Section Modulus calculation and optimization
SECTION MODULUS CALCULATION AND OPTIMIZATION
AIM:
To come up with a new section that has an improved section modulus compared to the previous one.
SECTION MODULUS:
It is the ratio of area moment of inertia about the neutral axis and to the distance of outermost fiber from the neutral axis.
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 second moment of area and polar second moment of area for stiffness.
Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus.
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
CALCULATION:
CASE 1:
I (Max) = 8.905871264e+07[mm^4]
I (Min) = 3.031341925e+05[mm^4]
S = I/Y
I = Min value is considered
I = 3.031341925e+05 mm^4
I = 303134.1925 mm^4
Y = Total distance/2 Total distance = 876.8553 mm
Y = 876.8553/2
Y = 438.42765mm
S = 303134.1925 mm^4/438.42765mm
S = 691.412 mm^3
CASE 2:
The hood inner panel’s curve is offset by 0.5mm outwards and section inertia analysis is done same as case 1 for a closed curve.
I (Max) = 8.903142847e+07[mm^4]
I (Min) = 3.076414815e+05[mm^4]
S = I/Y
I = Min value is considered
I = 3.076414815e+05 mm^4
I = 307641.4815 mm^4
Y = Total distance/2 Total distance = 876.8553 mm
Y = 876.8553/2
Y = 438.42765mm
S = 307641.4815 mm^4/438.42765mm
S = 701.692 mm^3
S2 = 701.692 mm^3 > S1 = 691.412 mm^3
S2 > S1 : I2 > I1
CONCLUSION :
The section modulus value of case 2 is higher than the case 1, The new section has an improved section modulus compared to the previous one as we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase.