Section Modulus calculation and optimization

Section modulus:-

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

The formula of section modulus is given by,

S=I / Ymax

Where,
I = Moment of inertia (mm^4)
Y = Distance between neutral axes and outermost fiber (mm)

Steps to calculate section modulus:-

• Step 1:- Find location of centroid of given cross section.
• Step 2:- Find moment of inertia about neutral axis
• Step 3:- Find YmaxYmax from neutral axis.
• Step 4:- Find elastic section modulus using the formula provided above.

Moment of inertia is nothing but offering resistance against the moment, bending or twisting. So higher the moment of inertia higher will be its resistance to deform .

Here the sectional modulus of hood design before optimization

Momemt of inertia is calculated by NX-CAD software

I_max – 1.613903391 x 10^7 (mm^4)

I_min – 2.081560826 x 10^5 (mm^4)

Y = Total length / 2

= 488.4485/2

=244.22425 mm

section modulus for max. = 1.613903391 x 10^7 / 244.22425

= 66.083 x 10^3 mm^3

section modulus for min. = 2.081560826 x 10^5 / 244.22425

= 0.852x 10^3 mm^3

So for this hood design section modulus range from 0.852x10^3 mm^3 to 66.083x10^3 mm^3 .

Optimized design

Inorder to increase the sectional modulus, cross sectional area has to be increased. So here the optmized design:-

I_max – 1.602469874 x 10^7 (mm^4)

I_min – 2.307239093 x 10^5 (mm^4)

Y = Total length / 2

= 488.4485/2

=244.22425 mm

section modulus for max. =1.602469874 x 10^7 / 244.22425

= 65.6098 x 10^3 mm^3

section modulus for min. = 2.307239093 x 10^5 / 244.22425

= 0.9447 x 10^3 mm^3

So for this hood design section modulus range from 65.6098 x 10^3 mm^3 to 0.9447 x 10^3 mm^3.

The section modulus is increased by increasing the sectional area.

Conclusion

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

Thus sectional modulus for hood design is calculated and optimized design is also done to increase the section modulus of the hood.