Section Modulus calculation and optimization
Title- calculation of section modulus of hood design and also come up with improved section modulus
Introduction
SECTION MODULUS
- Section modulus is the ratio of total moment resisted by the section to the stress in the extreme fibre.
- Section modulus give us idea about how much of load the given structure can take.
- If the section modulus increases the moment of resistance increases and hence its load bearing capacity.
- S=I/Y ,
Where S= section modulus
I=moment of inertia of a section
Y=distance from neutral axis to any given fibre.
| 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) |  [4] |
NA indicates neutral axis | |
| Circle |  [3] |
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 |
,
HOW TO CALCULATE MOMENTOF INERTIA MATHEMATICALLY?
LET US UNDERSTAND MOI BY A GIVEN PROBLEM
calculate moi of given I section to understand how to find moi
c
Question-using the section from previous hood design calculate the section modulus and also come up with a new section that has improved the section modulus of the previous section and mention what changes made that increased the length?
Sol-
CASE 1
Hood design
MOI (max) = 4.96600*10^06[mm^4]
`OI (MIN)= 1.4080*10^04[mm^4`
s= 10.5*10^03mm^3
CASE 2
hood optimised design
by adding +0.8 mm in the depth of hood
Moment of inertia (max)=4.98809*10^06[mm^4]
Moment of inertia(min)=1.417748*10^04[mm^4]
value of y=443.175mm
section modulus=moi/y
=11.2*10^03mm^4
percentage increase in optimised one= 100*(11.2-10.5)/10.5
=6%
CONCLUSION
- By comparing the values we can clearly say that the section modulus of the optimized hood increases by 5.5%
- moment of inertia increases by increasing depth of hood.
- it seems if we increase the gap between inner and outer panel moi also increases.