Section Modulus calculation and optimization
SECTION MODULUS
Section modulus is a direct measure of a strength of any cross sectional area of an object about an reference axis.
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)
MOMENT OF INERTIA
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.
By Bending moment equation,
M/I=f/y=E/R
where, M= Bending moment (KNmm)
I= Moment of inertia (Kg.mm)
f= Bending stress (N/mm^2)
y= Distance from neutral axis (mm)
E= Modulus of Elasticity (N/mm^2)
R= Radius of curvature (mm)
Ymax= Width/2
Ymax= 245.152mm
For minimum moment of inertia,
Imin= 1.190204 X 10^5 mm^4
S=Imin/Ymax
S= 485.494 mm^3
For maximum moment of inertia,
Imax= 1.543470X 10^7 mm^4
S=Imax/Ymax
S= 62969.096mm^3
Conclusion: Thus, for hood the section modulus varies from 485.496 mm^3 (min) to 62969.096 mm^3 (max)
Optimised design
To increase the section modulus it is recommended to increase the cross sectional area of the hood,
Ymax= Width/2
Ymax= 245.152mm
For minimum moment of inertia,
Imin= 1.452496 X 10^5 mm^4
S=Imin/Ymax
S= 592.487 mm^3
For maximum moment of inertia,
Imax= 1.554762X 10^7 mm^4
S=Imax/Ymax
S= 63420.326mm^3
Conclusion: Thus, for hood the section modulus varies from 592.487 mm^3 (min) to 63420.326 mm^3 (max) after increasing the cross sectional area.