Assignment On Plastic Structural Behavior | Engineer Laboratory

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UniversityFaculty of EngineeringLaboratory Report 1:Plastic Behaviour of Beams & FramesWritten by:Group 22:Test Date:Due Date:1|P a g e
Table of Contents1Executive Summary............................................................................................................32Test 1.1 – Plastic moment capacity....................................................................................42.1.1Plastic Section Modulus.......................................................................................42.1.2Elastic Section Modulus.......................................................................................42.1.3Shape factor.........................................................................................................52.1.4Plastic Moment....................................................................................................53Test 1.2 - Plastic Behaviour of a Continuous Beam...........................................................63.1Introduction.................................................................................................................63.2Theoretical Analysis.....................................................................................................63.2.1Collapse Load.......................................................................................................63.3Experimental Procedure..............................................................................................73.4Results.........................................................................................................................83.4.1Testing images......................................................................................................83.4.2Test Measurements.............................................................................................83.4.3Comparison..........................................................................................................93.5Conclusion.................................................................................................................104Test 1.3 - Plastic behaviour of a frame............................................................................114.1Introduction...............................................................................................................114.2Theoretical Analysis...................................................................................................114.2.1Method of virtual work......................................................................................114.2.2Beam Mechanism...............................................................................................124.2.3Sway Mechanism...............................................................................................134.2.4Combined Mechanism.......................................................................................144.2.5Interaction Diagram...........................................................................................154.3Experimental Procedure............................................................................................184.4Experimental Results.................................................................................................194.4.1Testing Images....................................................................................................194.4.2Test Measurement.............................................................................................194.4.3Comparison........................................................................................................204.5Conclusion.................................................................................................................212|P a g e
5References........................................................................................................................221Executive SummaryKnowing the plastic behaviour of a structure or structural member is important foran engineer to consider during the design process. Modern design standards andprocedures are based on the design utilising the elastic range of a member, as this ismore conservative when compared to the plastic limit.Ideally it would be preferred to carry out large scale in-situ testing of steel structuresto determine these characteristics, however this is not a feasible option for themajority of sites & practicing engineers. This is where testing samples within thelaboratory is able to provide us with all the relevant data within a time & costeffective manner which can be translated to the in-situ structure.This report looks at the laboratory testing of a continuous span beam & a rigid fixedfoot portal frame to determine their plastic properties. The goal is to determine thecollapse loads required to form a plastic hinge.3|P a g e
2Test 1.1 – Plastic moment capacity2.1.1Plastic Section ModulusThe plastic section modulus is used to describe the characteristic of a member inwhich it exhibits a plastic behaviour. The modulus is dependent on the position ofthe plastic neutral axis. The plastic neutral axis divides the cross section into twoequal areas, in order for the area under compression to equal to the area undertensionThe plastic section modulus for a member with a circular cross section isdetermined by the following equation;S=d36S=Plasticsectionmodulus,(mm3)d=Sectiondiamter,(mm)S=d36S=(3.20mm)36S=5.4613mm32.1.2Elastic Section ModulusThe elastic section modulus is a geometric property of a member determined by thefirst moment of area taken about the neutral axis.The elastic section modulus for a member with a circular cross section isdetermined by the following equation;Z=π×d332Z=Elasticsectionmodulus,(mm3)d=Sectiondiamter,(mm)Z=π×d332Z=π×(3.20mm)332Z=3.2170mm34|P a g e
2.1.3Shape factorThe shape factor is a numerical means of relating the plastic section modulus to theelastic section modulus for a particular cross sectional shape of a member. Thetypical value for a circular cross-section is 1.7. The shape factor for the membertested is calculated below;ShapeFactor=SZShapeFactor=Plasticsectionmodulus,(mm3)Elasticsectionmodulus,(mm3)S=Plasticsectionmodulus,(mm3)Z=Elasticsectionmodulus,(mm3)ShapeFactor=5.46133.2170ShapeFactor=1.6976ShapeFactor1.702.1.4Plastic MomentThe plastic moment(Mp)of a structural member is defined as the point in which theentire cross section has reached its yield stress. Theoretically, this is the maximumbending moment in which the section can resist before a plastic hinge forms. Thishinge will continue to deform under additional loading until such point in which thematerial fails.The Plastic moment of a member is determined by the following equation;Mp=S×σyMp=Plasticmoment,(Nm)S=Plasticsectionmodulus,(m3)σy=Yieldstress,(MPa)5|P a g e
3Test 1.2 - Plastic Behaviour of a Continuous Beam3.1IntroductionThe aim of this experimental testing is to obtain an understanding on the behaviourof a continuous span beam subjected to vertical forces. The loading action of eachspan will be based on a specified ratio. Key items to watch for will be the locationand severity of plastic hinges during the gradual loading process.3.2Theoretical Analysis3.2.1Collapse LoadTo determine the theoretical load at which a plastic hinge will form in themember the virtual work method is used. The method involves balancing theexternal work with the internal work and solving for the unknown collapse load.Data;L=0.30mMp=Plasticmoment,(Nm)ExternalWork=InternalWorkExternalWork=Vc×(L2)×θInternalWork=3×Mp×θVc×(L2)×θ=3×Mp×θVc×(0.30m2)×θ=3×1.36Nm×θVc×0.15m×θ=4.08Nm×θVc×0.15m=4.08NmVc=4.08Nm0.15mVc=27.20NWc=Vc2Wc=27.20N2Wc=13.60N6|P a g e
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