Section Modulus calculation and optimization

INTRODUCTI0N;

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 second moment of area and polar second moment of area 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

ELASTIC SECTION MODULUS;

For general design, the elastic section modulus is used, applicable up to the yield point for most metals and other common materials.

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

.

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.

The plastic section modulus depends on the location of the plastic neutral axis (PNA).The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant, and equal compressive and tensile yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.

SECTION MODULUS 1

S=1.429071e-13mm4

SECTION MODULUS 2

S=1.522142e-13mm4

Note;

Y=280

.