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.

OR

It is the ratio of moment of inertion to distance b/w the neutral axis to exttrim end of the object.

OR

When we produce the component in industry we have to find the minimum cross section of the body and we have to imprrove that , it means we when we produce the product within the lower section area it will get diflexction or bend in in this case when that part is going under some load it will bend and it will break, so we have to avoid it and make it withstad to load and reduce the diflextction by change the orientation of the product . Then only that product will have better life and strength.

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:-

Here we caluclate the section modulus with some following steps.

Befor this we get the cross section area from Section Inertia Analysis Command.

• Step 1:- Find location of centroid of given cross section which is taken from the HOOD.
• Step 2:- Find moment of inertia about neutral axis.
• Step 3:- Find YmaxYmax from neutral axis.
• Step 4:- Find 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 i shown the sectional modulus of hood design before optimization

Momemt of inertia is calculated by NX-CAD software, It is automatic caluclation .

IN FIRST CASE : (S1) TOTAL LENGTH :

I_max –1.562048788 (mm^4)

I_min –1.314542953 (mm^4)

Here we need Y value ( Distance b/w outer most edge from neutral axis).

TOTAL LENGTH : 487.415 mm.

Y = Total length / 2

= 487.415/2

=243.70 mm

1) S1 CALCULATION :

section modulus for max. =1.562048788 / 243.70

= 0.00640972007 x 10^3

section modulus for min. = 1.314542953 x 10^5 / 243.70

= 0.00539410321 x 10^3

So for this hood design section modulus range from 0.00640972007 x 10^3 to 0.00539410321 x 10^3

Optimized design (S2)

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

I_max – 1.56148326 (mm^4)

I_min – 1.493897949 (mm^4)

Here we need Y value ( Distance b/w outer most edge from neutral axis).

TOTAL LENGTH : 487.415 mm.

Y = Total length / 2

= 487.415/2

= 243.70 mm

2 ) S2 CALCULATION :

section modulus for max. = 1.56148326 / 243.70

=0.00640739951 x 10^3

section modulus for min. =1.493897949 / 243.70

= 0.00613006955 x 10^3

So for this hood design section modulus range from 0.00640739951 x 10^3 to 0.00613006955 x 10^3

It is final value , if the section modulus is increased from 0.00539410321 x 10^3 to 0.00613006955 x 10^3 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.

So here we consider the S2 value for produce the HOOD , that is 0.00613006955 x 10^3.