In this video, examples on shear force and bending moment diagram for cantilever beam is explained in following Timestamps:

0:00 – Mechanics of Solid Lecture series – Outlines on Examples based on Reaction of Beam
1:04 – Support reaction
2:24 – Calculation of shear force
4:03 – Drawing shear force diagram
4:39 – Calculation of bending moment
6:20 – Drawing bending moment diagram

Following points are covered in this video:

1. Shear Force Calculation
2. Shear Force Diagram
3. Bending Moment Calculation
4. Bending Moment Diagram
5. Example based on shear force and bending moment diagram for cantilever beam subjected to point loads and UVL.

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

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Details of Sign Convection for SF & BM:

In structural analysis, sign conventions are used for shear force (SF) and bending moment (BM) to indicate the direction and sense of the internal forces and moments developed in a beam. The following are the commonly used sign conventions for SF and BM:

Shear Force Sign Convention:

Positive shear force (upward direction): When the external loads acting on the beam tend to create a clockwise rotation of the beam section to the left of the section being considered.

Negative shear force (downward direction): When the external loads acting on the beam tend to create a counterclockwise rotation of the beam section to the left of the section being considered.

Bending Moment Sign Convention:

Positive bending moment (concave upward): When the external loads acting on the beam tend to create a sagging or concave upward deformation of the beam.

Negative bending moment (concave downward): When the external loads acting on the beam tend to create a hogging or concave downward deformation of the beam.

In other words, the positive shear force and bending moment cause upward deflection and concave upward deformation of the beam, while the negative shear force and bending moment cause downward deflection and concave downward deformation of the beam.

It is important to note that the sign conventions for SF and BM may vary depending on the coordinate system and the orientation of the beam. Hence, it is important to use a consistent sign convention throughout the analysis and design of the structure.

Details of Shear Force Diagram and Bending Moment Diagram:

Shear force diagram (SFD) and bending moment diagram (BMD) are graphical representations of the variation of shear force and bending moment along the length of a beam. These diagrams are important tools used in the design and analysis of beams and help to identify the maximum values of shear force and bending moment that the beam will experience.

The SFD is a graph of the shear force along the length of the beam, while the BMD is a graph of the bending moment along the length of the beam. The SFD and BMD are usually plotted on the same set of axes with the length of the beam along the x-axis and the shear force or bending moment along the y-axis.

The following are the steps involved in drawing the SFD and BMD:

Determine the reactions at the supports and draw the free body diagram of the beam.

Cut the beam at a section and consider the left or right part of the beam. Draw the forces acting on the left or right part of the beam and apply the equations of equilibrium to determine the shear force at the section.

Move to the next section and repeat the process to determine the shear force at that section. Plot the shear force on the SFD diagram with positive values indicating upward forces and negative values indicating downward forces.

Determine the bending moment at each section by integrating the shear force along the length of the beam. Plot the bending moment on the BMD diagram with positive values indicating sagging or concave upward deformation and negative values indicating hogging or concave downward deformation.

Continue the process until the entire length of the beam is covered. The resulting SFD and BMD diagrams provide a clear understanding of the internal forces and moments developed in the beam and can be used to determine the required strength and size of the beam and the type and size of the supports needed to ensure the beam remains stable and safe under the applied loads.