# finite element set up for beam

• posted

Hi,

I think this question should be pretty simple.

I have a rectangular 2D cantilever beam with an external point load in the downward direction at the free (right-hand) top corner of the beam (the beam is horizontal). The beam cannot delfec in the x- direction because it is constrained with rollers against a vertical wall.

This beam is broken into 2 triangular elements (split by a diagonal line which joins the bottom left corner to the top right. There is a node at each of the four corners of the beam, and the beam is fixed to the wall at its left-hand end.

Im just setting the equations up to anallyse the beam, and i am wondering if the vertiacl forces acting on the two left-hand nodes should both be equal to the applied force in the opposite direction, or both equal to half the applied force?

also would I be right in thinking that a horizontal force would need to act at the bottom left node to balance moments? - this would mean the bottom right element is not in horizontal equilibrium.

Thanks for any help,

• posted
30N 60N /| \ | | | | 3cm | | _____________________________________________________________ \|/ |

----- | W |

---------- | |

------------ | A |

------------ | 1 cm |

------------ | L /|\ 3

--------------------- | |

----------- | L |

----------- | |

------- | |_-_________\__________________________________________________| / 180N

• posted

that was my attempt at drawing it- whoops!

• posted

First off, these sounds like very odd elements...you normally want all the element dimensions to be approximately equal or your assumed basis functions may be too far from reality. These elements sound like they are extremely skewed.

Why are you setting these forces at all? You should be able to set the displacements (zero) and get the reactions as a solution to the problem, not as an input.

You do need a horizontal reaction force to balance moments...that's the realization of the compressive and tensile forces in the top and bottom of the beam. The bottom element should be in eqilibrium because it will have a reaction force at the bottom left node and a balancing force at the top right node (transmitted throught the top left element).

Tom.

• posted

Call me crazy but shouldn't beams be modeled with beam elements?

Just apply loads & specify boundary conditions....the analysis will take care of the rest.

cheers Bob

• posted

Thanks to both of you who replied.

I have since used the equation KU=F where k is the nxn stifness matrix, U is the nx1 displacement vector and F is the nx1 force vector.

Basically, what I dont understand is why in the question (in which this funny element set-up is defined), the stiffness matrices are given for both the elements.

I think that the displacements the bottom right-hand corner can be found from analysing the bottom right elelemnt alone, using the row of the equation KU=F as simultaneous equations.

Is the stiffness matrix of the top left-hand element needed at all? I only need to find the displacenment of te bottom right-hand corner of the beam

• posted

Yes. K is for the assembly of elements. Then apply the constraints and solve for the unknown Us.

• posted

Because you need both. A single element won't capture the true response of the beam.

They can't, because the global K matrix will have contributions from both elements at the top right and bottom left nodes. If you leave out the upper element, the K matrix will be wrong.

Yes. It influences the stiffness at the nodes it has in common with the bottom right element.

Right, but the displacement of the bottom-right node (bottom right corner of the lower element) is a function of applied load and the displacement of the other nodes of that element. The left node is fixed by the support, but the upper right node is free to move. This node is also attached to the top left element, so the displacement of the bottom right corner is a function of the displacement of both elements.

Tom.

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