Section Modulus calculation and optimization

Aim

To calculate section modulus of hood and optimize the design to have improved section modulus.

Section 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.

There are two types of section moduli,

1. Elastic section modulus ,

2. 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)

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 area (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. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre. It is also often used to determine the yield moment (My) such that My = S × σy, where σy is the yield strength of the material.

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. 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'

FIRST CASE STUDY OF DESIGN

The Intersection of the design was taken and then section Inertia Analysis was done-

Moment of inertia(max) = 5.8053439×10^5×mm^4

Moment of inertia(min) = 2.380902×10^3×mm^4

Y=485.7599/2=242.8799 mm

S=I/Y

S=2.380902×10^3/242.87= 9.803 mm^3

SECOND CASE STUDY OF DESIGN AFTER OPTIMIZATION

By ofseting the depth of the inner panel by 0.5 mm

Here,

Moment of inertia(max) = 8.600495×10^5×mm^4

Moment of inertia(min) = 3.29593×10^3×mm^4

Y=485.7599/2=242.8799 mm

S=I/Y

S=3.29593×10^3/242.87= 13.57 mm^3

Conclusion

So, here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design(depth).so it concluded that Strength of material is directly proportional to the moment of interia, thus increasing the sectional area increase the increases strength of component.

As just by increasing depth to 0.5 mm the section modulus is increased from 9.8 to 13.57