?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%2F18186%2F&rft.title=In-Plane+Nonlinear+Stability+Analysis+of+Shallow+Arches+with+Elastic+Supports&rft.creator=Gu%2C+Mengzhe&rft.description=Classical+buckling+theory+has+been+researched+extensively+to+determine+the+in-plane+buckling+behavior+of+parabolic%2C+circular+and+catenary+arches.+To+simplify+the+analyses%2C+several+assumptions+are+made.+However%2C+these+simplified+assumptions+are+not+valid+for+shallow+arches+under+significant+vertical+load+which+are+characterized+by+their+high+geometric+non-linearity.+Prebuckling+displacements+should+be+accounted+for+for+accurate+in-plane+buckling+analysis+of+shallow+arches.+%0D%0AIn+reality%2C+the+supports+of+arches+are+not+necessarily+pin-+or+fixed-connections.+An+arch+may+be+supported+by+elastic+foundations+or+other+structural+elements+that+provide+elastic+restraint+at+the+supports.+In+this+work%2C+elastic+foundations+are+represented+by+horizontal+and+rotational+springs.+These+support+restraints+may+have+a+significant+influence+on+the+in-plane+buckling+behavior.%0D%0AIn-plane+non-linear+stability+analysis+of+shallow+arches+is+performed+in+this+thesis.+Energy+equations+are+derived+by+considering+the+total+potential+energy+of+the+arch+structure.+The+vanishing+of+first+variation+of+total+potential+energy+characterizes+the+equilibrium+state%2C+while+the+second+variation+of+total+potential+energy+falling+to+zero+represents+the+transition+from+a+stable+state+to+an+unstable+state%2C+from+which+the+critical+condition+may+be+obtained.%0D%0AFinally%2C+this+thesis+discusses+the+effects+of+horizontal+and+rotational+restraints+in+calculation+of+in-plane+buckling+strength+of+shallow+arches.+Several+examples+are+considered+to+illustrate+the+application+of+the+theory%2C+presented+in+this+research+for+general+practice.&rft.date=2013-06-27&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%2F18186%2F1%2FMengzhe_Gu_ETD_2013.pdf&rft.identifier=++Gu%2C+Mengzhe++(2013)+In-Plane+Nonlinear+Stability+Analysis+of+Shallow+Arches+with+Elastic+Supports.++Master's+Thesis%2C+University+of+Pittsburgh.++++(Unpublished)++