Section Modulus calculation and optimization
Aim: -
To find the section modulus of the hood and optimization to improve the overall section modulus.
Objective: -
Use the section from your Hood design and calculate the section modulus using the formula S= I/y.
Section Modulus: -
The section modulus (S) is geometrical property of the cross section used for designing beams and flexural members. It does not represent anything physically.
Formula of section Modulus: - (The section modulus is a cross-sectional geometric property of structural elements such as beams, columns, slabs, etc. and it is used to calculate stresses in Cross-sections. In general, it can be said that the greater the dimensions of a cross-section under a given load, the greater the Section modulus and the smaller the bending stress.)
Which is equal to yield stress.
Therefore
S=I/y, Where
S= Section modulus (mm^3)
I = Moment of inertia of the section to the stress in the extreme end of the object (mm^4)
Y= Distance between the neutral axis and extreme end of the object (mm).
Area Moment of Inertia: -
The area moment of inertia of a beam cross section area measures the beam ability to resist bending. The larger the moment of inertia less will be the bend.
Where,
M = Bending Moment
I = Area moment of Inertia
E = Young modulus
R = Radius of gyration
Neutral Axis:-
When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibre of the beams are subjected to maximum tensi
This picture contains the following scene, Diagram of a beam on its narrow edge supported at both ends. A man is walking on a straight beam. Diagram of a beam resting on its flat side supported at both ends. A man is walking on the straight beam and its bending in the middle
Calculation:-
Case 1: Before Optimization
The hood which was already created is imported and the section inertia analysis is done.
We have to make sure that the curve obtained is a single/closed curve.
I (MAX) = 9.007542316e+07 (mm^4)
I (MIN) = 2.846332211e+05 (mm^4)
As per the section modulus equation,
S = I/Y
I = MOI (min) Value is considered
Y = Total distance / 2, Total distance = 880.1648 mm
Y = 880.1648 / 2
= 440.0824 mm
Therefore, S = 284633.2211mm^4 /440.0824 mm
S = 646.7725 mm^3
Case 2: After Optimization
The hood inner panel’s curve is offset by 0.5 mm outwards and section inertia analysis is done same as case 1 for a closed curve.
I (MAX) = 9.721317976e+07 (mm^4)
I (MIN) = 3.153347058e+05 (mm^4)
As per the section modulus equation,
S = I/Y
I = MOI (min) Value is considered
Y = Total distance / 2, Total distance = 880.1648 mm
Y = 880.1648 / 2
= 440.0824 mm
Therefore, S = 315334.7058 mm^4 / 440.0824 mm
S = 716.5355 mm^3
Optimization methods: -
Increasing the offset distance
Increasing the emboss
Increasing the thickness ( strength ) of the material
Table: -
|
S. no. |
Case no |
I (min) (mm^4) |
Y value(mm) |
Sm (mm^3) |
|
1 |
1) Before optimization |
2.846332211e+05 |
440.0824 |
S = 646.7725 |
|
2 |
2) After optimization |
3.153347058e+05 |
440.0824 |
S = 716.5355 |
Conclusion:-
Resulting by comparing case 1 & case 2,
The section modulus value of case 2 is higher than the case 1
As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase. Which the moment of inertia directly proportional to the strength of the material