Section Modulus calculation and optimization

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 ratio of the Moment of Inertia (I) of the beam cross-section about the neutral axis to the distance (Ymax) of extreme fiber from the neutral axis.

For a circular section, the section modulus: Z = I y max. where I = π 64 d 4 = Moment of Inertia.

It is the direct measure of the strength of the shaft section or beam section. The higher the section modulus of a structure, the more resistant it becomes to bending.

mathematically it is expressed as

S=I/Y

where S=section modulus

I=moment of inertia

Y= distance from the neutral axis to extreme end

Moment of inertia :

It is defined as the quantity expressed by the body resisting angular acceleration, which is the sum of the product of every particle's mass with its square distance from the axis of rotation.

it is directly proportional to the strength of the material, which can be calculated through section modulus.

Section modulus calculation of the hood design :

case 1:

Maximum moment of inertia = 4.776048246e+06[mm^4]

Minimum moment of inertia = 1.499059923e+04[mm^4]

The total distance of the hood Y = 878.4896mm

Distance between the neutral axis to the extreme end = (878.4896/2) = 439.248mm

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

S= 14990.59923/439.248

s= 34.1278mm^3

case 2:

Maximum moment of inertia = 4.784296572e+06[mm^4]

Minimum moment of inertia = 1.505336279e+04[mm^4]

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

S = 15053.36279mm^4/439.248mm

S=34.27076mm^3

From the above calculations, I got an improvement in section modulus for about increased 0.14296 mm³

so I also made an improvement in resistance to bending of my HOOD design.

Conclusion

The strength of the material is directly proportional to the moment of inertia, thus increasing the sectional area increases the increases strength of the component.

Thus sectional modulus for the hood design is calculated and an optimized design is also done to increase the section modulus of the hood.