Graph of bending moment doesn't return to 0

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Discussion Overview

The discussion revolves around the behavior of bending moment diagrams (BMD) in structural analysis, particularly focusing on why a bending moment diagram does not return to zero as expected. Participants explore the implications of load placement, moment calculations, and conventions for graphing bending moments and shear forces.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that their bending moment diagram does not return to zero and questions if there is an issue with the problem statement.
  • Another participant explains that the bending moment at a certain point is influenced by loads and torques at different locations, suggesting that the beam does not "know" about loads beneath certain points.
  • There is a discussion about the conventions for defining positive and negative curvature in bending moment diagrams, with some participants advocating for a "smiley face" convention while others express uncertainty.
  • A participant presents their calculations for moments about a point and seeks validation of their approach, indicating confusion about the influence of loads on the bending moment at different points.
  • Some participants express differing opinions on whether the upper or lower part of the graph should be considered positive, with references to consistent definitions being important.
  • One participant describes a simplified example to clarify the concept of torque and stress distribution along a beam, emphasizing that the beam's response does not depend on how the torque is generated.
  • There is a recurring question about whether positive values on the graph should always be oriented upwards, with some participants asserting that this is a standard convention.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the conventions for graphing bending moments and the interpretation of the bending moment diagram. There is no consensus on the correct approach to defining positive and negative values in the context of the bending moment diagram.

Contextual Notes

Participants highlight the importance of consistent definitions for positive and negative values in bending moment diagrams, but there is uncertainty regarding the application of these conventions. The discussion also reflects varying interpretations of how loads affect bending moments at specific points along a beam.

chetzread
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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 ...
 

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chetzread said:
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.
 
haruspex said:
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 ?
 
haruspex said:
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 ...
 

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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.
 
chetzread said:
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.
 
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Mapes said:
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?
 
haruspex said:
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
 
chetzread said:
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 (:smile:) bending moment. Others do the opposite.
 
  • #10
chetzread said:
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.
 
  • #11
Mapes said:
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 (:smile:) bending moment. Others do the opposite.
ya , from my definition , 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...
 
  • #12
chetzread said:
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...
 
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  • #13
Mapes said:
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?
chetzread said:
ya , from my definition , 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...
 
  • #14
On the graph, positive should always be upwards.
 
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  • #15
Mapes said:
On the graph, positive should always be upwards.
is it a must that positive should always be upwards ?
 
  • #16
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.
 

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