5CONCRETE DECK DESIGN Problem Statement: Use the approximate method of analysis [4.6.2] to design the deck of the reinforced concrete T-Beam bridge section of Fig.E for a HL-93 live load and a PL-2 performance level concrete barrier (Fig.7.45).The T-Beams supporting the deck are 2440 mm on the centers and have a stem width of 350 mm. The deck overhangs the exterior T-Beam approximately 0.4 of the distance between T-Beams. Allow for sacrificial wear of 15mm of concrete surface and for a future wearing surface of 75mm thick bituminous overlay. Use fc’=30 MPa, fy=400Mpa, and compare the selected reinforcement with that obtained by the empirical method [A9.7.2]
6A. DECK THICKNESSThe minimum thickness for concrete deck slabs is 175 mm [A ].Traditional minimum depths of slabs are based on the deck span length S to control deflection to give [ Table A ]Use hs = 190 mm for the structural thickness of the deck. By adding the15 mm allowance for the sacrificial surface, the dead weight of the deckslab is based on h= 205mm. Because the portion of the deck thatoverhangs the exterior girder must be designed for a collision loadon the barrier, its thickness has been increased by 25mm to ho=230mm
7B. WEIGHTS OF THE COMPONENTS [ TABLE A3.5.1-1 ] For a 1mm width of a transverse strip.BarrierPb = 2400 x 10-9 Kg/mm3 x 9.81 N/Kg x mm2= 4.65 N/mmFuture Wearing SurfaceWDW = 2250 x x x 75 = 1.66 x 10-3 N/mmSlab 205mm thickWs = 2400 x x x 205 = 4.83 x 10-3 N/mmCantilever OverhangingWo = 2400 x x x 230 = 5.42 x N/mm
8C. BENDING MOMENT FORCE EFFECTS – GENERAL An approximate analysis of strips perpendicular to girders is considered acceptable [A9.6.1]. The extreme positive moment in any deck panel between girders shall be taken to apply to all positive moment regions. Similarly, the extreme negative moment over any girder shall be taken to apply to all negative moment regions [A ]. The strips shall be treated as continuous beams with span lengths equal to the center-to-centre distance between girders. The girders are assumed to be rigid [A ]For ease in applying the load factors, the bending moments will separately be determined for the deck slab, overhang, barrier, future wearing surface, and vehicle live load.
91. DECK SLAB h = 205 mm, Ws = 4.83 x 10–3 N/mm, S = 2440 mm Placement of the deck slab dead load and results of a moment distribution analysis for negative and positive moments in a 1-mm wide strip is given in figure E7.1-2A deck analysis design aid based on influence lines is given in Table A.1 of Appendix A. For a uniform load, the tabulated areas are multiplied by S for Shears and S2 for moments.Fig.E7.1-2: Moment distribution for deck slab dead load.
101. DECK SLAB R200 = Ws (Net area w/o cantilever) S = 4.83 x 10-3 (0.3928) 2440 = 4.63 N/mmM204 = Ws (Net area w/o cantilever) S2= 4.83 x 10-3 (0.0772) 24402= 2220 N mm/mmM300 = Ws (Net area w/o cantilever) S2= 4.83 x 10-3 ( ) 24402= N mm/mmComparing the results from the design aid with those from moment distribution shows good agreement. In determining the remainder of the bending moment force effects, the design aid of Table A.1 will be used.
