A REFINED SHEAR DEFORMATION THEORY FOR FLEXURE OF THICK BEAMS
Keywords:
HYPERBOLIC SHEAR DEFORMATION THEORY, STATIC FLEXURE, GENERAL SOLUTION OF BEAMS, PROPORTIONALITY CONSTANT.Abstract
A HYPERBOLIC SHEAR DEFORMATION THEORY (HPSDT) TAKING INTO ACCOUNT TRANSVERSE SHEAR DEFORMATION EFFECTS, IS USED FOR THE STATIC FLEXURE ANALYSIS OF THICK ISOTROPIC BEAMS. THE DISPLACEMENT FIELD OF THE THEORY CONTAINS TWO VARIABLES. THE HYPERBOLIC SINE FUNCTION IS USED IN THE DISPLACEMENT FIELD IN TERMS OF THICKNESS COORDINATE TO REPRESENT SHEAR DEFORMATION.  THE TRANSVERSE SHEAR STRESS CAN BE OBTAINED DIRECTLY FROM THE USE OF CONSTITUTIVE RELATIONS, SATISFYING THE SHEAR STRESS-FREE BOUNDARY CONDITIONS AT TOP AND BOTTOM OF THE BEAM. HENCE, THE THEORY OBVIATES THE NEED OF SHEAR CORRECTION FACTOR. GOVERNING DIFFERENTIAL EQUATIONS AND BOUNDARY CONDITIONS OF THE THEORY ARE OBTAINED USING THE PRINCIPLE OF VIRTUAL WORK. GENERAL SOLUTIONS OF THICK ISOTROPIC SIMPLY SUPPORTED, CANTILEVER AND FIXED BEAMS SUBJECTED TO UNIFORMLY DISTRIBUTED AND CONCENTRATED LOADS ARE OBTAINED. EXPRESSIONS FOR TRANSVERSE DISPLACEMENT OF BEAMS ARE OBTAINED AND CONTRIBUTION DUE TO SHEAR DEFORMATION TO THE MAXIMUM TRANSVERSE DISPLACEMENT IS INVESTIGATED. THE RESULTS OF THE PRESENT THEORY ARE COMPARED WITH THOSE OF OTHER REFINED SHEAR DEFORMATION THEORIES OF BEAM TO VERIFY THE ACCURACY OF THE THEORY.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).