Section Modulus calculation and optimization
Section Modulus
Section Modulus is a geometric property used to calculate the bending stresses in a structural member. Mathematically, it is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.
Section modulus is a direct measure of strength of any sectional area of an object about a reference axis (neutral axis). Strength is the capability for supporting greater loads. So, higher the strength, higher will be the capability to support greater loads.
Section modulus S = I/Y
I = moment of inertia (min)
Y= distance from the reference line (neutral axis) to one of the extreme end of an object.
Moment of inertia is the resistance against moment, bending or twisting when we apply an external load on the body.
Case 1
According to the question, I calculated the section modulus of my hood design with the help of the given formula.
The values of my design are:
Moment of inertia (min.), I = 1.563065906 x 10^4 mm^4
The distance between the extreme ends of hood = 880.1mm
So, Y= 880.1/2 = 440.05 mm
Therefore, Section Modulus, S = 1.563065906 x 10^4/440.05
= 35.5201887513 mm^3.
Figure 1. Section curve of hood design.
Figure 2. Details of section inertia analysis.
Case 2
In the second case, I modified a section curve to improve the moment of inertia and thereby the section modulus. To increase the moment of inertia the area of cross section should be increased. To increase the area of cross section, I offseted the curve of the inner panel downwards to a distance 0.5mm. Since clearance of about 90-100 mm should be maintained between the hood and the components inside, further offsetting cannot be feasible.
The values of the improved design are:
I (min.) = 1.580270407 x 10^4 mm^4
Y = 440.05mm
Therefore S = 1.580270407x10^4 / 440.05 = 35.9111557096mm^3
Figure 3. Improved section curve.
Figure 4. Details of new section curve analysis.
Inference
After improving the Moment of Inertia by offsetting the inner curve, it was proved that the section modulus can also be improved, thereby improving the strength.