Want to learn how to write expressions for the shear force and bending moment for a beam? In this tutorial, I break down how to analyze a cantilever beam with a triangular distributed load, a point load, and a concentrated couple moment.
This is Example 14 in my Shear Force and Bending Moment series, which is selected from Craig's Mechanics of Materials. In this example, you'll learn:
- How to find the location and magnitude of the resultant force of a triangular load.
- How to determine the support reactions of a determinate cantilever beam by writing the equations of equilibrium for the beam.
- How to cut the beam at different sections and write expressions for the shear force and bending moment at each section.
- How to draw the shear force and bending moment diagrams (sfd & bmd) using the expressions that you determined for them.
This video is designed to help civil engineering students and structural engineers develop a deeper understanding of beam analysis. Whether you're studying for your exams, working on assignments, or applying these concepts in real-world structural design, this video breaks everything down step by step to make shear force and bending moment calculations easier to understand and apply.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
0:00 - Intro
0:14 - Question
1:02 - Step 1: Drawing the FBD of the entire beam
2:02 - Step 2: Writing the equations of equilibrium for the entire beam and determining the support reactions
4:24 - Step 3: Cutting the beam at different sections and drawing the FBDs of the two segments of each cut section
8:17 - Step 4: Writing the equations of equilibrium for any of the cut segments of each section and determining their V & M
16:15 - Drawing the shear force and bending moment diagrams using the determined equations for them
19:06 - Showing the shear force and bending moment diagrams plotted using MATLAB
19:18 - Outro
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