{"title":"Bending of Beams with Symmetrically Varying Mechanical Properties Under Generalized Load – Shear effect","authors":"K. Magnucki, J. Lewiński","doi":"10.24423/ENGTRANS.987.20190509","DOIUrl":null,"url":null,"abstract":"The paper is devoted to simply supported beams with symmetrically varying mechanical properties in the depth direction. Generalized load of the beams includes the load types from uniformly distributed to point load (three-point bending). This load is analytically described with the use of a certain function including a dimensionless parameter. The value of the parameter is decisive for the load type. The individual nonlinear “polynomial” hypothesis is applied to deformation of a planar cross section. Based on the definitions of the bending moment and the shear transverse force the differential equation of equilibrium is obtained. The equation is analytically solved and the deflections are calculated for an exemplary beam family. The results of the study are specified in tables.","PeriodicalId":38552,"journal":{"name":"Engineering Transactions","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Transactions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24423/ENGTRANS.987.20190509","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 7
Abstract
The paper is devoted to simply supported beams with symmetrically varying mechanical properties in the depth direction. Generalized load of the beams includes the load types from uniformly distributed to point load (three-point bending). This load is analytically described with the use of a certain function including a dimensionless parameter. The value of the parameter is decisive for the load type. The individual nonlinear “polynomial” hypothesis is applied to deformation of a planar cross section. Based on the definitions of the bending moment and the shear transverse force the differential equation of equilibrium is obtained. The equation is analytically solved and the deflections are calculated for an exemplary beam family. The results of the study are specified in tables.
期刊介绍：
Engineering Transactions (formerly Rozprawy Inżynierskie) is a refereed international journal founded in 1952. The journal promotes research and practice in engineering science and provides a forum for interdisciplinary publications combining mechanics with: Material science, Mechatronics, Biomechanics and Biotechnologies, Environmental science, Photonics, Information technologies, Other engineering applications. The journal publishes original papers covering a broad area of research activities including: experimental and hybrid techniques, analytical and numerical approaches. Review articles and special issues are also welcome. Following long tradition, all articles are peer reviewed and our expert referees ensure that the papers accepted for publication comply with high scientific standards. Engineering Transactions is a quarterly journal intended to be interesting and useful for the researchers and practitioners in academic and industrial communities.
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