Section Modulus calculation and optimization

Section Modulus of a car hood

Objective: To calculate the section modulus of a car hood and also to improve the strength of the hood by making changes in the hood section.

Introduction: Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It is a direct measure of the strength of the cross-section. A component that has a larger section modulus will be stronger and capable of withstanding higher loads/stress.

There are two types of section modulus:

• Elastic section modulus - For general design, the elastic section modulus is used, 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 inertia (or area moment of inertia, not to be confused with 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 (M_y) such that M_y = S × σ_y, where σ_y is the yield strength of the material.
  
  
• Plastic section modulus - The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.The plastic section modulus depends on the location of the plastic neutral axis (PNA).

  The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:

  Zp = AcYc + AtYt.

Calculation of section modulus

The image below shows the cross-section of a car hood whose section modulus is to be measured

Section of modulus of 1st section

Max.moment of inertia = 4.79*10^6 mm^4

min. moment of inertia = 1.52*10^4 mm^4

Y = 241.56mm

Section modulus (Z) is given by

Z= I/y

where I = second moment of inertia

y = distance of neutral axis from the outermost surface.

Z = 1.52*10^4/241.56

Z = 62.92 mm^3.

The section modulus can be increased by increasing the cross - sectional area of the hood or by making changes to its cross - section.

The image below shows the changes made in the cross-section. The cross -section area is increased by 1.02 mm^2.

The section modulus for the section 2

Max.moment of inertia = 4.88*10^6 mm^4

min.moment of inertia = 1.6*10^4 mm^4

Y = 241.56mm

Section modulus Z = 1.6*10^4/241.56

Z = 66.23 mm^3.

Conclusion

Thus by making changes or by increasing the cross- sectional area, the strength of the component can be improved. The section modulus is calculated for the hood and changes are made so as to increase its strength.