Beam Deflection with single support

[awiest82]

Hello

I am trying to setup a problem to represent a pipeline crossing over another perpendicular pipeline on the seabed. I am trying to represent the problem as a simple beam and having some issues with the supports i am selecting and the boundary conditions.

Attached is a picture representing the problem, but using the boundary conditions i select and trying to solve for the 5 unknowns i get two possible answers for one of the unknowns, P_0. I think one of my boundary conditions are wrong.

I using symmetry and the crossing pipe is fixed at the location of the crossed pipe. At the point where the pipe touches down i am using a hinged support.

I am trying to solve for P_0, M_0 and L

Not looking for a solution just a correction or validation of the boundary conditions i have selected.

Thanks.

 

[OldEngr63]

You have no way to know L. How far out does the pipe come into full contact with the floor? This means the point at which the pipe is fully supported by the floor, with no support coming from the elevated section. The pipe on the floor is what is called a "beam on an elastic foundation," a fairly tough problem. I don't think you will get an acceptable model with the approach you are using.

Here is a reference: http://www.engineeringmechanics.cz/pdf/19_6_381.pdf

 

[awiest82]

Lets neglect the floor stiffness for right now and assume its rigid and inelastic.

L is an unknown that we are trying to solve. I actually already have an answer that someone else did and was asked to validate, but am having an issue replicating. This is an excerpt from the document i am trying to validate:"Five conditions allow us to find the integration constants and the following unknowns: L, Mo, and Po. Note, for convenience the origin (x = 0 and y = 0) has been taken at the peak of the lift. The boundary conditions are: y(0) = 0

y’(0) = 0

y(L) = - δf (5.1-3)

y’(L) = 0

y”(L) = 0where, the primes (‘) denoted derivatives with respect to the independent variable “x.” Algebraic simplification, after applying four of the conditions, results in a final set of equations that may be solved for the distance to the touchdown point, L. They are:

This completes the solution and allows calculation of the bending moment at any point in the span using Equation 5.1-2, once Mo and Po are known. This allows the maximum bending stresses in the pipe to be computed and the concentrated force on the crossing pipe and its support (which may include the crossed pipe) to be determined for further analyses."I get two different equations fro Po, the one shown above or a similar but not quite one depending on the equations i combine.

 

[OldEngr63]

Can you show us the complete solution as given in your source document, please?

 

[awiest82]

Therein lies the problem. I am being to ask to validate something where no work was shown and only the final result.

 

[OldEngr63]

Looks to me like one difficulty lies in the fact that y''(x) is discontinuous at x = L. To set y''(L) = 0 implies that there is no bending moment at that point as you approach a fixed end from the left (this is not a simple support). That is certainly contrary to all intuition. Why would you expect that to be true? On the other hand, as you approach x = L from the right, y'' is clearly zero all along. I think this is a flaw in the model. (When you have a beam built into a wall, a cantilever, you certainly don't expect zero moment at the wall.)

 

[Nidum]

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