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. The higher the structure's section modulus, the more resistant 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 the design include an area for tension and shear, the radius of gyration for compression, and the 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 the Neutral axis to the end (unit mm)
• The Unit of a “section modulus” is (mm3)

Elastic section modulus:

• The elastic section modulus is used for a general design, applying up to the yield point for most metals and other common materials.
• The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with a moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (My) such that My = S × σy, where σy is the yield strength of the material.

First Design Study

• Moment of inertia(max) = 4.874721653×10^6×mm^4
• Moment of inertia(min) = 1.479902216×10^3×mm^4
• Y=878.8751/2=439.43755 mm
• S=I/Y
• S=1.479902216×10^3/439.43755= 3.3677mm^3

Hood Design Optimization

By increasing the depth of the inner panel by 0.8 mm

• Moment of inertia(max) = 4.895327527×10^6×mm^4
• Moment of inertia(min) = 1.511574723×10^4×mm^4
• Y=878.8751/2=439.43755 mm
• S=I/Y
• S=1.511574723×10^4/439.43755=3.4399mm^3

Conclusion:

• So, here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design(depth).