Section Modulus calculation and optimization
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
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 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
FIRST CASE
- 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.
CALCULATIONS
M1 = 1.085 x 10^-6 MM^4
M2 = 1.449 x 10^-4 MM^4
As per the section modulus equation
S = I/Y
I = Moment of inertia (Min) value is considered
Y = Total length/2 so Total length is 483.346 mm
Y = 483.346/2 = 241.673 mm
Therefore
S = 1.085 x 10^6/241.673
=4489.53 mm^3
SECOND CASE
After Optimization
The hood inner panel’s curve is offset by 1mm inwards and section inertia analysis is done same as first case for a closed curve.
CALCULATIONS
M1 = 9.914 x 10^-7 MM^4
M2 = 1.339 x 10^-4 MM^4
As per the section modulus equation
S = I/Y
I = Moment of inertia (Min) value is considered
Y = Total length/2 so Total length is 483.346 mm
Y = 483.346/2 = 241.673 mm
Therefore
S = 9.914 x 10^7/241.673
=410223.73 mm^3
Increasing the gap in between the outer and the inner panel leads to increament in the section modulus,so resistant to bending will also be get increased due to this strength of the hood will increase.
S = (410223.73 - 4489.53)
= 405734.2/4489.53 = 90.3734
= 90.373 *100 = 9037.36 %