Section Modulus calculation and optimization
Objective
To calculate the section modulus for the designed hood and optimized hood using NX cad.
Section Modulus
Section Modulus is the ratio of total moment resisted by the section to the stress in extreme fibre. Section Modulus is a geometric property of the given cross-section. It depends on the cross-section of the designed part or structure. Section modulus gives the idea about how much of the structure can bear.
Section modulus of the optimized design increases when the moment of resistance increases and hence it's load-bearing capacity increases.
Higher the Section Modulus higher will be the resistance to bending.
Section modulus can be calculated using the formula.
S = I/Y.
where, I = Moment of Inertia of the Section.
Y = Distance between neutral axis and extreme end of the design.
So, here we will take a section of our designed hood and optimized hoods for calculating the section modulus.
We will take the section along the length of the hood and find the Moment of Inertia using Section Inertia Analysis tool in NX Cad.
Section Modulus of Initial Hood Design.
From the above information analysis, Minimum and Maximum values of the moment of Inertia are obtained.
I (Max) = 88882996.24 mm^4.
I (Min) = 262004.45 mm^4.
Y = 880.8mm /2 = 440.4 mm.
We know that Section Modulus (S) = I/Y.
Maximun Section Modulus ( S[Max] ) = I[Max]/Y.
S[Max] = 88882996.24 mm^4 / 440.4 mm
= 201823.34 mm^3
S[Max] = 201823.34 mm^3.
Similarly, Maximun Section Modulus ( S[Min] ) = I[Min]/Y.
S[Min] = 262004.45 mm^4 / 440.4 mm
= 594.924 mm^3
S[Min] = 594.924 mm^3.
Section Modulus is represented as
S = ∑ Mi*(Ai)^2
Section Modulus is proportional to Area of Section (A) and Mass (M) of the body and inversely proportional to the distance between the neutral axis and extreme end of the design (Y) .
Section Modulus of Optimized Hood Design-1.
Here, Sectional Area is increased by offsetting the inner pannel to 0.2mm (outwards) and outer panel to 0.2mm (outwards).
From the above information analysis, Minimum and Maximum values of the moment of Inertia are obtained from the optimized design-1.
I (Max) = 89066716.33 mm^4.
I (Min) = 267073.50 mm^4.
Y = 880.8mm /2 = 440.4mm.
We know that Section Modulus (S) = I/Y.
Maximun Section Modulus ( S[Max] ) = I[Max]/Y.
S[Max] = 89066716.33 mm^4 / 440.4mm
= 202240.5 mm^3
S[Max] = 202240.5 mm^3.
Similarly, Maximun Section Modulus ( S[Min] ) = I[Min]/Y.
S[Min] = 267073.5 mm^4 / 440.4mm
= 606.434 mm^3
S[Min] = 606.434 mm^3.
Section Modulus of Optimized Hood Design-2
Here, Sectional Area is increased by offsetting the inner pannel to 0.1mm (outwards) and outer panel to 0.3mm (outwards).
From the above information analysis, Minimum and Maximum values of Moment of Inertia are obtained from the optimized design-2.
I (Max) = 89223853.03 mm^4.
I (Min) =267402.69 mm^4.
Y = 880.8mm /2 = 440.4mm.
We know that Section Modulus (S) = I/Y.
Maximun Section Modulus ( S[Max] ) = I[Max]/Y.
S[Max] = 89223853.03 mm^4 / 440.4mm
= 262597 mm^3
S[Max] = 262597 mm^3.
Similarly, Maximun Section Modulus ( S[Min] ) = I[Min]/Y.
S[Min] = 267402.7 mm^4 / 440.4 mm
= 607.18 mm^3.
S[Min] = 607.18 mm^3.
By comparing, Section Modulus values of the designed hood with the optimized designs, we can say the optimized hood design-2 has more section modulus value i.e 607.18 mm^3 .
Section Modulus is directly proportional to the resistance to bending. So, Optimized hood design -2 is capable to withstand larger loads.
Conclusion
Section Modulus of the optimized hood is calculated using NX Cad.