Section Modulus calculation and optimization

AIM

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

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 (INAINA)
• 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 ineria higher will be its resistance to deform is higher.

Here the sectional modulus of hood design before optimization

Momemt of inertia is calculated by NX-CAD software

Imax - 8.414866931*10^5(mm^4)

Imin-7.765899837*10^3(mm^4)

Y= Total length/2

= 487.61/2

= 243.805mm

section modulus for max = 8.414866931*10^5 / 243.805mm

= 3.4514*10^3

section modulus for min = 7.765899837*10^3 / 243.805mm

= 0.03185*10^3

So for this hood design section modulus ranges from 3.4514*10^3 mm to 0.03185*10^3 mm

OPTIMIZED DESIGN

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

Imax- 1.475216129*10^6 (mm^4)

Imin-1.397325598*10^4(mm^4)

Y = Total length / 2

= 487.61/2

= 243.805mm

section modulus for max = 1.475216129*10^6 / 243.805mm

= 6.0508*10^4mm

section modulus for min = 1.397325598*10^4 / 243.805mm

= 0.0573*10^3mm

so for this optimized design the section modulus ranges from 6.0508*10^3mm to 0.0573*10^3mm

EMBOSS

In order to increase the section modulus we create an emboss here is the design

Imax-1.492410863*10^6 (mm^6)

Imin-1.665950331*10^4 (mm^4)

Y = Total length / 2

= 487.61/2

= 243.805mm

Section modulus for max = 1.492410863*10^6 / 243.805mm

= 6.1213*10^4mm

section modulus for min = 1.665950331*10^4 / 243.805mm

= 0.0683*10^3

so for this hood modulus ranges from = 6.1213*10^3mm to 0.0683*10^3

It is evident that if the section modulus is increased from 3.4514*10^3 to 6.0508*10^4mm to 6.1213*10^4mm by increasing the sectional area and emboss

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.