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Bridge DesignBridge Design

Structural Engineering Structural Engineering

Final Year Final Year

History of Bridge History of Bridge DevelopmentDevelopment

Bridge is one of the oldest Bridge is one of the oldest instrument of our Civilization.instrument of our Civilization.

In pre-historic times bridge formed In pre-historic times bridge formed with fallen trees or logs of woodwith fallen trees or logs of wood

Suspension Bridges with creepers Suspension Bridges with creepers of treeof tree

Oldest bridge in record is built on Oldest bridge in record is built on river Niles in about 2650 B.C but river Niles in about 2650 B.C but no details are availableno details are available

History History

A wooden bridge built by the queen of A wooden bridge built by the queen of Babylon in the year 783 B.C. This bridge has Babylon in the year 783 B.C. This bridge has wooden platform supported on stone pierswooden platform supported on stone piers

Alexander while returning from India used a Alexander while returning from India used a boat bridge in 326 BCboat bridge in 326 BC

Primitive Arch bridge was built in Persia, Primitive Arch bridge was built in Persia, Greece and Rome Greece and Rome

Oldest Existing Bridge in 350 B.C consist of Oldest Existing Bridge in 350 B.C consist of 20 arches each of 7.5 m span total length is 20 arches each of 7.5 m span total length is 380 m in Babylon380 m in Babylon

X-istics of ancient BridgesX-istics of ancient Bridges

1.1. Crossing to the Right-Angle to Crossing to the Right-Angle to the Streamthe Stream

2.2. Hump in the CenterHump in the Center

3.3. Narrow WidthNarrow Width

4.4. Absence of Foot-PathAbsence of Foot-Path

5.5. AestheticsAesthetics

Evolution of Bridge Evolution of Bridge EngineeringEngineering

Resulting Combination of the evolution Resulting Combination of the evolution ofof Structures Structures Materials of ConstructionMaterials of Construction Method of DesignMethod of Design Method of FabricationMethod of Fabrication

Timber & Stone replaced by Timber & Stone replaced by Wrought Iron ----- Mild Steel ----- Wrought Iron ----- Mild Steel -----

Concrete----- Pre-stressed------ Concrete----- Pre-stressed------ Suspension bridges---Suspension bridges---

Span RangeSpan Range

TypeType MaterialMaterial Span Range (m)Span Range (m)

SlabSlab ConcreteConcrete 0-120-12

BeamBeam ConcreteConcrete

SteelSteel

12-21012-210

30-30030-300

TrussTruss SteelSteel 90-55090-550

Arch RibArch Rib ConcreteConcrete

SteelSteel

90-13090-130

120-370120-370

Arch TrussArch Truss SteelSteel 240-520240-520

CableCable ConcreteConcrete

SteelSteel

90-27090-270

90-35090-350

SuspensionSuspension SteelSteel 300-1400300-1400

Components of a BridgeComponents of a Bridge

1.1. Super StructureSuper Structure Structural members, beams, Structural members, beams,

girders, handrails, flooring, girders, handrails, flooring, arches, cables.arches, cables.

2.2. Sub StructureSub Structure AbutmentsAbutments PiersPiers Wing WallsWing Walls Foundations for Piers & Foundations for Piers &

AbutmentsAbutments

Basic DefinitionsBasic Definitions

BridgeBridge A structure facilitating a communication A structure facilitating a communication

route for carrying road, railway, route for carrying road, railway, pedestrian traffic or other moving loads pedestrian traffic or other moving loads over a depressionover a depression

CausewayCauseway It’s a pucca submersible bridge It’s a pucca submersible bridge

which allows flood water to pass which allows flood water to pass over it. It is provided on less over it. It is provided on less important routes in order to reduce important routes in order to reduce the construction cost of cross the construction cost of cross drainage structuresdrainage structures

DefinitionsDefinitions

Foot BridgeFoot Bridge Bridge Exclusively used for carrying Bridge Exclusively used for carrying

pedestrians, cycles & animalspedestrians, cycles & animals CulvertCulvert

When a Small stream crosses a road When a Small stream crosses a road with linear water way less than 6 with linear water way less than 6 metersmeters

