Dist. FactorsLive Load Distribution Factor Calculation Options:Calculate the Live Load Distrtibution Factors using:AASHTO LRFD with TxDOT policiesWhen using AASHTO LRFD:use the Lever Rule when outside the Range of ApplicabilityWhen using the Lever Rule:ignore the Range of Applicability for the Skew FactorLLDF Option :1ROA Option :3Skew Option :2TXDOTCounty:AnyHighway:AnyDesign:BRGDate:11/18/082007 LRFD SpecsConsistant with TxDOT LRFD Bridge Manual July 2008.BRIDGEC-S-J:XXX-XX-XXXXID #:XXXXCk Dsn:Date:Rev. 8/08 - (No Interim)Directions:DIVISIONDescrip:U-beam SuperstructureFile:distribution_factors_u.xlsSheet:LRFD Distribution Factors*Live Load Distribution Factors are calculated according to AASHTO LRFD Bridge Design Specifications, 4th Edition (2007, with no interim revisions) as prescribed by TxDOT policies (LRFD Design Manual July 2008) and practices. The Lever Rule is used when outside the Range of Applicability. The Range of Applicability for the Skew Correction Factors is ignored.Indicates areas for user inputsInputIndicates program values that may be overidden*Beam Designation =U40BeamIndicates calculated valuesBeam Type =U-BeamNo. Beams, Nb =4d =40inIndicates commentsCLbrg to CLbrg, L =98.4ftCF =34.9inIndicates diagnostic messagesBeam Spacing, S =9.3ftAvg. Skew Angle, =15.0deg0Note: Use ctrl+a to print all concrete calculationsSlab Overhang, OH =6.75ft060.550Use ctrl+t to print all steel calculationsRail Width, RW =1ft043.460Use ctrl+r to print results onlyRoadway Width, W =39.3ftUse ctrl+l to print lever rule onlyNo. Design Lanes, NL =3lanesd = Overall depth of beam.0CF = Distance from the beam centerline to the intersection of the midline of the thinnest part of the outside web to the top of the flange.*For typical cross sections ( b & c ). Table 4.6.2.2.1-1ResultsThe Final LLDF for may be modified according to the following TxDOT policies: When the Roadway width is greater than or equal to 20ft, Exterior beams are designed for two or more lanes loaded only. When the Roadway width is less than 20ft, all beams are designed for one lane loaded only. For Exterior beams the lever rule value is multiplied by 0.9 to account for the interior beam taking some of the load due to continuity. For Exterior beams, the multiple presence factor is 1 for one lane loaded. In no case shall the LLDF for the exterior beams be less than the LLDF for the interior beams. When there are two or less beams the live load is equally distributed between the beams. In no case shall the LLDF be less than mNLNb.Final LLDFInterior Shear LLDF, gVinterior0.926Interior Moment LLDF, gMinterior0.638Exterior Shear LLDF, gVexterior1.004Exterior Moment LLDF, gMexterior0.64600CALCULATIONS:000Range of Applicability (ROA) ChecksShear LLDF Correction for Skew (Table 4.6.2.2.3c-1)Check :0 15 60OKCheck S:6' 9.3' 11.5'OK0Check L:20' 98.4' 140'OKCorr. =Check d:18'' 40'' 65''OKCheck Nb:4 3OK=1.0 + sqrt(98.4*40 / 12.0) / (6*9.3) * tan (15)Corr. =1.087Moment LLDF Correction for Skew (Table 4.6.2.2.2e-1)Check :0 15 60OKSet =15Corr. =1.05 - 0.25 tan 1.00=1.05 - 0.25 (tan 15) 1.0Corr. =0.983INTERIOR BEAM: Concrete0Shear LL Distribution Per Lane (Table 4.6.2.2.3a-1):One Lane LoadedLever Rule(Table 3.6.1.1.2)mg = 0.676 * 1.2 =0.811Modify for Skew:skew correction =1.087mg = 0.811 * 1.087 =0.882Equationg =g = (9.3/10)^0.6 * [40/(12.0*98.4)]^0.1 =0.680Modify for Skew:skew correction =1.087g = 0.680 * 1.087 =0.739Range of Applicability (ROA) ChecksCheck S:6' 9.3' 18'OKCheck d:18'' 40'' 65''OKCheck L:20' 98.4' 140'OKCheck Nb:4 3OKUse Equation from Table 4.6.2.2.3a-1 