112. OVERHANG The parameters are ho = 230 mm, Wo = 5.42 x 10-3 N/mm2 L = 990 mmPlacement of the overhang dead load is shown in the figure E By using the design aid Table A.1, the reaction on the exterior T-Beam and the bending moments are:Fig.E7.1-3Overhang dead load placement
122. OVERHANG R200 = Wo (Net area cantilever) L = 5.42 x 10-3 ( x 990/2440) 990 = 6.75 N/mmM200 = Wo (Net area cantilever) L2= 5.42 x 10-3 ( ) 9902 = N mm/mmM204 = Wo (Net area cantilever) L2= 5.42 x 10-3 ( ) 9902 = N mm/mmM300 = Wo (Net area cantilever) L2= 5.42 x 10-3 (0.1350) = N mm/mm
133. BARRIER The parameters are Pb = 4.65 N/mm L = 990 – 127 = 863 mm Placement of the center of gravity of the barrier dead load is shown in figure E By using the design aid Table A.1 for the concentrated barrier load, the intensity of the load is multiplied by the influence line ordinate for shears and reactions. For bending moments, the influence line ordinate is multiplied by the cantilever length L.Fig.E7.1-4Barrier dead load placement
143. BARRIER R200 = Pb (Influence line ordinate) = 4.65( x 863/2440) = 6.74 N/mmM200 = Pb (Influence line ordinate) L= 4.65( ) (863) = N mm/mmM204 = Pb (Influence line ordinate) L= 4.65 ( ) (863) = N mm/mmM300 = Pb (Influence line ordinate) L= 4.65 (0.2700) (863) = 1083 N mm/mm
154. FUTURE WEARING SURFACE FWS = WDW = 1.66 x 10-3 N/mm2The 75mm bituminous overlay is placed curb to curb as shown in figure E The length of the loaded cantilever is reduced by the base width of the barrier to giveL = 990 – 380 = 610 mm.Fig. E7.1-5: Future wearing surface dead load placement
164. FUTURE WEARING SURFACE If we use the design aid Table A.1, we haveR200 = WDW [(Net area cantilever) L + (Net area w/o cantilever) S]= 1.66 x 10-3 [( x 610/2440) x (0.3928) x 2440)]= N/mmM200 = WDW (Net area cantilever) L2= 1.66 x 10-3 ( )(610)2 = N mm/mmM204 = WDW [(Net area cantilever) L2 + (Net area w/o cantilever) S2 ]= 1.66 x 10-3 [( )(610)2 + (0.0772)24402 ] = 611 N mm/mmM300 = WDW [(Net area cantilever) L2 + (Net area w/o cantilever) S2 ]= 1.66 x 10-3 [(0.1350)(610)2 + ( )24402 ] = N mm/mm
17D. VEHICULAR LIVE LOADWhere decks are designed using the approximate strip method [A ], and the strips are transverse, they shall be designed for the 145 KN axle of the design truck [A ]. Wheel loads on an axle are assumed to be equal and spaced 1800 mm apart [Fig.A ]. The design truck should be positioned transversely to produce maximum force effects such that the center of any wheel load is not closer than 300mm from the face of the curb for the design of the deck overhang and 600mm from the edge of the 3600 mm wide design lane for the design of all other components [A ]
18D. VEHICULAR LIVE LOADThe width of equivalent interior transverse strips (mm) over which the wheel loads can be considered distributed longitudinally in CIP concrete decks is given as[Table A ]Overhang, XPositive moment, SNegative moment, SWhere X is the distance from the wheel load to centerline of support and S is the spacing of the T-Beams. Here X=310 mm and S=2440 mm(Fig.E7.1-6)
19D. VEHICULAR LIVE LOADFigure E : Distribution of Wheel load on Overhang
20D. VEHICULAR LIVE LOADTire contact area [A ] shall be assumed as a rectangle with width of 510 mm and length given byWhere is the load factor, IM is the dynamic load allowance and P is the Wheel load.Here = 1.75, IM = 33% , P = 72.5 KN.
21Thus the tire contact area is 510 x 385mm D. VEHICULAR LIVE LOADThus the tire contact area is510 x 385mmwith the 510mm in the transverse direction as shown in Figure.E7.1-6
26D. VEHICULAR LIVE LOADFig.E7.1-7: Live load placement for maximum positive momentOne loaded lane, m = 1.2(b) Two loaded lanes, m = 1.0
27D. VEHICULAR LIVE LOADIf we use the influence line ordinates from Table A-1, the exterior girder reaction and positive bending moment with one loaded lane (m=1.2) are200204
28D. VEHICULAR LIVE LOAD Thus, the one loaded lane case governs. For two loaded lanes (m=1.0)Thus, the one loaded lane case governs.
29D. VEHICULAR LIVE LOAD 3. MAXIMUM INTERIOR NEGATIVE LIVE LOAD MOMENT. the critical placement of live load for maximum negative moment is at the first interior deck support with one loaded lane (m=1.2) as shown in Fig.E7.1-8.The equivalent transverse strip width isS = (2440) = 1830 mmUsing Table A-1, the bending moment at location 300 is
30D. VEHICULAR LIVE LOAD4. MAXIMUM LIVE LOAD REACTION ON EXTERIOR GIRDER
31E. STRENGTH LIMIT STATEThe gravity load combination can be stated as [Table A ]PPWhereDC = Dead load of structural components and non-structural attachements.DW= Dead load of wearing surfaces and utilities.LL = Vehicular live load.IM = Vehicular dynamic load allowance.
