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 modulus

• elastic section modulus
• plastic section modulus

ELASTIC SECTION MODULUS

The elastic section modulus is defined as S = I / y,

where

I is the second moment of area

y is the distance from the neutral axis to any given fibre

PLASTIC SECTION MODULUS

The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.

WE USE ELASTIC SECTION MODULUS FOR CALCULATION

CASE 1

I (max) = 4.813874623e+06[mm^4]

I (min) = 1.492639116e+04[mm^4]

Y = 451.230/2 = 225.619 mm

S (MAX) =4.813874623×10^6/225.619= 0.3479 mm^3

S (MIN) =1.492639116×10^4/225.619= 0.07193 mm^3

Its section modulus lies between 0.3479 mm^3 to 0.07193 mm^3

CASE 2

Just adjust the intersection point and get this values

I (max) = 5.167180377e+06[mm^4]

I (min) = 1.672018444e+04[mm^4]

Y = 451.230/2 = 225.619 mm

S (MAX) =5.167180337×10^6/225.619= 0.3735 mm^3

S (MIN) =1.672018444×10^4/225.619= 0.08057 mm^3

Its section modulus lies between 0.3735 mm^3 to 0.08057 mm^3.

conclusion

By this two case, case 2 is having more section by thing i coclude by adjusting the intersection point we get different section modulus.