Section Modulus calculation and optimization

Aim:

• Calculating the Section Modulus of the hood,compare them with different hood modifications and find out the best on it.

Introduction:

1. Section Modulus:

•  Section Modulus is the geometric property of the given cross-section of any shaft or beam structures. It is the direct measure of the strength of the shaft section or the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending.

•  The stress in the outermost section of beam is computed with the help of section modulus. It is indicated by S.

                  Section modulus :   

•  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.³(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,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.

    2.  Why we need Section Modulus?

•  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.
• More the section modulus, more the member is resistant to bending of the beam.
• It is significant for beam and flexural member design.

    3. Moment of Inertia:

• The moment of inertia of the cross-section of a body is its resistance to changes in its rotation. It depends on how far each part of the body's mass is from its centre.
• Moment of Inertia for various shapes

Tools Used:

• Intersection curve
• Project curve
• Datum plane
• Section Inertia Analysis
• Studio spline

Procedure:

• For proceeding the section modulus need a cross section of the hood.So create a Datum plane on the centre of the hood.

• Create a cross section by intersection curve option selecting the plane and hood as a reference.

• Select the Section inertia analysis to analyse the cross section of hood.

Calculation:

• For calculating section modulus we know S=I/Y
• In this case we need to consider the minimum value of section modulus i.e (S _min ),because the min value represent the load can withstand.
• S= Section Modulus.
• I= Moment of Inertia.
• Y= Distance between the neutral axis and the extreme end of the object. 

S=I/Y

S=[1.523912108e+004(mm4)/439.26]

S _min=34.69 mm3

Case 02:

• Offset the curve to 1mm upwards and do the section modulus analysis.

   S=I/Y

   S=[1.533202076e+004(mm4)/439.26]

   S _min=34.91 mm3

Case-03:

• Offset the curve to 1mm upwards and do the section modulus analysis

 S=I/Y

   S=[1.944173653e+004(mm4)/439.26]

   S _min=44.27 mm3

The above comparision table shows that case03 as good strength and as higher value of section modulus as compare to other two cases.

Conclusion:

• The Section modulus of the hood is measured and founded the best strength value and learned about the process involved on section modulus and the calculations.