Section Modulus calculation and optimization

SECTION MODULUS CALCULATION OF THE HOOD

AIM:

To Calculate the section modulus of the hood design by using Catia v5 and improve the strength of the hood design.

INTRODUCTION:

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.

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 i.e.., The elastic section modulus and The plastic section modulus.

S = I/Y

Were,

S = Section Modulus (mm^3),

I = Moment of Inertia (mm^4),

y = distance between the neutral axis and the extreme end of the object (mm).

ELASTIC SECTION MODULUS:

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 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.

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, and equal compressive and tensile yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.

Section modulus can also be defined by using the simple bending theory as,

we know that, M / I = σ / Y

Therefore, S = M / σ

i.e., section modulus is also expressed as the ratio of bending moment to the bending stress of a given object within the elastic limit.

IMPORTANT:

• It is significant for beam and flexural member design.
• More the section modulus, more the member is resistant to bending of the beam.
• It is easier to calculate stresses in beam and an exact measure of strength of steel.
• If two beams are made of same material and comparing the “section modulus” of two beams, the beam with bigger section modulus will be tougher and more capable to withstand larger loads.

ANALYSIS:

CASE 1:

The Inertia Analysis of the Hood Section brings out the following results.

Where the section modulus

S = I/Y

i.e.,

I = 4.883e-007 m⁴

= 4.883x10⁵ mm⁴

Y = 239.5645 mm

S = 4.883x10⁵ / 239.5645

= 2038.281 mm³

The section modulus of case 1

S = 2038.281 mm³

CASE 2:

After increasing the area by modifying the gap between the Inner panel and Outer panel of the Hood, without altering the standard design constraints, we get the following values after Inertia Analysis

Where the section modulus

S = I/Y

i.e.,

I = 5.179e-007 m⁴

= 5.179x10⁵ mm⁴

Y = 239.5645 mm

S = 5.179x10⁵ / 239.5645

= 2161.2839 mm³

The section modulus of case 1

S = 2161.2839 mm³

CONCLUSION

The Section Modulus in the CASE 2 is higher than the section modulus in the CASE 1. Thereby the variation provided in the CASE 1 & CASE 2 is 0.5 mm gap from the inner panel and outer panel. Increasing the gap between the outer and the inner panel leads to higher the section modulus value, hence resistant to bending will also get increased due to the strength of the hood increased.