Section Modulus calculation and optimization

Aim : To find the section modulus of the hood and optimisation to improve the overall section modulus.

Section Modulus: The section modulus (S) is geometric property of the cross section used for designing beams and flexural members. It does not represent anything physically.

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

Where yield strength of stainless steel is 520MPa = 520 N/mm^2

Case 1:

MOI (max) = 5.561437238e+06 (mm^4)

MOI (min) = 1.716060293e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = 485.7599/2= 242.8799 mm

Therefore, S = 706.57mm3

Case 2:

MOI (max) = 4.779392677e+06 (mm^4)

MOI (min) = 1.420487134e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = 485.7599/2= 242.8799 mm

Therefore, S = 586.978 mm3

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).