Moment at Two Ends of Beam: Understanding Variations and Direction

In summary, the moment is always 0 kN-m in the first case, opposite to the 20kNm at the opposite end in the second case, and linear in between in the third case.
  • #1
chetzread
801
1

Homework Statement


in the first diagram , i notice that the moment is constant throughout the beam...

why in the second notes, for the moment 20kNm at 2 ends of beam, why the moment varies from -20kNm to 0 from one end to another end?

hbaHRJu.jpg

ii7MFar.jpg


Homework Equations

The Attempt at a Solution


Which is correct? Which is wrong?
i'm confused...
another thing that i noticed is why no matter moment is clockwise or anticlockwise, the moment is always -20kNm??(as we can see ,moment is anticlockwise on the left , clockwise on the right...)
 
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  • #2
chetzread said:

Homework Statement


in the first diagram , i notice that the moment is constant throughout the beam...

why in the second notes, for the moment 20kNm at 2 ends of beam, why the moment varies from -20kNm to 0 from one end to another end?

hbaHRJu.jpg

ii7MFar.jpg


Homework Equations

The Attempt at a Solution


Which is correct? Which is wrong?
i'm confused...
another thing that i noticed is why no matter moment is clockwise or anticlockwise, the moment is always -20kNm??(as we can see ,moment is anticlockwise on the left , clockwise on the right...)
You can't compare beams willy-nilly. The support conditions influence how the forces and moments distribute within the beam.

In the first case, you have a cantilever beam, with the left end fixed and a couple applied at the opposite end. In order to maintain static equilibrium, there will be a constant moment present along the length of the beam, as shown in Fig. (b). The fixed end of the cantilever has a reactive couple, which combines with the applied couple to make a zero net moment for the beam.

In the other two beam cases, the beam is pinned at each end and a couple of magnitude 20 kN-m is also applied at each end. Pinned connections cannot support a moment, so the moment diagram shows the magnitude of each couple where it is applied and a zero moment at the opposite end of the beam, with a linear slope in between.
 
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  • #3
SteamKing said:
You can't compare beams willy-nilly. The support conditions influence how the forces and moments distribute within the beam.

In the first case, you have a cantilever beam, with the left end fixed and a couple applied at the opposite end. In order to maintain static equilibrium, there will be a constant moment present along the length of the beam, as shown in Fig. (b). The fixed end of the cantilever has a reactive couple, which combines with the applied couple to make a zero net moment for the beam.

In the other two beam cases, the beam is pinned at each end and a couple of magnitude 20 kN-m is also applied at each end. Pinned connections cannot support a moment, so the moment diagram shows the magnitude of each couple where it is applied and a zero moment at the opposite end of the beam, with a linear slope in between.
why moment at the opposite end of the beam will be 0 ? why not positive 20kNm ?
 
  • #4
chetzread said:
why moment at the opposite end of the beam will be 0 ? why not positive 20kNm ?
I explained that in my post.

If you are not going to read the replies to your questions, what are you doing on this site?
 
  • #5
SteamKing said:
You can't compare beams willy-nilly. The support conditions influence how the forces and moments distribute within the beam.

In the first case, you have a cantilever beam, with the left end fixed and a couple applied at the opposite end. In order to maintain static equilibrium, there will be a constant moment present along the length of the beam, as shown in Fig. (b). The fixed end of the cantilever has a reactive couple, which combines with the applied couple to make a zero net moment for the beam.

In the other two beam cases, the beam is pinned at each end and a couple of magnitude 20 kN-m is also applied at each end. Pinned connections cannot support a moment, so the moment diagram shows the magnitude of each couple where it is applied and a zero moment at the opposite end of the beam, with a linear slope in between.
why not positive 20kNm ? why it's 0 ? we can see , the moment 20kNm at the left ( anticlockwise) is opposite to the moment on the right (clockwise)
 

Related to Moment at Two Ends of Beam: Understanding Variations and Direction

1. What is a moment at two ends of a beam?

A moment at two ends of a beam refers to the force or torque applied to the beam at each end that causes it to rotate or bend. This moment is typically measured in units of Newton-meters (N-m) and is an important factor in understanding the stability and strength of a beam.

2. How do variations in moments affect beams?

Variations in moments can significantly affect the behavior of a beam. If the moments at both ends of a beam are equal, the beam will remain static. However, if there are differences in the moments, the beam will rotate or bend, potentially causing it to fail or become unstable. This is why it is important for engineers to carefully consider and calculate moments when designing structures.

3. How is the direction of a moment determined?

The direction of a moment is determined by the direction of the force applied to the beam and the distance from the point of application to the point of rotation. The right-hand rule is often used to determine the direction of the moment, where the thumb points in the direction of the force and the curled fingers point in the direction of rotation.

4. What are some real-world applications of understanding moments at two ends of beams?

Understanding moments at two ends of beams is crucial for engineers and architects when designing and constructing buildings, bridges, and other structures. It is also important in the design and analysis of machinery and other mechanical systems. Additionally, moments are essential in understanding the behavior of beams in earthquake and wind load scenarios.

5. How can moments at two ends of beams be calculated?

Moments at two ends of beams can be calculated using the formula: M = F x d, where M is the moment, F is the force applied, and d is the distance from the point of application to the point of rotation. The units for force and distance should be consistent (e.g. N-m or lb-ft) to ensure accurate calculations.

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