Section Modulus calculation and optimization
1. Brief explanation about Section Modulus?
Ans: -
Section Modulus: It is the ratio of area moment of inertia about the neutral axis and to the distance of outermost fiber from the neutral axis.
Z = I/Y` [ units: mm3 or m3]
Where as,
Z, S = Section Modulus
I = Area moment of inertia
Y = Distance from neutral axis to the outermost fiber
Area moment of inertia: Area moment of inertia will depict the resistance offered by the body towards bending due to its cross section.
Neutral Axis: It’s a layer in a particular cross-section where, there will be either in tension or compression.
Example: Consider a bar as shown in figure below,
CASE 1: Bar is subjected to the load at center by fixing at both ends with the help of support A and B. Cut section view is shown to the right side of the bar with dimensions of b and d.
Area moment of inertia of the above-mentioned rectangular cross section is `= bd^3 /12`
CASE 2: The bar mentioned above is rotated to 90 degrees. Compared to CASE 1, in CASE 2 the bar is difficult to bend.
Area moment of inertia of the above mentioned rectangular cross section is `= db^3 /12`
By visual inspection itself we can say bd. Area moment of inertia in CASE 2 is greater than CASE 1. Therefore, resistance offered by a cross section towards bending is more in the case of case 2 so as the strength.
We can also prove it by bending equations.
`M/I = σ /Y = E /R`
We will consider the first two terms and we will rearrange them,
`M = I/Y * σ`
Where as,
M- bending moment (resistance towards bending)
I - area moment of inertia
Y - distance from outer most fiber to neutral axis
σ - Bending stress.
Here, I / Y is section modulus. So M is directly proportional to the section modulus and therefore to the area moment of inertia. By this we can say that if section modulus is more then the strength of cross section is more.
Here, we got the value as 876.47 mm /2 =438.21 mm is the Y value.
Note: -
Please refer the pdf file attached below for the section modulus of the hood.