Section Modulus calculation and optimization

Section Modulus of The Hood

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 is the ratio of Moment of Inertia (I) of the beam cross-section about the neutral axis to the distance (ymax) of extreme fiber from the neutral axis.

        Therefore,

          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

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

Case 1 : 

The Hood which was already created is imported and the section inertia analysis is done.

We have to make sure that the curve obtained is a single/closed curve.

                                                                     fig: 1.1

                                                                                fig:1.2

MOI (max) =4.832518775e+06(mm^4)

MOI (min) = 1.503510429e+04(mm^4)

Section Modulus Equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2, Total distance =882.104579mm

Y =882.104579 / 2

   = 441.0522 mm

Therefore, S = 15035.104/441.0522

                    S = 35.13 mm^3

Case 2 : Optimization 

The hood inner panel’s curve is offset by 2mm outwards and section inertia analysis is done same as case 1 for a closed curve.

                                                                     fig: 1.3

                                                                        fig : 1.4

MOI (max) = 4.8772264e+06 [mm^4]

MOI (min) =1.63171721e+04[mm^4]

As per section modulus equation,

S = I / Y

I = MOI (min) value is considered

Y = Total distance /2, Total distance =882.104579mm

Y =882.104579 / 2

   = 441.0522 mm

Therefore, S = 16317.172 mm^4 / 441.0522 mm

                   S =  36.99601mm^3

Conclusion : 

If We comparing case 1 & case 2,

The section area is directly proportional to the moment of inertia & section modulus.

The section modulus value of case 2 is higher than the case 1. Section 2 having more strength than section 1.