{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/74079"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/74079","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Stress analysis of parabolic arches and their dynamic behavior","abstract":"This thesis is concerned with both the static and dynamic analysis of parabolic arches. In the dynamic part, special attention is given to the free vibration of such arches. The following procedure is followed. The loading conditions are assumed and a infinitesimal segment of the arch is taken so as the differential equations relating deflections and slope changes on both ends of the segment are developed. These obtain a set of general equations for elastic parabolic arches. In dynamics, the equations of general curved structure are developed through considerations of dynamic equilibrium. A sudden removal of loading is assumed to cause the structure to vibrate freely. Then, a method of separating variables for partial differential equations is used to get the equations of deflection components. Each special characteristic function is derived for each special set of boundary conditions so as to get an unlimited number of modes of free vibrations. The Fourier series is employed to determine the coefficients of the dynamic equations, and to get a series-form solution for deflections. Finally, two numerical examples are given to represent the practical application. Two kinds of parabolic arches, one with two-hinged supports and the other with fixed-ends are considered in each procedure.","abstract_html":"This thesis is concerned with both the static and dynamic analysis of parabolic arches. In the dynamic part, special attention is given to the free vibration of such arches. The following procedure is followed. The loading conditions are assumed and a infinitesimal segment of the arch is taken so as the differential equations relating deflections and slope changes on both ends of the segment are developed. These obtain a set of general equations for elastic parabolic arches. In dynamics, the equations of general curved structure are developed through considerations of dynamic equilibrium. A sudden removal of loading is assumed to cause the structure to vibrate freely. Then, a method of separating variables for partial differential equations is used to get the equations of deflection components. Each special characteristic function is derived for each special set of boundary conditions so as to get an unlimited number of modes of free vibrations. The Fourier series is employed to determine the coefficients of the dynamic equations, and to get a series-form solution for deflections. Finally, two numerical examples are given to represent the practical application. Two kinds of parabolic arches, one with two-hinged supports and the other with fixed-ends are considered in each procedure.","abstract_has_math":false,"creators":["Hou, Shou-nien"],"institution":"Virginia Polytechnic Institute","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Structural Engineering","degree_department":"Structural Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1958,"date_issued":"1958","date_published":"1958","updated_at":"2026-07-22T22:20:02Z","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/10919/74079","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Structural Engineering"]},{"key":"dc:creator","label":"Author","values":["Hou, Shou-nien"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-01-10T20:34:42Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-01-10T20:34:42Z"]},{"key":"dc:date.issued","label":"Date","values":["1958"]},{"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":["Structural 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/10919/74079"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is concerned with both the static and dynamic analysis of parabolic arches. In the dynamic part, special attention is given to the free vibration of such arches. The following procedure is followed. The loading conditions are assumed and a infinitesimal segment of the arch is taken so as the differential equations relating deflections and slope changes on both ends of the segment are developed. These obtain a set of general equations for elastic parabolic arches. In dynamics, the equations of general curved structure are developed through considerations of dynamic equilibrium. A sudden removal of loading is assumed to cause the structure to vibrate freely. Then, a method of separating variables for partial differential equations is used to get the equations of deflection components. Each special characteristic function is derived for each special set of boundary conditions so as to get an unlimited number of modes of free vibrations. The Fourier series is employed to determine the coefficients of the dynamic equations, and to get a series-form solution for deflections. Finally, two numerical examples are given to represent the practical application. Two kinds of parabolic arches, one with two-hinged supports and the other with fixed-ends are considered in each procedure."]},{"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":["Stress analysis of parabolic arches and their dynamic behavior"]}]}],"canonical_facts":{"dc:contributor.department":["Structural Engineering"],"dc:creator":["Hou, Shou-nien"],"dc:date.accessioned":["2017-01-10T20:34:42Z"],"dc:date.available":["2017-01-10T20:34:42Z"],"dc:date.issued":["1958"],"dc:description.abstract":["This thesis is concerned with both the static and dynamic analysis of parabolic arches. In the dynamic part, special attention is given to the free vibration of such arches. The following procedure is followed. The loading conditions are assumed and a infinitesimal segment of the arch is taken so as the differential equations relating deflections and slope changes on both ends of the segment are developed. These obtain a set of general equations for elastic parabolic arches. In dynamics, the equations of general curved structure are developed through considerations of dynamic equilibrium. A sudden removal of loading is assumed to cause the structure to vibrate freely. Then, a method of separating variables for partial differential equations is used to get the equations of deflection components. Each special characteristic function is derived for each special set of boundary conditions so as to get an unlimited number of modes of free vibrations. The Fourier series is employed to determine the coefficients of the dynamic equations, and to get a series-form solution for deflections. Finally, two numerical examples are given to represent the practical application. Two kinds of parabolic arches, one with two-hinged supports and the other with fixed-ends are considered in each procedure."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/74079"],"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":["Stress analysis of parabolic arches and their dynamic behavior"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Structural Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-22T22:20:02Z"}