Section Modulus calculation and optimization

Section of modulus: Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. 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.

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)

Section Of Modulus Equations:

Section of Modulus calculations:

Case 1 : Section of modulus of existing section.

MOI (max) = 4.823941189e+06 (mm^4)

MOI (min) = 1.436304691e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2,

Total distance =880.1413mm

Y = 880.1413 / 2

= 440.07065mm

Therefore, S = 14363.04691 mm^4/440.07065 mm

S = 32.63804 mm^3

Case 2 : Offset the section to 0.5 mm

MOI (max) = 4.814992559e+06 (mm^4)

MOI (min) = 1.454654820e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2,

Total distance =880.1413mm

Y = 880.1413 / 2

= 440.07065mm

Therefore, S = 14546.54820 mm^4/440.07065 mm

S = 33.055029 mm^3

So it is clear from above calculation that strength of the material is directly proportional to the moment of inertia, hence increase in sectional area there is have increase in overall mass of an object ,hence have increase in strength