Section Modulus calculation and optimization
AIM
1. To Understand the concept of section modulus and it's role in design.
2. To Calculate section modulus of designed hood.
3. To optimize the existing hood design with improved section modulus and understand the changes required.
INTRODUCTION
Section modulus can be termed as the ratio of area of moment of inertia about the neutral axis to the distance of outermost fiber from the neutral axis.
S=I/y
Where,
S is the section modulus.
I is the moment of inertia.
y is the distance from neutral axis to outermost fiber.
From Bending Equation,
M/I = f/y = E/R
Where,
M is bending moment.
I is moment of inertia of cross-section.
f is stress at a fiber from a distance of "y" from neutral axis.
E is Young's Modulus.
R is radius of curvature of bend structure.
M = I. f/y
i.e. M = S. f
M refers to bending moment meaning the resistance towards bending.
If M has to reach a max. value S has to be maximum, whereas S is directly proportional to I, Which in turn shows that I should be maximum value.
Calculation of section modulus on designed hood
Cross section to be evaluated:
Section inertia analysis for the region gives the maximum and minimum moment of inertia as follows:
For the analysis, considering Moment of inertia minimum to find out minimum strength of the hood,
MOI min = 2.862542641 x 10^5 mm^4
Distance between neutral axis and extreme end,
y = 879.9513/2 = 439.9756 mm
Now,
section modulus of initial hood design, S1 = MOI min/y
S1 = 2.862542641 x 10^5 / 439.9756 mm^3
S1 = 650.6139 mm^3
Calculation of section modulus on modified hood
For modified design the cross-section from initial hood design is slightly modified and the lower section is slightly offset to a value of .5mm. The new cross-section to be evaluated :
Section inertia analysis for the region gives the maximum and minimum moment of inertia as follows:
For the analysis, considering Moment of inertia minimum to find out minimum strength of the hood,
MOI min = 2.901491968 x 10^5 mm^4
Distance between neutral axis and extreme end remains same as no changes were made in that aspect,
y = 879.9513/2 = 439.9756 mm
Now,
section modulus of modified hood design, S2 = MOI min/y
S2 = 2.901491968 x 10^5 / 439.9756 mm^3
S2 = 659.4665 mm^3
Comparison between the designs
| Initial Design | Modified Design | |
|---|---|---|
| MOI min (mm^4) | 2.862542641 x 10^5 | 2.901491968 x 10^5 |
| MOI max (mm^4) | 9.127985355 x 10^7 | 9.111344025 x 10^7 |
| Distance, y (mm) | 439.9756 | 439.9756 |
| Section Modulus, S (mm^3) | 650.6139 | 659.4665 |
CONCLUSION
The existing hood design was analyzed and obtained MOI for the section, using this value the section modulus was calculated. This benchmark helps to optimize the next iteration of the design. In this specific case the section was slightly modified to obtain a better value for MOI which in turn results in a better section modulus value. This ultimately translates to the optimized strength of the designed hood.