Section Modulus calculation and optimization
Section modulus
It is the ratio of area of moment of inertia about the neutral axis and to the distance of outermost fiber from the neutral axis.
Z=I/Y
Whereas,
Z= section modulus
I=Area moment of Inertia
Y=Distance from the neutral axis to the outermost fiber.
The sectional modulus of hood design before optimization
I max =9.004750779*10^7 (mm^4)
I min =3.041752136*10^5 (mm^4)
Y = 875.7120 / 2= 437.856 mm
S=I/Y
Section modulus for max = 9.004750779*10^7 /437.856
=2.05655*10^5
Section modulus for min =3.041752136*10^5 / 437.856
=6.94692*10^2
So for this hood design section modulus range from 2.05655*10^5 mm^3 to 6.94692*10^2 mm^3
Optimized design
In order to increase the sectional modulus, cross sectional area has to be increased.
I max = 8.988490649*10^7 (mm^4)
I min =3.094412137*10^5 (mm^4)
Y = 437.856 mm
Section modulus for max =8.988490649*10^7 /437.856
=2.05284*10^5
Section modulus for min =3.094412137*10^5 / 437.856
=7.06715*10^2
So, for this hood design section modulus range from 2.05284*10^5mm^3 to 7.06715*10^2 mm^3
Z1< Z2
Since, Z2 > Z1 the strength of the hood is increased.
Section modulus
Section modulus is a way to describe the strength and stiffness of a shape, like a beam or a bar. It helps engineers design these structures. There are different kinds of section moduli for different purposes. The main idea is that the shape and size of a cross-section affect how strong and rigid the structure is. So, section modulus helps us understand and calculate these effects.
S= I/Y
Here,
S = Section modulus
I= Moment of Inertia (Unit mm 4)
Y= Distance from Neutral axis to the extreme end (unit mm)
The Unit of a “section modulus” is (mm3)
Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.
Moment of Inertia is expressed as I = m × r2
where,
m = Sum of the product of the mass.
r = Distance from the axis of the rotation.
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.