Boundary condition of pinned/fixed/roller support

In summary, the conversation discusses the question of whether the shear force is discontinuous at the ends and center of a beam with point reaction forces and a point load. It is agreed that the shear force is discontinuous, but the question from the homework specifically asks for the value of the shear force at x = L. The diagrams provided for the fixed support are incorrect, as R1 and R2 should not be equal.
  • #1
yecko
Gold Member
277
15

Homework Statement


-bg38psihf5D0qL_m6G_y_Xc7YM58NoqLQFCzpWt2lxa5OeFJ0mIjzSP21WdVymtDm7lZQbPNWOeg&owa=outlook.office.jpg
[/B]

Homework Equations


shear bending diagram

The Attempt at a Solution


May I ask for supports like these, if shear force V= 0 or not when x=L?
From the shear diagram, it is a shape increase from -0.5P to 0 there.
As the shear go back to zero is owing to the reaction force by R2, right before x=L V=-0.5P, while right after V=0.

Thank you.
 

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    -bg38psihf5D0qL_m6G_y_Xc7YM58NoqLQFCzpWt2lxa5OeFJ0mIjzSP21WdVymtDm7lZQbPNWOeg&owa=outlook.office.jpg
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  • #2
yecko said:

Homework Statement


View attachment 225582[/B]

Homework Equations


shear bending diagram

The Attempt at a Solution


May I ask for supports like these, if shear force V= 0 or not when x=L?
From the shear diagram, it is a shape increase from -0.5P to 0 there.
As the shear go back to zero is owing to the reaction force by R2, right before x=L V=-0.5P, while right after V=0.

Thank you.
If you are asking whether the shear force is discontinuous at the ends (where point reaction forces are applied) and at the center (where a point load is applied), then yes.
 
  • #3
Yes, it is discontinuous, yet the question from my homework is asking if the shear force at x=L V=0?
 
  • #4
yecko said:
Yes, it is discontinuous, yet the question from my homework is asking if the shear force at x=L V=0?
I don't know how to answer that if it is discontinuous at x = L.
 
  • #5
I agree with Chet that it makes no sense to ask for the value of a function at a discontinuity.
But I would like to point out that your diagrams are wrong for the fixed support. R1 and R2 will not be equal there.
 

1. What is the difference between a pinned, fixed, and roller support?

A pinned support allows for rotation and translation in all directions, while a fixed support does not allow for any rotation or translation. A roller support only allows for translation along one direction.

2. How do I know which boundary condition to use for my analysis?

The type of support depends on the structural system and the type of loading it is subjected to. Generally, a pinned support is used for beams or trusses, a fixed support is used for columns or frames, and a roller support is used for structures with a horizontal or inclined plane.

3. Can I have multiple boundary conditions on one structural element?

It is not recommended to have multiple boundary conditions on one structural element. This can lead to unrealistic and inaccurate results. It is important to choose the appropriate boundary condition for each structural element.

4. What happens if I incorrectly specify the boundary condition?

Incorrectly specifying the boundary condition can result in inaccurate and unrealistic results. It is important to carefully consider the type of support used in order to accurately model the behavior of the structure.

5. How do boundary conditions affect the overall stability of a structure?

The boundary conditions play a crucial role in the stability of a structure. A fixed support provides the most stability, while a pinned support provides the least stability. The type of support used can also affect the distribution of forces within the structure.

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