Section Modulus calculation and optimization
SECTION MODULUS HOOD :
* To find section modulus of the hood and optimization to improve the overall section modulus.
* The section modulus is geometry property of the cross section used for designing beams and flexural members.it does not reprsent anything physically.
S=I/Y
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 objet(mm)
Area moment of inertia:
* The area moment of inertia of beams cross sectional area measure the beam ability to resist bending .the larger the moment of inertia less will be the bend.
M = Bending moment
I = Area moment of inertia
E = Youngs 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 fibres of the beam maximum tension .
Material data : stainless steel AISI 302 -cold rolled
where yield strength of stainless steel is 520Mpa = 520 N/mm^2
Case : 1 Before optimization:
Fig 1.1
Fig 1.2
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 =875.5680mm
Y = 875.5680 / 2
= 437.784 mm
Therefore, S = 319660.966 mm^4/437.784 mm
S = 730.179 mm^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.
Fig 1.3
Fig 1.4
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 =875.5680mm
Y = 875.5680 / 2
= 437.784 mm
Therefore, S = 326495.4768 mm^4 / 437.784 mm
S = 745.792 mm^3
Conclusion:
* Hence when comparing case 1 & case 2,
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 increases which means strength and load material also increase