Shear & Moment Equations | Overhanging Beam (Method of Sections)

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 an overhanging beam with a rectangular distributed load over the middle span and two concentrated loads at the ends.

This is Example 12 in my Shear Force and Bending Moment series, which is selected from Hibbeler's Structural Analysis. In this example, you'll learn:

How to determine the support reactions 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 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
0:09 - Question
0:52 - Step 1: Drawing the FBD of the entire beam
1:44 - Step 2: Writing the equations of equilibrium for the entire beam and determining the support reactions
4:47 - Step 3: Cutting the beam at different sections and drawing the FBDs of the two segments of each cut section
9:03 - Step 4: Writing the equations of equilibrium for any of the cut segments of each section and determining their V & M
13:37 - Drawing the shear force and bending moment diagrams using the determined equations for them
16:43 - Outro

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