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    Stiffness-Matrix Formulation of Beams with Shear Effect on Elastic Foundation

    Source: Journal of Structural Engineering:;1995:;Volume ( 121 ):;issue: 009
    Author:
    Metin Aydoğan
    DOI: 10.1061/(ASCE)0733-9445(1995)121:9(1265)
    Publisher: American Society of Civil Engineers
    Abstract: A stiffness matrix for a beam element with shear effect on an elastic foundation is developed using the differential-equation approach for plane-frame analysis. Small-displacement theory and linear-elastic material are assumed. The contribution of the shear stresses to the deflection of the beam in addition to the bending stresses is considered. Shear effect is represented by a second-order term of the derivative of beam deflection in the differential equation. This fact is also taken into account in the boundary conditions of the beam element. The complex variables are used in the solution of the differential equation. Stiffness and loading matrices for a beam element resting on Winkler foundation are derived by means of a computer program coded in FORTRAN language. Using this element, the effects of the shear forces on deflections and internal forces in the beams on an elastic foundation are investigated. The results of this finite-element analysis are exact for the Winkler assumption. It is shown that the deflections due to shear effect are influenced particularly with the modulus of the foundation and for the beams that have small span to height ratio. Also, numerical examples are given to demonstrate this fact.
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      Stiffness-Matrix Formulation of Beams with Shear Effect on Elastic Foundation

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    http://yetl.yabesh.ir/yetl1/handle/yetl/32303
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    contributor authorMetin Aydoğan
    date accessioned2017-05-08T20:56:03Z
    date available2017-05-08T20:56:03Z
    date copyrightSeptember 1995
    date issued1995
    identifier other%28asce%290733-9445%281995%29121%3A9%281265%29.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/32303
    description abstractA stiffness matrix for a beam element with shear effect on an elastic foundation is developed using the differential-equation approach for plane-frame analysis. Small-displacement theory and linear-elastic material are assumed. The contribution of the shear stresses to the deflection of the beam in addition to the bending stresses is considered. Shear effect is represented by a second-order term of the derivative of beam deflection in the differential equation. This fact is also taken into account in the boundary conditions of the beam element. The complex variables are used in the solution of the differential equation. Stiffness and loading matrices for a beam element resting on Winkler foundation are derived by means of a computer program coded in FORTRAN language. Using this element, the effects of the shear forces on deflections and internal forces in the beams on an elastic foundation are investigated. The results of this finite-element analysis are exact for the Winkler assumption. It is shown that the deflections due to shear effect are influenced particularly with the modulus of the foundation and for the beams that have small span to height ratio. Also, numerical examples are given to demonstrate this fact.
    publisherAmerican Society of Civil Engineers
    titleStiffness-Matrix Formulation of Beams with Shear Effect on Elastic Foundation
    typeJournal Paper
    journal volume121
    journal issue9
    journal titleJournal of Structural Engineering
    identifier doi10.1061/(ASCE)0733-9445(1995)121:9(1265)
    treeJournal of Structural Engineering:;1995:;Volume ( 121 ):;issue: 009
    contenttypeFulltext
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