Procedure

Steps for the Area Method:
  • Calculate Support Reactions: Draw a Free-Body Diagram of the entire beam and use static equilibrium (ΣFy=0\Sigma F_y = 0, ΣM=0\Sigma M = 0) to calculate all external support reaction forces.
  • Draw the Shear Diagram (VV):
  • Start from the far left side of the beam at V=0V = 0.
  • Move left to right. When you encounter a concentrated point load (or an upward support reaction), jump the shear line directly up or down by the exact magnitude of that load.
  • For a uniformly distributed load, the change in shear equals the area under the load curve (w×Lw \times L). A constant downward load creates a straight, negatively-sloped line on the shear diagram.
  • The shear diagram must return exactly to zero at the far right end of the beam to satisfy overall vertical equilibrium.
  • Locate Points of Zero Shear: Find the exact xx-coordinates where the shear diagram crosses the horizontal axis (V=0V=0). These critical locations indicate where the maximum (or minimum) bending moments occur. You may need to use similar triangles to find the exact xx distance if it crosses along a sloped line.
  • Draw the Moment Diagram (MM):
  • Start from the left side. For a simply supported or roller end, the moment starts at M=0M = 0. For a fixed cantilever end, it starts at the value of the fixed end moment.
  • Moving left to right, the change in moment between two points equals the calculated area of the shear diagram between those points.
  • Degree Rule: If the load is constant (degree 0), shear is linear (degree 1), and moment is parabolic (degree 2).
  • The moment diagram must return exactly to zero at the right end (unless there is a fixed support or an externally applied concentrated moment at that right end).

Shear & Moment Diagram Generator

Simply supported beam with a single concentrated point load.

10 kN
RAR_A = 5.0
RBR_B = 5.0
10 m

Shear Force Diagram (VV)

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Bending Moment Diagram (MM)Max: 25.0 kN·m

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Determining Maximum Bending Moment

Consider a simply supported beam of length LL with a concentrated load PP placed exactly at its center. Find the maximum bending moment using the area method.

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Drawing Diagrams for a Uniformly Distributed Load

A cantilever beam of length LL is fixed at its right end and subjected to a uniform downward distributed load ww over its entire length. Find the maximum shear and bending moment.

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