Section Modulus calculation and optimization
SECTION MODULUS OF THE HOOD
Objectives: To find the section modulus of the hood and optimisation to improve the overall section modulus.
SECTION MODULUS: The section modulus (s) is geometric property of the cross section used for designing beams and flexural members. It does not repesent anything physically.
FORMULA OF SECTION MODULUS:It may be defined as the ration of total mpment resisted by the section to the strees in the extreme fibre which is equal to yield stress.
There fore: S=I/Y,where
S=section modulus(mm^3)
I=moment of inertia of the section about the bending axis(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 beams cross section area measure the beam ability to resist bending. The large the moment of inertia less will be the bend.
where,
M=Bending moment
I=Area moment of inertia
E=Youngs modulus
R=Radius of gyration
NATURAL AXIS:
When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibres of the beams are subjected to maximum tension.
CALCULATION:
Case 1: Before optimization.
The hood which are 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.
MOI (max)= 8.928754301e+ 07[mm^4]
MOI (min)=3.196609661e+05 [mm^4]
As per the section modulus equation .
S=I/Y
I=MOI(min) value is considered
Y=Total distance/2, Total distance=87505680mm
Y=87505680/2
=4370784mm
Therefore, S=730.179mm^3
Case 2:After optimization:
The hood inner panel's curve is offset by 0.5mm outwards and section inertia analysis is done same as.
Case 1 for a closed curve
MOI (max)=8.910657812e^07 mm^4
MOI (min)=3.264954768e^05 mm^4
As per section modulus equation,
S=I/Y
I=MOI (min) value is considered
Y=Total distance/2 Total distance=875.5680 mm
Y=875.5680/2
=437.784 mm
Therefore,S= 326495.4768 mm^4/437.784mm
S=745.792mm^3
CONCLUSION:
Hence when comparing case1&case2,
1. The section modulus value of case 2 is higher than the case 1
2. As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase
So, here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design (depth).