33E. STRENGTH LIMIT STATEThe T-Beam stem width is 350mm, so the design sections will be 175mm on either side of the support centerline used in the analysis. The critical negative moment section is at the interior face of the exterior support as shown in the free body diagram[Fig. E7.1-10]Back
34E. STRENGTH LIMIT STATEThe values of the loads in Fig E are for a 1-mathematical model strip. The concentrated wheel load is for one loaded lane, that is,W = 1.2(72500)1400 = N/mmDeck Slab:s
41F. Selection Of Reinforcement Maximum reinforcement keeping in view the ductility requirements is limited by [A ]Minimum reinforcement [ ] for components containing no prestressing steel is satisfied if
43F. Selection Of Reinforcement POSITIVE MOMENT REINFORCEMENT :
44F. Selection Of Reinforcement Check DuctilityCheck Moment Strength
45F. Selection Of Reinforcement 2. Negative Moment ReinforcementBack
46F. Selection Of Reinforcement Check Moment StrengthFor transverse top bars,Use No. mm.
47F. Selection Of Reinforcement 3. DISTRIBUTION REINFORCEMENT:Secondary reinforcement is placed in the bottom of the slab to distribute the wheel loads in the longitudinal direction of the bridge to the primary reinforcement in the transverse direction. The required area is a percentage of the primary positive moment reinforcement. For primary reinforcement perpendicular to traffic [A ]Where Se is the effective span length [A ]. Se is the distance face to face of stems, that is,Se= = 2090mm
49F. Selection Of Reinforcement 4. SHRINKAGE AND TEMPRATURE REINFORCEMENT.The minimum amount of reinforcement in each direction shall be [A ]Where Ag is the gross area of the section for the full 205 mm thickness.For members greater than 150 mm in thickness, the shrinkage and temperature reinforcement is to be distributed equally on both faces.Use 450 mm, Provided As = mm2/mm
50G. CONTROL OF CRACKING-GENERAL Cracking is controlled by limiting the tensile stress in the reinforcement under service loads fs to an allowable tensile stress fsa [A ]WhereZ = N/mm for severe exposure conditions.dc = Depth of concrete from extreme tension fiber to center of closest bar mmA = Effective concrete tensile area per bar having the same centroid as the reinforcement.
51G. CONTROL OF CRACKING-GENERAL M = MDC + MDW MLLc
52G. CONTROL OF CRACKING-GENERAL Where= density of concrete = 2400 Kg/m3.f’c = 30 MPa.So thatUse n = 7
53G. CONTROL OF CRACKING-GENERAL 1. CHECK OF POSITIVE MOMENT REINFORCEMENT.The service I positive moment at Location 204 isThe calculation of the transformed section properties is based on a 1-mm wide doubly reinforced section shown in the Figure E7.1-12
54G. CONTROL OF CRACKING-GENERAL Sum of statical moments about the neutral axis yields
55G. CONTROL OF CRACKING-GENERAL The positive moment tensile reinforcement of No.15 bars at 25mm on centers is located 33 mm from the extreme tension fiber. Therefore,cysasays
56G. CONTROL OF CRACKING-GENERAL 2. CHECK OF NEGATIVE REINFORCEMENT:The service I negative moment at location isThe cross section for the negative moment is shown in Fig.E
57G. CONTROL OF CRACKING-GENERAL Balancing the statical moments about the neutral axis gives
58G. CONTROL OF CRACKING-GENERAL The negative moment tensile reinforcement of No.15 bars at 225 mm on centers is located 53 mm from the tension face. Therefore dc is the maximum value of 50mm, andsasa
59H. FATIGUE LIMIT STATEThe investigation for fatigue is not required in concrete decks for multigirder applications [A9.5.3]
60TRADITIONAL DESIGN FOR INTERIOR SPANS The design sketch in Fig.E summerizes the arrangement of the transverse and longitudinal reinforcement in four layers for the interior spans of the deck. The exterior span and deck overhang have special requirements that must be dealt with separately.
61J. EMPERICAL DESIGN OF CONCRETE DECK SLABS Research has shown that the primary structural action of the concrete deck is not flexure, but internal arching. The arching creates an internal compression dome. Only a minimum amount of isotropic reinforcement is required for local flexural resistance.
62J. EMPERICAL DESIGN OF CONCRETE DECK SLABS 1. DESIGN CONDITIONS [A ]Design depth excludes the loss due to wear, h=190mm. The following conditions must be satisfied:
64J. EMPERICAL DESIGN OF CONCRETE DECK SLABS 3. EMPERICAL DESIGN SUMMARYwhile using the empirical design approach there is no need of using any analysis. When the design conditions have been met, the minimum reinforcement in all four layers is predetermined. The design sketch in the Fig.E summarizes the reinforcement arrangement for the interior deck spans.