because all criteria is OK.gVint1 =0.739Two or More Lanes LoadedLever Rule(Table 3.6.1.1.2)mg = Max( 0.959 * 1.0 , 0.959 * 0.85 , 0.959 * 0.65 ) =0.959Modify for Skew:skew correction =1.087mg = 0.959 * 1.087 =1.042Equationg =g = (9.3/7.4)^0.8 * [40/(12.0*98.4)]^0.1 =0.852Modify for Skew:skew correction =1.087g = 0.852 * 1.087 =0.926Range of Applicability (ROA) Checks(same as for one lane loaded)Use Equation from Table 4.6.2.2.3a-1 because all criteria is OK.gVint2+ =0.926TxDOT Policy states gVInterior must be mNLNbmNLNb =0.85 * 3 / 4 =0.638Is W 20ft ?Yes>>TxDOT Policy states that if W 20ft, gVInterior is the Maximum of: gVint1, gVint2+, and mNL/Nb.0TxDOT Policy states that if W < 20ft, gVInterior is the Maximum of: gVint1, and mNL/Nb.gVinterior =0.926INTERIOR BEAM: Concrete0Moment LL Distribution Per Lane (Table 4.6.2.2.2b-1):One Lane LoadedLever Rule(Table 3.6.1.1.2)mg = 0.676 * 1.2 =0.811Modify for Skew:skew correction =0.983mg = 0.811 * 0.983 =0.797Equationg =g = (9.3/3.0)^0.35 * [(9.3*40)/(12.0*98.4^2)]^0.25 =0.352Modify for Skew:skew correction =0.983g = 0.352 * 0.983 =0.346Range of Applicability (ROA) ChecksCheck S:6' 9.3' 18'OKCheck L:20' 98.4' 140'OKCheck d:18'' 40'' 65''OKCheck Nb:4 3OKUse Equation from Table 4.6.2.2.2b-1 because all criteria is OK.gMint1 =0.346Two or More Lanes LoadedLever Rule(Table 3.6.1.1.2)mg = Max( 0.959 * 1.0 , 0.959 * 0.85 , 0.959 * 0.65 ) =0.959Modify for Skew:skew correction =0.983mg = 0.959 * 0.983 =0.943Equationg =g = (9.3/6.3)^0.6 * [(9.3*40)/(12.0*98.4^2)]^0.125 =0.614Modify for Skew:skew correction =0.983g = 0.614 * 0.983 =0.604Range of Applicability (ROA) Checks(same as for one lane loaded)Use Equation from Table 4.6.2.2.2b-1 because all criteria is OK.gMint2+ =0.604TxDOT Policy states gMInterior must be mNLNbmNLNb =0.85 * 3 / 4 =0.638Is W 20ft ?Yes>>TxDOT Policy states that if W 20ft, gMInterior is the Maximum of: gMint1, gMint2+, and mNL/Nb.0TxDOT Policy states that if W < 20ft, gMInterior is the Maximum of: gMint1, and mNL/Nb.gMinterior =0.638EXTERIOR BEAM: Concrete0Shear LL Distribution Per Lane (Table 4.6.2.2.3b-1):One Lane LoadedLever Rule(Table 3.6.1.1.2)mg = 1.081 * 1.0 * 0.9 =0.973TxDOT uses a multiple presence factor of 1.0 for one lane loaded, and multiplies the lever rule by 0.9 to account for continuity on the exterior beam.Modify for Skew:skew correction =1.087mg = 0.973 * 1.087 =1.058Use Lever Rule, as per AASHTO LRFD Table 4.6.2.2.3b-1.gVext1 =1.058Two or More Lanes LoadedLever Rule(Table 3.6.1.1.2)mg = Max( 1.135 * 1.0 , 1.135 * 0.85 , 1.135 * 0.65 ) * 0.9 =1.022TxDOT multiplies the lever rule by 0.9 to account for continuity on the exterior beam.Modify for Skew:skew correction =1.087mg = 1.022 * 1.087 =1.111Equationde = dist. b/w outer web to curbde = OH - RW - CFde =6.8ft - 1ft - 2.9 ft =2.8 fte =e = 0.8 + (2.8/10) =1.084g = e*gVint2+Eqg = 1.084 * 0.926 =1.004Skew Correction is included in gV(interior).Range of Applicability (ROA) ChecksInterior ROA is implicitly applied to the exterior beam.Check Interior Beam ROA:OKCheck de:0' 2.8' 4.5'OKCheck S:9.3' 18'OKUse Equation from Table 4.6.2.2.3b-1 because all criteria is OK.gVext2+ =1.004TxDOT Policy states gVExterior must be gVinteriorgVinterior =0.926Is Nb < 3 ?No0TxDOT Policy states that if Nb < 3 beams, gVExterior is mNL/Nb.mNLNb =0.85 * 3 / 4 =0.638Is W 20ft ?Yes>>TxDOT Policy states that if W 20ft, gVExterior is the Maximum of: gVinterior, gVext2+, and mNL/Nb.0TxDOT Policy states that if W < 20ft, gVExterior is the Maximum of: gVinterior, gVext1, and mNL/Nb.gVexterior =1.004EXTERIOR BEAM: Concrete0Moment