Section Modulus calculation and optimization

Aim 

To calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus. 

S=I/Y

Here,

S = Section modulus

I= Moment of Inertia (Unit mm 4)

Y= Distance from Neutral axis to the extreme end (unit mm)

The Unit of a “section modulus” is (mm3)

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 Changing the position can show the difference in bending which is because of the centroid distance from extreme fiber end.In Layman's terms, in this position there is more material from axis to the specific direction, to resist the load which makes less bend amd improves the strength.

case-1

For my hood design the moment of inertia values are,

Maximum moment of inertia = 1.563959205e+07[mm^4]

Minimum moment of inertia = 1.819266580e+05[mm^4] = 4.3604[mm^4]

The total distance of the hood Y = 947.77 mm

Distance between the neutral axis to the extreme end = (947.77/2) =473.885 mm

To find section modulus of  HOOD section, we have to calculate

S= 181926.6580/473.885

S = 383.904656193mm3

case-2

In order to increase the resistance to bending of HOOD, We have to make an improvement in section modulus of HOOD

So I have made some changes in my HOOD design and its section is given as follows,

Maximum moment of inertia = 1.559785106e+07[mm^4]

Minimum moment of inertia = 1.869087589e+05[mm^4] 

distance of the hood Y  = 4.4574[mm^4]

To find section modulus of new HOOD section, we have to calculate

S = 186908.7589/4.4574

S = 41932.2382779mm3

Conclusion:

These calculation is necessary to know the design actual withstand capability of product. As we increase sectional area, the moment of inertia & section modulus increases  it means capacity of material also increases