Section Modulus calculation and optimization
SECTION MODULUS OF THE HOOD
OBJECTIVE:
To find the section modulus of the hood and optimisation to improve the overall section modulus.
Section modulus: the section modulus (s) is a geometric property of the cross section used for designing beams and flexural members. It does not represent anything physically.
Formula of section modulus: it may be defined as the ration of total moment resisted by the section to the stress 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 sectional 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 = 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 beams are subjected to maximum tension.
CALCULATION:
CASE 1: BEFORE OPTIMIZATION
The existing hood profile inertia analysis is completed.
We have to make sure that the curve obtained is a single/closed curve.
Moment of inertia (I -max) = 2.953e+008mm4
Moment of inertia (I -min) = 7.32e+006mm4
Y = 487.2mm / 2 = 243.6 mm
S (max) = I -max / y ( 2.953 / 243.6 ) = 0.0121 x 10^8 mm4
S (min) = I -min / y ( 7.32 / 243.6 ) = 0.0300 x 10^6 mm4 = 300 mm4
CASE 2: AFTER OPTIMIZATION
The hood profile is modified with some minor extension of profile
Moment of inertia (I -max) = 3.137e+008mm4
Moment of inertia (I -min) = 8.154e+006mm4
Y = 487.2mm / 2 = 243.6 mm
S (max) = I -max / y ( 3.137 / 243.6 ) = 0.0128 x 10^8 mm4
S (min) = I -min / y ( 8.154 / 243.6 ) = 0.0334 x 10^6 mm4 = 334 mm 4
CONCLUSION:
Hence when comparing case 1 & case 2,
In this study, we take the minimum of inertia moment to analyze the minimum limit of hood deformation. Thus the section modulus of the front hood was calculated and compared with the new design.
From the result, we found out that increasing the cross-section area would give a better section modulus and helps in increasing the strength of the hood.