Section Modulus calculation and optimization

 SECTION MODULUS OF AN HOOD

• Section modulus is used to calculate the direct measure of strength of any sectional area of an object with an reference axis or neutral axis.
• Strength means capable of supporting loads, so higher the strength higher capablity of supporting greater loads.
• This strength can be measured directly from Section modulus formula, and is defined below.
• Section modulus is represented with a symbol  'S'.

                                                                                        S=I/Y

         where 'I' is the moment of inertia

         'Y' is the distance from the reference axis (neutral axis) to one of the extreme point 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 it provides against the deformation property.
• So, higher the value of moment of inertia ,higher will be the resistance, hence we can say that moment of inertia is directly proportional to the strength of the material.Therefore, 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.

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

Here the moment of inertia was calculated and below the values are tabulated

I_MAX:1.786X10⁶mm⁴

I_min:1.55x10⁸mm⁴

Total length of 'Y' value was 490.029mm

At neutral axis we need Y/2=490.029/2=245.0145mm

1)Section modulus(S):-I/Y=1.786X10⁶mm⁴mm⁴/245.0145mm

                                                =7.289X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=1.55x10⁸mm⁴/245.0145mm

                                                =6.32x10³mm³(minimum strength).

So the strength of an hood varies from 0.0632x10³mm³to 7.289X10³mm³

Now, we offset the inner panel by 0.5mm outside i.e increasing in cross sectional area,the results shown below.

Obtained values

I_MAX:1.859X10⁶mm⁴

I_min:1.609x10⁸mm⁴

Total length of 'Y' value was 490.029mm

At neutral axis we need Y/2=490.029/2=245.0145mm

1)Section modulus(S):-I/Y=1.859X10⁶mm⁴/245.0145mm

                                                =7.58X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=1.609x10⁸mm⁴/245.0145mm

                                                =6.56x10³mm³(minimum strength).

So the strength of an hood varies from 7.58X10³mm³ to 6.56x10³mm³.

• So, here when comparing both the hoods there is a change  in both MAX and MIN strength values,i.e the value of minimum strength was increased from 6.32x10³mm³ to 6.56x10³mm³, and maximum strength was also increased from 7.289X10³mm³ to 7.58X10³mm³ with increase in cross sectional area it results in increase in strength.
• Here just by increase in cross sectional area by 0.5mm the minimum load carrying capacity or strength was increased by approximately 5%.
• The strength of the 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 sectional area  increase the overall strength.