Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMIZATION - 

OBJECTIVE - To get a section of hood and find the section modulus of it and to come up with a new section which has increased the section modulus of the previous section .

INTRODUCTION - Section modulus is a geometric property for a given cross-section used in design of beam and 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.

Elastic section modulus - 

For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.The elastic section modulus is defined as S = I / y, where I is the second moment of inertia (or area moment of inertia, not to be confused with moment of inertia) and 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 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 plastic neutral axis  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 yielding stress, the area above and below the PNA will be equal, but for composite sections, this maynot be equal . 

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:

the Plastic Section Modulus can also be called the 'First moment of area'

Section modulus is calculated by formula -

                   S=I/Y

 where , S - Section modulus .

             I - Moment of inertia . 

             Y- Distance from neutral axis to the most extreme point . 

DESIGN PROCEDURE - 

1. For existing Hood section - 

So , moment of inertia (min) I = 2.3723e+05 mm^4

      Distance of neutral axis to extreme end (Y) = 439.5mm .

     Section modulus (s) = I/Y = 2.3723e+05 / 439.5 mm = 539.77 mm^3

2 . Changes in section -

We have made a change in section by increasing the base by 20mm . now we will see what is the value of section modulus we get for this modified section . 

3 . For modified Hood section - 

So , moment of inertia (min) I = 2.6676e+05 mm^4

      Distance of neutral axis to extreme end (Y) = 439.5mm .

     Section modulus (s) = I/Y = 2.6676e+05 / 439.5 mm = 606.96 mm^3

OBSERVATION -  

 As we  observe the values of section modulus of hood section and modified hood section , the section modulus of modified hood section is more than the original hood section.  so , if we increase the section  we get a better result of section modulus . 

CONCLUSION - 

So , by doing some change in section of hood we get a increased value of section modulus , this will in turn increase the strength of hood .