Section Modulus calculation and optimization

Aim:

The main objective of this project is to understand and learn the basic tools and advanced tools used in NX and calculation as well as section modulus and optimization of Car Hood done in the previous challenge.

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 the design include an area for tension and shear, the radius of gyration for compression, and the 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.

Use the Section from your Hood design and calculate the section modulus using the formula

S=I/Y

S= Section Modulus

I= Moment of inertia

Y= Distance between the neutral axis and the extreme end of the object

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 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 (M_y) such that M_y = S ⋅ σ_y, where σ_y is the yield strength of the material.

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, 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:

The plastic section modulus is used to calculate the plastic moment, M_p, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, F_y, by M_p = F_y ⋅ 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: -

Section modulus(S)

Another property used in beam design is section modulus

The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the Strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

It includes the idea that most of the work in bending is being done by the extreme fibers of the beam, ie the top and bottom fibers of the section. The distance of the fibers from top to bottom is therefore built into the calculation.

The elastic modulus is denoted by S. To calculate S, the distance (y) to the extreme fibers from the centroid (or neutral axis) must be found as that is where the maximum stress could cause failure.

Moment Of Inertia:

The moment of inertia is defined as the product of mass of section and the square of the distance between the reference axis and the centroid of the section.

The moment of inertia I is also defined as the ratio of the net angular momentum L of a system to its angular velocity ω around a principal axis

Section Modulus calculation and optimization:

1. Hood Design

Calculation of Section Modulus of main Hood:

Moment of Inertia (MOI), Imax = 8.338247302 x 10^5 [mm^4]

Moment of Inertia (MOI), Imin = 5.987031706 x 10^3 [mm^4]

Distance between the neutral axis and the extreme end of the object, y = 487.1834mm / 2 = 243.591mm

Section Modulus,

S = Moment of Inertia (MOI), I / Distance between the neutral axis and the extreme end of the object (y)

For Maximum (MOI),

S = (8.338247302 x 10^5 mm^4) / (243.591mm)

Smax = 3.42305229 x 10^3 mm^3

For Minimum (MOI),

S = (5.987031706 x 10^3 mm^4) / (243.591mm)

Smin = 0.0245782139 x 10^3 mm^3

Hood Optimized Design:

After some Changes

Moment of Inertia (MOI), Imax = 8.236250016 x 10^5 [mm^4]

Moment of Inertia (MOI), Imin = 6.622151809 x 10^3 [mm^4]

Distance between the neutral axis and the extreme end of the object, y = 487.1834mm / 2 = 243.591 mm

Section Modulus, S = Moment of Inertia (MOI), I / Distance between the neutral axis and the extreme end of the

object (y)

For Maximum (MOI),

S = (8.236250016 x 10^5 mm^4) / (243.591 mm)

Smax = 3.38117994 x 10^3 mm^3

For Minimum (MOI),

S = (6.622151809 x 10^3 mm^4) / (243.591 mm)

Smin = 0.0271855356 x 10^3 mm^3

Conclusion:

Section Modulus of Car Hood was calculated and optimized

Found some better results after some changes with the section modulus or optimization.