Understanding Negative Shear Force in Beams: Explanation and Graph Analysis

[chetzread]

Homework Statement

in this notes, the shear force is negative because at LHS, shear force cause the beam to turn counterclockwise , am i right?
at RHS, the shear force cause the beam to turn anticlockwise, so that the shear force is also negative?

Homework Equations

The Attempt at a Solution

Why the moment change from -ve to +ve at the moment graph?
Is it wrong?
Shoudlnt the graph look like this? (red line)

 

[chetzread]

bump

 

[PhanthomJay]

It is not wrong. The shear starts off negative and remains negative because therrre are no forces applied in between end points. Then from the calculus of beam theory, the slope of the moment diagram at a given point is equal to the shear at that point, so the slope of the moment diagram is always negative. The applied couple is a dicontinuity which adds a positive moment at that point.

 

[chetzread]

It is not wrong. The shear starts off negative and remains negative because therrre are no forces applied in between end points. Then from the calculus of beam theory, the slope of the moment diagram at a given point is equal to the shear at that point, so the slope of the moment diagram is always negative. The applied couple is a dicontinuity which adds a positive moment at that point.

can you explain in another way without the draw of moment and shear force graph ?
why the shear force is negative throughout the beam ? As we can see , the shear force acted upward at the left of beam , the shear force acted downward at the right of the beam ... the sign convention that the author used are not consistent... ( the assume upward as positive on the left , assume downward shear force as positive on the right . )
Is it wrong ?

 

[PhanthomJay]

The reaction acts down at the left and up at the right. So by convention, the shear is downward negative starting at left, then stays constant negative because there is no load applied in between until the right end, then the reaction acts up there and thus the shear goes up back to 0.

 

[chetzread]

The reaction acts down at the left and up at the right. So by convention, the shear is downward negative starting at left, then stays constant negative because there is no load applied in between until the right end, then the reaction acts up there and thus the shear goes up back to 0.

So, shear force graph is " cumulative " ??

 

[PhanthomJay]

So, shear force graph is " cumulative " ??

Not sure what you mean by "cumulative.". The shear force is a constant value of -M_o/2L at any point along the beam between end points.

 

[chetzread]

Not sure what you mean by "cumulative.". The shear force is a constant value of -M_o(L/2 ) at any point along the beam between end points.

ok , now can you explain why the moment change from -ve to positive value ?

 

[PhanthomJay]

The moment is increasingly negative up to the middle. Then the applied couple jumps it up to a positive value, then it decreases to zero at the end. You might want to visualize how the beam deflects under that applied twisting moment. The left part of the beam is a hogging moment like sort of an upside down u shape and the right part is a sagging moment upright u shape. Hogging is negative moment and sagging is positive.