# How to formulate pin joints in finite element modeling of solid frames

In frame analysis with finite element every node can be assumed with 6 Degree of Freedom (3 translation DoF and 3 rotational DoF). There are formulations over the web for creating stiffness matrix etc. of frame elements like this one. These formulation does model rigid joints which means element is totally connected to nodes, but i need a document to describe how to model pinned joints like this image:

• A pin restricts all relative translation and 2 dof of relative rotation. Therefore, you should impose that the nodes being "pinned" have this property. Implementation of this is straightforward after assembly of the full FE system. You must use 2 nodes at the joint--one for each part. If you only use a single node that gets shared between parts, you will be effectively saying that those two pieces are rigidly connected. – Tyler Olsen Jun 29 '15 at 23:00
• @TylerOlsen thanks it is good idea, but this solution also increases the DoFs also computation time. i was looking for a solution to just take one node for this pin joints. Like what is described in page 11 of manual of this file: mathworks.com/matlabcentral/fileexchange/… – epsi1on Jul 2 '15 at 14:42
• There's really no way to get around the issue of adding dofs. You're removing a constraint from the physical system, which by definition is adding a degree of freedom. If you want to track the rotation for each frame piece in the joint separately, then you have to add dofs to your computation. Fortunately, frame FEM simulations tend to be rather small compared to continuum simulations, so you should still be fine. How big are your problems? – Tyler Olsen Jul 2 '15 at 15:20
• in the pdf file i sent in my last comment it is shown how local frame stiffness matrix can be changed for modeling a hinged beam. with no adding new DoFs. I wanted to add this to a opensource library named BriefFiniteElementdotNET – epsi1on Jul 2 '15 at 15:40
• I'm not sure what they mean by "member release" so I can't speak to that directly. If that's what you're looking for, then it sounds like your question has already been answered. – Tyler Olsen Jul 2 '15 at 16:00

A pin restricts all relative translation and 2 dof of relative rotation. Therefore, you should impose that the nodes being "pinned" have this property. Implementation of this is straightforward after assembly of the full FE system. You must use 2 nodes at the joint--one for each part. If you only use a single node that gets shared between parts, you will be effectively saying that those two pieces are rigidly connected.

Truss elements, as opposed to beam elements, don't usually include rotational freedoms so there's no need to release them to model a pin-joint. The structure illustrated could be modelled with a 2-D beam element for the left-hand part (encastre at the wall) and a 2-D truss element for the right hand element (roller supported at the end). The beam element will include rotational freedoms but, because the truss element won't, the joint will act as a pin.

In pseudo-code:

nodes
node(1)... coordinates of left-hand end
node(2)... coordinates of joint
node(3)... coordinates of right-hand end

elements
elem[1],type=2Dbeam.... joins node(1) to node(2)
elem[2],type=2Dtruss... joins node(2) to node(3)

constraints
node(1)   disp(x)=0,disp(y)=0,rotation=0
node(3)   disp(y)=0


This is for the simplest case, with a point load at the joint.

• Yes your solution can be used for this case, but not applicable to 3d problems where 3d beams have complicated end releases. I was seeking for a general solution... – epsi1on Aug 28 '15 at 6:23