Section Modulus calculation and optimization
SECTION MODULUS OPTIMIZATION
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 the design include an area for tension and shear, the 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.
There are two types of section moduli, the elastic section modulus, and the plastic section modulus.
- The elastic section modulus is defined as S = I / y,
where,
I is the moment of inertia
Y is the distance from the neutral axis to any given fiber.
- The plastic section modulus is the sum of the areas of the cross-section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:
Zp= Acyc+ Atyr
Section modulus calculation:
CASE 1:
In this select the designed hood and extract the outer surface of that and convert it into the sketch.
Apply the moment of inertia to the closed section of the hood.
Now calculate the section modulus by considering the minimum moment of inertia,
We have,
I (max) = 4.74e+06[mm^4]
I (min) = 1.462e+04[mm^4]
y in mm = 874.2972/2
Then S = I/y
S = 1.462686566e*10^4/874.2972/2
S = 39759.94/437.1486
S = 90.95 mm^3
CASE 2:
By changing the design of the hood and calculating the section modulus.
Apply the moment of inertia to the closed section of the hood.
Now calculate the section modulus by considering the minimum moment of inertia,
We have,
I (max) = 4.706e+06[mm^4]
I (min) = 1.675e+04[mm^4]
y in mm = 874.2972/2
Then S = I/y
S = 1.675193809e*10^4/874.2972/2
S = 45536.4889/437.1486
S = 104.1670 mm^3
therefore by comparing the results the modified part got the more section modulus which gives rise to the stiffnes of hood.
CONCLUSION:
- Calculated the section modulus of the designed hood and made the changes in the hood in order to improve the stiffness of the hood.
- By considering the minimum moment of inertia along the x-axis calculated the section modulus and optimized by improving the resistance against the bending stress.