{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/76263"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/76263","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Analysis of a circular arch by the Rayleigh-Ritz method","abstract":"The Rayleigh-Ritz method is a convenient tool for the analysis of deflections in structures subjected to external forces. Bending moment relations can be developed and reliable values obtained for bending moments. In this thesis the Rayleigh-Ritz method is used for the analysis of a single-span, pin-connected circular arch subjected to uniform load along the arch. The method is explained, equations for deflections and moments are developed and the results of an illustrated problem are tabulated. The illustrated problem is also solved by a conventional method using the dummy load and virtual work techniques. Results are compared and found to be good. In both methods, account is taken of bending and axial forces; shear distortion is neglected. For the Rayleigh-Ritz method where undetermined coefficients are evaluated, a tabulation of the rate of convergence is presented. Computer programs for both methods are included.","abstract_html":"The Rayleigh-Ritz method is a convenient tool for the analysis of deflections in structures subjected to external forces. Bending moment relations can be developed and reliable values obtained for bending moments. In this thesis the Rayleigh-Ritz method is used for the analysis of a single-span, pin-connected circular arch subjected to uniform load along the arch. The method is explained, equations for deflections and moments are developed and the results of an illustrated problem are tabulated. The illustrated problem is also solved by a conventional method using the dummy load and virtual work techniques. Results are compared and found to be good. In both methods, account is taken of bending and axial forces; shear distortion is neglected. For the Rayleigh-Ritz method where undetermined coefficients are evaluated, a tabulation of the rate of convergence is presented. Computer programs for both methods are included.","abstract_has_math":false,"creators":["Chang, Ming-ke"],"institution":"Virginia Polytechnic Institute","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Civil Engineering","degree_department":"Civil Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1966,"date_issued":"1966","date_published":"1966","updated_at":"2026-07-22T22:19:31Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/76263","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Civil Engineering"]},{"key":"dc:creator","label":"Author","values":["Chang, Ming-ke"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-03-10T20:13:48Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-03-10T20:13:48Z"]},{"key":"dc:date.issued","label":"Date","values":["1966"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Civil Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/76263"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Rayleigh-Ritz method is a convenient tool for the analysis of deflections in structures subjected to external forces. Bending moment relations can be developed and reliable values obtained for bending moments. In this thesis the Rayleigh-Ritz method is used for the analysis of a single-span, pin-connected circular arch subjected to uniform load along the arch. The method is explained, equations for deflections and moments are developed and the results of an illustrated problem are tabulated. The illustrated problem is also solved by a conventional method using the dummy load and virtual work techniques. Results are compared and found to be good. In both methods, account is taken of bending and axial forces; shear distortion is neglected. For the Rayleigh-Ritz method where undetermined coefficients are evaluated, a tabulation of the rate of convergence is presented. Computer programs for both methods are included."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Analysis of a circular arch by the Rayleigh-Ritz method"]}]}],"canonical_facts":{"dc:contributor.department":["Civil Engineering"],"dc:creator":["Chang, Ming-ke"],"dc:date.accessioned":["2017-03-10T20:13:48Z"],"dc:date.available":["2017-03-10T20:13:48Z"],"dc:date.issued":["1966"],"dc:description.abstract":["The Rayleigh-Ritz method is a convenient tool for the analysis of deflections in structures subjected to external forces. Bending moment relations can be developed and reliable values obtained for bending moments. In this thesis the Rayleigh-Ritz method is used for the analysis of a single-span, pin-connected circular arch subjected to uniform load along the arch. The method is explained, equations for deflections and moments are developed and the results of an illustrated problem are tabulated. The illustrated problem is also solved by a conventional method using the dummy load and virtual work techniques. Results are compared and found to be good. In both methods, account is taken of bending and axial forces; shear distortion is neglected. For the Rayleigh-Ritz method where undetermined coefficients are evaluated, a tabulation of the rate of convergence is presented. Computer programs for both methods are included."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/76263"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Analysis of a circular arch by the Rayleigh-Ritz method"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-22T22:19:31Z"}