Section Modulus calculation and optimization
Aim: To calculate the section modulus of the designed hood and try out another way to increase the section modulus of the same hood by some means.
Theory:
What is Section Modulus (S)?
Section Modulus is the total moment resisted by the section to the stress in the extreme fibre. It gives an idea about how much load the structure can take. A high section modulus means better load-bearing capacity.
The formula for S is :
S = I / Y
where S is the section modulus, I is the moment of inertia, and Y is the distance between the neutral axis and extreme fibre.
What is Moment of Inertia (I)?
Moment of inertia aka angular mass or rotational inertia can be defined w.r.t. rotation axis, as a quantity that decides the amount of torque required for a desired angular acceleration or a property of a body due to which it resists angular acceleration. The formula for moment of inertia is the “sum of the product of mass” of each particle with the “square of its distance from the axis of the rotation”.
The formula of Moment of Inertia is expressed as I = Σ miri2.
Scenario 1:
This is the designed hood previously made. Make a plane (front plane) on the surface. This is the plane with which the section is to be done.
Using intersection command, intersect the hood with this newly made plane.
Extract the outer curve of the outer panel and the inner curve of the inner panel. These are the 2 curves to be used for finding the section modulus.
Extracting the outer curve of the outer panel intersection
Extracting the inner curves of the inner panel intersection
Hiding all unwanted curves. This is what we are going on to work on.
Connect the gaps with lines.
Join the ends
Next up, fill the closed sketch using "Fill" command
Measure the Moment of Inertia using the "Measure Inertia" tool
M1 and M2 are the inertia values. Convert these values to mm^4. For calculating the section modulus, we take the smaller value of M (which is M1 here)
To get the Y value, we need to take the overall length of the section. For that, we can make a sketch and create 2 lines/axes and measure the distance between them. Half of that distance will be the value of Y.
Making an axis from the created point (similarly on the other side too)
The distance was found to be 884.146mm.
Finally calculating the S (section modulus) value
M1 = 2.638 x 10^(-6) m^(4)
= 2.638 x 10^(-6) x 10^(12) mm^(4)
M1 = 2.638 x 10^(6) mm^(4)
M2 = 9.846 X 10^(8) mm^(4)
We need to take the lowest value of M1. The lowest value of M determines the starting point of breakage. Here M1<M2, so M1 is to be taken.
Y is the distance between the neutral axis and the extreme end of the object. The overall length was found to be 884.146 mm. Taking the half of this value will give us Y.
Y = 884.146 mm / 2 = 442.073 mm
I / Y = 2.638 x 10^(6) mm^(4) / 442.073 mm
So, S1 = 5967.34 mm^(3)
Scenario 2:
We have to find a way to increase the section modulus of the hood by changing the section.
Make a parallel curve of the inner panel curve downwards for 0.5mm. Then try measuring the MI again.
In scenario 2, M1 has slightly increased to 2.742 x 10^6 mm^4 and M2 has become 0.001 x 10^12 mm^4.
Doing the calculation
M1 = 2.742 x 10^(-6) m^(4)
= 2.742 x 10^(-6) x 10^(12) mm^(4)
Therefore, M1 = 2.742 x 10^(6) mm^(4)
M2 = 0.001 x 10^(12) mm^(4)
Here M1<M2, so M1 is to be taken.
Y value remains the same.
Hence,
S2 = (2.742 x 10^(6) mm^(4)) / 442.073 mm
Therefore, S2 = 6202.595 mm^(3)
From this, we can see that S1 = 5967.34 and S2 = 6202.595.
Hence we have successfully improved the section modulus by offsetting the inner panel curve downwards/inwards to 0.5mm.