Section Modulus calculation and optimization
Aim: To calculate the section modulus by using the hood design.
Objective: 1.Description.
2.Elastic section modulus.
3.Plastic section modulus.
4.Calculating the section modulus 1st set.
5.Calculating the section modulus 2nd set.
6.Conclusion.
1.Description :
Section modulus is a geometric property of any taken 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 intertia for stiffness.
There are two type of section modulus, are discussed below.
2.Elastic section modulus :
For general design, the elastic section modulus is used and applying up to the yeild point for the most metals and other common materials.
The elastic section modulus is defined as S=I/Y.
Where, S= Section modulus.
I= Is the second moment of area (or area moment of inertia,).
Y= Is the distance from the neutral axis to any given fibre. It is often reported using (Y=C).
Area wise section modulus equations given below fig 2.1(a)
Fig 2.1(a)
3.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 deformation, 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 yilding 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 area 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 PNA.
ZP : A Cy C + A Ty T(displaystyle Z_(P)=A_(C)y_(C)+A_(T)y_(T))
The plastic Section Modulus can also be calculated the 'First moment of area'
Fig 3.1(a)
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 limit of material. This could be shown mathematically with the formula.
Shape factor for a rectangular is 1.5.
4.Calculating the section modulus 1st set.
For calculating the first set section modulus. We was used the hood section this is shown in below fig 4.1(a).
Fig 4.1(a) In which contains the first set values.
Fig 4.1(b) In this fig contains the length (Y).
Formula for Section modulus is (S=I/Y)
Where, I-Moment of Inertia.
Y-Distance between neutral axis and extreme end of the object.
S-Section modulus.
In this First set value of I=270340.522mm*4
Y=440mm
S=I/Y
S=270340.522/440
S=614.14mm*3
5.Calculating the section modulus 2nd set.
In this we are changing the sketch size which one is used in the first set. Then make comparision between both of them. Hence it will be help to increse the strength of the componets or sections. In fig 5.1(a) shown 2nd set values.
Fig 5.1(a) changes in emboss and obtained value.
In this I=271601.88mm*4
Y=440mm
S=I/Y
S=271601.88/440
S=617.27mm*3.
6.Conclusion.
This calculation is necessarly to know the design actual withstand capability of product. As we increase sectional area, the moment of inertia & section modulus increases it means the strength of material also increses.