LL Distribution Per Lane (Table 4.6.2.2.2d-1):One Lane LoadedLever Rule(Table 3.6.1.1.2)mg = 1.081 * 1.0 * 0.9 =0.973TxDOT uses a multiple presence factor of 1.0 for one lane loaded, and multiplies the lever rule by 0.9 to account for continuity (exterior beam, Moment LLDF).Modify for Skew:skew correction =0.983mg = 0.973 * 0.983 =0.956Use Lever Rule, as per AASHTO LRFD Table 4.6.2.2.2d-1.gVext1 =0.956Two or More Lanes LoadedLever Rule(Table 3.6.1.1.2)mg = Max( 1.135 * 1.0 , 1.135 * 0.85 , 1.135 * 0.65 ) * 0.9 =1.022TxDOT multiplies the lever rule by 0.9 to account for continuity on the exterior beam.Modify for Skew:skew correction =0.983mg = 1.022 * 0.983 =1.005Equatione =e = 0.97 + (2.8/28.5) =1.070g = e*gMint2+Eqg = 1.07 * 0.604 =0.646Skew Correction is included in gV(interior).Range of Applicability (ROA) ChecksInterior ROA is implicitly applied to the exterior beam.Check Interior Beam ROA:OKCheck de:0' 2.8' 4.5'OKCheck S:6' 9.3' 18'OKUse Equation from Table 4.6.2.2.2d-1 because all criteria is OK.gMext2+ =0.646TxDOT Policy states gMExterior must be gMinteriorgMinterior =0.638Is Nb < 3 ?No0TxDOT Policy states that if Nb < 3 beams, gMExterior is mNL/Nb.mNLNb =0.85 * 3 / 4 =0.638Is W 20ft ?Yes>>TxDOT Policy states that if W 20ft, gMExterior is the Maximum of: gMinterior, gMext2+, and mNL/Nb.0TxDOT Policy states that if W < 20ft, gMExterior is the Maximum of: gMinterior, gMext1, and mNL/Nb.gMexterior =0.646LEVER RULES =9.3 ft0INTERIOR0For S < 4:One Lane ==0.5000For 4 S < 6:One Lane ==0.500Two Lanes ==0.784>>For 6 S < 10:One Lane ==0.676Two Lanes ==0.9590For 10 S < 12:One Lane ==0.676Two Lanes ==0.9190For 12 S < 16:One Lane ==0.676Two Lanes ==0.919Three Lanes ==0.7700For 16 S < 18:One Lane ==0.676Two Lanes ==0.919Three Lanes ==0.770Four Lanes ==0.405LEVER RULES =9.3 ft0INTERIOR (con't)0For 18 S < 22:One Lane ==0.676Two Lanes ==0.919Three Lanes ==0.297Four Lanes ==-0.0680For 22 S 24:One Lane ==0.676Two Lanes ==0.919Three Lanes ==0.297Four Lanes ==-0.757EXTERIORS =9.3 ftOH =6.8 ftRW =1.0 ftX = S+OH-RW-2ft =13.0 ft00For X < 6:One Lane ==0.7030For 6 X < 12:One Lane ==1.081>>For 12 X < 18:One Lane ==1.081Two Lanes ==1.135LEVER RULEEXTERIOR (con't)S =9.3 ftOH =6.8 ft0RW =1.0 ftX = S+OH-RW-2ft =13.0 ft0For 18 X < 24:One Lane ==1.081Two Lanes ==0.8650For 24 X < 30:One Lane ==1.081Two Lanes ==0.865Three Lanes ==0.2700For 30 X < 36:One Lane ==1.081Two Lanes ==0.865Three Lanes ==-0.6490For 36 X < 42:One Lane ==1.081Two Lanes ==0.865Three Lanes ==-0.649Four Lanes ==-1.8920For 42 X 48:One Lane ==1.081Two Lanes ==0.865Three Lanes ==-0.649Four Lanes ==-3.459INTERIOREXTERIOROne Lane Loaded=0.676One Lane Loaded=1.081Two Lanes Loaded=0.959Two Lanes Loaded=1.135Three Lanes Loaded=0.959Three Lanes Loaded=1.135Four Lanes Loaded=0.959Four Lanes Loaded=1.135INTERIOR BEAM: SteelBeams are not SteelLever Rule(Table 3.6.1.1.2)mg = Max( 0.676*1.2 , 0.959*1.0 , 0.959*0.85 , 0.959*0.65 ) =0.959Steel beams have no Skew Correction.Equation(Table 4.6.2.2.2b-1)g = 0.05 + 0.85 * 3/4 + 0.425/3 =0.829Steel beams have no Skew Correction.Range of Applicability (ROA) ChecksCheck NL/Nb:0.5 0.75 1.5OKCheck Nb:4 4OKUse Equation because all criteria is OK.ginterior =0.829EXTERIOR BEAM: SteelBeams are not SteelLever Rule(Table 3.6.1.1.2)mg = Max( 1.081*1.2 , 1.135*1.0 , 1.135*0.85 ) =1.297Steel beams have no Skew Correction.Equationg = 0.05 + 0.85 * 3/4 + 0.425/3 =0.829Steel beams have no Skew Correction.Range of Applicability (ROA) ChecksCheck NL/Nb:0.5 0.75 1.5OKCheck Nb:4 4OKCheck de:2.8' 3'OKUse Equation because all criteria is OK.ginterior =0.829

