Section Modulus calculation and optimization

Section modulus is a geometric property of a cross-sectional shape that measures its resistance to bending. It quantifies the shape's ability to withstand applied bending moments without excessive deflection or failure. The section modulus is an important parameter used in structural engineering and design calculations.

Mathematically, the section modulus (denoted as "S") is calculated as the ratio of the moment of inertia (I) of a cross-sectional shape about a neutral axis to the distance (c) from the neutral axis to the outermost fiber of the shape. It is typically expressed in units of length cubed

The section modulus formula is given by:

S = I / Y

Where:
- S is the section modulus
- I is the moment of inertia of the cross-sectional shape about the neutral axis
- Y is the distance from the neutral axis to the outermost fiber of the shape

The moment of inertia represents the resistance of a shape to bending. It depends on the shape's geometry and distribution of material around the neutral axis. A larger moment of inertia indicates a greater resistance to bending.

The distance "Y" is the perpendicular distance from the neutral axis to the outermost fiber of the shape. It represents the "height" of the shape's cross-section, as measured from the neutral axis to the farthest point.

The section modulus provides an indication of a cross-sectional shape's bending strength. Shapes with larger section modulus values have greater resistance to bending moments and are therefore more suitable for applications where bending loads are significant. Conversely, shapes with smaller section modulus values are less resistant to bending and may be more prone to deflection or failure under applied bending loads.

Original Hood Design 1

Section Modulus

I = 2.74 x 10^5 mm^4

Distance between Neutral Axis and extreme end of the Object

Distance between 2 outer ends of the hood = 876.45

Y = 876.45/2

Y =  438.22 mm

Section Modulus = I/Y

S = 2.74 x 10^5 mm^4/438.22 mm

S = 625.25 mm^3

 Hood Design 2 

Section Modulus

I = 2.802 x 10^5 mm^4

Distance between Neutral Axis and extreme end of the Object

Distance between 2 outer ends of the hood = 876.45

Y = 876.45/2

Y =  438.22 mm

Section Modulus = I/Y

S =  2.802 x 10^5 mm^4 / 438.22 mm

S = 639.40 mm^3

In the Above mentioned 2 Hoods the second hood is having high section modulus of 639.40 mm^3 

As per the rules if the area of the moment of inertia is more the strengths will also be increased.

In the above 1st intersection of the hood the S = 625.25 mm^3 &

in the 2nd intersection the S= 639.40 mm^3.

as it can be seen from the 2 section modulus values it can be said that the second hood is much stronger when compared to first hood.

The strength of the hood is achieved by increasing the dimensions of the hood, that is enlarging the thickness of the hollow section in the hood without changing the Y ( distance from neutral fibre to the outer part of section).

the hood inner and outer parts are offsetted so that the area inside the hood is increased.

As it can be seen from the below image the inner hood is offsetted b 0.7mm