Radius of Gyration and Section of Modulus is explained with following timestamps:

0:00 – Mechanics of Solid Lecture series
0:12 – Outlines on the session
0:27 – Radius of Gyration
4:19 – Definition of Radius of Gyration
5:33 – Section Modulus or Modulus of Section

Following points are covered in this video:
1. Radius of Gyration
2. Definition of Radius of Gyration
3. Section Modulus or Modulus of Section

Engineering Funda channel is all about Engineering and Technology. Here this video is a part of Mechanics of Solids or Engineering Mechanics.

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Details of Radius of Gyration and Section of Modulus:

The radius of gyration, also known as the gyradius, is a measure of how far the mass of an object is distributed from its axis of rotation. It is denoted by the symbol k and has units of length. The radius of gyration is defined as the square root of the ratio of the moment of inertia of an object to its mass:

k = sqrt(I/m)

where k is the radius of gyration, I is the moment of inertia of the object, and m is its mass. The radius of gyration is useful for calculating the torque required to rotate an object and for analyzing the stability of rotating systems.

The section modulus is a geometric property of a cross-sectional shape that is used to measure its resistance to bending. It is denoted by the symbol Z and has units of length to the power of 3. The section modulus is defined as the ratio of the moment of inertia of a cross-section to the distance from the neutral axis to the outermost edge of the section:

Z = I / y

where Z is the section modulus, I is the moment of inertia of the cross-section, and y is the distance from the neutral axis to the outermost edge of the section. The section modulus is used to design beams and other structural members that are subject to bending forces.

The section modulus can be used in conjunction with the bending stress equation to determine the maximum stress that a structural member can withstand before it fails due to bending. The bending stress equation is:

σ = M * y / Z

where σ is the bending stress, M is the bending moment applied to the member, y is the distance from the neutral axis to the point where the stress is being calculated, and Z is the section modulus of the cross-section.