Section Modulus calculation and optimization

Section modulus is the measure of the strength of any section with respect to neutral axis.

The strength is measured by the section modulus formula.

S=I/Y

Were

S: suction modulus

I: moment of inertia

resistnce offered to any load creating moment , bending or twisting.

Y : distance from neutral axis to any extreme end

so as the moment of inertia increses strength of the material also increases and hence higher the section modulus .the strength of the material can be calculated by the calculation of section modulus.

but the value of Y will change the section modulus value irrespectivly.

ie if we change 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 we are now going to calculate the value of section modulus of our hood panel.

Given data

I_MAX:-8.770037226 x 10^5 mm⁴

I_min:-6.947773486 x 10^3 mm⁴

The distance is measured between the extreme end is 492.458 mm

so we can take the value ashalf of this

ie Y=246.229

Then as per the formula

S max=I max / Y

=8.770037226 x 10^5 /246.229

=3.561740 x 10^3 mm³(Maximum strength).

similarly

S min =I min / Y

=6.947773486 x 10^3 / 246.229

=0.028216714 x 10^3 (minimum strength).

So the strength of an hood varies from 0.028216714 x 10^3 to 3.561740 x 10^3mm³

Now we are going to increas the section area by some increase in the offset values.

let the new section be

HERE

I_MAX:-8.885563447X10⁵mm⁴

I_min:-6.976176880x10³mm⁴

now S =8.885563447 x 10^ 5 / 246.229

=3.608658379 x10^ 3 mm3 (Maximum strength).

and

S =6.976176880 X 10^3 / 246.229

=0.02833206844 x 10 ^3 mm3 (minimum strength).

So the strength of an hood varies from 0.02833206844 x 10 ^3 mm³to 3.608658379 x10^ 3 mm³.

for section 1

strength varies from

0.028216714 x 10^3 to 3.561740 x 10^3mm³

for section 2

strength varies from

0.02833206844 x 10 ^3 mm³to 3.608658379 x10^ 3 mm³.

from this the mininum strength and maximum strength is increased by increase in the area.

we know,if higher the mass , the force required to move the object is also high due to offering more resistance ias per the Newtons law .This resistance is called MOMENT OF INERTIA.

CONCLUSION:

Increase in the cross sectional area will increase the strength of the hood by increasing the moment of inertia and mass of material.