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The cyclic plastic moment of [P-M2-M3|P-M2-M3 hinges] and [fiber|kb:Caltrans vs. fiber hinge] [hinges|kb:Hinge] will lead to ratcheting behavior, or accumulation of plastic deformation, in the axial direction. According to plasticity theory and the behavior of structural systems, this type of [nonlinear|kb:Nonlinear] response is expected.

Ratcheting is a real effect in which the length of a reinforced-concrete member tends to grow in each direction under cyclic bending. On the tension side, steel yields and concrete cracks such that load transfers only through steel reinforcement. On the compression side, both steel and concrete carry load, causing less compressive deformation than tensile. If restraint prevents the member from axial elongation, additional compressive forces will result. Otherwise, with each displacement excursion, axial lengthening (on the tension side of the neutral axis) will exceed axial shortening (on the compressive side), leading to the accumulation of plastic axial strain.

Axial ratcheting occurs because plastic yielding keeps some tensile deformation from being recovered upon unloading. [Fiber hinges|kb:Caltrans vs. fiber hinge] capture this effect directly by evaluating the localized behavior of longitudinal concrete and steel fibers. [P-M2-M3 hinges|kb:P-M2-M3 hinges] capture ratcheting through formulation associated with plasticity theory and the assumption that plastic deformation occurs normal to the yield surface. This normal includes an axial component except at the balance point, where pure bending occurs.

Ratcheting can be observed in other structural configurations, such as with pile-foundation sinking under cyclic bending.


h1. See Also

* [tp:Hinge response when yield point changes] test problem, load cases 4a, 4b, and 4c


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*Related Incidents:*
* {incident:no=18341|comment=Ratcheting for PMM hinges explained by bm.}
* {incident:no=48618|comment=Additional explanation for interacting and fiber PMM hinges.}
** {email:date=10/16/2012|from=bm|to=ma|subject=fiber vs. PMM hinge, axial effects|comment=fiber vs. PMM hinge, axial effects|id=9538306}
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