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Plastic Behaviour of Beams and Frames

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Added on  2019-10-18

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This report entails an experimentation of the behaviour of ductile material. The following report will specifically observe the enabling of plastic hinges due to bending caused by loadings. The plastic hinges that from are regions of localised plasticity where an increase in rotations occurs due to plastic moment of the beam section being equal to a constant bending moment. This report aims to observe the development of plastic collapse mechanisms and compare experimentally determined plastic collapse values against theoretical ones.

Plastic Behaviour of Beams and Frames

   Added on 2019-10-18

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Plastic Behaviour of Beams and Frames
Plastic Behaviour of Beams and Frames_1
ContentsIntroduction...........................................................................................................................................1Background Information........................................................................................................................1Test 1.1..................................................................................................................................................21.1.0 Laboratory Test Set-Up.............................................................................................................21.1.1 Test Results...............................................................................................................................21.1.2 Analysis.....................................................................................................................................21.1.3 Discussion.................................................................................................................................3Test 1.2..................................................................................................................................................31.2.0 Laboratory Test Set-Up.............................................................................................................31.2.1 Results......................................................................................................................................41.2.2 Analysis.....................................................................................................................................41.2.3 Discussion.................................................................................................................................6Test 1.3..................................................................................................................................................61.3.0 Laboratory Test Set-Up.............................................................................................................61.3.1 Results......................................................................................................................................71.3.2 Analysis.....................................................................................................................................81.3.3 Discussion...............................................................................................................................10Conclusion...........................................................................................................................................11
Plastic Behaviour of Beams and Frames_2
IntroductionThe following report entails an experimentation of the behaviour of ductile material. The following report will specifically observe the enabling of plastic hinges due to bending caused by loadings. The plastic hinges that from are regions of localised plasticity where an increase in rotations occurs due to plastic moment of the beam section being equal to a constant bending moment. This report aims to observe the development of plastic collapse mechanisms and compare experimentally determined plastic collapse values against theoretical ones.Background InformationPlastic collapse methods are used in obtaining failure loads of structures. The method involves analysis of structure mechanics after the onset of plasticity at certain points along the structure that are unable to withhold loads any longer. An elastic analysis is used mainly for practical design however a plastic analysis is used for considering a wide spectrum of responses along the structure when it is performing in the inelastic region and when designing for the ultimate loading.For simple beam structures, the moment curve relationship for a rectangular cross section isshown above. For M<My, the beam behaves elastically however at A; the moment M = the yield moment My and the relationship loses its linear behaviour. The moment then further moves towards the fully plastic moment Mp and the curve relationship tends to infinity. Theratio of Mp to the yield moment is known as the shape factor Sf. When a load is applied to the structure, it is in its elastic state and will resist deformation; however, when it reaches the point of zero resistance, plastic hinges form. When the plastic hinges in the structure equal n+1 the structure will collapse (n = degree of indeterminacy of the structure).
Plastic Behaviour of Beams and Frames_3
Test 1.11.1.0 Laboratory Test Set-Up1.Metal rod placed under tension machine2.Rod is stretched from both sides until failure occurs1.1.1 Test ResultsDiameter (d) = 3.2mmYield Stress (σy) = 245MPa1.1.2 AnalysisThe plastic collapse method aims to determine the failure load of a structure by finding the onset of plasticity at certain points along the structure. The Plastic Moment of the circular rod in this experiment is found by utilizing the following calculation:Mp=SσyWhere Mp = Plastic Moment S = Plastic Section Modulusσy = Yield StressCircular Rod:Ac=AT=AsemicircleAsemicircle=πd24S=(A¿¿c×h)+(AT×h)=2Ah¿y=2d3πh=y2Where h = distance to the plastic neutral axis of semicircle; y = distance to centroid∴S=πd24×2d3πy
Plastic Behaviour of Beams and Frames_4

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