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    Effect of Curvature on Stability of Curved Beams

    Source: Journal of Structural Engineering:;1987:;Volume ( 113 ):;issue: 006
    Author:
    Yeong‐Bin Yang
    ,
    Shyh‐Rong Kuo
    DOI: 10.1061/(ASCE)0733-9445(1987)113:6(1185)
    Publisher: American Society of Civil Engineers
    Abstract: This paper intends to derive the nonlinear differential equations of equilibrium for a horizontally curved I‐beam. Based on the principle of virtual displacements, the equilibrium of a bar is established for its deformed or buckled configuration using a Lagrangian approach. Central to the consideration of the effect of curvature is the expression of various quantities in cylindrical coordinates and the incorporation of radial stresses in the virtual work statement. The governing differential equations are obtained for the curved beam as the Euler‐Lagrange equations of the functional using a variational procedure. Rationality of the present theory is demonstrated for some typical examples, where the sources of errors in existing theories are traced. Also illustrated is the inconsistency involved in a conventional finite element analysis in which a curved beam is represented by several straight beam elements.
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      Effect of Curvature on Stability of Curved Beams

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    contributor authorYeong‐Bin Yang
    contributor authorShyh‐Rong Kuo
    date accessioned2017-05-08T20:52:32Z
    date available2017-05-08T20:52:32Z
    date copyrightJune 1987
    date issued1987
    identifier other%28asce%290733-9445%281987%29113%3A6%281185%29.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/30090
    description abstractThis paper intends to derive the nonlinear differential equations of equilibrium for a horizontally curved I‐beam. Based on the principle of virtual displacements, the equilibrium of a bar is established for its deformed or buckled configuration using a Lagrangian approach. Central to the consideration of the effect of curvature is the expression of various quantities in cylindrical coordinates and the incorporation of radial stresses in the virtual work statement. The governing differential equations are obtained for the curved beam as the Euler‐Lagrange equations of the functional using a variational procedure. Rationality of the present theory is demonstrated for some typical examples, where the sources of errors in existing theories are traced. Also illustrated is the inconsistency involved in a conventional finite element analysis in which a curved beam is represented by several straight beam elements.
    publisherAmerican Society of Civil Engineers
    titleEffect of Curvature on Stability of Curved Beams
    typeJournal Paper
    journal volume113
    journal issue6
    journal titleJournal of Structural Engineering
    identifier doi10.1061/(ASCE)0733-9445(1987)113:6(1185)
    treeJournal of Structural Engineering:;1987:;Volume ( 113 ):;issue: 006
    contenttypeFulltext
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