In this video, stresses in bars of varying sections are explained and an example is solved in following timestamps:
0:00 – Mechanics of Solid Lecture series
0:16 – Outlines on the session
0:36 – Stress in the bars of varying sections
6:23 – Example on stresses in the bars of varying sections

Following points are covered in this video:
1. Stress in the bars of varying sections Non-Prismatic Bars
2. Example on stresses in the bars of varying sections

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

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Details of Stresses in Bars of Varying Sections:

Stresses in bars of varying sections, also known as non-prismatic bars, are more difficult to analyze than prismatic bars due to the variation of cross-sectional area along the length of the bar. The stresses in non-prismatic bars depend on the geometry of the cross-sectional area and the distribution of the load along the length of the bar.

One approach to analyzing non-prismatic bars is to divide the bar into small prismatic segments, and then use the principles of equilibrium and compatibility to determine the stresses and strains in each segment. This method is known as the method of sections.

Another approach is to use the concept of the centroidal axis. The centroidal axis is an imaginary line that runs through the centroid of the cross-sectional area of the bar. By considering the bar as a prismatic bar with an equivalent cross-sectional area and moment of inertia about its centroidal axis, the stresses and strains in the non-prismatic bar can be determined using the equations for prismatic bars.

In general, the stress in a non-prismatic bar will be highest at the point of maximum cross-sectional area reduction or at points of abrupt changes in the cross-sectional area. The stress distribution can be determined by analyzing the load and geometry of the cross-sectional area at each point along the length of the bar.

In summary, stresses in bars of varying sections, or non-prismatic bars, can be analyzed using the method of sections or by considering the bar as a prismatic bar with an equivalent cross-sectional area and moment of inertia about its centroidal axis. The stress distribution along the length of the bar will depend on the geometry of the cross-sectional area and the distribution of the load.