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{{distinguish|living hinge}}
{{distinguish|living hinge}}
[[File:plastic hinges.jpg|thumb|300px|Diagram of a structure featuring plastic hinges]]
[[File:plastic hinges.jpg|thumb|300px|Diagram of a structure featuring plastic hinges]]
In the [[structural engineering]] [[beam theory]], '''plastic hinge''' is the deformation of a section of a [[Beam (structure)|beam]] where [[plastic bending]] occurs.<ref>{{Cite book

In the [[structural engineering]] [[beam theory]], the term "plastic hinge" is used to describe the deformation of a section of a [[Beam (structure)|beam]] where [[plastic bending]] occurs.<ref>{{Cite book
| edition = 2
| edition = 2
| publisher = Butterworth-Heinemann
| publisher = Butterworth-Heinemann
Line 10: Line 9:
| title = Structural and Stress Analysis, Second Edition
| title = Structural and Stress Analysis, Second Edition
| date = 2005-04-29
| date = 2005-04-29
}}</ref> In [[earthquake engineering]] '''plastic hinge''' is also a type of energy [[Damping ratio|damping]] device allowing [[Plasticity (physics)|plastic]] rotation [deformation] of an otherwise rigid column connection.<ref>[http://mceer.buffalo.edu/education/reu/04Proceedings/12Long_Bergad.pdf Analysis of Rotational Column with Plastic Hinge] Michael Long and Corey Bergad, retrieved November 5, 2006</ref>
}}</ref> In [[earthquake engineering]] plastic hinge is also a type of energy [[Damping ratio|damping]] device allowing [[Plasticity (physics)|plastic]] rotation [deformation] of an otherwise rigid column connection.<ref>[http://mceer.buffalo.edu/education/reu/04Proceedings/12Long_Bergad.pdf Analysis of Rotational Column with Plastic Hinge] Michael Long and Corey Bergad, retrieved November 5, 2006</ref>


==Plastic behaviour==
==Plastic behaviour==
In plastic [[Limit state design|limit analysis]] of structural members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as [[Plastic Moment|plastic moment]] (M<sub>p</sub>). Member behaviour between M<sub>yp</sub> and M<sub>p</sub> is considered to be elastic. When M<sub>p</sub> is reached, a plastic hinge is formed in the member. In contrast to a [[friction]]less hinge permitting free rotation, it is postulated that the plastic hinge allows large rotations to occur at constant plastic moment M<sub>p</sub>.
In plastic [[Limit state design|limit analysis]] of structural members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as [[plastic moment]] (M<sub>p</sub>). Member behaviour between M<sub>yp</sub> and M<sub>p</sub> is considered to be elastic. When M<sub>p</sub> is reached, a plastic hinge is formed in the member. In contrast to a [[friction]]less hinge permitting free rotation, it is postulated that the plastic hinge allows large rotations to occur at constant plastic moment M<sub>p</sub>.

Plastic hinges extend along short lengths of beams. Actual values of these lengths depend on cross-sections and load distributions. But detailed analyses have shown that it is sufficiently accurate to consider beams rigid-plastic, with plasticity confined to plastic hinges at points. While this assumption is sufficient for [[Limit state design|limit state analysis]], finite element formulations are available to account for the spread of plasticity along plastic hinge lengths.<ref>{{cite journal | doi = 10.1061/(ASCE)0733-9445(2006)132:2(244) | volume=132 | title=Plastic Hinge Integration Methods for Force-Based Beam–Column Elements | year=2006 | journal=Journal of Structural Engineering | pages=244–252 | last1 = Scott | first1 = Michael H. | last2 = Fenves | first2 = Gregory L.}}</ref>

By inserting a plastic hinge at a plastic limit load into a statically determinate beam, a kinematic mechanism permitting an unbounded displacement of the system can be formed. It is known as the collapse mechanism. For each degree of static indeterminacy of the beam, an additional plastic hinge must be added to form a collapse mechanism


