Section Modulus calculation and optimization

QUESTION:

Use the Section from your Hood design and calculate the section modulus using the formula S = I/y

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 improved the section modulus of the previous section and mention what change you made that has increased the 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.

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:

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.