User:EML4500.f08.RAMROD.E/HW7

Frame Element Definition
A frame element is an element that is made up of a beam element and a truss element. Recall that for a truss element, all deformations were axial while in a beam element, the deformation was transverse to the axis. Knowing this, we can assume that for a frame element, the deformation will be some linear combination of both axial and transverse displacements at each node.

Model Problem for Frame
As with other types of elements, we will do our simple analysis using a model problem. The model here is a two-bar frame with nodes 1 and 3 simply supported and node 2 is a rigid connection between elements 1 and 2, as shown in the diagram below:



Combining the two elemental FBDs to a global FBD is shown in the picture below.



Elemental and Global Stiffness Matrices
The next step is deriving the stiffness matrix for our model problem. Since there are more dof's at each node now, the elemental stiffness matrices will each be a 6x6 matrix. We combine them very similarly as with trusses, with the overlapping dof's being at node two, such that the global stiffness matrix will be a 9x9 and be made up as shown below: