{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/45528"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/45528","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A general procedure for analysis of elastic rings in space","abstract":"The purpose of this thesis has been achieved. Vector notation has been used in developing the equations necessary for the analysis of three dimensional elastic rings. An elastic centroid for the elastic ring has been located with a tabular procedure for exacting the solution to the problem. For a comparison of the solutions between the method based on three elastic centroids with the method based on one elastic centroid, one need refer to Figures 7 and 10. Comparing the two methods, it is the author's opinion that the method herein presented is superior if for no other reason than simplicity. The development of the six equations can be readily followed and the tabular form of Figure 7 presented as an orderly means for obtaining the coefficients of the six unknowns. Figure 10 presents a method involving a similar tabular form as in Figure 7 along with the additional calculations that must be made before the correction moments and shears can be obtained. The necessity of these additional terms serves to obscure the physical significance of the final equations.","abstract_html":"The purpose of this thesis has been achieved. Vector notation has been used in developing the equations necessary for the analysis of three dimensional elastic rings. An elastic centroid for the elastic ring has been located with a tabular procedure for exacting the solution to the problem. For a comparison of the solutions between the method based on three elastic centroids with the method based on one elastic centroid, one need refer to Figures 7 and 10. Comparing the two methods, it is the author's opinion that the method herein presented is superior if for no other reason than simplicity. The development of the six equations can be readily followed and the tabular form of Figure 7 presented as an orderly means for obtaining the coefficients of the six unknowns. Figure 10 presents a method involving a similar tabular form as in Figure 7 along with the additional calculations that must be made before the correction moments and shears can be obtained. The necessity of these additional terms serves to obscure the physical significance of the final equations.","abstract_has_math":false,"creators":["Liessner, Walter Carl"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Applied Mechanics","degree_department":"Applied Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Pletta, Dan H."],"committee_members":["Pardue, Louis A.","Whittemore, John A."],"year":1957,"date_issued":"1957-10-14","date_published":"1957-10-14","updated_at":"2026-07-24T05:56:14Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-11072012-040243"],"render_values":[{"text":"etd-11072012-040243","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/45528","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Pletta, Dan H."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Pardue, Louis A.","Whittemore, John A."]},{"key":"dc:contributor.department","label":"Department","values":["Applied Mechanics"]},{"key":"dc:creator","label":"Author","values":["Liessner, Walter Carl"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:49:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:49:13Z","2012-11-07"]},{"key":"dc:date.issued","label":"Date","values":["1957-10-14"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"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":["Applied Mechanics"]},{"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"]},{"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.other","label":"Dc Identifier Other","values":["etd-11072012-040243"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/45528"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of this thesis has been achieved. Vector notation has been used in developing the equations necessary for the analysis of three dimensional elastic rings. An elastic centroid for the elastic ring has been located with a tabular procedure for exacting the solution to the problem. For a comparison of the solutions between the method based on three elastic centroids with the method based on one elastic centroid, one need refer to Figures 7 and 10. Comparing the two methods, it is the author's opinion that the method herein presented is superior if for no other reason than simplicity. The development of the six equations can be readily followed and the tabular form of Figure 7 presented as an orderly means for obtaining the coefficients of the six unknowns. Figure 10 presents a method involving a similar tabular form as in Figure 7 along with the additional calculations that must be made before the correction moments and shears can be obtained. The necessity of these additional terms serves to obscure the physical significance of the final equations."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A general procedure for analysis of elastic rings in space"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Pletta, Dan H."],"dc:contributor.committeemember":["Pardue, Louis A.","Whittemore, John A."],"dc:contributor.department":["Applied Mechanics"],"dc:creator":["Liessner, Walter Carl"],"dc:date.accessioned":["2014-03-14T21:49:13Z"],"dc:date.available":["2014-03-14T21:49:13Z","2012-11-07"],"dc:date.issued":["1957-10-14"],"dc:description.abstract":["The purpose of this thesis has been achieved. Vector notation has been used in developing the equations necessary for the analysis of three dimensional elastic rings. An elastic centroid for the elastic ring has been located with a tabular procedure for exacting the solution to the problem. For a comparison of the solutions between the method based on three elastic centroids with the method based on one elastic centroid, one need refer to Figures 7 and 10. Comparing the two methods, it is the author's opinion that the method herein presented is superior if for no other reason than simplicity. The development of the six equations can be readily followed and the tabular form of Figure 7 presented as an orderly means for obtaining the coefficients of the six unknowns. Figure 10 presents a method involving a similar tabular form as in Figure 7 along with the additional calculations that must be made before the correction moments and shears can be obtained. The necessity of these additional terms serves to obscure the physical significance of the final equations."],"dc:description.degree":["Master of Science"],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-11072012-040243"],"dc:identifier.uri":["http://hdl.handle.net/10919/45528"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["A general procedure for analysis of elastic rings in space"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Applied Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-24T05:56:14Z"}