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.
It is denoted by Z.
Z = I/ymax
Mathematically By bending stress equation,
M/I = σmax/ymax
M = σmax × (I/ymax)
M = σmax × Z
Where,
I = Moment of Inertia(m⁴)
y = distance from NA to extreme layer(m)
The unit of section modulus is m³.
Calculations
Now we will calculate the section modulus of the hood
1st Iteration
Here is the section of Hood for 1st iteration -
Here is the moment of inertia analysis -
Here is the length of extreme ends -
As per the formula
S = I/Y
I = 2.43 x 10^5
Y = L/2 = 885/2 = 442.5
So S = 2.43 X 10^5/442.5
= 0.00549 x 10^5 M^3
2nd Iteration
Here is the section of hood for 2nd iteration -
Here is the moment of inertia analysis -
As per the formula
S = I/Y
I = 2.56 x 10^5
Y = L/2 = 885/2 = 442.5
So S = 2.56 X 10^5/442.5
= 0.00578 x 10^5 M^3
The percentage difference between 1st iteration and 2nd iteration is -
5.28%
So the strength increased by 5.28% after we changed the shape of the hood a little as shown in the 2nd iteration section image