Section Modulus calculation and optimization

Objectice:-

         Use the Section from your Hood design and calculate the Section Modulus using the formula.

Section Modulus:-

         Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It is the ration of moment of inertia and the distance of the topmost or the bottommost fiber from the neutral axis. It represents the strength of the section. The section modulus depends upon the moment of inertia which again depends not only on the total area of the cross-section but also on the disposition of the area with respect to neutral axis.

                   S = I/y

                   Where, 

                          S = Section Modulus,

                          I = Moment of Inertia,

                          y = distance between the neutral axis and the extreme end of the object.

Calculation Of Section Modulus For Hood:-

To calculate the section modulus first we need to cut the solid model at the middle by the plane. You may see the plane that is the pane i used to cut the model.

 

 This is how it looks like after sectioning and made it as closed curve. Then using the sketch we need to make it closed curve to perform the section inertia to calculate the section modulus.

After Performing the section inertia.

Section 1:-

MOI (Max) : 9.469835087e+007[mm^4]

MOI (Min) : 2.817391064e+005[mm^4]

Section Modulus Equation :

                S = I / Y.

Here the MOI (Min) is considered as the value of inertia (I).

I = 2.817391064*10^5,

I = 281739.1064.

Y = Total Distance / 2,

Total Distance = 880.4513,

Y = 880.4513 / 2,

Y = 440.22565.

Therefore S = 2,81,739.1064  / 440.22565,

               S = 639.98 mm^3.           

After Optimization:-

Offsetting the curve of inner panel to 1mm outwards.

Section 2:-

MOI (Max) = 9.484190555e+007[mm^4]

MOI (Min) = 2.966493037e+005[mm^4]

Here the MOI (Min) is considered as the value of inertia (I).

I = 2.966493037*10^5,

I = 296649.3037.

Y = Total Distance / 2,

Total Distance = 880.4513,

Y = 880.4513 / 2,

Y = 440.22565.

Therefore S = 296649.3037 / 440.22565,

               S = 673.85 mm^3.

Conclusion:-

• The value of Section Modulus of original section is small(639.98 mm^3) when compared to the value after optimization(673.85 mm^3).
• Therefore the value of section modulus will increase if the cross-section area increases.