Asymmetric bending principle of second moment of A derivation

Thread starter yonese
Start date Mar 28, 2021
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Bending Derivation Moment Principle

In summary, the asymmetric bending principle is a concept in physics and engineering that describes how a beam or structure will behave when subjected to an off-center load. It is derived from the second moment of area and is used in calculations to determine the bending stress and deflection of a beam. The principle is derived by analyzing the forces and moments acting on a small element of a beam, and it is essential in the design and analysis of various structures. However, it has limitations in its assumptions and its applicability to beams under elastic deformation only.

Mar 28, 2021

yonese

TL;DR Summary: I don't understand how the radius and offset of the Mohr's circle can be simplified down to the principal Iq and Ip equations - where does the load F go? This was taken from a worked example with inverted L section carrying a load. My teacher hasn't explained how he jumps to these steps and I don't understand how the load F gets removed and the 6 simplifies to a 3. I have tried to solve for simultaneous equations using the radius and offset equation, but still stuck. Thanks.

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Mar 30, 2021

Dr.D

Perhaps you could post a picture to show what problem you are considering?

What is the asymmetric bending principle?

The asymmetric bending principle is a concept in structural mechanics that states that when a beam or other structural element is subjected to a bending moment, the neutral axis (the line of zero stress) will not be in the exact center of the cross-section. Instead, it will be shifted towards the side of the cross-section with the greater moment of inertia.

What is the second moment of area?

The second moment of area, also known as the moment of inertia, is a measure of an object's resistance to bending. It is calculated by summing the products of each infinitesimal area element in the object and the square of its distance from a chosen axis. In the asymmetric bending principle, the second moment of area is used to determine the location of the neutral axis.

How is the asymmetric bending principle derived?

The asymmetric bending principle can be derived using the basic principles of statics and calculus. The key steps involve determining the equations for the bending moment and the curvature of the beam, and then using these equations to find the location of the neutral axis. The full derivation involves some complex mathematical calculations, but the final result is a simple formula that can be used to determine the position of the neutral axis.

What are the practical applications of the asymmetric bending principle?

The asymmetric bending principle is used in the design and analysis of various structural elements, such as beams, columns, and frames. It is particularly useful in situations where the loading is not symmetric, such as in cantilever beams or beams with eccentric loads. Understanding the principle can help engineers design more efficient and reliable structures.

Are there any limitations or assumptions in the asymmetric bending principle?

Like any mathematical model, the asymmetric bending principle has some limitations and assumptions. It assumes that the material is homogeneous and isotropic, and that the beam is loaded in a linear elastic range. It also does not take into account any non-uniformities or imperfections in the material or the structure. These limitations should be considered when applying the principle in practical applications.