Section Modulus calculation and optimization
Aim - To calculate section modulus of hood and optimize the design to have improved section modulus.
Section modulus - Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness.
TYPES OF SECTION MODULUS - There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.
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).
Section Modulus Calculation and Optimization:
- Hood Main Design:
Calculation of Section Modulus of main Hood:
Moment of Inertia (MOI), Imax = 9.069480176 x 10^7 [mm^4]
Moment of Inertia (MOI), Imin = 2.950173723 x 10^5 [mm^4]
Distance between the neutral axis and the extreme end of the object, y = 876.8171 mm / 2 = 438.40855 mm
Section Modulus, S = Moment of Inertia (MOI), I / Distance between the neutral axis and the extreme end of the object (y)
S = I/y
For Maximum (MOI),
S = ( 9.069480176 x 10^7 mm^4) / (438.40855 mm)
S= 2.06872794246 x 10^5 mm^4
For Minimum (MOI),
S = (2.950173723 x 10^5 mm^4) / (438.40855 mm)
S= 6.7292796251 x 10^2 mm^4
2.Hood Optimized Design:
Calculation of Section Modulus of Optimized Hood:
Moment of Inertia (MOI), Imax = 9.052755367 x 10^7 [mm^4]
Moment of Inertia (MOI), Imin = 2.989494730 x 10^5 [mm^4]
Distance between the neutral axis and the extreme end of the object, y = 876.8171 mm / 2 = 438.40855 mm
Section Modulus, S = Moment of Inertia (MOI), I / Distance between the neutral axis and the extreme end of the object (y)
S = I/y
For Maximum (MOI),
S = ( 9.052755367 x 10^7) / (438.40855 mm)
S= 2.0649130513 x 10^5 mm^4
For Minimum (MOI),
S = (2.989494730 x 10^5 mm^4) / (438.40855 mm)
S= 6.8189699539 x 10^2 mm^4
Conclusion:
The section modulus of the Front Hood of a car was calculated and compared with the optimized hood and found the better result.