65K. COMPARISON OF REINFORCEMENT QUANTITIES The weight of reinforcement for the traditional and empirical design methods are compared in Table.E7.1-1 for a 1-m wide transverse strip. Significant saving, in this case 74% of the traditionally designed reinforcement is required, can be made by adopting the empirical design method.(Area = 1m x 14.18m)
66L. DECK OVERHANG DESIGNThe traditional and the empirical methods does not include the design of the deck overhang.The design loads for the deck overhang are applied to a free body diagram of a cantilever that is independent of the deck spans.The resulting overhang design can then be incorporated into either the traditional or the empirical design by anchoring the overhang reinforcement into the first deck span.
67Two limit states must be investigated. L. DECK OVERHANG DESIGNTwo limit states must be investigated.Strength I [A13.6.1] and Extreme Event II [A13.6.2]The strength limit state considers vertical gravity forces and it seldom governs, unless the cantilever span is very long.
68L. DECK OVERHANG DESIGNThe extreme event limit state considers horizontal forces caused by the collision of a vehicle with the barrier.The extreme limit state usually governs the design of the deck overhang.
691. STRENGTH I LIMIT STATE: L. DECK OVERHANG DESIGN1. STRENGTH I LIMIT STATE:The design negative moment is taken at the exterior face of the support as shown in the Fig.E7.1-6 for the loads given in Fig.EBecause the overhang has a single load path and is, therefore, a nonredundant member, then
72L. DECK OVERHANG DESIGN 2. EXTREME EVENT II LIMIT STATE the forces to be transmitted to the deck overhand due to a vehicular collision with the concrete barrier are determined from a strength analysis of the barrier.In this design problem, the barriers are to be designed for a performance level PL-2, which is suitable for“High-speed main line structures on freeways, expressways, highways and areas with a mixture of heavy vehicles and maximum tolerable speeds”
73L. DECK OVERHANG DESIGNThe maximum edge thickness of the deck overhand is 200mm[A ] and the minimum height of barrier for a PL-2 is 810mm.The transverse and longitudinal forces are distributed over a length of barrier of 1070mm. This length represents the approximate diameter of a truck tire, which is in contact with the wall at the time of impact.The design philosophy is that if any failures are to occur they should be in the barrier, which can readily be repaired, rather than in the deck overhang.The resistance factors are taken as 1.0 and the vehicle collision load factor is 1.0
74M. CONCRETE BARRIER STRENGTH All traffic railing systems shall be proven satisfactory through crash testing for a desired performance level [A ]. If a previously tested system is used with only minor modification that do not change its performance, then additional crash testing is not required [A ]The concrete barrier shown in theFig.E (Next Slide) is similar to the profile and reinforcement arrangement to traffic barrier type T5 analyzed by Hirsh(1978) and tested by Buth et al (1990)
75M. CONCRETE BARRIER STRENGTH Fig. W (Concrete Barrier and connection to deck overhang.)
78M. CONCRETE BARRIER STRENGTH 1. MOMENT STRENGTH OF WALL ABOUTVERTICAL AXIS,MWH.The moment strength about the vertical axis is based on the horizontal reinforcement in the wall. The thickness of the barrier wall varies and it is convenient to divide it for calculation purposes into three segments as shown in Fig. E7.1-18
80M. CONCRETE BARRIER STRENGTH Neglecting the contribution of compressive reinforcement, the positive and negative bending strengths of segment I are approximately equal and calculated asnI
81M. CONCRETE BARRIER STRENGTH For segment II, the moment strengths are slightly different. Considering the moment positive if it produces tension on the straight face, we haven posn negn II
82M. CONCRETE BARRIER STRENGTH For segment III, the positive and negative bending strengths are equal andnIIInInIInIII
83M. CONCRETE BARRIER STRENGTH Now considering the wall to have uniform thickness and same area as the actual wall and comparing it with the value of MwH.This value is close to the one previously calculated and is easier to find
84M. CONCRETE BARRIER STRENGTH 2. MOMENT STRENGTH OF WALL ABOUT HORIZONTAL AXISThe moment strength about the horizontal axis is determined from the vertical reinforcement in the wall.The yield lines that cross the vertical reinforcement (Fig.E ) produce only tension in the sloping wall, so that the only negative bending strength need to be calculated.Matching the spacing of the vertical bars in the barrier with the spacing of the bottom bars in the deck, the vertical bars become No.15 at 225mm(As = mm2/mm) for the traditional design (Fig.E7.1-14).
