?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%2F9926%2F&rft.title=LATERAL-TORSIONAL+BUCKLING+OF+STRUCTURES+WITH+MONOSYMMETRIC+CROSS-SECTIONS&rft.creator=Vensko%2C+Matthew+John&rft.description=Lateral-torsional+buckling+is+a+method+of+failure+that+occurs+when+the+in-plane+bending+capacity+of+a+member+exceeds+its+resistance+to+out-of-plane+lateral+buckling+and+twisting.+The+lateral-torsional+buckling+of+beam-columns+with+doubly-symmetric+cross-sections+is+a+topic+that+has+been+long+discussed+and+well+covered.+The+buckling+of+members+with+monosymmetric+cross-sections+is+an+underdeveloped+topic%2C+with+its+derivations+complicated+by+the+fact+that+the+centroid+and+the+shear+center+of+the+cross-section+do+not+coincide.+In+this+paper%2C+the+total+potential+energy+equation+of+a+beam-column+element+with+a+monosymmetric+cross-section+will+be+derived+to+predict+the+lateral-torsional+buckling+load.+The+total+potential+energy+equation+is+the+sum+of+the+strain+energy+and+the+potential+energy+of+the+external+loads.+The+theorem+of+minimum+total+potential+energy+exerts+that+setting+the+second+variation+of+this+equation+equal+to+zero+will+represent+a+transition+from+a+stable+to+an+unstable+state.+The+buckling+loads+can+then+be+identified+when+this+transition+takes+place.+This+thesis+will+derive+energy+equations+in+both+dimensional+and+non-dimensional+forms+assuming+that+the+beam-column+is+without+prebuckling+deformations.+This+dimensional+buckling+equation+will+then+be+expanded+to+include+prebuckling+deformations.+The+ability+of+these+equations+to+predict+the+lateral-torsional+buckling+loads+of+a+structure+is+demonstrated+for+different+loading+and+boundary+conditions.+The+accuracy+of+these+predictions+is+dependent+on+the+ability+to+select+a+suitable+shape+function+to+mimic+the+buckled+shape+of+the+beam-column.+The+results+provided+by+the+buckling+equations+derived+in+this+thesis%2C+using+a+suitable+shape+function%2C+are+compared+to+examples+in+existing+literature+considering+the+same+boundary+and+loading+conditions.The+finite+element+method+is+then+used%2C+along+with+the+energy+equations%2C+to+derive+element+elastic+and+geometric+stiffness+matrices.+These+element+stiffness+matrices+can+be+transformed+into+global+stiffness+matrices.+Boundary+conditions+can+then+be+enforced+and+a+generalized+eigenvalue+problem+can+then+be+used+to+determine+the+buckling+loads.+The+element+elastic+and+geometric+stiffness+matrices+are+presented+in+this+thesis+so+that+future+research+can+apply+them+to+a+computer+software+program+to+predict+lateral-torsional+buckling+loads+of+complex+systems+containing+members+with+monosymmetric+cross-sections.&rft.date=2009-01-28&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%2F9926%2F1%2Fvensko_matt_j_2008.pdf&rft.identifier=++Vensko%2C+Matthew+John++(2009)+LATERAL-TORSIONAL+BUCKLING+OF+STRUCTURES+WITH+MONOSYMMETRIC+CROSS-SECTIONS.++Master's+Thesis%2C+University+of+Pittsburgh.++++(Unpublished)++