&R&8

&P of &N-Input data in fields-Data in BLUE are set to default but may be changedGREENClick to Reset Defaults

TablesInterior Beam Reaction for given number of vehiclesReaction Times MPFSpacing1 Vehicle2 Vehicles3 Vehicles4 VehiclesSpacing1 Vehicle2 Vehicles3 Vehicles4 VehiclesSpacingMaxControllingPrestressed Beams30.50.50.50.530.60.50.4250.32530.6001 VehicleTypeB (in)C (in) or bfb (in)D (in) or d (in)E (in)F (in)G (in)H (in)J (in) or tw (in)K (in) or x (in)yt (in)yb (in)A (in2)I (in4)Weight (plf)CF (in)4.50.50.55555555560.55555555560.55555555564.50.60.55555555560.47222222220.36111111114.50.6001 VehicleU4055894033.2557.52710.138.3751723.6616.3979.9183108102134.924.70.50.57446808510.57446808510.57446808514.70.60.57446808510.48829787230.37340425534.70.6001 VehicleU5455965447.2564.530.524.1311.8820.531.5822.361120403020116738.424.80.50.58333333330.58333333330.58333333334.80.60.58333333330.49583333330.37916666674.80.6001 Vehicle4B204855.004.010.199.815922808661617.384.90.50.59183673470.59183673470.59183673474.90.60.59183673470.50306122450.38469387764.90.6001 Vehicle5B206055.004.010.129.887183523474823.3850.50.60.60.650.60.60.510.3950.6001 Vehicle4B284845.005.014.3813.626796874570716.385.10.50.60784313730.60784313730.60784313735.10.60.60784313730.51666666670.39509803925.10.6082 Vehicles5B286045.005.014.2613.748058537083822.385.20.50.61538461540.61538461540.61538461545.20.60.61538461540.52307692310.45.20.6152 Vehicles4B344845.005.017.9216.0879911565583216.385.30.50.62264150940.62264150940.62264150945.30.60.62264150940.5292452830.40471698115.30.6232 Vehicles5B346045.005.017.7216.2892514216196322.3860.50.66666666670.66666666670.666666666760.60.66666666670.56666666670.433333333360.6672 Vehicles4B404845.005.021.3118.6991917660795716.386.20.51612903230.69354838710.69354838710.69354838716.20.61935483870.69354838710.5895161290.45080645166.20.6942 Vehicles5B406045.005.021.0718.931045215300108822.386.70.5522388060.75373134330.75373134330.75373134336.70.66268656720.75373134330.64067164180.48992537316.70.7542 VehiclesSteel6143.466.90.56521739130.77536231880.77536231880.77536231886.90.67826086960.77536231880.6590579710.50398550726.90.7752 VehiclesOther6143.467.10.57746478870.79577464790.79577464790.79577464797.10.69295774650.79577464790.67640845070.51725352117.10.7962 Vehicles123456789101112131415167.30.58904109590.81506849320.81506849320.81506849327.30.70684931510.81506849320.69280821920.52979452057.30.8152 Vehicles7.50.60.83333333330.83333333330.83333333337.50.720.83333333330.70833333330.54166666677.50.8332 VehiclesCF is the distance from the beam centerline to the intersection of the midline of the thinnest part of the outside web to the top of the flange.7.70.61038961040.85064935060.85064935060.85064935067.70.73246753250.85064935060.72305194810.55292207797.70.8512 VehiclesCF = 55" / 2 + D * 1/4 - 5" / 2 / cos(arc tan(1/4))CF = bfb - x - tw/27.90.62025316460.86708860760.86708860760.86708860767.90.74430379750.86708860760.73702531650.56360759497.90.8672 Vehicles8.10.62962962960.88271604940.88271604940.88271604948.10.75555555560.88271604940.7503086420.57376543218.10.8832 VehiclesMultiple Presence8.30.63855421690.89759036140.89759036140.89759036148.30.76626506020.89759036140.76295180720.58343373498.30.8982 