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

The real-world design of beams requires a detailed understanding of how the internal shear force [i]V[/i] and bending moments [i]M [/i]vary at each point along the beam’s length. [br][br]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. [br]

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

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

The intensity of the distributed load curve at that point The area under the distributed load curve The intensity of the moment diagram at that point The area under the moment diagram

Between any two points along a beam, the change in shear [math]\Delta V[/math]is equal to,

The intensity of the distributed load between the points The area under the distributed load curve between the points The area under the moment diagram between the points The intensity of the moment diagram between the points

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

The area under the distributed load curve The intensity of the shear curve at that point The area under the shear curve The intensity of the distributed load curve at that point

Between any two points along a beam, the change in moment[math]\Delta M[/math]is equal to,

The intensity of the distributed load between the points The area under the shear diagram between the points The intensity of the shear diagram between the points The area under the distributed load curve between the points

If a concentrated force acts upward on the beam, on the shear diagram the shear force [i]V[/i] will,

Jump upward by the same amount Go to zero Jump upward by twice the amount Jump downward by twice the amount Jump downward by the same amount Remain unchanged

At points where shear is equal to 0 ([math]V=0[/math]), the moment diagram will,

Also be equal to 0 Equal the area under the distributed load curve Reach a minimum or maximum since [math]\frac{dM}{dx}=0[/math] Equal the area under the shear curve before shear was equal to 0

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

Jump upward by the same magnitude of the couple moment Go to zero Be unaffected Jump downward by the same magnitude of the couple moment

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

Go to zero Jump upward by the same magnitude of the couple moment Be unaffected Jump downward by the same magnitude of the couple moment

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. [br][br]Drag and move the red dots to change the shape of the distributed load, and the location of point[br]loads and couple moments on the beam. [br][br]Use the sliders to change their magnitudes and directions. [br][br]Use the Figure to answer the following questions.

For a uniformly distributed load[math]w_a=w_b[/math], the shape of the shear curve is linear because,

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

For a uniformly distributed load[math]w_a=w_b[/math], the shape of the moment curve is,

Parabolic Zero Linear Cubic

For a uniformly distributed load[math]w_a=w_b=200[/math]N/m with a beam length of 3m, what is the correct expression for the change in moment[math]\Delta M[/math]between a and b?

[math]\Delta M=\frac{1}{2}\cdot\left(6m\right)\cdot\left(600m\right)[/math] [math]\Delta M=\frac{1}{2}\cdot\left(3m\right)\cdot\left(300m\right)[/math] [math]\Delta M=\frac{1}{2}\cdot\left(3m\right)\cdot\left(600m\right)[/math] [math]\Delta M=\left(3m\right)\cdot\left(600m\right)[/math]

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?[br]

It changes from parabolic to linear It doesn't change at all It changes from linear to cubic It changes from parabolic to cubic It changes from linear to parabolic

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?

It changes from parabolic to cubic It changes from linear to cubic It changes from parabolic to linear It doesn't change at all It changes from linear to parabolic

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?

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

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. [br][br]Use the above Figure to answer the following questions.[br]

When only a single point load acts on the cantilever beam, why is the slope of the shear force diagram [math]\frac{dV}{dx}=0[/math] up to the point load?

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

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?

Zero Half the magnitude of the point load Twice the magnitude of the point load Equal to the magnitude of the point load

If the point load acts at the free end of the beam, where is the max shear [math]V_{max}[/math]located?

Uniformly distributed at every point up to the point load At the fixed support At the free end of the beam In the middle of the beam

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

A parabolic curve A cubic curve A linear slope A horizontal line

If a point load [i]P[/i] acts at a distance [i]x[/i] along the cantilever, what is the magnitude of the maximum bending moment [math]M_{max}[/math]at the support?

[math]Px[/math] [math]\frac{Px^2}{2}[/math] [math]Px^2[/math] [math]\frac{Px}{2}[/math]

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?

It would stay the same It would be cut in half It would quadruple It would double

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

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

Use the Figure to Draw Shear and Moment Diagrams

Cantilever with a Point Load

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