Section Modulus calculation and optimization
Section modulus give us idea about how much of load the given structure can take. If the section modulus increases the moment of resistance increases and hence its load bearing capacity. S=I/Y, Where S= section modulus I=moment of inertia of a section Y=distance from neutral axis to any given fibre.
Aim:
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 fibre which is equal to yield stress.
Which is equal to yield stress.
Therefore
S=I/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 a 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
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 (MAX) = 4.532796634+06 (mm^4)
I (MIN) = 1.172289501e+04 (mm^4)
As per the section modulus equation,
S = I/Y
I = MOI (min) Value is considered
Total distance = 855.6618 mm
Y = Total distance / 2,
Y = 855.6618/ 2
= 427.8309 mm
Therefore, S = 1.17228*10^6/427.8309 mm
S = 2740.05454mm^3
Case 2: After Optimization
The hood inner panel’s curve is offset by 1mm outwards and section inertia analysis is done same as case 1 for a closed curve.
I (MAX) = 4.504835313e+06 (mm^4)
I (MIN) = 1.257102826e+04 (mm^4)
As per the section modulus equation,
S = I/Y
I = MOI (min) Value is considered
Total distance = 855.6618 mm
Y = Total distance / 2,
Y = 855.6618/ 2
= 427.8309 mm
Therefore, S = 1.257102*10^6/427.8309 mm
S = 2938.3151146867mm^3
