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 / Y

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 =9.231593941e+07[mm^4]

imin =2.725496960e+05[mm^4]

Y=TOTAL LENGHT/2

880.5/2  =  440.25mm

section modulus for max. =   9.23159394*10^7/440.25

                                                                                 = 209.689*10^3

section modulus for min. =2.725496960*10^5/440.25

                                                                               =6.190793*10^2

So for this hood design section modulus range from  209.689*10^3[mm^4]    to      6.190793*10^2 [mm^4]

Optimized design 

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

 i max =9.264959611e+07[mm^4]

i min = 2.816056707e+05[mm^4] 

Y=TOTAL LENGHT/2

880.5/2  =  440.25mm  

section modulus for max= I/Y 

                      9.264959611*10^7/440.25

                                                                  =210.447691*10^3

section modulus for min. =2.81605671*10^5/440.25

                                                                             =6.39649451*10^2

So for this hood design section modulus range from 210.447691*10^3[mm^4]   to   

6.39649451*10^2 [mm^4]

proof here  increasing the sectional area increases section modulus

1.thickness increassed section modulus increases

2. increasing the sectional area increases section modulus

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.