User:Eml4500.f08.bike.pataky

Mon
A frame element is defined as an element with a truss or bar element and a beam element. This gives the frame element both axial and transverse deformations.



The frame shown above has a rigid connection between its two elements. This means that the angle between the two elements will stay constant after deformation.

Next the frame will be broken down into its two elements. The free body diagrams for these elements are shown below.



In the free body diagram above, a new degree of freedom is introduced for each node. This new degree of freedom is the moment around the node and adds two degrees of freedom. This brings the total to six degrees of freedom for element 1.



As with element 1, element 2 has the two new degrees of freedom.

In general, the degrees of freedom shown above for each element would be the general forces previously used. However, the new rotational degrees of freedom, $$d_3^{(e)}$$ and $$d_6^{(e)}$$, are now the bending moments, $$f_3^{(e)}$$ and $$f_6^{(e)}$$ instead of forces.



The global diagram contains nine degrees of freedom now. All three nodes now contain bending moments just like the elements do.

The elemental stiffness matrices $$\textbf{k}^{(e)}_{6x6}$$ where e = 1,2 are used to make the global stiffness matrix $$\textbf{K}_{9x9}$$. For the current frame element, the global matrix would look like the picture shown below.