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

Autore:Ana Kwon

Argomento:Vettori 2D (Due dimensioni), Diagrammi, Vettori

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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A
The intensity of the distributed load curve at that point
B
The intensity of the moment diagram at that point
C
The area under the distributed load curve
D
The area under the moment diagram

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

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A
The intensity of the distributed load between the points
B
The intensity of the moment diagram between the points
C
The area under the distributed load curve between the points
D
The area under the moment diagram between the points

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

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A
The intensity of the distributed load curve at that point
B
The intensity of the shear curve at that point
C
The area under the distributed load curve
D
The area under the shear curve

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

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A
The intensity of the distributed load between the points
B
The intensity of the shear diagram between the points
C
The area under the distributed load curve between the points
D
The area under the shear diagram between the points

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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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A
Remain unchanged
B
Jump downward by the same amount
C
Jump downward by twice the amount
D
Jump upward by the same amount
E
Jump upward by twice the amount
F
Go to zero

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

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A
Also be equal to 0
B
Reach a minimum or maximum since
C
Equal the area under the shear curve before shear was equal to 0
D
Equal the area under the distributed load curve

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

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A
Be unaffected
B
Jump downward by the same magnitude of the couple moment
C
Jump upward by the same magnitude of the couple moment
D
Go to zero

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

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A
Be unaffected
B
Jump downward by the same magnitude of the couple moment
C
Jump upward by the same magnitude of the couple moment
D
Go to zero

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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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A
The intensity of the distributed load is constant
B
The shear curve is always linear
C
The shear curve always has to go to zero
D
The beam is a cantilever

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

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A
Linear
B
Parabolic
C
Cubic
D
Zero

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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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A
B
C
D

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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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A
It changes from parabolic to linear
B
It changes from linear to parabolic
C
It changes from parabolic to cubic
D
It changes from linear to cubic
E
It doesn't change at all

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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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A
It changes from parabolic to linear
B
It changes from linear to parabolic
C
It changes from parabolic to cubic
D
It changes from linear to cubic
E
It doesn't change at all

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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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A
Because the intensity of the distributed load is decreasing
B
Because the intensity of the distributed load is increasing
C
Because the distributed load is constant
D
Because the slope of the shear curve always decreases along the beam for cantilever beams

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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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A
The slope of shear is always zero on a cantilever beam
B
There is no distributed load between x=0 and the applied point load
C
The point load does not affect the shear force diagram

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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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A
Zero
B
Equal to the magnitude of the point load
C
Half the magnitude of the point load
D
Twice the magnitude 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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A
At the fixed support
B
At the free end of the beam
C
In the middle of the beam
D
Uniformly distributed at every point up to the point load

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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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A
A horizontal line
B
A linear slope
C
A parabolic curve
D
A cubic curve

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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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A
B
C
D

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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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A
It would double
B
It would be cut in half
C
It would stay the same
D
It would quadruple

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