Beam DesignCVEN3302 Assignment 1Column loading (for the purpose of SpaceGass)PG1350kNGiven in Assignment DataPQ1000kNGiven in Assignment DataFactored Column LoadingP*3120kNP*/21560kNFrom SlabsAS/NZS 1170.0:2002Section 4Combinations of Actions4.2Combinations of actions fro ultimate limit state4.2.1Stability1.2G+1.5Q4.2.2Strength1.2G+1.5QTable 4.1S0.7L0.4AS/NZS 1170.0:2002Section 7Confirmation Methods7.2Ultimate Limit State7.2.2StrengthRdEdRd=RuRCB Equation 2.11Values of Page 61RCB 2EDProperties of SlabTributary Area42m2Area of Slab parts acting on beam B4Tributary Width6mWidth of Slab parts acting on beam B4 parallel to slab directionp0.031From Slab DesginSteel Weight1kN/m3AS1170.1:2002 Appendix ASlab Thicknes0.25mFrom Slab DesginConcrete Unit Weight24kN/m3AS1170.1:2002 Appendix ASlab Unit Weight25kN/m3Slab Unit Pressure6.25kPa or kN/m2Dead Imposed Load1.0kPa or kN/m2Given in Assignment DataLive Load (Office)3.0kPa or kN/m2AS1170.1:2002 Table 3.1Slab Line Load37.5kN/mDead Load6.0kN/mLive Load (Office)18.0kN/mG43.5kN/mQ18.0kN/m1.35G58.7kN/mRCB Equation 2.11.2G52.21.5Q271.2G+1.5Q79.2kN/m(governs)RCB Equation 2.2Spacegass ResultsSpan 1Span 2Span 3Span 1Span 2Span 3dweb=480Support 1mid spansupport 2midspansupport 3midspanfixed enddweb=625Support 1mid spansupport 2midspansupport 3midspanfixed endD=730-1155.07728.13-1377.330-1297.3200D=875-1171.42738.66-1397.53687.93-1316.18667.01-1533.32Beam Design (Beam-Slab T-Section)Material Propertiesf'c32MPaimpliesEc30100MPaRCB Table A.10.8260.83RCB Equation 3.6020.9040.85RCB Equation 3.61fsy500MPaES200000MPan6.6DurabilityExposure ClassificationA2AS3600-2009 Table 4.3f'c32MPaminimum Cover25mmAS3600-2009 Table 4.10.3.2

FireFRP3hrsas50mmAS3600-2009 Table 5.4.1(B)b550mmAS3600-2009 Table 5.4.1(B) Combination 3minimum cover24mmDurability governs, take minimum cover25mmMake consistant with slab30mm(Cover to the bottom longitudinal reinforcement)Distance to top slab reinforcement20mm(assumed)StirrupsR1010mmS0.7rc25kN/m3L0.4/span1/250mm/mm26.88mm

Slab's6000Beam Span7000mmbef1240Assuming 450x450 columnst250Lo6720mmRCB Equation 2.25Ln6600mmD625Trial Depthdweb375D733.3333333333mmRCB Table C.1D1730mmbw400D2625mmbw1438mmCROSS-SECTION OF BEAM PERPINDICULAR TO LOGITUDINALbw2400mmSpan7000a4900mmRCB0.8RCB Table 2.1t250

Take N28 barsLo6720d28mmAmm2RCB Table B.4Ln6600No.450450Astmm2CROSS-SECTION OF BEAM PARALLEL TO LOGITUDINALDesign for DeflectionS.W beam-slab41250000kN/mm41.3kN/mwG47.3kN/m(Self weight + unfactored line load calculated in the 'From Slab Section Above)wQ18.0kN/m(Self weight + unfactored line load calculated in the 'From Slab Section Above)Time-dependent effective service load:Span 1Span 2Span 3TakingSupport 1mid spansupport 2midspansupport 3midspanfixed endkcs21-1155.07728.13-1377.33639.23-1297.32656.44-1544.45Then2-1171.42738.66-1397.53687.93-1316.18667.01-1533.32Fd.ef168.8kN/mFoster Lecture Notes3-1211.67760.41-1437.31708.72-1355.03687.21-1578.024-680.35420.01-784.33393.93-745.59379.36-898.565-636.34391.81-730.24367.84-695.11354.15-842.286-615.38378.38-704.48355.47-671.05342.02-815.47

Considering Span 1 (End Span):Considering Span 2 (Interior Span):Considering Span 3 (End Span):

Fom SpacegassFom SpacegassFom SpacegassML-615.38kNmML-704.48kNmML-671.05kNmMM378.38kNmMM355.47kNmMM342.02kNmMR-704.48kNmMR-671.05kNmMR-815.47kNm

Second Moment of AreaRCB Equation 3.46Second Moment of AreaRCB Equation 3.46Second Moment of AreaRCB Equation 3.46Rearranging for Moment of AreaRearranging for Moment of AreaRearranging for Moment of AreaIef.av>1.433E+09mm4Ief.av>1.267E+09mm4Ief.av>1.124E+09mm4Taking the largest of the three:Ief.av MAX1.433E+09mm4(Desgin for Span 1 governs)

Checking the Trial Section:AssumeIg is 4*iefavIg5.73E+09mm4(Compare with trial section's I gross)Beambef11240mmRCB Equation 3.7921240mm31240mmbef1240mmIg)O.K.

Tiral Section:D625mmDesign for StrengthChecking minimum reinforcements for strength1.2G47.3kN/m(No patterning is needed as (3/4)*G>>Q)1.5Q18.0kN/mw*65.3kN/m

Span 1Span 2Span 3Support 1mid spansupport 2midspansupport 3midspanfixed endMoments-251.38145.17-266.08139.76-253.56132.49-349.99Since desgin for span 1 governsThenThe moment capacity Mu of the section should not be less than 1.2 Mcro1.2 Mcrois equal to1.2f'ct.pZZtop3.008E+07mm3Zbottom1.714E+07mm3

At supports1.2 Mcro1.225E+08Nmm1.2 McrokNmMuis equalto M*/phi332.6>122.5OKAt mid-span1.2 Mcro6.982E+07Nmm1.2 McrokNmMu181.5>69.8OKThe min. reo. Requirments are satisfied along span 1 (Beam 4)Longitudinal reinforcements:Check A4 for equationsPositive Bending(Assume N28bars)dn=t=250mmd571mmM3760672000Nmm3760.672kNm(Capacity if NA were to be at lower edge of flange)At mid Span Mu is181.5>>229.37kNNo critical web crushingultimate shear strengthVuc123bvdofcv(Ast/bvdo)^1/311.1319>1.12131bv400mmdo571mmf'c32MPafcv3.17Ast3100mm2Asc775mm2Vuc123336N123.3kNphiVcu86.3kN