85M. CONCRETE BARRIER STRENGTH For segment I, the average wall thickness is 175mm and the moment strength about the horizontal axis becomesAt the bottom of the wall the vertical reinforcement at the wider spread is not anchored into the deck overhang. Only the hairpin dowel at a narrower spread is anchored. the effective depth of the hairpin dowel is [Fig.E7.1-17]d= = 224 mm
87M. CONCRETE BARRIER STRENGTH 3. CRITICAL LENTH OF YIELD LINE PATTERN,LCNow with moment strengths and Lt=1070mm known, Eq.E7.1-9 yieldsttbwcc
88M. CONCRETE BARRIER STRENGTH 4. NOMINAL RESISTANCE TO TRANVERSELOAD,RWFrom Eq.E7.1-8, We haveccwbwct
89M. CONCRETE BARRIER STRENGTH 5. SHEAR TRANSFER BETWEEN BARRIER AND DECKThe nominal resistance Rw must be transferred acroass a cold joint by shear friction. Free body diagrams of the forces transferred from the barrier to the deck overhang are shown in the Fig.E7.1-19c
90M. CONCRETE BARRIER STRENGTH The nominal shear resistance Vn of the interface plane is given by [A ]ncvvfc
91M. CONCRETE BARRIER STRENGTH The last two factors are for concrete placed against hardened concrete clean and free of laitance, but not intentionally roughened. Therefore for a 1-mm wide design stripncvvffy
92M. CONCRETE BARRIER STRENGTH The minimum cross-sectional area of dowels across the shear plane is [A ]vvfy
93M. CONCRETE BARRIER STRENGTH The basic development length lhb for a hooked bar with fy = 400 MPa. Is given by [A ]and shall not be less than 8db or 150mm. For a No.15 bar, db=16mm andwhich is greater than 8(16) = 128mm and 150mm. The modifications factors of 0.7 for adequate cover and 1.2 for epoxy coated bars [A ] apply, so that the development length lhb is changed tolhb=0.7(1.2)lhb = 0.74(292) = 245mm
95M. CONCRETE BARRIER STRENGTH The standard 90o hook with an extension of 12db=12(16)=192mm at the free end of the bar is adequate [A ]
96M. CONCRETE BARRIER STRENGTH 6. TOP REINFORCEMENT IN DECK OVERHANGThe top reinforcement must resist the negative bending moment over the exterior beam due to the collision and the dead load of the overhang. Based on the strength of the 90o hooks, the collision moment MCT (Fig.E7.1-19) distributed over a wall length of (Lc+2H) is
97M. CONCRETE BARRIER STRENGTH The dead load moments were calculated previously for strength I so that for the Extreme Event II limit state, we haveu
98M. CONCRETE BARRIER STRENGTH Bundling a No.10 bar with No.15 bar at 225mm on centers, the negative moment strength becomessn
99M. CONCRETE BARRIER STRENGTH this moment strength will be reduced because of the axial tension forceT = Rw/(Lc+2H)By assuming the moment interaction curve between moment and axial tension as a straight line (Fig.E7.1-20]
1107.10.2: SOLID SLAB BRIDGE DESIGN PROBLEM STATEMENT:Design the simply supported solid slab bridge of Fig with a span length of 10670mm center to center of bearing for a HL-93 live load. The roadway width is 13400mm curb to curb. Allow for a future wearing surface of 75mm thick bituminous overlay. Use fc’=30MPa and fy=400 MPa. Follow the slab bridge outline in Appendix A5.4 and the beam and girder bridge outline in section 5-Appendix A5.3 of the AASHTO (1994) LRFD bridge specifications.
141I. INVESTIGATE SERVICE LIMIT STATE DESIGN LANE LOADLane
142I. INVESTIGATE SERVICE LIMIT STATE The live load deflection estimate of 17mm is conservative because Ie was based on the maximum moment at midspan rather than an average Ie over the entire span.Also, the additional stiffness provided by the concrete barriers has been neglected, as well as the compression reinforcement in the top of the slab.Bridges typically deflect less than the calculations predict and as a result the deflection check has been made optional.
143I. INVESTIGATE SERVICE LIMIT STATE 5. Concrete stresses [A ].As there is no prestressing therefore concrete stresses does not apply.
144I. INVESTIGATE SERVICE LIMIT STATE 5. FATIGUE [A5.5.3]Fatigue load should be one truck with 9000-mm axle spacing [A ]. As the rear axle spacing is large, therefore the maximum moment results when the two front axles are on the bridge. as shown in Fig.E7.2-8, the two axle loads are placed on the bridge.No multiple presence factor is applied (m=1). From Fig.E7.2-8