?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fd-scholarship-dev.library.pitt.edu%2F7028%2F&rft.title=ELASTIC+FLEXURAL-TORSIONAL+BUCKLING+ANALYSIS+USING+FINITE+ELEMENT+METHOD+AND+OBJECT-ORIENTED+TECHNOLOGY+WITH+C%2FC%2B%2B&rft.creator=Roberts%2C+Erin+Renee&rft.description=Flexural-torsional+buckling+is+an+important+limit+state+that+must+be+considered+in+structural+steel+design.+Flexural-torsional+buckling+occurs+when+a+structural+member+experiences+significant+out-of-plane+bending+and+twisting.+This+type+of+failure+occurs+suddenly+in+members+with+a+much+greater+in-plane+bending+stiffness+than+torsional+or+lateral+bending+stiffness.+Flexural-torsional+buckling+loads+may+be+predicted+using+energy+methods.+This+thesis+considers+the+total+potential+energy+equation+for+the+flexural-torsional+buckling+of+a+beam-column+element.+The+energy+equation+is+formulated+by+summing+the+strain+energy+and+the+potential+energy+of+the+external+loads.+Setting+the+second+variation+of+the+total+potential+energy+equation+equal+to+zero+provides+the+equilibrium+position+where+the+member+transitions+from+a+stable+state+to+an+unstable+state.+The+finite+element+method+is+applied+in+conjunction+with+the+energy+method+to+analyze+the+flexural-torsional+buckling+problem.+To+apply+the+finite+element+method%2C+the+displacement+functions+are+assumed+to+be+cubic+polynomials%2C+and+the+shape+functions+are+used+to+derive+the+element+stiffness+and+element+geometric+stiffness+matrices.+The+element+stiffness+and+geometric+stiffness+matrices+are+assembled+to+obtain+the+global+stiffness+matrices+of+the+structure.+The+final+finite+element+equation+obtained+is+in+the+form+of+an+eigenvalue+problem.+The+flexural-torsional+buckling+loads+of+the+structure+are+determined+by+solving+for+the+eigenvalue+of+the+equation.+The+finite+element+method+is+compatible+with+software+development+so+that+computer+technology+may+be+utilized+to+aid+in+the+analysis+process.+One+of+the+most+preferred+types+of+software+development+is+the+object-oriented+approach.+Object-oriented+technology+is+a+technique+of+organizing+the+software+around+real+world+objects.+An+existing+finite+element+software+package+which+calculates+the+elastic+flexural-torsional+buckling+loads+of+a+plane+frame+was+obtained+from+previous+research.+This+program+is+refactored+into+an+object-oriented+design+to+improve+the+structure+of+the+software+and+increase+its+flexibility.+Several+examples+are+presented+to+compare+the+results+of+the+software+package+to+existing+solutions.+These+examples+show+that+the+program+provides+acceptable+results+when+analyzing+a+beam-column+or+plane+frame+structure+subjected+to+concentrated+moments+and+concentrated%2C+axial%2C+and+distributed+loads.&rft.date=2004-06-09&rft.type=University+of+Pittsburgh+ETD&rft.type=PeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fd-scholarship-dev.library.pitt.edu%2F7028%2F1%2Froberts_etd2004.pdf&rft.identifier=++Roberts%2C+Erin+Renee++(2004)+ELASTIC+FLEXURAL-TORSIONAL+BUCKLING+ANALYSIS+USING+FINITE+ELEMENT+METHOD+AND+OBJECT-ORIENTED+TECHNOLOGY+WITH+C%2FC%2B%2B.++Master's+Thesis%2C+University+of+Pittsburgh.++++(Unpublished)++