Procedure
Steps for the Area Method:
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Calculate Support Reactions: Draw a Free-Body Diagram of the entire beam and use static equilibrium (, ) to calculate all external support reaction forces.
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Draw the Shear Diagram ():
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Start from the far left side of the beam at .
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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.
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For a uniformly distributed load, the change in shear equals the area under the load curve (). A constant downward load creates a straight, negatively-sloped line on the shear diagram.
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The shear diagram must return exactly to zero at the far right end of the beam to satisfy overall vertical equilibrium.
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Locate Points of Zero Shear: Find the exact -coordinates where the shear diagram crosses the horizontal axis (). These critical locations indicate where the maximum (or minimum) bending moments occur. You may need to use similar triangles to find the exact distance if it crosses along a sloped line.
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Draw the Moment Diagram ():
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Start from the left side. For a simply supported or roller end, the moment starts at . For a fixed cantilever end, it starts at the value of the fixed end moment.
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Moving left to right, the change in moment between two points equals the calculated area of the shear diagram between those points.
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Degree Rule: If the load is constant (degree 0), shear is linear (degree 1), and moment is parabolic (degree 2).
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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
= 5.0
= 5.0
10 m
Shear Force Diagram ()
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Bending Moment Diagram ()Max: 25.0 kN·m
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Determining Maximum Bending Moment
Consider a simply supported beam of length with a concentrated load placed exactly at its center. Find the maximum bending moment using the area method.
Step-by-Step Solution
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Drawing Diagrams for a Uniformly Distributed Load
A cantilever beam of length is fixed at its right end and subjected to a uniform downward distributed load over its entire length. Find the maximum shear and bending moment.
Step-by-Step Solution
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