Section Modulus calculation and optimization
Report
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 geometry 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 ratio of total moment resisted by the section to the stress in the extreme fiber which is equal to yield stress.
Which is equal to yield stress .
Therefore
S/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 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 subected to maxmum compression ,while the botttom most fibre of the beams are subjected to maximum tension.
#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(mix)=9.302672194e+07[mm^4]
I(min)=2.873737748e+07[mm^4]
as per the section modulus equation,
S=I/Y
I=MOI(min)value is considered
Y=total distance/2,total distanec = 885.7763mm
Y=885.7763mm/2
Y=442.88815mm
Therefore ,
S= 287373.7748mm^4/442.88815mm
S=648.863mm^4
Case2:- After Optimization
The hood inner panels curve is offset outwards and section inertia analysis is done same as case 1 for a closed curve .
I(mix)=1.116537365e+08[mm^4]
I(min)=3.383802794e+05[mm^4]
as per the section modulus equation,
S=I/Y
I=MOI(min)value is considered
Y=total distance/2,total distanec = 885.7763mm
Y=885.7763mm/2
Y=442.88815mm
Therefore ,
S= 338380.2794mm^4/442.88815mm
S=764.031mm^4
Conclusion :-
Resulting by comparing case 1and case2,
1. The section modulus value of case 2 is higher than the case 1 .
2. as we increase the seectionn area the moment of inertia and section modulus increase which means strenght and load materisl also increase . which the moment of inertia directly proportonal to the strenght of the material.