{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/45549"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/45549","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Effects of shear deformations on the vibrational frequencies of wide-flanged structures","abstract":"The well-known Timoshenko beam equations (which include transverse shear deformation and rotary inertia effects) are extended for a wide-flanged structure to include the additional shear lag deformation of the flanges; thus, cross-sections of the beam are allowed to distort instead of remaining plane sections. The effect of relative flange bending (bending of the flanges relative to the web) is also included and the integro-differential equations appropriate to the problem are derived. The frequency equation is given in closed form (neglecting the relative flange bending) and solutions for various values of the nondimensional parameters are given. A reduction of the elementary frequency by as much as 40 percent in the first mode is shown.","abstract_html":"The well-known Timoshenko beam equations (which include transverse shear deformation and rotary inertia effects) are extended for a wide-flanged structure to include the additional shear lag deformation of the flanges; thus, cross-sections of the beam are allowed to distort instead of remaining plane sections. The effect of relative flange bending (bending of the flanges relative to the web) is also included and the integro-differential equations appropriate to the problem are derived. The frequency equation is given in closed form (neglecting the relative flange bending) and solutions for various values of the nondimensional parameters are given. A reduction of the elementary frequency by as much as 40 percent in the first mode is shown.","abstract_has_math":false,"creators":["Weidman, Deene J."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1961,"date_issued":"1961-03-05","date_published":"1961-03-05","updated_at":"2026-07-22T22:18:49Z","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-11092012-040048"],"render_values":[{"text":"etd-11092012-040048","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/45549","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Weidman, Deene J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:49:15Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:49:15Z","2012-11-09"]},{"key":"dc:date.issued","label":"Date","values":["1961-03-05"]},{"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":["Engineering 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-11092012-040048"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/45549"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The well-known Timoshenko beam equations (which include transverse shear deformation and rotary inertia effects) are extended for a wide-flanged structure to include the additional shear lag deformation of the flanges; thus, cross-sections of the beam are allowed to distort instead of remaining plane sections. The effect of relative flange bending (bending of the flanges relative to the web) is also included and the integro-differential equations appropriate to the problem are derived. The frequency equation is given in closed form (neglecting the relative flange bending) and solutions for various values of the nondimensional parameters are given. A reduction of the elementary frequency by as much as 40 percent in the first mode is shown."]},{"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":["Effects of shear deformations on the vibrational frequencies of wide-flanged structures"]}]}],"canonical_facts":{"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Weidman, Deene J."],"dc:date.accessioned":["2014-03-14T21:49:15Z"],"dc:date.available":["2014-03-14T21:49:15Z","2012-11-09"],"dc:date.issued":["1961-03-05"],"dc:description.abstract":["The well-known Timoshenko beam equations (which include transverse shear deformation and rotary inertia effects) are extended for a wide-flanged structure to include the additional shear lag deformation of the flanges; thus, cross-sections of the beam are allowed to distort instead of remaining plane sections. The effect of relative flange bending (bending of the flanges relative to the web) is also included and the integro-differential equations appropriate to the problem are derived. The frequency equation is given in closed form (neglecting the relative flange bending) and solutions for various values of the nondimensional parameters are given. 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