Section Modulus calculation and optimization
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
Moment of inertia (max)=4.78578`*10^4mm^4
Moment of inertia(min)=1.88739⋅104mm41.88739⋅104mm4
value of y=440mm
section modulus=moi (min)/y
1.88739⋅1041.88739⋅104/ 440
=42.89mm^3
CASE 2
hood optimised design
by adding +0.6 mm in the depth of hood
MOI (max) = 7.46052`*10^4 mm^4
MOI (MIN)= 2.94221*10^4 mm^4
s=66.89 mm^3
comparing case 1 and 2
percentage increase in optimised one= (66.89-42.89)/42.89
=5.5%
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.