Section Modulus calculation and optimization

Aim: To find Section  Modulus of the hood using NX_CAD 

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. There are two types of section moduli, the elastic section modulus and the 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 fiber. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber, as seen in the table below. It is also often used to determine the yield moment (My) such that My = S ⋅ σ_y, where σ_y is the yield strength of the material.

Moment of inertia for hallow component:

There are two cases in which the term “moment of inertia” is used:

• Area moment of inertia: a geometric cross-sectional property (also known as second moment of area)
• Mass moment of inertia or polar moment of inertia: resistance of a mass to changes in rotational velocity

Section modulus and area moment of inertia are closely related, however, as they are both properties of a beam’s cross-sectional area.

Area moment of inertia can be used to calculate the stress in a beam due to an applied bending moment at any distance from the neutral axis using the following equation:

where σ is the stress in the beam, y is the distance from the neutral axis passing through the centroid, and I is the area moment of inertia.

Since the stress is greatest at the farthest distance from the neutral axis, section modulus combines both the area moment of inertia and the maximum distance from the neutral axis into one term:

Therefore, the equation for maximum bending stress becomes:

Section Modulus Analysis:

Section 1:

Minimum moment of inertia for the given below section is calculated by using section inertia analysis Feature of NX_CAD

Section Modulus:

S = I/Z

I = Moment of inertia

Z = Distance from the neutral axis to the outermost fiber.

S = Section Modulus.

Here Minimum moment of inertia is taken in to consideration to increase the stability of the components towards the forces applied on the body.

I_min = 1.53523977e+04mm⁴

Z = 440.2mm

S = 34.8759mm³

Section 2:

The above section got modified and calculated the section modulus by using same feature as above.

Section Modulus:

S = I/Z

I = Moment of inertia

Z = Distance from the neutral axis to the outermost fiber.

S = Section Modulus.

Here Minimum moment of inertia is taken in to consideration to increase the stability of the components towards the forces applied on the body.

I_min = 1.735198985e+04mm⁴

Z = 440.2mm

S = 39.41mm³

Conclusion:

From the above Comparison second Section modulus it has been proved that Increasing of Area moment of inertia leads to increase the Section modulus.

Hence, we required more force to bend the second section.