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'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 NX-software obtained values are

I_MAX:-8.485481X10⁵mm⁴

I_min:-3.18672x10³mm⁴

Total length of 'Y' value was 488.8252mm

So,at neutral axis we need 'Y' value:-Y/2=488.8252/2=244.412mm

1)Section modulus(S):-I/Y=8.485481X10⁵mm⁴/244.412mm

                                                =3.471X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=3.18672x10³mm⁴/244.412mm

                                                =0.013x10³mm³(minimum strength).

So the strength of an hood varies from 0.013x10³mm³to 3.471X10³mm³

Now, one more trail is that, here the inner panel curve offsetting outside by 1mmi.e increasing in cross sectional area,the results shown below.

I obtained the values of

I_MAX:-8.4462X10⁵mm⁴

I_min:-3.61202x10³mm⁴

Total length of 'Y' value was 488.8252mm

So,at neutral axis we need 'Y' value:-Y/2=488.8252/2=244.412mm

1)Section modulus(S):-I/Y=8.4462X10⁵mm⁴/244.412mm

                                                =3.455X10³mm³(Maximum strength).

2) Section modulus(S):-I/Y=3.61202x10³mm⁴/244.412mm

                                                =0.014x10³mm³(minimum strength).

So the strength of an hood varies from 0.014x10³mm³to 3.455X10³mm³.

• 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 1mm the value of minimum strength was increased from 0.013x10³mm³ to 0.014x10³mm³,Hence with increase in cross sectional area results in increase in strength.
• But, when we seen the value of maximum strength its slightly decreases from 3.471X10³mm³ to 3.455X10³mm³,i think this due to design of hood, here what we want to know that when increase in cross sectional area there will be increase in minimum strength or maximum strength or increase in both.
• So Newton's first law also 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, i.e when increase in cross sectional area by 1mm the minimum load carrying capacity or strength was increased by approximately 8% percentage what we observed from the above discussion.
• 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 there is have increase in overall mass of an object ,hence have increase in strength.