Section Modulus calculation and optimization

AIM:

To calculate section modulus of hood and optimize the design to have improved section modulus

SECTION MODULAS:

Section modulus is a direct measurement of a strength of any cross sectional area of an object about an reference axis.

SECTION MODULAS FORMULA:

It is the ratio of area of moment of inertia about the neutral axis and to the distance of outermost fiber from the neutral axis.

                                     S = I / Y

S= Section modulus (mm^3)

I = Moment of inertia of the section to the stress in the extreme end of the object (mm^4)

Y= Distance between the neutral axis and extreme end of the object (mm).

CASE 1: BEFORE OPTIMIZATION

Imax = 8.978142385 x 10^7 (mm^4)

Imin = 2.746490946 x 10^5 (mm^4)

 

Y = Total length / 2

 Y = 876.4574 / 2

Y = 438.2287mm

Smax =   8.978142385 x 10^7 /  438.2287

          = 2.04873 x 10^5 mm ^3

Smin =  2.746490946 x 10^5 /  438.2287

       = 6.26 x 10^2 mm^3

So, for this car hood design section modulus ranges from 2.04873 x 10^5 mm ^3 to 6.26 x 10^2 mm^3

CASE 2: AFTER OPTIMIZATION

Imax = 8.973916531 x 10^7 (mm^4)

Imin = 2.809224477 x 10^5 (mm^4)

 

Y = Total length / 2

 Y = 876.4574 / 2

Y = 438.2287mm

Smax =  8.973916531 x 10^7 /  438.2287

          = 2.04777 x 10^5 mm ^3

Smin =  2.809224477 x 10^5 /  438.2287

       = 6.41 x 10^2 mm^3

So, for this car hood design section modulus ranges from 2.04777 x 10^5 mm ^3 to 6.41 x 10^2 mm^3

It is proven that if the section modulus is enhanced from  6.26 x 10^2 mm^3 to 6.41 x 10^2 mm^3 by increasing the sectional area.

After calculation the difference between these two values is 0.15 x 10^2  mm^3 .

CONCLUSION:

           Strength of  material is directly proportional to the moment of interia, thus increasing the sectional area increase the  strength of component.

                                                                                    CASE 2 > CASE 1