Section Modulus calculation and optimization

Aim:

To Calculate the Section modulus of the hood and to improve it.

Formulas used:

`S = I/y mm^3`

Where,

S - Section modulus mm³

y - The distance between neutral y-axis and the extreme fibre of the section mm

I - The second moment of inertia of the section mm⁴

Definition:

Section modulus is a geometric property for a given cross-section used generally and oftenly in the design of beams or flexural members. 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 and y is the distance from the neutral axis to any given fibre.

Case-1:

The section from the hood outer panel and the hood inner panel is taken and is made to be a closed geometry by filling the gaps with lines and trimming unwanted edges. The Sectional Inertia Analysis Command is used to find the properties of the section.

Calculation of Section Modulus:

`S = I/y mm^3`

For , MOI minimum value is considered MOI_min = 1.448526431 * 10⁴ mm⁴

The total length of the section is L = 877.4626 mm

y = L/2 = 877.4626/2 = 438.7313 mm

S = 1.448526431 * 10⁴/438.7313

S = 33.01625462 mm³ .

Case-2:

Then the section is extended by an offset of 0.8 mm from the lowest filament of the section and the analysis is carried out same as above case.

Calculation of Section Modulus:

`S = I/y mm^3`

For , MOI minimum value is considered MOI_min = 1.480949247 * 10⁴ mm⁴

The total length of the section is L = 877.4626 mm

y = L/2 = 877.4626/2 = 438.7313 mm

S = 1.480949247 * 10⁴/438.7313

S = 33.75526768 mm³ .

Observations and Inferences:

On comparing the results from case 1 and 2 it is found that case 2 has higher and improved sectional modulus with improved sectional area and moment of inertia.

It is evident that when the moment of inertia increases, the sectional modulus also increases.

For this particular section the feature embosses were not removed to form a simpler closed geometry and thus it resulted in a very small improvement.

Study Case	MOI	Section Modulus
1	1.448526431 * 104	33.01625462
2	1.480949247 * 104	33.75526768

Result and Conclusion:

Hence the sectional modulus analysis is carried out in the cross section of the hood without design compromise.