Section Modulus calculation and optimization

Section Modulus

Section Modulus is termed as the ratio of Moment of Inertia and the distance from Neutral Axis to the extreme end. And also it is the measure of strength of given member. It is indicated by "S".

`S=I/y`

I - Moment of Inertia

y - Distance from the neutral axis to extreme end.

Unit of Section Modulus is `mm^3`

Moment of Inertia

It is defined as the ratio of the net angular momentum "L" of a system to its angular velocity "`omega`" around a principal axis.

`I = L/omega`

Unit of Moment of inertia is `mm`

Section Modulus Calculation of Car Hood

Case-1: Existing Hood design

First we go with the existing hood panel to calculate the section modulus.

The max and min moment of inertia is obtained for the hood by using the NX software.

`I_max = 4.774109094 X 10^6 mm^4`

`I_min = 1.648837356 X 10^4 mm^4`

`y = 440.2439 mm`

`S_max = I_max/y`

`S_max = 4.774109094 X 10^6 //440.2439`

`S_max = 1.08442^4 mm^3`

`S_min = I_min/y`

`S_min = 1.648837356 X 10^4 //440.2439`

`S_min = 0.003745 X 10^4 mm^3`

Case-2: Modified Section

A offset of inner panel to 1mm outside from the existing panel is done to modify the design and to optimize the section modulus

The below pictures show the new `I_max`and `I_min` with respect to the changes made.

`I_max = 4.795993846 X 10^6 mm^4`

`I_min = 1.733864483 X 10^4 mm^4`

`y = 440.2439 mm`

`S_max = I_max/y`

`S_max = 4.795993846 X 10^6//440.2439`

`S_max = 1.0893 X 10^4 mm^3`

`S_min = I_min/y`

`S_min = 1.733864483 X10^4//440.2439`

`S_min = 0.003938 X 10^4 mm^3`

Conclusion

Therefore by comparing the case-1 & case-2, as the Section modulus is directly proportional to the Moment of inertia, thus by increasing the section area the moment of inertia get increased which tends to increse in section modulus. So, higher the section area of particular part will result in high strength.