Graph of bending moment doesn't return to 0

[chetzread]

Homework Statement

I gt VA and VB = 85 N and 65 N respectively ... but , my bending moment diagram doesn't return to 0 ... Is there something wrong with the question ?

Homework Equations

The Attempt at a Solution

I found that if i didnt include both the moment of 75(0.05) = 3.75Nm , the bending moment graph return to 0 perfectly ...

 

[haruspex]

my bending moment diagram doesn't return to 0

You have the bending moment suddenly diminishing at 200mm. The beam does not "know" the load is beneath that point. What it feels is the load and torque at the 250mm point.

 

[chetzread]

You have the bending moment suddenly diminishing at 200mm. The beam does not "know" the load is beneath that point. What it feels is the load and torque at the 250mm point.

do you mean the beam 'feel ' the load and moment only at 250mm from A , but not 200mm from A ? so , i should ' bring down ' the graph for both SFD and BMD only at 250mm from A ?

 

[chetzread]

You have the bending moment suddenly diminishing at 200mm. The beam does not "know" the load is beneath that point. What it feels is the load and torque at the 250mm point.

here's my sketch of BMD and SFD , are they correct ? For the BMD , i do in 2 ways , which are upper part of graph as positive and lower part of graph as negative ...

 

[Mapes]

A return to zero moment at the end (where there is zero applied moment) is a good sign. Remember that your shear force (moment) diagrams mean little without stating a convention for which direction (curvature) is positive and which is negative. Positive curvature is often defined as a "smiley face"; i.e., a beam under such curvature would curve upward while moving from left to right. However, this is just a convention.

 

[haruspex]

here's my sketch of BMD and SFD , are they correct ? For the BMD , i do in 2 ways , which are upper part of graph as positive and lower part of graph as negative ...

Yes, that looks better.

 

[chetzread]

smiley face"; i.e., a beam under such curvature would curve upward while moving from left to right.

Do you mean the graph is positive downwards? Or do you assume that the graph is positive upwards?

 

[chetzread]

Yes, that looks better.

do you mean the beam 'feel ' the load and moment only at 250mm from A , but not 200mm from A ? so , i should ' bring down ' the graph for both SFD and BMD only at 250mm from A ?

why when i calculate the moment about A , it's 75(0.2) + 75(0.45) -VB(0.75) = 0
VB = 65N , VA = 85N

Here's my ans which satisified the ans given , is my concept and equation correct ?

You ssaid that the beam will only feel the load and moment about C and D , so i am not sure about my ans

 

[Mapes]

Do you mean the graph is positive downwards? Or do you assume that the graph is positive upwards?

It doesn't matter, as long as your definitions are consistent. I find it easy to associate a beam that curves like a smile with a positive () bending moment. Others do the opposite.

 

[haruspex]

do you mean the beam 'feel ' the load and moment only at 250mm from A , but not 200mm from A ? so , i should ' bring down ' the graph for both SFD and BMD only at 250mm from A ?

why when i calculate the moment about A , it's 75(0.2) + 75(0.45) -VB(0.75) = 0
VB = 65N , VA = 85N

Here's my ans which satisified the ans given , is my concept and equation correct ?

You ssaid that the beam will only feel the load and moment about C and D , so i am not sure about my ans

I think your difficulty is conceptual, so I'll describe a simpler example. Consider first a rod under tension T. At each point in the rod there is a force T pulling on it on one side balanced by an equal and opposite force on the other. But the stress at that point is the magnitude of these forces.
Now consider a horizontal 2m beam AB, midpoint C.
At the left (A) there is a 1N force acting down. At the right, a 1N force acting up. At C, a 2Nm torque clockwise.
The beam is therefore in equilibrium. If we look at any point on the beam, the sum of torques due to applied torques and forces on one side is equal and opposite to the sum on the other side. As for the rod, the torsional stress at the point is the magnitude of these opposing torque sums.
Perhaps the torque at C comes from some L-shaped descender attached there. Let's say it descends .5m, then goes off to the right for 4m to point D, where there is a downward force of .5 N. That provides the 2Nm torque. But the beam itself does not care how that torque is generated. It could have been 10m to point D and a force there of .2N, it makes no difference to the stresses at points along the beam.

 

[chetzread]

It doesn't matter, as long as your definitions are consistent. I find it easy to associate a beam that curves like a smile with a positive () bending moment. Others do the opposite.

ya , from my definiton , smile curve is positive bending moment , my problem now is should i put the upper graph or lower graph of bending moment as positive ...
I was told that we can either the upper graph or lower graph of bending moment as positive ...
Correct me if i am wrong ... P/s : I let positive y-axis as positive for shear force diagram all the times...

 

[Mapes]

my problem now is should i put the upper graph or lower graph of bending moment as positive ...

Looks like those downward 75 N loads and the end constraints are going to make the beam look more smiley than frowney...

 

[chetzread]

Looks like those downward 75 N loads and the end constraints are going to make the beam look more smiley than frowney...

So, which is correct? Upper side of graph or lower side of graph should be positive?

ya , from my definiton , smile curve is positive bending moment , my problem now is should i put the upper graph or lower graph of bending moment as positive ...
I was told that we can either the upper graph or lower graph of bending moment as positive ...
Correct me if i am wrong ... P/s : I let positive y-axis as positive for shear force diagram all the times...

 

[Mapes]

On the graph, positive should always be upwards.

 

[chetzread]

On the graph, positive should always be upwards.

is it a must that positive should always be upwards ?

 

[Mapes]

I was going to say I've never seen a case where it isn't, but then I found this example in an image search. It seems like a recipe for confusion.