VehiclesFactor8.50.64705882350.91176470590.91176470590.91176470598.50.77647058820.91176470590.7750.59264705888.50.9122 VehiclesNo. Lanesm8.70.65517241380.92528735630.92528735630.92528735638.70.78620689660.92528735630.78649425290.60143678168.70.9252 Vehicles11.208.90.66292134830.93820224720.93820224720.93820224728.90.7955056180.93820224720.79747191010.60983146078.90.9382 Vehicles21.009.10.67032967030.95054945050.95054945050.95054945059.10.80439560440.95054945050.8079670330.61785714299.10.9512 Vehicles30.859.30.67741935480.96236559140.96236559140.96236559149.30.81290322580.96236559140.81801075270.62553763449.30.9622 Vehicles40.659.50.68421052630.97368421050.97368421050.97368421059.50.82105263160.97368421050.82763157890.63289473689.50.9742 Vehicles9.70.69072164950.98453608250.98453608250.98453608259.70.82886597940.98453608250.83685567010.63994845369.70.9852 VehiclesS =9.39.90.6969696970.99494949490.99494949490.99494949499.90.83636363640.99494949490.84570707070.64671717179.90.9952 VehiclesX =13.010.10.7029702971.00990099011.01485148511.014851485110.10.84356435641.00990099010.86262376240.659653465310.11.0102 VehiclesLane Width =12.0010.30.70873786411.02912621361.04368932041.043689320410.30.85048543691.02912621360.88713592230.678398058310.31.0292 VehiclesLever Rule - 12.00 ft Lane10.50.71428571431.04761904761.07142857141.071428571410.50.85714285711.04761904760.91071428570.696428571410.51.0482 VehiclesNo. LanesInteriorExterior10.70.71962616821.06542056071.09813084111.098130841110.70.86355140191.06542056070.9334112150.713785046710.71.0652 Vehiclesgg10.90.72477064221.08256880731.1238532111.12385321110.90.86972477061.08256880730.95527522940.730504587210.91.0832 Vehicles10.6761.08111.10.72972972971.09909909911.14864864861.148648648611.10.87567567571.09909909910.97635135140.746621621611.11.0992 Vehicles20.9591.13511.30.73451327431.11504424781.17256637171.172566371711.30.88141592921.11504424780.99668141590.762168141611.31.1152 Vehicles30.9591.13511.50.73913043481.13043478261.19565217391.195652173911.50.88695652171.13043478261.01630434780.77717391311.51.1302 Vehicles40.9591.13511.70.74358974361.14529914531.21794871791.217948717911.70.89230769231.14529914531.03525641030.791666666711.71.1452 Vehicles50.9591.13511.90.74789915971.15966386551.23949579831.239495798311.90.89747899161.15966386551.05357142860.805672268911.91.1602 Vehicles60.9591.13512.10.75206611571.1735537191.26033057851.260330578512.10.90247933881.1735537191.07128099170.81921487612.11.1742 Vehicles70.9591.13512.30.7560975611.18699186991.28048780491.280487804912.30.90731707321.18699186991.08841463410.832317073212.31.1872 Vehicles80.9591.135130.76923076921.23076923081.34615384621.3461538462130.92307692311.23076923081.14423076920.875131.2312 Vehicles90.9591.135140.78571428571.28571428571.42857142861.4285714286140.94285714291.28571428571.21428571430.9285714286141.2862 Vehicles100.9591.135150.81.33333333331.51.5333333333150.961.33333333331.2750.9966666667151.3332 Vehicles110.9591.135160.81251.3751.56251.625160.9751.3751.3281251.05625161.3752 Vehicles120.9591.135130.9591.135140.9591.135150.9591.135mg1 =0.8110.973mg2+ =0.9591.022mg =0.9591.022Lever Rule for Interior Beam is controlled by 2 Lanes Loaded and = 0.959Lever Rule for Exterior Beam is controlled by 2 Lanes Loaded and = 1.022

