Beam Deflections via Computer Algebra Systems

摘要

Computer algebra software can be used to replace the traditional paper andpencil approach for generating mathematical symbolic solutions. The user must only define problems in a software understandable format, and then the computer rapidly performs the actual calculations. Computer algebra software can be used to supplement traditional solution techniques in mechanics of materials courses.Beam deflection is a topic normally included in undergraduate mechanics of materials courses. Although most mechanics of materials texts include a number of beam deflection solutionmethods, studentsare normally shown only one, or possibly two methods due to course time constraints.Beam deflections at any point along the length of a beam can be determined using the double-integration method, however a number of dependent solution steps are required to develop the deflection equation. A plot of the deflection curve can then be created from the deflection equation. Unfortunately, developing deflection curves using the double-integration method can be both long and tedious if done by hand, and any changes to the original beam loading will require that all calculations be repeated.Computer algebra software can be used to help automate the beam deflection process. Once a moment equation has been developed, the software is used to perform the integrations, solve for the constants of integration, develop the final deflection equation and then plot a deflection curve. The rapid computational speed of the software allows the user to analyze a large number of problems in a minimum amount of time.An example problem is included to illustrate using computer algebra software as a supplement to traditional double-integration beam deflection hand calculations.