Section Modulus calculation and optimization
Section Modulus calculation and optimization
SECTION MODULUS
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 moment of inertia and polar moment of inertia 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.
DEFINITION
Section modulus is the ratio of moment of inertia about neutral axis upon the farthest point of section from neutral axis.
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 .
SECTION MODULUS CALCULATION
A Section of Hood Design is taken for the calculation of section modulus.
CASE 1 - Before Optimization
Section inertia analysis is carried out for the closed section of the designed hood.
By Section Inertia Analysis we have,
MOI (max) = 8.189619735e+05(mm^4)
MOI (min) = 3.494251651e+03(mm^4)
Y = 481.92 mm/2
= 240.96 mm
By Section Modulus formula,
S = I/y
= 3.494251651e+03 mm^4 / 240.96 mm
= 14.5013 mm^3
S = 14.5013 mm^3
CASE 2 - After Optimization
The inner pannel curve's of the hood is offseted outwards by a distance of 1 mm and the section inertia analysis is carried out as above.
By Section Inertia Analysis we have,
MOI (max) = 8.158003854e+05 mm^4
MOI (min) = 3.743298859e+03 mm^4
Y = 481.92 mm/2
= 240.96 mm
By Section Modulus formula,
S = I/y
= 3.743298859e+03 mm^4 / 240.96 mm
= 15.5349 mm^3
S = 15.5349 mm^3
CONCLUSION
By Comparing the above cases the value of section modulus in case 2 is greater than that of case 1. As we increase the cross-sectional area, the moment of inertia and section modulus increases hence,the strength and the load material also increases.