Section Modulus calculation and optimization

REPORT ON SECTION MODULUS OF HOOD DESIGN

AIM: To calculate the section modulus of the interesction curve of the hood before and after optimazation being done on it.

 Section modulus: Section modulus is the ratio of Moment of Inertia (I) of beam of cross-section about the neutral axis to the maximum distance (y) between the extreme fiber and neutral axis. It genrally represents the bending strength of a cross section of material about the reference axis, like how much a material capable of resistance to the bending. Section modulus is geometric property i.e.,

  S= I/ymax

  where I= Moment of Inertia (m^4)

            Ymax= Distance between the extreme layer and neutral axis (m)

          So unit of section modulus is m^3

There are two types of section modulus:

> Elastic section modulus

>Plastic section modulus

Steps to calculate section modulus:

• Step 1: Form an intersection between the hood and desired plane
• Step 2: Take extreme curve of outer panel and inner panel and join them by sketch modification to form a close curve
• Step 3: Determine the maximum distance between neutral axis and extreme fiber
• Step 4: Use section Inertia analysis to determine max. and min. moment of inertia of section 
• Step 5 : Calculate the section modulus by formula S= I/Ymax

Moment of inertia can be understood as the resistance against the moment, bending or twisting so higher the moment of inertia higher will be its resistance to deform.

Here is the image of maximum distance b/w NA and extreme fiber  and Moment of Inertia calculated from NX CAD software

Imax. = 1.566313658 x 10^7 (mm^4)

Imin.= 1.707797232 x 10^5 (mm^4)

Y= Total length/2

 = 487.4152/2

 = 243.71mm

So, Section Modulus max. = Imax./Y = 1.566313658 x 10^7 / 243.71

                                        = 6.4269 x 10^4 (mm^3)

     Section Modulus min. = Imin./Y = 1.707797232 x 10^5 / 243.71

                                   =0.07007497 x 10^4 (mm^3)

So for this hood design section modulus ranges from 6.4269 x 10^4 mm^3 to 0.07007497 x 10^4 mm^3

Optimized design 

so to increase the section modulus of the hood design we need to increase its cross sectional area so that its MOI increase which ultimately lead to increase its section modulus, calculation of MOI for optimized design are as shown:

Imax.= 1.566294182 x 10^7 mm^4

Imin.= 1.908428495 x 10^5 mm^4

Y = Total length/2

  = 487.4152/2

  = 243.71 mm

Section modulus max. = 1.566294182 x 10^ 7 /243.71

                               = 6.4269 x 10^4 mm^3

Section modulus min. = 1.908428495 x 10^5 / 243.71

                               =0.078307 x 10^4 mm^3

so for this optimized hood design section modulus ranges from 6.4269 x 10^4 mm^3 to 0.078307 x 10^4 mm^3

It is evident that section modulus is increased from 0.07007497 x 10^4 mm^3 to 0.078307 x 10^4 mm^3 by increasing the design cross sectional area.

Conclusion

So by increasing the cross sectional area of design we increase its Moment of Inertia which ultimately increases its section modulus and hence component's strength. Because, section modulus is directly proptional to the Moment of Inertia for a component.

Therefore we determined section modulus for hood design before and after optimization to see the increase in section modulus.