A kind of displacement mode of spatial beam element considering the effect of warping and distortion

A kind of displacement mode of spatial beam element considering the effect of warping and distortion | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A kind of displacement mode of spatial beam element considering the effect of warping and distortion Jiaxin Lu, Manyi Liu, Jun Dong, Yao Zhang, Kun Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7109621/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Based on the theory of elasticity and torsional geometry, the displacement mode of a single node 6-degree-of-freedom,low order spatial beam element with the ability to calculate bending distortion was reproduced,and the construction method of Bm_ZY was improved, realizing its application on any cross-section. Furthermore,the accuracy of Gaussian integration was explored through the self-developed ZQFEM finite element program, and the contributions of shear and bending deformations to torsional stiffness were separated. Finally, the influence of cross-sectional shape and wall thickness on buckling distortion was studied through a cantilever beam example, and the reliability of the commercial software Midas Civil was explored. The analysis results indicate that the Bm_ZY element has the ability to analyze the coupling effects of torsion, shear, and bending. Gaussian integration using more than eight points reduced weak integration errors to within 10%. Numerical examples once again confirm that the constrained torsional effect significantly increases the torsional stiffness of the cross-section; The Bm_ZY unit has a exhibits consistent deformation behavior under applied stress. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing Python Element construction Finite element analysis Torsion Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7109621","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":492288543,"identity":"486e8ae3-37a9-4c74-9083-76c82a1f268d","order_by":0,"name":"Jiaxin Lu","email":"","orcid":"","institution":"Liaoning Technical University","correspondingAuthor":false,"prefix":"","firstName":"Jiaxin","middleName":"","lastName":"Lu","suffix":""},{"id":492288544,"identity":"4b180b23-3590-4de7-a1d5-9bf72e7f4255","order_by":1,"name":"Manyi Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtUlEQVRIiWNgGAWjYBACPmYGBmYQgx+IJYjSwgbTItlAtBYGqBaDA0RrYecx/FxQccdu8/GzD2/8YLCT020g6DAeY+kZZ54lbzuTbmzZw5BsbHaAsBYzZt62w8lmN9jYpBkYDiRuI07Lv8PJxjNI09Jw2M5AgngtbMXSPMcOJ0icSWO27DEgwi/8/Ic3fuapOWzP336M8caPCjs5glpgILEBTBkQqRwE7ElQOwpGwSgYBSMNAACOCTQ6mk40hgAAAABJRU5ErkJggg==","orcid":"","institution":"Liaoning Technical University","correspondingAuthor":true,"prefix":"","firstName":"Manyi","middleName":"","lastName":"Liu","suffix":""},{"id":492288545,"identity":"cf8573ef-0769-4a43-a539-5fb4c4a70080","order_by":2,"name":"Jun Dong","email":"","orcid":"","institution":"Beijing University of Civil Engineering and Architecture","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Dong","suffix":""},{"id":492288546,"identity":"633acb5e-8273-4e02-ba32-b669e53e4f86","order_by":3,"name":"Yao Zhang","email":"","orcid":"","institution":"Beijing University of Civil Engineering and Architecture","correspondingAuthor":false,"prefix":"","firstName":"Yao","middleName":"","lastName":"Zhang","suffix":""},{"id":492288547,"identity":"095a3f83-2a42-425f-86fe-ff54c7e04177","order_by":4,"name":"Kun Chen","email":"","orcid":"","institution":"Beijing University of Civil Engineering and Architecture","correspondingAuthor":false,"prefix":"","firstName":"Kun","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2025-07-12 17:53:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7109621/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7109621/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88804109,"identity":"7b42a391-22a6-4825-85eb-53f1c510475f","added_by":"auto","created_at":"2025-08-11 14:39:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":664396,"visible":true,"origin":"","legend":"","description":"","filename":"beamelementwarping.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7109621/v1_covered_8dabddb8-9a7b-4eb8-a7bf-cdf088799ca4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A kind of displacement mode of spatial beam element considering the effect of warping and distortion","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Python, Element construction, Finite element analysis, Torsion","lastPublishedDoi":"10.21203/rs.3.rs-7109621/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7109621/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Based on the theory of elasticity and torsional geometry, the displacement mode of a single node 6-degree-of-freedom,low order spatial beam element with the ability to calculate bending distortion was reproduced,and the construction method of Bm_ZY was improved, realizing its application on any cross-section. 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