Plastic hinges extend along short lengths of beams. Actual values of these lengths depend on cross-sections and load distributions.<ref>{{cite journal |last1=Megalooikonomou |first1=Konstantinos G. |last2=Tastani |first2=Souzana P. |last3=Pantazopoulou |first3=Stavroula J. |title=Effect of Yield Penetration on Column Plastic Hinge Length |journal=Engineering Structures |year=2018 |volume=156 |pages=161–174 |doi= 10.1016/j.engstruct.2017.11.003|bibcode=2018EngSt.156..161M }}</ref> But detailed analyses have shown that it is sufficiently accurate to consider beams rigid-plastic, with plasticity confined to plastic hinges at points. While this assumption is sufficient for [[Limit state design|limit state analysis]], finite element formulations are available to account for the spread of plasticity along plastic hinge lengths.<ref>{{cite journal | doi = 10.1061/(ASCE)0733-9445(2006)132:2(244) | volume=132 | title=Plastic Hinge Integration Methods for Force-Based Beam–Column Elements | year=2006 | journal=Journal of Structural Engineering | pages=244–252 | last1 = Scott | first1 = Michael H. | last2 = Fenves | first2 = Gregory L.| issue=2 }}</ref>
Sufficient number of plastic hinges(N) required to make a collapse mechanism (unstable structure):


By inserting a plastic hinge at a plastic limit load into a statically determinate beam, a kinematic mechanism permitting an unbounded displacement of the system can be formed. It is known as the collapse mechanism. For each degree of static indeterminacy of the beam, an additional plastic hinge must be added to form a collapse mechanism.{{cn|date=August 2024}}
N=Degree of static indeterminacy + 1


==References==
==References==
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[[Category:Building engineering]]
[[Category:Building engineering]]
[[Category:Structural engineering]]
[[Category:Structural engineering]]
4. Megalooikonomou, K.G., Tastani, S. P., and Pantazopoulou, S. J. (2018) Effect of Yield Penetration on Column Plastic
Hinge Length. Engineering Structures, Elsevier, 156:161-174, https://doi.org/10.1016/j.engstruct.2017.11.003

Latest revision as of 02:49, 27 August 2024

Diagram of a structure featuring plastic hinges

In the structural engineering beam theory, plastic hinge is the deformation of a section of a beam where plastic bending occurs.[1] In earthquake engineering plastic hinge is also a type of energy damping device allowing plastic rotation [deformation] of an otherwise rigid column connection.[2]

Plastic behaviour

[edit]

In plastic limit analysis of structural members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as plastic moment (Mp). Member behaviour between Myp and Mp is considered to be elastic. When Mp is reached, a plastic hinge is formed in the member. In contrast to a frictionless hinge permitting free rotation, it is postulated that the plastic hinge allows large rotations to occur at constant plastic moment Mp.

Plastic hinges extend along short lengths of beams. Actual values of these lengths depend on cross-sections and load distributions.[3] But detailed analyses have shown that it is sufficiently accurate to consider beams rigid-plastic, with plasticity confined to plastic hinges at points. While this assumption is sufficient for limit state analysis, finite element formulations are available to account for the spread of plasticity along plastic hinge lengths.[4]

By inserting a plastic hinge at a plastic limit load into a statically determinate beam, a kinematic mechanism permitting an unbounded displacement of the system can be formed. It is known as the collapse mechanism. For each degree of static indeterminacy of the beam, an additional plastic hinge must be added to form a collapse mechanism.[citation needed]

References

[edit]
  1. ^ Megson, T.H.G. (2005-04-29). Structural and Stress Analysis, Second Edition (2 ed.). Butterworth-Heinemann. ISBN 0-7506-6221-2.
  2. ^ Analysis of Rotational Column with Plastic Hinge Michael Long and Corey Bergad, retrieved November 5, 2006
  3. ^ Megalooikonomou, Konstantinos G.; Tastani, Souzana P.; Pantazopoulou, Stavroula J. (2018). "Effect of Yield Penetration on Column Plastic Hinge Length". Engineering Structures. 156: 161–174. Bibcode:2018EngSt.156..161M. doi:10.1016/j.engstruct.2017.11.003.
  4. ^ Scott, Michael H.; Fenves, Gregory L. (2006). "Plastic Hinge Integration Methods for Force-Based Beam–Column Elements". Journal of Structural Engineering. 132 (2): 244–252. doi:10.1061/(ASCE)0733-9445(2006)132:2(244).