Section Modulus calculation and optimization
Aim:- To determine the hood's section modulus and do optimisation to enhance the section modulus overall.
Section Modulus:-Section modulus is a direct measure of a strength of any cross sectional area of an object about an reference axis.
The formula of section modulus is given by,
S=I / Ymax
Where,
I = Moment of inertia (mm^4)
Y = Distance between neutral axes and outermost fiber (mm)
Steps to determine section modulus:-
- Find location of centroid of given cross section.
- Find moment of inertia about neutral axis.
- Find YmaxYmax from neutral axis.
- Find elastic section modulus using the formula provided above.
Area Moment Of Inertia:- The capacity of a beam to resist bending is measured by the area moment of inertia of its cross section. Less bend will occur when the moment of inertia increases.
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.
Imax =9.038206964 x 10^7 (mm^4)
Imin =2.692728187 x 10^5 (mm^4)
Y = 880.8102 / 2
= 440.4051
section modulus (S)= Imin/ Y
section modulus (S) = 2.692728187 x 10^5 / 440.4051
= .61142x 10^3
So for this hood design section modulus range from 0.61142 x 10^3 mm^3 = 611.42mm^3.
CASE 2: After optimization
The hood inner panel’s curve is offset by 2mm outwards and section inertia analysis is done same as case 1 for a closed curve.
Imax = 9.00179327 x 10^7 (mm^4)
Imin = 2.849808772 x 10^5 (mm^4)
Y = Total length / 2
= 880.8108/2
=440.4054 mm
section modulus (S)= Imin/ Y
section modulus = 2.849808772 x 10^5 / 440.4054
= 0.64708 x 10^3
So for this hood design section modulus is 0.64708 x 10^3 mm^3= 647.08mm^3
Hence on comparing both the cases,
1. The section modulus value of case 2 (optimised case) 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