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.

Introduction:

What is Section Modulus? 

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It defines the strength of beams which depends upon the cross-section area of that beam. 

Though section modulus is generally calculated for the extreme tensile or compressive fibers in a bending beam, compression is often the most critical case due to onset of flexural torsional (F/T) buckling. Generally (except for brittle materials like concrete) tensile extreme fibers have a higher allowable stress or capacity than compressive fibers.

In the case of T-sections if there are tensile fibers at the bottom of the T they may still be more critical than the compressive fibers at the top due to a generally much larger distance from the neutral axis so despite having a higher allowable stress the elastic section modulus is also lower. In this case F/T buckling must still be assessed as the beam length and restraints may result in reduced compressive member bending allowable stress or capacity.

Formula for calculating Section Modulus:

S or Z = I/y

S or Z - Section modulus of material

I- Moment of inertia 

y- Length of extreme fiber from the neutral axis

The Unit of a “section modulus” is (mm3)

 For symmetrical sections the value of Z is the same above or below the centroid.

For asymmetrical sections, two values are found: Z max and Z min

SIGNIFICANCE OF  SECTION MODULUS:

• Section modulus is the important factor for design of 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

 ROLE OF CROSS SECTION IN SECTION MODULUS:

• 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 max and the minimum section modulus is S min.

From The Existing Design 

The Intersection of the design was taken and then section Inertia Analysis was done

 

Moment of inertia(max) = 8.19398×10^5×mm^4

Moment of inertia(min) = 5.34031×10^3×mm^4

Y=485.7599/2=242.8799 mm

S=I/Y

S=5.34031×10^3/242.87= 21.98 mm^3

Hood Design Optimization

By increasing the depth of the inner panel by 0.5 mm

Here,

Moment of inertia(max) = 8.16698×10^5×mm^4

Moment of inertia(min) = 5.51216×10^3×mm^4

Y=485.7599/2=242.8799 mm

S=I/Y

S=5.51216×10^3/242.87=22.69 mm^3

Conclusion

               So, here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design(depth).

   also, 

•  Importance of section modulus when it comes to the selection of right material or right design which will

     have more strength.

•   Factors affecting Section modulus and how to enhance the strength of a material by using section

     modulus as a check parameter.