Section Modulus calculation and optimization
Section Modulus calculation and optimization
Objective :
- Use the Section from your Hood design and calculate the Section Modulus using the formula :
Z = I/y
Where,
Z = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
- A new section that has improved the section modulus of the my previous hood design. Calculate section modulus of the previously created design of car hood by taking a cross-section of it and analyzing the result.
- To come up with a new design that would increase or improve the section modulus of the existing car hood and optimize our design to obtain better results.
Brief explanation about the Section Modulus :
- It 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.
- There are two types of section modulus :
1. The elastic section modulus
2. The plastic section modulus.
- For general design, the Elastic section modulus is used, applying up to the yield point for most metals and other common materials.
- The elastic section modulus is defined as Z = I / y, where I is the second moment of area (or area moment of inertia, and y is the distance from the neutral axis to any given fibre.
- 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 which is maximum allowable load in a mechanical component.
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 Z max and the minimum section modulus is Z min.
Procedure of Hood Section Modulus :
- In the Hood design case we use Elastic section modulus. Model preparation as below.
- Copied two parts of Hood outer panel and inner panel in another new part model which is named as Section modulus, then created the section geometry of the outer most geometry of hood outer panel and lower most geometry of hood inner panel and joined them with lines as we need closed profile to measure the inertia, then later using “Measure the Inertia” option in Catia noted the Moment of inertia ‘ I ’ value and then proceeded with the calculation to measure the allowable strength of the section 1.
- Find the below the images and calculation taken from Catia model of for your reference.
Calculation of Section Modulus of Hood :
- See the below the images and calculation taken from Catia model of for your reference.
- Section 1 :
Calculation of Section 1:
- Calculating Section modulus of existing design by using NX-CAD by taking cross-section of hood along x-x axis and calculating moment of inertia.
- As, our hood shape is asymmetrical there will be two values of section modulus
so,
Imin= 2.499589375 X 10^5 mm^4
y= 439.32 mm
Zmin= Imin/y
= 2.499589375X 10^5/439.32
= 568.967 mm^3.
This is the result of section modulus our initial hood design.
Section 2 :
- To improve this value of section modulus we need to optimize our present hood design.
- For that purpose, we will offset the outer panel of our hood by 0.5mm to increase the sectional area of our hood and thereby increase in section modulus.
- The reason behind providing offset to the outer panel
As we know that section modulus
Z= Σmi*Ai^2/y
where 'A' is the area
'M' is the mass of the body
From the above equation, it can be observed that Section modulus is directly proportional to the sectional area of the body.
That's why we can increase the section modulus by increasing the sectional area by offsetting the outer panel and reducing the emboss depth.
As the section area will increase Moment of inertia will also increase thereby Section Modulus of our hood will increase.
Calculation of Section 2 :
- Here in the above sectional report we can see that section area is increased as compared to previous section area in old design of our hood.
- Also the Moment of inertia has been significantly changed as it is function of section area.
- Now we will calculate the section modulus
Imin= 2.610029335 X 10^5 mm^4
y= 439.32 mm
Zmin= Imin/y
= 2.610029335 X 10^5/439.32
= 594.106 mm^3.
Hence the section modulus of our hood has been increased as compared with the previous value which is 568.967 mm^3 and the new value is 594.106 mm^3.
Difference between Section Modulus Z = Section 2 Zmin - Section 1 Zmin = 594.106 mm^3 - 568.967 mm^3 Difference between Section Modulus Z = 25.139 mm^3.
Conclusion :
- Hence, from the above study, it is clear that optimization helps to improve the results in a design as we have increased the Section Modulus of our hood.
- Gain crucial insight about Section Modulus its relationship with bending stress, Moment of inertia and got an idea of how the section modulus changes with respect to change in section area of a body and its effect on the value of section modulus.
- 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.