Section Modulus calculation and optimization
SECTION MODULUS CALCULATION AND OPTIMIZATION
Aim
To calculate the section modulus of the previously designed hood for analysing its strength and optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more the resistive it becomes to bending.
Section modulus
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. 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.
Section modulus Calculation
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 (mm3)
There are two types of section modulus,
- Elastic section modulus
- Plastic section modulus.
Elastic 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 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, as seen in the table below. 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.
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 following are few iterations performed over the Car Hood or Bonnet cross -section.
Section#:1
Type: Hollow
CG : (0.010902150, 749.935654199, -970.091117505) [mm]
MOI (Max) : 5.050094240 e+06[mm^6]
MOI (Min) : 1.716003375 e+04[mm^4]
Principal Directions:
Max: (0.000003667, 0.987503153, 0.157599250)
Min: (1.000000000, -0.000003621, 0.000000578)
Section Length: 3.721993600e+03[mm]
Section Area: 74.439290245[mm^2]
Distance of Extreme Layer from Neutral Axis (Y) - 895.8/2 = 447.9mm
Section Modulus (s) = I / Y = 17160.03375 / 447.9 = 38.31 [mm^3]
From the section#: 1, using Minimum Moment of Inertia and extreme distance of layer, we got the section modulus(S) value is 38.31[mm^3].
Section#:2
Type: Hollow
In this section modulus to increase of inner panel distance from the previous section#:1. Offset of the inner panel 2mm.
CG : (-0.001639473, 748.798804181, -970.272551568) [mm]
MOI (Max) : 5.093458285 e+06[mm^6]
MOI (Min) : 1.839820887 e+04[mm^4]
Principal Directions:
Max : (-0.00000556, 0.987503153, 0.157599250)
Min : (1.000000000, 0.000000579, 0.000000088)
Section Length : 3.732729175+03[mm]
Section Area : 74.654573661[mm^2]
Section Modulus (s) = I / Y = 18398.20887 / 447.9 = 41.08 [mm^3]
From the section#: 1, using Minimum Moment of Inertia and extreme distance of layer, we got the section modulus(S) value is 41.08[mm^3].
Conclusion
Different section, as shown above, were tried in order to achieve a higher moment of inertia. It is observed that increasing the gap between the inner and outer panels has resulted to improve the section modulus. Hence it is the best to add more geometric features to the master section to more the stiffness of section. However, this could result in an increase in manufacturing cost.