Section Modulus calculation and optimization
Aim
To calculate section modulus of hood and optimize the design to have improved section modulus.
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 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.
Changing the position can show the difference in bending which is because of the centroid distance from extreme fiber end.
In Layman's terms, in this position there is more material from axis to the specific direction, to resist the load which makes less bend amd improves the strength.
Elastic section modulus
For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.
The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (My) such that My = S × σy, where σy is the yield strength of the material.
| Cross-sectional shape | Figure | Equation | Comment |
|---|---|---|---|
| Rectangle |  |
Solid arrow represents neutral axis | |
| doubly symmetric I-section (major axis) | 
|
NA indicates neutral axis | |
| doubly symmetric I-section (minor axis) |  |
NA indicates neutral axis | |
| Circle |  |
Solid arrow represents neutral axis | |
| Circular hollow section |  |
Solid arrow represents neutral axis | |
| Rectangular hollow section |  |
NA indicates neutral axis | |
| Diamond |  |
NA indicates neutral axis | |
| C-channel | |
NA indicates neutral axis |
,
Steps to calculate section modulus:-
- Step 1:- Find location of centroid of given cross section.
- Step 2:- Find moment of inertia about neutral axis
- Step 3:- Find YmaxYmax from neutral axis.
- Step 4:- Find elastic section modulus using the formula provided above
Here the sectional modulus of hood design before optimization
Momemt of inertia is calculated by NX-CAD software
I MAX – 9.06301234 x 10^5 (mm^4)
I MIN – 2.619922086 x 10^3 (mm^4)
Y- 879.5180/2= 439.759
Z1-2.619922086 x 10^3/439.759
Z1=5.95MM^3
OPTIMISED DESIGN OF HOOD
I MAX – 9.033276788 x 10^5 (mm^4)
I MIN -2.56987526 X10^3 (mm^4)
Y- 879.5180/2= 439.759
Z2 -2.56987526 X10^3/439.759
5.84MM ^3
PERCENTAGE DECREASE IN SECTION MODULOUS = Z1-Z2/Z1X 100
=1.84%
Conclusion
So, here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design.