Section Modulus calculation and optimization

Aim

To calculate the Section Modulus of the Hood design and findout the improved Section Modulus which will increase the strength.

Section Modulus

Section modulous is the resistance to bending.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.

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

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

The equation for the Section Modulus is derived from the Equation of the Bending Moment

Equation for the Bending Moment

σ/Y=M/I=E/R

where σ=Bending stress

Y=Distance from the Neutral axis

I = Moment of Inertia

M = Bending moment

R = Radius of curvature

E = Young's Modulous

CASE 1

MOI (min) = 6.5489460e+03 (mm^4)

Y = Total distance/2 = 486.87/2 =243.435 mm

S= 6548.946/243.435=26.90mm^3

Now we need to offset the curve to 3mm and check the section modulus again.

CASE 2

MOI (min) = 7.481650284e+03 (mm^4)

Y = Total distance/2 = 486.87/2 =243.435 mm

S= 7481.65/243.435=30.74mm^3

From this experiment we can reach to the conclusion that Case 2 value is higher than that of the Case 1 value.

So,if the depth is increased,the section modulus and the Moment of inertia value is increased.