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. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section Modulus:

Section modulus is indicated as follows:

S = Section Modulus

I = Moment of Inertia

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

Here, I is “moment of inertia” and y is distance from “neutral axis” to top or bottom of fiber.

Unit of a “section modulus” is in (mm3).

Section modulus depends only on the cross section shape of the beam. Cross section shapes like rectangular, square, circular, I section and T, composite section etc.

For symmetric sections, the value of “section modulus” is for both above and below of centroid of the fiber.

An asymmetric section has two values for top and bottom of the fiber due to different distance from centroid to the top and bottom of the material, the maximum “section modulus” is S m ax and the minimum section modulus is S min.

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.

Importance:

• 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.

SIGNIFICANCE 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.

1. Section modulus is the important factor for design of beam and flexural member
2. Higher the value of section modulus, higher will be the resistance of member to bending
3. It is required to calculate stresses in beams.
4. It is used to calculate strength of the steel structure
5. More the section modulus, it can withstand more load and it is also considered to be more tougher.

Below picture referes to the distance between hood from one end to extreme end.

The total distance of the hood Y = (881.926 mm.)

Calculation for the Hood Section of Modulus:

Let,

Moment of Inertia (max. & min.)values of Hood part.

MOI (max) : (7.478842125e+06) [mm^4]

MOI (min) : (2.211100141e+04) [mm^4]

The total distance of the hood Y = (881.926 mm.)

Distance between the neutral axis to the extreme end = (881.926/2) = 440.963 mm.

For Asymmetric has two values for the top and bottom of the centroid ie., S(max) and S(min).

For S(max) and S(min)

Section modulus is the ratio of second moment of area and distance from N.A (Neutral axis) to the extremeend is given by S = I/Y

S(min) = I(min)/Y = (2.211100141e+04) / ( 440.963 ) = (6.019643900) [mm^3]

Case 2:

By offsetting the inner panel by 0.5mm

Let,

Moment of Inertia (max. & min.)values of Hood part.

MOI (max) : (7.59930880e+06) [mm^4]

MOI (min) : (2.243229842e+04) [mm^4]

The total distance of the hood Y = (881.926 mm.)

Distance between the neutral axis to the extreme end = (881.926/2) = 440.963 mm.

For Asymmetric has two values for the top and bottom of the centroid ie., S(max) and S(min).

For S(max) and S(min)

Section modulus is the ratio of second moment of area and distance from N.A (Neutral axis) to the extremeend is given by S = I/Y

S(min) = I(min)/Y = (2.243229842e+04) / ( 440.963 ) = (6.0068019724) [mm^3]

CONCLUSION:

Thus I calculated the section modulus of Hood design and also there is improved in section modulus of the previous section Finally i concluded that there is Increase in Sectional area it increases the Overall mass of an object and also strength of an object.