Section Modulus calculation and optimization
Report on section modulus calculation on hood:
Objective:
In this case we’re going to analyze the strength of hood that we designed previously and optimize the strength of itself during the bending on the other hand we are going to analyze the hood by increasing the depth of inner panel then we compare the values we got from that and find which one is giving more value, because more value means more strength.
What is 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 moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such, then there’re couple of types in section modulus that is,
- Elastic section modulus
- Plastic section modulus
And then here we got the formula S= I/ Y we’re going to calculate the section modulus of hood with this formula, hence
S = section modulus
I = inertia (mm4)
Y= distance from the neutral axis to extreme point (mm)
Then unit of “section modulus” (mm3).
Elastic section modulus:
The elastic section modulus is defined as the ratio of the second moment of area (or moment of inertia) and the distance from the neutral axis to any given (or extreme) fiber. It can also be defined in terms of the first moment of area.
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 location 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 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 can also be called the 'First moment of area'
The plastic section modulus is used to calculate the plastic moment, Mp, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, Fy, by Mp=Fy*Z. Plastic section modulus and elastic section modulus are related by a shape factor which can be denoted by 'k', used for an indication of capacity beyond elastic limit of material. This could be shown mathematically with the formula: -
K= z/s
Shape factor for a rectangular section is 1.5.
Design study at first time:
In this case we have the results
Moment of inertia (maximum) = 8.969798557 e + 0 7 mm^4
Moment of inertia (minimum) = 2.591113520 e + 05 mm^4
Y= 439.92mm
S = 2.591113520 e +05/439.92
Hence,
S = 588.99 mm^3
At another time analyzed by increasing depth by 0.5 mm
In this case we have the results
Moment of inertia (maximum) = 9.371711520 e + 07 mm^4
Moment of inertia (minimum) = 2.633201699 e + 05 mm^4
Y = 439.92mm
Hence,
S = 2.633201699 e + 05/ 439.92
S = 598.56 mm^3
Conclusion:
As I've mention before we’ve analyzed the hood and calculated the section modulus by changing the depth of hood about 0.5 mm, remain more value will give more strength.