Section Modulus Calculation and Optimization

Section Modulus Calculation and Optimization

Objective:

To calculate the section modulus for the previously designed hood and optimize it for better resistance to bending.

Material of the hood:

Stainless Steel AISI 302 (Cold-rolled)

Y = 520 Mpa.

SECTION MODULUS:

• Section modulus may be defined as the ratio of total moment resisted by the section to the stress in the extreme fibre which is equal to the yield stress.
• It is a geometric property for a given cross-section used in the design of beams or flexural members and it depends only on the cross-section shape of the beam or structure.
• There are two types of section moduli, the elastic section modulus (S) and the plastic section modulus (Z).

Section modulus is given by,

`S= I/y`

where, I = second moment of inertia or area moment of inertia, `mm^4`

y = distance between the neutral axis and the extreme end of the object, `m`

Importance of Section Modulus:

The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads. Higher the section modulus, higher will be the resistance to bending.

SECTION ANALYSIS:

1. Section Modulus of the hood before optimization :

From the Section Analysis, the following maximum and minimum values of moment of inertia are obtained:

`Imax = 824081.9892 mm^4`

`Imin = 3397.006489 mm^4`

`y = 243.87 mm`

`Smax = (Imax)/y = 824081.9892/243.87 = 3379.18559 mm^3`

`Smin = (Imin)/y = 3397.006489/243.87 = 13.929 mm^3`

2. Section Modulus of the hood after optimization :

The value for Section Modulus of the body can be increased by offsetting the outer panel. In the second part, the outer panel is offset by 1.7 mm.

From the Section Analysis, the following maximum and minimum values of moment of inertia are obtained:

`Imax = 818054.2469 mm^4`

`Imin = 3844.854508 mm^4`

`y = 243.87 mm`

`Smax = (Imax)/y = 818054.2469/243.87 = 3354.46856 mm^3`

`Smin = (Imin)/y = 3844.854508/243.87 = 15.766 mm^3`

CONCLUSION:

• By comparing both the design, I found out that the minimum section modulus of the optimized hood increased by ~ 13%.
• Moment of Inertia increases with increase if section area.
• If we increase the distance between the inner and the outer panel of the hood, then the section modulus also increases.