Section Modulus calculation and optimization
Section modulus:
Section modulus is a geometric property for a given cross-section used 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 moment of inertia) and
Y is the distance from the neutral axis to any given fiber.
It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber.
The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.
Design study:
Without Modification,
Moment of inertia, I max = 4.776647150*10^6 mm4
Moment of inertia, I min = 1.502636898*10^4 mm4
Distance from NA to extreme fiber, y = 879.8/2 = 439.9 mm
Then Min. Section modulus, S min = I / y = 1.50263*10^4/439.9 = 34.15 mm3.
Max. Section modulus, S max = I / y = 4.776647150*10^6/439.9 = 10858.48 mm3
With modification (thickness of inner panel is increased by 0.2 mm),
Moment of inertia, I max = 4.77913934*10^6 mm4
Moment of inertia, I min = 1.51408246*10^4 mm4
Distance from NA to extreme fiber, y = 879.8/2 = 439.9 mm
Then Min. Section modulus, S min = I / y = 1.51408*10^4/439.9 = 34.41 mm3.
Max. Section modulus, S max = I / y = 4.77913934*10^6/439.9 = 10864.14 mm3.
Conclusion:
By increasing the thickness of the inner panel, we observe that the section modulus also increases. Therefore, by increasing the section modulus, the strength is also increasing.