Linear algebra concept, Civil Engineering

Scenario: You are working for a structural engineering firm and you have been assigned the task of computing the code checks on a new structural design. Though another commercial program was used to do the analysis, you have been instructed to use an in-house code to re-check the analysis results, and to add your code checks to the in-house code. Fortunately for you, the model from the other code is available, and the in-house code is already able to read it. The assignment wil l lead you through to the solution, as usual. Background: A frame is a set of beams and/or columns rigidly connected at their ends. Generally, beams are loaded axially and along their length, but in this assignment, all loads (forces) will be applied at joints, for example, see Fig. 2.

A frame is specified by giving the locations of all the nodes or joints. For this project, the nodes are specified in a file that contains a list of x-y coordinates like:

0.0 0.0

1.0 2.0

3.0 -2.0

each line contains the coordiante of one joint. The joints are numbered according to their appearance in the file, i.e. the first coordinates is for joint 1, second pair for joint 2, etc. The beams are specified by three pieces of information, an index of the joint at each end, and a number indicating which material properties are to be applied to this beam (more on that later). Thus, a beam connectivity file might look like:

1 2 1
3 7 1
11 114 5

where, in the first line, for aexample, the beam starts at node 1, connects to node 2, and uses material properties 1. The last beam in this example has one end at node 11, connecting to node 114, and uses material properties number 5. Each beam has three properties that define it (for this assignment, in reality there are several others). We will use the cross-sectional area, bending moment of inertia and Young's modulus as our three properties. Since is is common that many of the same types of beams are used in a structure, it is wasteful to list the full proprties for each beam. Instead, a list of material properties is tabulated, and each beam has an index to which properties to use. In the above table the last number indicates which beam properties in the array of properties should be used for that beam.

Once the structural geometry and material properties have been specified, the support conditions and loads must be specified. For this project, we provide files containing the necessary information, and functions to process them for you, so you needn't be too concerned about it here.

Posted Date: 3/11/2013 2:11:24 AM | Location : United States

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