Section Modulus calculation and optimization

What is SECTION MODULUS

• Section Modulus is the geometric property of the given cross-section of any structures.
• It is the direct measure of the strength of any structure.
• Higher the section modulus of a structure, the more the resistive it becomes to bending.
• FORMULA `S=I/Y`

  • S = Section modulus ( `mm^3`)

  • I= Moment of Inertia (`mm^4`)

  • Y= Distance from Neutral axis to the extreme end (mm)

• 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.

Design Study

Max MOI = I_{MAX =}`8.3137 * 10^5 mm^4`

Min MOI = I_MAX= `0.0508 * 10^5 mm^4`

Total lenght = 489.6984 mm

Y`= 244.8492 mm`

Max Section Modulus = `(8.3137 * 10^5) / 244.8492 = 3.395436864 * 10^3 mm^3`

Min Section Modulus = `(0.0508 * 10^5) / 244.8492 = 0.020747*10^3 mm^3`

So the strength of an hood varies from `0.020747*10^3 mm^3`to `3.395436864 * 10^3 mm^3`

Now lets increase the area of panel by offsetting inner panel by 2mm

Max MOI = I_{MAX =}`8.4442 * 10^5 mm^4`

Min MOI = I_MIN= `0.0596 * 10^5 mm^4`

Total lenght = 489.6984 mm

Y`= 244.8492 mm`

`Max Section Modulus`=(8.4442 * 10^5) / 244.8492 = 3.44873497 * 10^3 mm^3`

Min Section Modulus = `(0.0596 * 10^5) / 244.8492 = 0.024341*10^3 mm^3`

So the strength of an hood varies from `0.024341*10^3 mm^3`to `3.44873497 * 10^3 mm^3`

Comparison

Case No.	Max Section Modulus	Max Section Modulus	Area
1st Case	`3.395436864 * 10^3 mm^3`	`0.020747*10^3 mm^3`	`40.8642 mm^3`
2nd Case	`3.44873497 * 10^3 mm^3`	`0.024341*10^3 mm^3`	`41.0742 mm^3`

As we can see clearly by increasing the area, the value of maximum and minimum section modulus increases.

Which means the overall strenghth of the hood increases.

CONCLUSION:-

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