Property used in beam design is section modulus (S).
Section modulus is the ratio of moment of inertia about neutral axis upon the farthest point
of section from neutral axis.
A beam that has a larger section modulus than another will be stronger and capable of
supporting greater loads, The section modulus is denoted by S. To calculate S, the distance
(y) to the extreme structure of boundary from the centroid (or neutral axis) must be found as that is where
the maximum stress could cause failure.
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*sigmay`
where `sigmay`is the yield strength of material.
SIGNIFICANCE OF SECTION MODULUS:
- Section modulus is the important factor for design of beam and flexural member design.
- More the section modulus, more the member is resistant to bending of the beam.
- It is easier to calculate stresses in beam and an exact measure of strength of steel.
- If two beams are made of same material and comparing the “section modulus” of two
beams, the beam with bigger section modulus will be tougher and more capable to
withstand larger loads.
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 5.727024013e+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= 5.727024013e+04 mm^3
Modified section of hood-
In this New Hood design, minimum Moment of Inertia(MOI) is 9.564367050e+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= 9.564367050e+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 3.8373430370e+04 mm^3.
The model files and Report are attached to the google drive, the link to which is attached below-
https://drive.google.com/drive/folders/1MMvrJxwcJQ139Pxwu-Zy0C3bgvsfkyAn?usp=sharing