Section Modulus calculation and optimization

                                          SECTION MODULUS CALCULATION & OPTIMATION

INTRODUCTION:

• What is section modulus?
• Types of section modulus
• Section modulus of hood
• Conclusion

SECTION MODULUS

            Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. 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.

Section Modulus is also referred to as the Polar Modulus or the Torsional Sectional

Section modulus is defined as the ratio of moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibres

Polar moment of inertia

         Polar moment of inertia measures the resistance to torsion. Polar Moment of Inertia is also called the second polar moment of area. It is usually denoted by IZ. However, sometimes J or JZ is also used. Polar Moment of Inertia can be represented mathematically with the given by  

                                                                

Location of neutral axis

        For axis-symmetric, isotropic sections the neutral axis is located at centroid axis. For curved sections of neutral axis is located at the point where tensile stresses are equal to compressive stresses.

TYPES OF SECTION MODULUS

1. Elastic section modulus
2. Plastic section modulus

1. 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 area (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 edge of the material. 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.

2. Plastic section modulus

           The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behaviour 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 PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.

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:

                                                                        

The Plastic Section Modulus can also be called the 'First moment of area'

The plastic section modulus is used to calculate the plastic moment, M_p, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, F_y, by M_p=F_y*Z. Plastic section modulus and elastic section modulus are related by a shape factor which can be denoted by 'k', used for an indication of capacity beyond elastic limit of material. This could be shown mathematically with the formula:

                                                                            

SECTION MODULUS OF HOOD

AIM:

      To calculate the section modulus for the previously designed hood and optimized hood.

PREVIOUSLY DESIGNED HOOD:

                                        

CALCULATION AND COMPARISION:

Section modulus(S) = I/y

I is moment of inertia, here we take moment of inertia value for I as it starts acting on the part in earlier stage of crash.

y is the distance between the neutral axis to the edge of the cross section.

y=439.5 mm

Comparing CASE I, CASEII, and CASE III from the above table CASE III have more resistance towards the external load.

Strength of component is directly proportional to the area moment of inertia (Section Modulus)

This is achieved by implementing geometrical modification at the rib sections of the model. Therefore design is optimized.

RESULT:

            Hence, the section modulus for the previously designed hood has been calculated under different cases and optimized the hood.

CONCLUSION:

           From different values of section modulus of above three cases, we conclude that while offsetting the inner panel to a 3 mm outside, we get an improved section modulus and this is providing a good stiffness to the hood while comparing to the master section. So, the section modulus analysis of our hood is analysed and a better stiffness is achieved comparing to the master section by offsetting the inner panel to an additional value.