Section Modulus calculation and optimization

                                   SECTION MODULUS CALCULATION AND OPTIMIZATION

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

SECTION MODULUS

Section Modulus is a geometric property used to calculate the bending stresses in a structural member.It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.It gives us an idea about how much of the load the given structure can take.

therefor,

S=I/Y

where s= section modulus in mm^3

          i= area moment of inertia

          Y = distance between nuetral axis and extreme end

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.

NUETRAL 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.

CALCULATION

befor optimization

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.

MOI (MAX) =8.2164*10^5 MM^4

MOI (MIN) =3.6302*10^3 MM^4

By equation,

S=I/Y

Y= 478.06/2 =239.03

S = 3.6302*10^3/239.03 = 15.187 MM^3

AFTER OPTIMIZATION

MOI (MAX) = 8.1932*10^5 MM^4

MOI (MIN) = 3.7908*10^3 MM^4

Y = 478.06/2 =239.03

S = M/Y

   = 3.7908*10^3 /239.03

   = 15.859

CONCLUSION

Hence when comparing both cases,

1. The section modulus value of case 2 has increased.

2. As we increase the section area, the moment of inertia & section modulus increases which means strength and resistance will increase.