Section Modulus calculation and optimization

Section Modulus

Section Modulus is given by the ration of (Momentum inertia of the cross-section/ Distance between the centre to the end of the cross section).

This is a geometric property through which we can find how much a body could sustain the force by taking its cross-section into consideration.

Formula

S = I/Y

I = Moment of inertia

Y = Distance between the Center of the hood to end point of the hood

Moment of inertia of the Hood cross-section is calculated by the Section inertia analysis command. Moment of inertia depends upon the Cross-sectioanal area at given instace. Moment of inertia is directly proportional to Area of cross section.

Distance is measured by the Distace command.

As Shown in the above picture the distace Y has been Calculated as 438.0034mm which mostly equal to 438mm.

The Moment of inertia has been calculated as MOI (min) as 1.46*10^4 mm^4

We know S = I/Y

therefore S = (1.46*10^4)/438

S = 33.33 mm^3

Therefore Section modulus of designed hood has been calculated as 33.33mm^3

Optimizing Cross sectioanl area

Optimizing the hood inner panel design changes the are of cross section of the closed cross section hence the moment of inertia changes.

As shown below we increased the area of cross section by changing the inner panel

Cross sectioanl area has been increased so the moment of inertia aslo increases

The obtained moment of inertia is 1.54*10^4 mm^4

The y value does not change

As we know S= I/Y

we get S = 1.54*10^4/438

therefore S = 35.15 mm^3

hence proved that when the area changes moment of inertia also changes .

They are directly proportional.

Conclusion

The Section modulus of the designed hood has been calculated as 33.33 mm^3 and also the optimized design hood section modulus has also been calculated as 31.15 mm^3.