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    On Timoshenko Beams of Rectangular Cross-Section

    Source: Journal of Applied Mechanics:;2004:;volume( 071 ):;issue: 003::page 359
    Author:
    James R. Hutchinson
    ,
    Professor Emeritus
    ,
    Life Mem. ASME
    DOI: 10.1115/1.1751186
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: It was recently shown that the shear coefficient for a rectangular Timoshenko beam is highly dependent on the aspect ratio of the beam. This research investigates the reasons for that behavior by comparison of the Timoshenko beam solution with a new three-dimensional solution for a simply supported beam. The new solution is a series solution that converges to any desired accuracy. Comparisons are also made to both elementary and Mindlin plates. The Mindlin plate solution is in excellent agreement with the three-dimensional solution for the simply supported case, and is used as a basis of comparison for a free-free beam. It is found that a shear coefficient which would cause matching of the three-dimensional and Mindlin solutions would have to be a function of the wave length as well as the aspect ratio. Physical explanations are given for the high dependence on aspect ratio and for the dependence on wave length.
    keyword(s): Stress , Waves , Poisson ratio , Shear (Mechanics) , Equations , Frequency , Boundary-value problems , Plates (structures) , Thickness AND Simply supported beams ,
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      On Timoshenko Beams of Rectangular Cross-Section

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    http://yetl.yabesh.ir/yetl1/handle/yetl/129497
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    contributor authorJames R. Hutchinson
    contributor authorProfessor Emeritus
    contributor authorLife Mem. ASME
    date accessioned2017-05-09T00:12:07Z
    date available2017-05-09T00:12:07Z
    date copyrightMay, 2004
    date issued2004
    identifier issn0021-8936
    identifier otherJAMCAV-26577#359_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/129497
    description abstractIt was recently shown that the shear coefficient for a rectangular Timoshenko beam is highly dependent on the aspect ratio of the beam. This research investigates the reasons for that behavior by comparison of the Timoshenko beam solution with a new three-dimensional solution for a simply supported beam. The new solution is a series solution that converges to any desired accuracy. Comparisons are also made to both elementary and Mindlin plates. The Mindlin plate solution is in excellent agreement with the three-dimensional solution for the simply supported case, and is used as a basis of comparison for a free-free beam. It is found that a shear coefficient which would cause matching of the three-dimensional and Mindlin solutions would have to be a function of the wave length as well as the aspect ratio. Physical explanations are given for the high dependence on aspect ratio and for the dependence on wave length.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleOn Timoshenko Beams of Rectangular Cross-Section
    typeJournal Paper
    journal volume71
    journal issue3
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.1751186
    journal fristpage359
    journal lastpage367
    identifier eissn1528-9036
    keywordsStress
    keywordsWaves
    keywordsPoisson ratio
    keywordsShear (Mechanics)
    keywordsEquations
    keywordsFrequency
    keywordsBoundary-value problems
    keywordsPlates (structures)
    keywordsThickness AND Simply supported beams
    treeJournal of Applied Mechanics:;2004:;volume( 071 ):;issue: 003
    contenttypeFulltext
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