Section Modulus calculation and optimization

AIM 

To  calculate section modulous 

SECTION MODULOUS 

section modulous is direcyty measure of strength of any cross sectional area of of an object about an refrence axis 

the formula of section modulous 

S=I/Ymax 

where 

s = section modulous 

I= Moment of inertia 

Y= distance between neutral axis and outermost fiber (mm)

STEPS TO CALCULATE 

• find location of centroid of given cross section
• find moment of inertia about neutral axis 
• find Ymax from neutral axis 
• find the elastic section modulous using the formula

HERE IS THE SECTION MODULUS 

Imax =5.96x10^5 (mm^4)

Imin =1.489x10^3(mm^4)

Y =Total length/2

= 488.81/2

=244.405mm

section modulous for maximum  = I/Ymax

      = 5.96x10^5/244.05

      = 2.4421225 x 10^3

section modulous for minimum =I/Ymax

         = 1.489x10^3/244.405

         = 0.00609x 10^3

So for this hood design section modulous range from 2.4421225x10^3 to 0.00609 x10^3

OPTIMIZED DESIGN 

in order to increse the section  modulous , cross sectional area has to be increase 

Imax=6.285x10^5 mm 

Imin =1.537x10^3mm

Y= total length /2

 =488.81/2

=244.405mm

section modulous for maximum  = I/Ymax

= 6.285x10^5/244.405

=2.57155x10^3

section modulous for minimum =I/Ymax

=1.537x10^3/244.405

=0.006288x10^3

so for this hood design section modulous range from 2.57155x10^3 to 1.537x10^3

CONCLUSION

the section modulous is increased from 2.4421225 x 10^3 to 2.57155x10^3

Strength of material is directly proportional to the moment of inertia thius increasing the sectional area 

the sectional modulous for hood design is calculated and optimized design is also done to increase the section modulous of hood