Tables00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

1 Vehicle2 Vehicles3 Vehicles4 VehiclesBeam Spacing (ft)LLDF (Including Multiple Presence Factor)Lever Rule - Controlling Number of Vehicles

These values include TxDOT's policy for U-Beams: 1) Multiply the result of the lever rule by 0.9 for Exterior Beams2) The multiple presence factor for One Lane Loaded = 1.0 for Exterior BeamsThese values include TxDOT's policy for U-Beams: 1) Multiply the result of the lever rule by 0.9 for Exterior Beams2) The multiple presence factor for One Lane Loaded = 1.0 for Exterior Beams3) For Exterior beams, single lane loaded is ignored when the Roadway width is 20ft.These values include TxDOT's policy for U-Beams: 1) Multiply the result of the lever rule by 0.9 for Exterior Beams2) The multiple presence factor for One Lane Loaded = 1.0 for Exterior Beams

MBD00471B96.unknown

MBD00E30B6C.unknown

MBD00E38B65.unknown

MBD00E3C876.unknown

MBD00E3AAA3.unknown

MBD00E347F5.unknown

MBD00E37666.unknown

MBD00E32C79.unknown

MBD004E493D.unknown

MBD004E493F.unknown

MBD004E576C.unknown

MBD004E493E.unknown

MBD00479708.unknown

MBD0047B09D.unknown

MBD00471B97.unknown

MBD003AF290.unknown

MBD003EBBCA.unknown

MBD00471831.unknown

MBD00471833.unknown

MBD00471B95.unknown

MBD00471832.unknown

MBD003EC93A.unknown

MBD004167FF.unknown

MBD0041AED9.unknown

MBD003EDB67.unknown

MBD003EC850.unknown

MBD003E1976.unknown

MBD003E1BD1.unknown

MBD003E9B4A.unknown

MBD003E1B58.unknown

MBD003E17AD.unknown

MBD003E18C9.unknown

MBD003DF7D8.unknown

MBD003909DF.unknown

MBD0039E42C.unknown

MBD003AC497.unknown

MBD003AC498.unknown

MBD003AC496.unknown

MBD003990DC.unknown

MBD0039BE6E.unknown

MBD003990DB.unknown

MBD0038C5D2.unknown

MBD0038D0E5.unknown

MBD0038E0C0.unknown

MBD0038C93D.unknown

MBD0038AE49.unknown

MBD0038B9B7.unknown

MBD00389F7F.unknown

MBD0038A25B.unknown

MBD00389955.unknown