Section Modulus calculation and optimization
SECTION MODULUS :-
Section modulus is defined as the ratio of polar moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibres. The common way of calculating Section_Modulus for a shaft requires is its diameters even if it is a solid or hollow shaft.
S = I/Y(max)
For general design, the elastic section modulus is used, applying up to the yeild point of most
metals and other common metals.
The elastic section modulus is defined as S= I/Y, where I is the moment of inertia and Y is
the distance from neutral axis to the outer most boundary.
It is often used as Y=c, where c is the distance of boundary from neutral axis. It can also be
defined from yield moment given by equation-
My=S⋅σy
where σyis the yield strength of material.
ROLE OF CROSS SECTION IN SECTION MODULUS:
- Section modulus depends only on the cross section shape of the beam. Cross section shapes like rectangular, square, circular, I section and T, composite section etc.
- For symmetric sections, the value of “section modulus” is for both above and below of centroid of the fiber.
- An asymmetric section has two values for top and bottom of the fiber due to different distance from centroid to the top and bottom of the material, the maximum “section modulus” is S max and the minimum section modulus is S min.
CALCULATIONS FOR SECTION MODULUS OF HOOD-
Initial Hood design and it\'s moment of inertia-
In this Hood design, minimum Moment of Inertia(MOI) is 1.4134e85450+04[mm^4].
We have, Stainless steel AISI 302 – cold-rolled which has yield strength = 520 MPa.
To find out section modulus
S=I/Y
Here, I is “moment of inertia” and y is distance from “neutral axis” to top or bottom of fiber.
Unit of a “section modulus” is mm^3
As we absorb above equation of Section modulus,
Section modulus is directly proportional to Moment of Inertia(MOI)
S α I
For unit Y distance, S= 3.589830444e+04 mm^3
Modified section of hood-
In this New Hood design, minimum Moment of Inertia(MOI) is 1.378345333e+04[mm^4].
We know, Stainless steel AISI 302 – cold-rolled has yield strength = 520 MPa.
To find out section modulus
S=I/Y
Here, I is “moment of inertia” and y is distance from “neutral axis” to top or bottom of fiber.
Unit of a “section modulus” is mm^3
We know that,
Section modulus is directly proportional to Moment of Inertia(MOI)
S α I
For unit Y distance, S= 3.6034298e+04 mm^3
RESULT-
Therefore, a small modification in Sectional area, results to variation of section modulus
between initial and and New hood is about 0.17364653e+04 mm^3.