Section Modulus calculation and optimization
Use the Section from your Hood design and calculate the Section Modulus using the formula
S = I/y
Where,
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
Come up with a new section that has an improved Section Modulus compared to the previous one and mention what changes you made which resulted in the increased strength.
Answer:
Section Modulus:
- It is defined as the ratio of the moment resisted by the section to the stress in the extreme fibre.
- It gives an idea that most of the work in bending is being done by the extreme fibres of the beam, ie the top and bottom fibres of the section.
- The distance of the fibres from top to bottom is therefore built into the calculation.
- If the section modulus increases the moment of resistance increases & hence its load bearing capacity.
- A section that has longer section modulus than another will be stronger and capable of supporting greater loads.
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 |
,
Calculation of Section Modulus:
- In this challenge I have taken my designed hood, for calculation.
- To calculate the moment of inertia, I have taken the hood section along the length of hood & find the inertia using 'section inertia analysis' tool in NX CAD.
- Then, the section modulus is calculated using the given formula i.e.
| S = I/y |
Where,
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
Fig. Moment of Inertia of hood section
Fig. Length of the Hood section
so, From the above images we find that,
I = moment of inertia(min.) = 3.1721*10^3 mm^4
y = distance from neutral axis to extreme end = 240.7 mm
Hence, S = 13.17mm^3
similarly, I have prepared a chart to optimize the section modulus, by extending the lowermost edge of inner panel & then calculated the moment of inertia for each extension of inner panel's edge:
SECTION MODULUS TO BE CALCULATED ON THE GIVEN COMPONENT - HOOD OUTER AND INNER PANEL ASSEMBLY
HOOD ASSEMBLY
PARTS REQUIRED FOR SECTION MODULUS:
HOOD OUTER PANEL:
HOOD INNER PANEL:
ASSEMBLY:
TABLE: OPTIMIZATION CHART OF HOOD SECTION ON EXTENDING THE INNER PANEL'S EDGE
| s. no. |
extension (mm) |
MOI(min.) (mm^4) |
Value of 'y' (mm) |
Section Modulus (mm^3) |
| 1 | 0.5 | 3.3114*10^3 | 240.7 | 13.7573743249 |
| 2 | 0.6 | 3.3400*10^3 | 240.7 | 13.8761944329 |
| 3 | 0.7 | 3.3688*10^3 | 240.7 | 13.9958454508 |
| 4 | 0.8 | 3.3979*10^3 | 240.7 | 14.1167428334 |
As 'Moment of inertia' is directly proportional to the 'section modulus', thus the value of section modulus is increasing with the value of moment of inertia.
CONCLUSION:
- The section modulus of my hood section is 13.17mm^3 .
- And after extending the lowermost edge of the inner panel & calculating the section modulus, we found that with the extent of lowermost edge of inner panel by 0.1mm, the section modulus is improved by 0.12 mm^3.
- Thus, the largest section modulus of hood section is 14.11 mm^3, which is the hood section with 0.8 extension of the lowermost edge of inner pnael.
- As the largest section modulus has better capability to withstand the load, therefore hood section with 0.8 extension of the lowermost edge of inner pnael is stronger.