Section Modulus calculation and optimization
Aim/Objective: To calculate the section modulus of the hood and to optimise and increase the performance and have better section modulus result.
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.
S=I/Y
Here,
S = Section modulus
I= Moment of Inertia (Unit mm^4)
Y= Distance from Neutral axis to the extreme end (unit mm)
The Unit of a “section modulus” is (mm^3)
There are two types of section moduli and they are
- Elastic section modulus
- Plastic section modulus.
Elastic section modulus
The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the 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. 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. For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.
Image of Elastic section modulus
Plastic section modulus
The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behaviour 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 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 the elastic limit of material.
K= Z/S
Section modulus calculation of hood design
Case 1:
Interaction from hood design
Moment of inertia MOI (Max): 4.775726041*10^6*mm^4
Moment of inertia MOI (Min): 1.344023222*10^4*mm^4
Y=880/2=440mm
S=I/Y
After substituting
S=1.344023222*10^4/440
=30.5455mm^3
Case 2:
By increasing the hood inner panel with 0.5mm and optimise the section modulus.
Moment of inertia MOI (Max): 4.782957095*10^6*mm^4
Moment of inertia MOI (Min): 1.372390106*10^4*mm^4
Y=880/2=440mm
S=I/Y
After substituting
S=1.372390106*10^4/440
=31.1906mm^3
Result:
From both the cases it's clear that by the change in the moment of inertia the section modulus is also increasing. By optimizing the hood the strength too increases proportionally.
Conclusion:
The section modulus can be improved by increasing the area Moment of inertia, The section modulus and moment of inertia are directly proportional to each other if MOI increases the sectional modulus increases. Thus providing good strength to the sheet metal.