User:Eml4500.f08.team.dwyer.jd/HW7 Nov 17 (Meeting 35)

Frame Elements

 * Frame element = truss(bar) element + beam element


 * A truss has axial deformation


 * A beam has transverse deformation (bends)

Model Frame Problem with 2 Elements:



FBD's:

 * Because the connection between the two elements is rigid, the angle between them will stay constant after deformation.

The free body diagrams of each element is shown below:



$$ rotational dofs and $$\left.\begin{matrix}f_{3}^{(e)}\\ f_{6}^{(e)} \end{matrix}\right\} $$ bending moments
 * Where $$\left.\begin{matrix}d_{3}^{(e)}\\ d_{6}^{(e)}\end{matrix}\right\}

2-D Frame Global DOF's:


There are now 9 total degrees of freedom, so:


 * 2 element stiffness matrix: $$\underline{k}_{(6x6)}^{(e)}$$, e=1,2
 * Global stiffness matrix: $$\underline{k}_{(9x9)}=A\underline{k}_{(6x6)}^{(e)}$$

The 9x9 global stiffness matrix will now look like this: