Chapter A Steel and Composites

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1、ASteelandCompositesA.1SteelStructuresA.1.1ImpactonSteelBeamsAnumberofsteelbeamsunderimpactareanalyzed.Thebeamsaretreatedasrate-sensitiveandtheinputenergyoftheimpactorisassumedtobehigh.Thestraineffects(rateofstrainoccurringataparticularsolution)foraparticularstateo

2、fstrainareincluded.Theimpactorisassumedtostrikeasteelbeamatmid-span.FigureA.1showsatypical8-node,isoparametric,finite-elementmeshforasteelbeamofrectangularcross-section.Thematerialisassumedtobeelastic/visco-perfectlyplastic.ProgramISOPARisusedtoanalyzethebeamwhens

3、ubjectedtoacone-shapedimpactor.Thefollowingdataareconsidered:PlateA.1givestheforce-timerelationswithdominantfrequencyandmodes.Acceleration-timerelationforthebeamisshowntherein.BritishbeamAmericanbeamSpanlengths,L:3–10mL=30ft−1Mass,M:30–57kgmwidthDeadweight=1,000l

4、b−1Impactorvelocity,vs:1–25msMF=DLF=1.4−3−3Densityofsteel,ρ:7,800kgm(386kipsin)F1(t)=222.4kN(50,000lb)−26−2Young’smodulus,Es:200GNm(30×10lbin)−2Yieldstress,σy:250MNmPoisson’sratio,v:0.3−1Strainrate,˙ε:40.4sFiniteelements:8-nodedisoparametricelements;200Assumedimp

5、actloads:triangularloads,load–timerelationsvary,typicalonesF1(t)max=222.4kN(50,000lb)tr=0.08s836ASteelandCompositesZXYFig.A.1.Finite-elementmeshofasteelbeamTheprocedureforsizingupthebeamusingtheUScodeforonecaseisasfollows:F1(t)+20,000lbdeadload−1L=30ft;1,000lbftd

6、eadloadofthebeamThebeamisassumedtobefixedatbothendsDLF>1.4;t/T<2(seetheresponsechartinChap.3)r3wL2FLF(t)dD1Mmax=++(DLF)1288=(1,000×302/12)+(20×30×103/8)+(50,000×30/8)1.4=412,500inlbZ=(M×12)/σ=(412×103×12)/(75×103)py3=65.92in3SectionadoptedZp=175.4in→24WF764I=2,0

7、96in3−1K=192EI/L=258,760lbinUniformlydistributedloadiftreatedseparately(seetablesinthissection)KL=1.0ConcentratedmassKM=1.0DistributedmassKM=0.37Mc=ΣKMM=(20,000×1.0+30,000×0.37)/(386×1,000)=0.081kips2in−1=0.081×103lbs2in−1−1ke=kKL=258,760×1.0lbin=258,760lbin−1A.1

8、SteelStructures83722=30MN/mcuF=355MN/my230×135×30steelbeamGradeS355UBPbeam.133.86.3Typicalsectionofanuncased9.69.6187.620683.6Hz(m=5)341.8Hz(m=7)15sec)305.2Hz(