How to solve this problem by the method of superposition?

In summary, the problem is that the table doesn't seem to be very helpful in understanding how to incorporate the moment at the pin into the deformation. However, by reversing the direction of the moment, the response will be reversed.
  • #1
link223
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Homework Statement
Please refer to the picture for a visual.

QUESTION 1: Determine the slope of the beam at A , measured counterclockwise from the positive x -axis.

QUESTION 2:
Determine the maximum deflection of the beam.
(Express your answer in terms of some or all of the variables L, E, I and M_0 in both cases .)
Relevant Equations
Table of deformation --> attachment to be used to determine the maximum deformation + slope via the method of superposition
1654968837880.png


Hello there,

I would like to get some help for this problem if possible.

The problem here is that, after looking at the table I don't really understand how I'd be able to incorporate the moment at the pin A into the deformation. as if you look at the first page 2nd block, there's that simply supported beam, but with a moment that is applied at the side of the roller.

So there are actually two questions here:
(1) for the pin: How do I determine the deformation due to the moment at A
(2) for the roller: the moment is in the opposite direction than shown in the table, does that imply that I could just take the opposite of the equation that is stated next to it for the slope and the deflection?

Thanks in advance!

a note: I do know that the elastic curve will be a 'parabolic' being concave down and deforming above the non-deformed state of the beam, but that is about it on this one.
 

Attachments

  • Deform.pdf
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  • #2
(1) For this case the pin and the roller represent identical support conditions. If your deflection table only supplies results for a moment acting at the right end of the beam, you can use these results for a moment acting at the left end by imagining viewing the beam from the back side.
(2) Reversing the direction of an applied load simply causes a reversal in sign in the response.
 
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  • #3
T1m0 said:
(1) For this case the pin and the roller represent identical support conditions. If your deflection table only supplies results for a moment acting at the right end of the beam, you can use these results for a moment acting at the left end by imagining viewing the beam from the back side.
(2) Reversing the direction of an applied load simply causes a reversal in sign in the response.
Thanks! I wasn't so sure about how to go about these scenarios, but I just need to plug and chug the cases basically.
 

FAQ: How to solve this problem by the method of superposition?

What is the method of superposition?

The method of superposition is a mathematical technique used to solve problems that involve multiple forces or inputs. It involves breaking down a complex problem into smaller, simpler problems and then combining the individual solutions to obtain the overall solution.

When should the method of superposition be used?

The method of superposition is most useful when dealing with linear systems, where the individual forces or inputs can be added together to obtain the total response. It is commonly used in physics, engineering, and other fields that involve analyzing systems with multiple inputs.

How does the method of superposition work?

The method of superposition works by using the principle of linearity, which states that the response of a system to a combination of inputs is equal to the sum of the responses to each individual input. This allows us to break down a complex system into simpler parts and then combine the solutions to obtain the overall solution.

What are the steps involved in using the method of superposition?

The steps involved in using the method of superposition are as follows:

  1. Identify the individual inputs or forces acting on the system.
  2. Solve for the response of the system to each individual input.
  3. Combine the individual solutions using the principle of linearity to obtain the overall response of the system.

Are there any limitations to the method of superposition?

Yes, there are some limitations to the method of superposition. It can only be used for linear systems, and it assumes that the individual inputs do not interact with each other. Additionally, it may not be applicable to all types of problems, such as those involving non-linear or time-dependent systems.

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