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 the geometric property of the given cross-section of any shaft or beam structures. It is the direct measure of the strength of the shaft section or the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending.
• Section modulus is defined as the ratio of polar moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibres.
• There are two types of section modulus, the elastic section modulus, and the plastic section modulus. The section modulus of different profiles can also be found as numerical values for common profiles in tables listing properties.
• Formula of Section Modulus: It may be defined as the ration of total moment resisted by the section to the stress in the extreme fibre which is equal to yield stress.

There fore

S = I/Y, Where

• S = Section modulus (mm^3)
• I = Moment of Inertia of the section about the bending axis. (mm^4)
• Y = Distance between the neutral axis and extreme end of the object (mm)

Area moment of Inertia:-

• The area moment of inertia of a beams cross sectional area measures the beam ability to resist bending. The larger the moment of inertia less will be the bend.

Where,

• M = Bending moment
• I = Area moment of Inertia
• E = Youngs modulus
• R = Radius of gyration

Neutral axis:- When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibres of the beams are subjected to maximum tension.

• Material Data: Stainless steel AISI 302 – cold rolled
• Where yield strength of stainless steel is 520MPa = 520 N/mm^2

Section Modulus Calculation:-

• Case 1:-The Intersection of the design was taken and then section Inertia Analysis was done.

Moment of inertia(max) = 1.58509×10^7(mm^4)

Moment of inertia(min) = 1.36088×10^5(mm^4)

Y = Total length/2

=484.3055/2

=242.1527mm

section modulus for max. = 1.58509×10^7/242.1527

= 6.5458×10^4

section modulus for min. = 1.36088×10^5/242.1527

= 0.5619×10^3

So for this hood design section modulus range from 6.5458×10^4(mm^3) to 0.5619×10^3(mm^3).

• Case 2:- Hood Design Optimization by increasing the depth of the inner panel by 2mm.

Moment of inertia(max) = 1.57730×10^7(mm^4)

Moment of inertia(min) = 1.53090×10^5(mm^4)

Y = Total length/2

=484.3055/2

=242.1527mm

section modulus for max. = 1.57730×10^7/242.1527

= 6.5136×10^4

section modulus for min. = 1.53090×10^5/242.1527

= 0.6322×10^3

So for this hood design section modulus range from 6.5136×10^(mm^3) to 0.6322×10^3(mm^3)

Conclusion:-

the strength of the section increases in area ion both maximum and minimum value.

by evaluting the above cases, we can say that moment of inertia is directly propotional to the strength of the material.