Section Modulus calculation and optimization

Section Modulus calculation and optimization

Aim

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

Section modulus:-

Section modulus is a direct measure of the strength of any cross-sectional area of an object about a 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 the location of the centroid of the given cross-section.
• Step 2:- Find the moment of inertia about the neutral axis
• Step 3:- Find YmaxYmax from the neutral axis.
• Step 4:- Find the 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 its resistance to deform is higher.

Here is the sectional modulus of hood design before optimization

The moment of inertia is calculated by NX-CAD software.

CASE - I

Calculation

Imax – 9.07092 x 10^7 (mm^4)

Imin – 2.9838 x 10^5 (mm^4)

Y = Total length / 2

= 878.2116 / 2

= 439.1058 mm

section modulus for max. = 9.07092 x 10^7 / 439.1058

= 2.06577 x 10^5

section modulus for min. = 2.9838 x 10^5 / 439.1058

= 0.679517 x 10^3

So for this hood design section modulus ranges from 2.06577 x 10^5 mm^3 to 0.679517 x 10^3 mm^3

CASE -II

Optimized design

To increase the sectional modulus, the cross-sectional area has to be increased. So here is the optimized design:-

Calculation

Imax – 9.15423 x 10^7 (mm^4)

Imin – 3.02441 x 10^5 (mm^4)

Y = Total length / 2

= 878.2116 / 2

= 439.1058 mm

section modulus for max. = 9.15423 x 10^7 / 439.1058

= 2.06897 x 10^5

section modulus for min. = 3.02441 x 10^5 / 439.1058

= 0.68876 x 10^3

So for this hood design section modulus ranges from 2.06197 x 10^5 mm^3 to 0.68876 x 10^3 mm^3

It is evident that if the section modulus is increased from 2.06577 x 10^5 mm^3 to 2.06897 x 10^5 mm^3 by increasing the sectional area.

Conclusion

The strength of the material is directly proportional to the moment of inertia, thus increasing the sectional area increases the increases strength of the component.

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