Displacement of the node, superposition of forces

In summary, Homework Statement: The student is trying to solve a problem concerning the deflection of a beam due to the application of distributed loads and a lever moment. They need to work out the slope of the horizontal beam at the point where the two join, and then add it to the deflection caused by the load applied at the bottom end.
  • #1
margareta
3
0

Homework Statement


Hi,
I was wondering if anybody has an idea how to divide the forces on this structure to get the dispacement of the node 4.
upload_2017-2-22_10-49-8.png

2. Formulas
I would like to solve this task by superpositioning forces working on different elements of the construction. (note different EI)
using basic values for basic beams:
upload_2017-2-22_10-58-51.png

The Attempt at a Solution


upload_2017-2-22_10-56-14.png

? should it be devided like this?
but then, how would i consider displacement at the node 2?
upload_2017-2-22_10-49-45.png

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  • #2
Proceed in six stages :

(1) Treat the vertical beam initially as just a lever which is applying a bending moment to the horizontal beam at the point where the two join .

(2) Work out the slope of the horizontal beam at the point where the two join .

(3) From that slope work out the displacement of the bottom of the vertical beam using geometry .

(4) Now treat the vertical beam as a cantilever fixed at the top to some fictional rigid structure .

(5) Work out the deflection caused by the load applied at the bottom end .

(6) Add the deflection from (3) to the deflection from (5) to get the total deflection .
 
Last edited:
  • #3
ok. I understand, however I have a question how to get the slope of the horizontal beam. Can I divide this beam into 4 elements like this:
upload_2017-2-22_11-29-15.png
 
  • #4
You can use superposition for this simple problem .

Work out the slope due to the distributed load and to the lever moment separately and add them together . Pay attention to signs when doing this .
 
  • #5
I guess I made some wrong superposition assumptions considering case 3,4. Could u please tell me, what kind of assumptions should i do to get the final displacement in this middle node. This task has to be solved using superposition of forces
upload_2017-2-22_12-21-29.png
 
  • #6
Your M as shown in top diagram is turning the wrong way .

You need to work out the slope at the joining point not the vertical deflection .
 
  • #7
Yes. I agree. On the top diagram it is just the exaple of how forces work in case of my beam. In case 2 i take the moment with correct sign.
i will try to find the formulas for calculating the change of the slope depending on the position of x. cause i need it for my case 3, where i want to calculate the angle in the middle of the beam.
 

1. What is displacement of the node?

Displacement of the node refers to the change in position of a specific point or node in a system. This can occur due to applied forces or external factors.

2. How is displacement of the node calculated?

Displacement of the node is typically calculated using mathematical equations that take into account the applied forces and the properties of the system, such as stiffness and mass.

3. What is superposition of forces?

Superposition of forces is a principle in physics that states that the total force on a system is equal to the sum of the individual forces acting on that system. This principle can be applied to the displacement of nodes in a system.

4. How does superposition of forces affect the displacement of nodes?

Superposition of forces can affect the displacement of nodes in a system by changing the overall forces acting on the system. This can result in a change in the displacement of specific nodes within the system.

5. What are some real-world applications of displacement of nodes and superposition of forces?

Displacement of nodes and superposition of forces have many real-world applications, including in engineering, structural analysis, and materials testing. They can also be used to model the behavior of various systems, such as bridges, buildings, and mechanical structures.

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