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Shear-Moment (V-M) Diagrams: Cantilever Beam

Author:Ana Kwon
The real-world design of beams requires a detailed understanding of how the internal shear force V and bending moments M vary at each point along the beam’s length. Shear and Moment diagrams, or V&M diagrams, provide a graphical description of how the internal shear and moment change along the length of a beam.

Conceptual Questions - Relationships between Distributed Load, Shear, and Moment

The slope of the shear diagram at a point along a beam is equal to,

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Between any two points along a beam, the change in shear is equal to,

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At a point along a beam, the slope of the moment diagram is equal to,

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Between any two points along a beam, the change in momentis equal to,

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If a concentrated force acts upward on the beam, on the shear diagram the shear force V will,

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At points where shear is equal to 0 (), the moment diagram will,

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If a clockwise couple moment acts at a location on the beam, the shear diagram will,

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If a clockwise couple moment acts at a location on the beam, the moment diagram will,

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Use the Figure to Draw Shear and Moment Diagrams

Use the interactive Figure below to determine the shear and moment diagrams for the cantilever beam with a distributed load. Drag and move the red dots to change the shape of the distributed load, and the location of point loads and couple moments on the beam. Use the sliders to change their magnitudes and directions. Use the Figure to answer the following questions.

For a uniformly distributed load, the shape of the shear curve is linear because,

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For a uniformly distributed load, the shape of the moment curve is,

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For a uniformly distributed loadN/m with a beam length of 3m, what is the correct expression for the change in momentbetween a and b?

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What happens to the shape of the shear curve as the distributed load changes from a uniformly varying load, starting from zero at the free end, to a uniformly distributed load?

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What happens to the shape of the moment curve as the distributed load changes from a uniformly varying load, starting from zero at the free end, to a uniformly distributed load?

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For a cantilever beam with a uniformly varying load starting at zero at the free end, why does the slope of the shear curve decrease along the length of the beam?

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Cantilever with a Point Load

Click and drag the red dot to move the location of the point load along the beam. Use the slider to change its magnitude. Use the above Figure to answer the following questions.

When only a single point load acts on the cantilever beam, why is the slope of the shear force diagram up to the point load?

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If the point load acts at the free end of the beam, what is the shear force just to the left of the point load?

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If the point load acts at the free end of the beam, where is the max shear located?

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What is the shape of the bending moment curve if the point load acts at the free end of the beam?

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If a point load P acts at a distance x along the cantilever, what is the magnitude of the maximum bending moment at the support?

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If the length of the beam were doubled while keeping the point load at the free end, what would happen to the magnitude of the bending moment at the support end of the beam?

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