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BDM Example 6_20180101

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Bending moment diagram
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  EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION ON A TYPE 7 & TYPE 10M BARRIER   1 CDOT Bridge Design ManualJanuary 2018  Design Example 6   EXAMPLE 6.1 - DECK DESIGN GENERAL INFORMATION 1.Approximate Elastic Method, or Equivalent Strip Method (AASHTO 4.6.2.1)2.Refined Methods (AASHTO 4.6.3.2)3.Empirical Design Method (AASHTO 9.7.2) MATERIAL AND SECTION PROPERTIES Structure typeGirder spacing, maximumS Gdr   = 8.00 ft. Number of girdersN Gdr   = 3 ea. Overall deck width W Deck  = 24.00 ft. Deck slab thicknesst Deck  = 8.00 in. Overhang thickness (average)t OH  = 9.00 in. Concrete top cover c Top  = 2.00 in.  AASHTO T.5.12.3-1Concrete bottom cover c Bot  = 1.00 in.  AASHTO T.5.12.3-1Wearing surfacet WS  = 3.00 in. Concrete strength f' c  = 4.50 ksi (Concrete Class D compressive strength) Reinforcement strength f  y = 60.00 ksi (Minimum yield strength of grade 60 steel) Concrete density  W C  = 0.150 kcf  Deck overlay density  W WS  = 0.145 kcf  Section 3.4.2 Allowance for future utilities  W Utl  = 0.005 ksf  Section 3.4.3Resistance factors  φ STR  = 0.90 (strength limit state)  AASHTO 5.5.4.2 φ EE  = 1.00 (extreme event limit state)  AASHTO 1.3.2.1Correction factor for source aggregate K 1  = 1.00  AASHTO 5.4.2.4Modulus of elasticity of reinforcementE s  = 29000 ksi  AASHTO 5.4.3.2Modulus of elasticity of concreteE c  =4435 ksi  AASHTO 5.4.2.4Modular ration = E S  / E C  =6.54Girder typeGirder web thickness web = 7.00 in. Girder top flange widthflange = 43.00 in. Barrier type Area of barrier section A B  = 3.24 ft. 2 Barrier weight  W Barrier   =0.486 kip/ft. (Refer to Example 6.3 and CDOT Bridge Worksheet B-606-7A for more details)BasedonAASHTOLRFDBridgeDesignSpecifications9.6.1,therearethreepermittedmethodsof deck analysis:Thisdesignexampleusesthe  ApproximateElasticMethod  (EquivalentStripMethod),inwhichthedeckisdividedintotransversestrips,assumedtobesupportedonrigidsupportsatthecenterofthegirders. CIP Concrete DeckBulb Tee - BT54Type 7            APPENDIX A EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION ON A TYPE 7 OR TYPE 10 M BARRIER  EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION ON A TYPE 7 & TYPE 10M BARRIER   2  CDOT Bridge Design ManualJanuary 2018  UNFACTORED DEAD LOADS Dead Load calculation for analysis model:DC Deck  = W C t Deck * 1 ft. = 0.100 klf  DC Overhang  = W C t OH * 1 ft. = 0.113 klf  DC Barrier   = 0.486 kip at 6.84 in. from edge of deck (see Example 6.3)DW WS  = W WS  t WS * 1 ft. = 0.036 klf  DW Utl  =  W Utl  1 ft. = 0.005 klf  Where:DC Deck  - self-weight of deck slabDC Overhang  - self-weigh of overhangDC Barrier   - weight of barrier DW WS  - weight of wearing surfaceDW Utl  - weight of utilities0.150 kcf * 8.0 in. / 12 in./ft. * 1.0 ft. =0.145 kcf * 3.0 in. / 12 in./ft. * 1.0 ft. =0.150 kcf * 9.0 in. / 12 in./ft. * 1.0 ft. =DeadLoadsmomentsarecalculatedfora1.00ft.widesectionofthebridgedeckusingapprovedstructuralanalysismethods.Thisincludescontinuousbeamequations,momentdistribution,simplebeamequations,orfiniteelementanalysis.DeadLoadbendingmomentsshownbelowareproducedbyacontinuousbeammodelinCSiBridge2017usingauniformloadfordeckandwearingsurfaceanda point load for barriers.0.005 ksf * 1 ft. = Typical Section  EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION ON A TYPE 7 & TYPE 10M BARRIER   3 CDOT Bridge Design ManualJanuary 2018  Results of analysis: Abbreviation :M 100  - moment at girder 1M 150  - moment between supportsM 200  - moment at girder 2M 100 (kip-ft) M 150 (kip-ft) M 200 (kip-ft) DC Deck 0.0000.403-0.795DC Overhang -0.904-0.2300.444DC Barrier -1.667-0.4250.818DW WS -0.1130.116-0.231DW Utl -0.0400.010-0.020 UNFACTORED LIVE LOADS Deck superstructure type - k  AASHTO T.4.6.2.2.1-1Design section = min of 1/3 flange width or 15.00 in. = 14.33 in.  AASHTO 4.6.2.1.6Maximum Live Loads per unit width:Positive Moment from LL+M LL  = 5.69 kip-ft.  AASHTO T. A4-1Negative Moment from LL-M LL  = -3.06 kip-ft. (interpolated)  AASHTO T. A4-1LoadInlieuofdetermininganequivalentstripwidthforbridgeswithdeckssupportedonthreeormoregirders,LiveLoadmomentcanbedeterminedusingAASHTOLRFDBridgeDesignSpecifications AppendixA4T.A4-1.ThistablelistspositiveandnegativeLiveLoadmomentscalculatedusingtheEquivalentStripMethod.Tablevaluesincludemultiplepresencefactorsandthedynamicloadallowance.Interpolationbetweengivenvaluesisallowed.Tousethistable,distancefromcenterlineof girder to design section for negative moment has to be calculated first.Ingeneral,LiveLoadeffectscanbecalculatedbymodelingthedeckasabeamsupportedongirders,withoneormoreaxlesplacedsidebyside.Theseloadsaremovedtransverselytomaximizethemoments.TodetermineLiveLoadmomentperunitwidthofthebridge,calculatedtotalLiveLoadmomentisdividedbyanequivalentstripwidth,calculatedperequationsfromAASHTOLRFDBridgeDesign Specifications T.4.6.2.1.3-1. General Pattern of Moment Distribution Diagram in Deck  EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION ON A TYPE 7 & TYPE 10M BARRIER   4 CDOT Bridge Design ManualJanuary 2018  FACTORED DESIGN LOADS M u  = η   [ γ DC M DC  + γ DW M DW  + m γ LL (M LL + IM)] η   = 1.0load modifier  γ  - load factors specified in AASHTO T.3.4.1-1, T.3.4.1-2m - multiple presence factor, included in values from AASHTO T. A4-1IM - dynamic load allowance, included in values from AASHTO T. A4-1 γ DC_max  γ DC_min  γ DW_max  γ DW_min  γ LL M 100 (kip-ft) M 150 (kip-ft) M 200 (kip-ft) Strength I1.250.901.500.651.75-8.8010.06-5.59Service I1.001.001.001.001.00-5.785.56-2.84Controlling positive factored moment +Mu =10.06 kip-ft. Controlling negative factored moment-Mu =-8.80 kip-ft. DECK SLAB STRENGTH DESIGN Width of the design sectionb = 12.00 in.  Resistance factor for tension-controlled section  φ STR    =0.90AASHTO 5.5.4.2 Positive Moment Capacity (bottom reinforcement) TryBar size# 5 Bar spacings = 9.00 in. Bar diameter d b  =0.625 in. Bar area A b  =0.31 in. 2 Load CombinationNote - it is conservative to use minimum load factors for positive values of M 100  and M 200  and negative values of M 150 . Load FactorsDesign MomentsConcretedecksmustbeinvestigatedforstrength,serviceandextremelimitstates.Fatigueandfracture limit states do not need to be investigated (AASHTO 9.5).Designofdeckreinforcement,includingflexuralresistance,limitsofreinforcement,andcontrolof crackingisbasedonAASHTOLRFDBridgeDesignSpecifications5.7.3(typicalrectangularbeamdesign).Thefollowingdesignmethodcanbeusedfornormalweightconcretewithspecifiedcompressivestrengthsupto15.0ksi.RefertoSection9,DeckandDeckSystems,ofthisBDMfor information about acceptable deck reinforcement sizes and spacing.
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