Section Modulus calculation and optimization
SECTION MODULUS :
It is a way of quantifying a cross-section of a given geometry. It is directly proportional to the area moment of inertia of the cross-section. Higher the section modulus, the more the moment of inertia, more stiffness and thus more resistance to deformation and bending. Section modulus can also be improved by varying the geometry of the cross-section. In other words, stiffness can be improved by just improving the geometry without the need for adding extra material.
SECTION MODULUS (S): I/Y(MAX)
I= AREA MOMENT OF INERTIA OR SECOND ORDER MOMENT OF INERTIA.
Y(MAX)= DISTANCE OF EXTREME LAYER FROM NEUTRAL AXIS.
Alternatively, it can also be defined by the below formula
M/I = σ/Y
M = σ*S
σ= YIELD STRENGTH
S= SECTION MODULUS
1. Inner and Outer panel with 2mm offset as per the actual master section.
I(MAX): 4.877 X 10^6 mm^4; Y:440.6 mm
S=I/Y= 11069 mm^3
Bending moment (M)=S*σ(yield)=5755880 N-mm
2. Inner and Outer panel with 2mm offset with geometry changes to the inner panel as shown below.
I(MAX): 5.2893 X 10^6 mm^4; Y:440.6 mm
S=I/Y= 12005 mm^3
Bending moment (M)=S*σ(yield)=6242600 N-mm
3. Inner and Outer panel with 5mm offset. No geometry changes.
I(MAX): 4.839 X 10^6 mm^4; Y:440.6 mm
S=I/Y= 10983 mm^3
Bending moment (M)=S*σ(yield)=5711160 N-mm
4. Inner and Outer panel with 4mm offset. No geometry changes.
I(MAX): 4.862 X 10^6 mm^4; Y:440.6 mm
S=I/Y= 11035 mm^3
Bending moment (M)=S*σ(yield)=5738200 N-mm
CONCLUSION: Different sections, as shown above, were tried in order to achieve a higher moment of inertia. It is observed that increasing the gap between the inner and outer panels has resulted in decreasing bending moments. No significant change in section modulus is observed just by increasing the gap between the panels. On the contrary, if we tend to add more geometric features to the master section resulted in a drastic increase in section modulus. Hence it is best to add more geometric features to the master section to improve the stiffness of a section. However, this could result in an increase in manufacturing cost.