1mm the value of minimum strength was increased from 0.03032×10³ mm³ to 0.03156×10³ mm³ and maximum strength was increased from 11.0438×10³ mm³ to 11.0564×10³ mm³. Hence with increase in cross sectional area results in increase in strength.
• So newton's first law 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 called it as a MOMENT OF INERTIA.
• In case of hood also same principle will work, that is when we increase cross sectional area by 1mm the minimum load carrying capacity or strength was increased by approximately 4% and maximum strength was increased by approximately 0.1%.
• The strength of material also depends upon the composition of 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 cross sectional area results in increase of the strength of material.