User:Eml4500.f08.ateam.rivero/w1

Week 1: Sept. 5, 2008 Continued
Example Problem:

The following example below, will show the steps described below in the recipe to solving simple truss problems. Trusses are composed of elements that only allow for axial loads. The elements are connected by nodes. This problem has a total of two elements and three nodes, where each node has two degree's of freedom. This problem will be composed of applying a load P to node two. Once the problem is solved we would be able to see the deflections and force reactions at each node.

Data:

Element Length: *L(1) = 4 *L(2) = 2

Young's Modulus: *E(1) = 3 *E(2) = 5

Cross Sectional Area: *A(1) = 1 *A(2) = 2

Inclination Angle: *Θ(1) = 30o *Θ(2) = 45o

Step 1: Global Picture

Labeling : Global degrees of freedom (dofs) and forces

The number inscribed in a green circle refers to a node value n. For example, in the problem being described the node values range from one through three. When numbering the displacement degrees of freedom (d1, . . . d6), you want to start at node 1 and the x displacement. This displacement degree of freedom would be labeled ( d1 ). This would be followed by node 1, y displacement; labeled ( d2 ). Next would be followed by node 2, x displacement; labeled ( d3 ). Next would be node 2, y displacement; labeled ( d4 ). One would continue this order until all the nodes are labeled with their corresponding degrees of freedom. The same systematic order would be followed to label the global forces ( F1, . . . F6 ).See image above for further explanation on labeling. These displacements and forces are then put into a matrix format as seen in the image below.