Section Modulus calculation and optimization

SECTION MODULUS

• It is the ratio of moment of Inertia of the cross section about the neutral axis to the distance of farthest end from the neutral axis.

    S = I/Y

S = Section modulus

I= Moment of inertia

Y= Distance from the center of axis of cross section to the farthest end.

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

• The section modulus of the cross sectional shape is significant in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.
• The unit of the Section modulus is mm³
• Section modulus can improved by varying the geometry of the cross section.

MOMENT OF INERTIA:

• Moment of inertia, quantitative measure of the rotational inertia of a body i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force).
• The formula for moment of inertia is the “sum of the product of mass” of each particle with the “square of its distance from the axis of the rotation”. The formula of Moment of Inertia is expressed as

                         I = Σ mr²

CASE 1: Initial hood design

MOI(min):1.550240974e +04(mm^4)

Y distance =440.6839mm

S =I/Y

  =1.55024097e+04/440.6839

  S =0.01864mm⁴

 

 

 

 

 

CASE 2: Optimized hood design

MOI(min): 2.006731839e+04(mm^4)

Y distance=440.6839mm

S = I/ Y

   =2.006731839e+04/440.15

   =0.021455mm⁴

This section is increased with 0.5mm clearance between inner and outer panel which increases the strenght of the hood.

CONCLUSION:

From comparing the case1 and case2

1. The section modulus value of case 2 is higher than the case 1
2. As we increase the section area between inner panel and outer panel the moment of inertia & section modulus increases which means that the strength of the hood and load material is strong enough.