CEE/CNE 210—Statics SSEBE Mechanics Group     Computing Project 2 Beam Analysis Program  The computing project Beam Analysis deals with load placement at various points along a beam

Computing Project 2

Beam Analysis

Program 

The computing project Beam Analysis deals with load placement at various points along a beam.  The concept is to model the relationship between location of load placement and the reaction forces at the end of the beam.  The location of a load has significant impact on the magnitude of the reaction forces.  Take the following beam diagram:

The steel beam is supported by cables AB and CD and a ball-and-socket joint at O.  The position of the vertical point load, P influences the reaction at O as well as the tension in each cable.

What you need to do

For this computing project, first you need to derive the equations for the tension in cable AB, the tension in cable CD and the reaction at O in terms of x, which represents the placement of the point load, P, measured from the axis origin, point O.  These equations can be implemented into your MATLAB program Beam.m in a while loop.  Use the while loop to vary the value of x between 0 and 6 m.  You should be able to get this working by adding only a few lines to the template code we have provided for you.

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Once you get your code working, use it to study how the reaction force, R changes with the value of x.  Determine the value of x, where the ratio R/P is minimum, where R represents the magnitude of the total reaction at O.  Create a plot to show how this ratio changes as x changes.

Then do some research and find a standard value for weight of a W8x24 beam.  Incorporate the self-weight value into your equations and then into your program (use correct units).  Discuss the differences between neglecting self-weight and including self-weight.  

You then need to explore this program by changing around parameters.  Your report will be evaluated based on your insight and the interest of your study.  This offers you the ability to discover and explore how loads on a beam work.  For example, you could change your code to account for placement of multiple loads or move the location of the cables.

Report

Write a report documenting your work and the results (in accord with the specifications given in the document CEE210 Guidelines for Computing Projects).  Include figures, plots, and results.  Discuss your discoveries and explorations.  Upload your report to Blackboard prior to the deadline.

Upload your .m program file to Blackboard as well and follow all of the typical submittal instructions for Statics Computing Projects.

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