Section Modulus calculation and optimization
AIM: To calculate the Section modulus of the Hood design and optimization to improve the overall section modulus
Use the Section from your Hood design and calculate the Section Modulus using the formula
S = I/y
Where,
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
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. Any relationship between these properties is highly dependent on the shape in question. Equations for the section modulus of common shapes are given below.
Neutral axis:The neutral axis of a beam is the line that passes through the centroidal depth of the beam where no longitudinal stress either compressive or tensile stress or no strain exists
CASE 1: Before optimization
Make sure to have a closed/single curve on a hood design before the section inertia analysis is done.
I (MAX) = 1.600870530e+007 (mm^4)
I (MIN) = 1.778660918e+005 (mm^4)
As per the section modulus equation,
S = I/Y
I = MOI (min) Value is considered
Y = Total distance / 2, Total distance =490.1352
Y = 490.1352 / 2
= 245.0676 mm
Therefore, S = 177866.091 mm^4 /245.067mm
S = 725.785mm^3
CASE 2: After optimization
I (MAX) = 1.591231363e+007 (mm^4)
I (MIN) = 2.450212823e+005 (mm^4)
As per the section modulus equation,
S = I/Y
I = MOI (min) Value is considered
Y = Total distance / 2, Total distance =490.1352
Y = 490.1352 / 2
= 245.0676 mm
Therefore, S = 245021.282 mm^4 /245.067mm
S =999.813mm^3
comparing case 1 and 2
percentage increase in optimised=(999.813+ 725.785)/245.067=7.04%
Conclusion:
Thus the section of mudulus increases, more strength the material have and section of modulus is directly propotional to the area of cross section