Section Modulus calculation and optimization

It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.

 

It is denoted by Z. or S

S = I/y

 Where, 

S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object

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.

case 1

Here the sectional modulus of hood design before optimization

 

I_max – 8.954696423x 10^7 (mm^4)

I_min-   2.940715834 x10^5 (mm^4)

Y = Total length / 2

   = 879.5901/2

   =439.79505 mm

section modulus for max. = I/Y = 8.954696423x 10^7 / 439.79505

                       S  = 203.610x10^3

section modulus for min. =I/Y=2.940715834x 10^5 / 439.79505

                      S   =6.6865 x 10^3

So for this hood design section modulus range from 203.610x10^3 mm^3 to 6.6865 x 10^3 mm^3

Case2:  Optimized design 

Inorder to increase the sectional modulus, cross sectional area has to be increased. So here the optmized design:-The hood inner panel’s curve is offset by 0.5mm outwards and section inertia analysis is done same as case 1 for a closed curve.

I_max = 8.964734464x 10^7 (mm^4)

I_min=  2.987281145 x10^5 (mm^4)

Y = Total length / 2

   = 879.5901/2

   =439.79505 mm

section modulus for max. =I/Y=8.964734464x 10^7  / 439.79505

                       S  = 203.83891x10^3 mm^3

section modulus for min. =I/Y =2.987281145 x10^5 /439.79505

                        S = 67.92439 x 10^3 mm^3

So for this hood design section modulus range from 203.83891 x 10^3 mm^3 to 67.92439 x 10^3 mm^3