Section Modulus calculation and optimization

Objective:

To study the section modulus of the hood design from challenge 3 and optimize the same for better strength of the hood.

Definition:

For a specific cross-section, section modulus is a geometric property that is employed in the construction of beams or flexural members.

The elastic section modulus is defined mathematically as S = I / y.

where I is the second moment of inertia (area moment of inertia) in mm⁴

and y (in mm) is the distance between the neutral axis and the extreme fibre/end of the object. It is basically calculated as 'half of the section width'. Section modulus is calculated in mm³ .

As large is the section modulus, the better the strength of the object in consideration. As per formula, it can be concluded that either increasing are moment of inertia (MOI) or decrasing the distance between the neutral axis and the extreme end of the object, one can increase the strength of the object.

CASE 1:

As can be seen from the images,

y= l/2 = 921.5869/2 = 460.79345 mm

and min MOI = 2.3646e+04 mm⁴

max MOI = 5.6804e+04 mm⁴

And we take minimum moment of inertia into design considerations.

Therefore section modulus as defined earlier as I/y,

S1= 2.3646e+04 ÷ 460.79345 = 51.32 mm³

CASE 2:

By increasing the gap between the inner pannel and outer panel, moment of inertia can be increased for the same length consideration. I have increased the gap by 0.4mm and hence the minimum moment of inertia has been increased as can be seen from the image.

In this case, min MOI = 2.4071e+04 mm⁴

Therefore,

section modulus for this case is,

S2= 2.4071e+04/460.79345= 52.24 mm³

Initial section modulus= 51.32 mm³

Optimized section modulus= 52.24 mm³

Conclusion: It can be concluded by above challenge that, one can increase section modulus by increasing the moment of inertia and hence the overall strength of the section in consideration.