Section Modulus calculation and optimization
SECTION MODULUS CALCULATION AND OPTIMISATION:
INTRODUTION OF SECTION MODULUS:
Section modulus 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 second moment of area and polar moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question.
Equations for the section moduli of common shares are given below:
There are two types of section moduli is here,
- Elastic section modulus
- Plastic section modulus
ELASTIC SECTION MODULUS:
For general design, the elastic section modulus is used, applicable up to the yield point for most metals and other common materials.
The elastic section modulus is defined as S = I/Y,
Where,
I - Area moment of inertia,
Y - Distance from the neutral axis to any given fibre.
It is often reported using Y = C, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (My) such that
My = S * σy,
where,
σy - yield strength of the material.
PLASTIC SECTION MODULUS:
The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.
The plastic section modulus depends on the locatio of the plastic neutral axis (PNA). The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant, and equal compressive and tensile yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.
The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:
Zp = Acyc + Atyt.
The plastic section modulus is not the 'First moment of area'. Both relate to the calculation of the centroid, but plastic section modulus is the sum of all areas on both sides of PNA and multiplied with the distance from the centroid of the corresponding areas to the centroid of the cross section, while the first moment of area is calculated based on either side of the "considering point" of the cross section and it is different along the cross section and depends on the point of consideration.
SECTION MODULUS FORMULA:
S = I / Y
where,
S - Section modulus
I - Moment of Inertia
Y - Distance from the neutral axis to the most extreme end of the object
CASE - 1:
- Use the intersection curve command on the hood outer panel and hood inner panel
- Form the closed curve of intersecting curve
- Get the area moment of inertia value using
- Measure the length from the neutral axis to the one of the extreme end (Y)
Calculate the section modulus:
I = 2.674*10^5 mm^4
Y = 876.46/2 = 438.23 mm
S = 610.18 mm^3
CASE - 2:
Increase the area of cross section using the method of increase the gap between the inner and outer panel by the value of 0.5 mm.
And then follow the same method for finding area moment of inertia. Value of Y is same as the case 1.
Calculation of section modulus
I = 2.72*10^5 mm^4
Y = 438.23 mm
S = 620.68 mm^3.
COMPARISON OF CASE 1 AND CASE 2:
When we compare the case 1 of section modulus to the case 2 of section modulus, case 2 section modulus is more than case 1. It means the section of modulus the section of modulus is directly propotional to the area of cross section, we can also said strength and load bearing capacity is more in case 2 than case 1.