Section Modulus calculation and optimization

AIM:

To calculate the section modulus use section of the Hood for analyzing its strength and then optimizing the hood panel for comparing the section modulus.

SECTION MODULUS:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric propertic used in design include area for tension, radius of gyration for compression, and 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 (s) and the plastic section modulus (z).

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

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)

Elastic section modulus:

The elastic section modulus is defined as S = I / y,

where I is the second moment of area (or moment of inertia) and y is the distance from the neutral axis to any given fiber. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber, It is also often used to determine the yield moment (My) such thatMy= 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 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 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 :-

Section Modulus Calculation:

For studying the section modulus we need the cross section of hood. For that I created a cross section using intersection curve.

Cross section of Hodd

Find the inertia using section inertia tool in NX:

Reslut:-

Here the minimum moment of inertia, I = 5.426697456e+03 [mm^4]

The distance between neutral axis and extreme end of the object, Y = 242.9 mm

Therefore the Section Modulus, S = I/Y

S = 5426.697456 [mm^4] / 242.9 [mm]

= 22.341 [mm^3]

Design OptimizationBy increasing the depth of the inner panel by 0.5 mm:

Here the minimum moment of inertia, I = 5.834009745e+03 [mm^4]

The distance between neutral axis and extreme end of the object, Y = 242.9 mm

Therefore the Section Modulus, S = I/Y

S = 5834.009745 [mm^4] / 242.9 [mm]

= 24.018 [mm^3]

CONCLUSION:

In this study, we take the minimum of inertia moment to analyze the minimum limit of hood deformation. Thus the section modulus of the front hood was calculated and compared with the new design.

From the result we found out that increasing the cross-section area would give a better section modulus and helps in increasing the strength of the hood.