Section Modulus calculation and optimization

Section Modulus:

Section Modulus is the geometric property of any given cross section of a shaft or beam structure, it is the direct measure of strength of that particular beam or shaft section. The resistance to bending by that structure is directly proportional to the section modulus of that structure, that is, higher the section modulus, higher the resistance to bending by that structure.

Section modulus can also be defined as the ratio of the moment of inertia to the distance from the neutral axis to the outer fibres.

Using the above statement to form a mathematical equation we get,

Where, S = The Section Modulus of the structure

I = The moment of inertia

Y = The distance from the neutral axis to the outermost fibres

The section modulus is taken with reference to the hood that was designed earlier, the image shows the hood assembly for which we are calculating the section modulus.

From this hood design, we extract a 2D sketch of it using the “Intersection Curve” command to extract the sketch. The image below shows what the extracted 2D sketch looks like.

The next thing to do is to calculate Y, which the distance from the neutral axis (Center point in the Y direction) to the outermost fibre (end point in any direction)

From the image above we can infer that Y = 440 mm

For the Moment of inertia, we can take different cases, starting from the original drawing and increasing the thickness of it to observe how the moment of inertia changes and in turn how it affect the Section modulus of the structure.

Cases for Calculation:

1. Case 1: Using the Hood that was designed for the previous challenge and calculating its section modulus

S = I/Y where in this case,

I = 1.643484268 x 10⁴ mm⁴

Y = 440 mm

Hence, S = 37.35191518 mm³

2. Case 2: Increasing the distance between the outer and inner panel by an additional 0.5 mm from the original distance.

I = 1.642419124 x 10⁴ mm⁴

Y = 440 mm

S = 37.32770736 mm³

3. Case 3: Increasing the distance the outer and inner panel by 2 mm from the original distance.

I = 1.639332469 x 10⁴ mm⁴

Y = 440 mm

S = 37.25755611 mm³

Result:

The moment of inertia for the 3 difference cases were taken and the section modulus of the structure was calculated and the results are shown above, from this we can infer that changing the distance between the outer and inner panel only affects the section modulus of the structure marginally with very small differences in values when comparing the three different cases.