Is Shear Force Always Maximum When Moment is Zero?

AI Thread Summary
The discussion centers on the relationship between shear force and bending moment in beams. It clarifies that while the textbook states shear force being zero indicates a maximum moment, this is not universally true, as demonstrated by a cantilever beam where both shear force and moment can be zero at the free end. The key point is that locations where shear force is zero can correspond to relative maxima or minima of the bending moment. In the specific case discussed, when shear force is zero, the moment is also zero, indicating a minimum. This highlights the need to consider the context of beam types when analyzing shear and moment relationships.
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Homework Statement


in the book , i was told that when the shear force is 0 , moment is maximum . However , in this question , i found that when the shear foce is 0 , the moment is also 0 . I'm wondering is the ststemnet true ?
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Homework Equations

The Attempt at a Solution

 
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chetzread said:

Homework Statement


in the book , i was told that when the shear force is 0 , moment is maximum . However , in this question , i found that when the shear foce is 0 , the moment is also 0 . I'm wondering is the ststemnet true ?
swF2bVW.jpg


Homework Equations

The Attempt at a Solution

Obviously, if the beam is a cantilever, the shear force and the bending moment can both be zero at the free end. You won't find the maximum moment there in any event.

I think what the author was trying to say was that since the derivative of the bending moment, dM/dx = V, the locations where the shear is zero are also possible locations where the bending moment has a relative maximum or minimum.
 
SteamKing said:
Obviously, if the beam is a cantilever, the shear force and the bending moment can both be zero at the free end. You won't find the maximum moment there in any event.

I think what the author was trying to say was that since the derivative of the bending moment, dM/dx = V, the locations where the shear is zero are also possible locations where the bending moment has a relative maximum or minimum.
so , for the above case , shear force = 0 , moment = 0(minimum) ?
 
chetzread said:
so , for the above case , shear force = 0 , moment = 0(minimum) ?
Obviously.
 
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