Deck BridgeDeck Bridge Bridges whose floorings are Bridges whose floorings are

supported at top of the super supported at top of the super structuresstructures


Through BridgeThrough Bridge Whose floorings are supported at the Whose floorings are supported at the

bottom of the super-structurebottom of the super-structure Cantilever BridgeCantilever Bridge

More or less fixed at one end and free More or less fixed at one end and free on the other end varying from 8m to on the other end varying from 8m to 20m20m

Square BridgeSquare Bridge Bridges at Right-Angle to the axis of Bridges at Right-Angle to the axis of

riverriver Skew BridgeSkew Bridge

Bridges which are not at Right-Bridges which are not at Right-AngleAngle


Suspension BridgeSuspension Bridge Bridges suspended on cables Bridges suspended on cables

anchored at endsanchored at ends ApronApron

It’s a layer of concrete, masonry It’s a layer of concrete, masonry stone, etc placed like flooring at stone, etc placed like flooring at the entrance or outlet of a culvert the entrance or outlet of a culvert to prevent scourto prevent scour

Curtain WallCurtain Wall It’s a thin wall used as a protection It’s a thin wall used as a protection

against scouring action of a streamagainst scouring action of a stream


Back WallBack Wall Retaining wall to support soil from Retaining wall to support soil from

approach roadapproach road Wing-wallWing-wall

Retaining the earth from later dimensionRetaining the earth from later dimension Floor SlabFloor Slab

Provides the carriage way for the Provides the carriage way for the movement of trafficmovement of traffic

StringersStringers These are the small beams which These are the small beams which

transfer the load from floor slab to transfer the load from floor slab to floor beamsfloor beams


Floor BeamFloor Beam Transfer the load from stringer to Transfer the load from stringer to

main girdermain girder GirderGirder

Carries the load of bridge & Carries the load of bridge & Transfer it to the piers & Transfer it to the piers & abutmentsabutments

BearingsBearings These behaves as shock absorbers These behaves as shock absorbers

and caries thermal stressesand caries thermal stresses


PiersPiers These are the intermediate supports of a These are the intermediate supports of a

bridge superstructuresbridge superstructures AbutmentsAbutments

These are the end supports of the These are the end supports of the superstructuresuperstructure

Effective SpanEffective Span The C/C distance between any two The C/C distance between any two

adjacent supportsadjacent supports Clear SpanClear Span

The clear distance between any two The clear distance between any two adjacent supportsadjacent supports


Free BoardFree Board Difference between the highest Difference between the highest

flood level and the formation level flood level and the formation level of road embankments on the of road embankments on the approachesapproaches

HeadroomHeadroom The vertical distance between the The vertical distance between the

highest point of a vehicle and the highest point of a vehicle and the lowest point of any protruding lowest point of any protruding member of a bridgemember of a bridge

Requirements of an Requirements of an Ideal BridgeIdeal Bridge

An ideal bridge meets following An ideal bridge meets following requirements to fulfill the three requirements to fulfill the three criteria of efficiency, criteria of efficiency, effectiveness and equityeffectiveness and equity

1.1. It serves the intended function It serves the intended function with utmost safety and with utmost safety and convenienceconvenience

2.2. It is aesthetically soundIt is aesthetically sound

3.3. It is economicalIt is economical

Selection of Selection of Bridge SiteBridge Site

1.1. Ground ReconnaissanceGround Reconnaissance2.2. Collection of hydraulic/ground dataCollection of hydraulic/ground data3.3. Subsoil InvestigationSubsoil Investigation4.4. Type of BridgeType of Bridge5.5. Engineering ConsiderationsEngineering Considerations6.6. Social ConsiderationsSocial Considerations7.7. Aesthetic ConsiderationsAesthetic Considerations8.8. Future RequirementsFuture Requirements9.9. Design AlternativesDesign Alternatives10.10. Strategically neededStrategically needed

Ideal Bridge SiteIdeal Bridge SiteCharacteristicsCharacteristics

1.1. Geologically SuitableGeologically Suitable2.2. The stream at bridge site should be The stream at bridge site should be

well defined and as narrow as well defined and as narrow as possiblepossible

3.3. There should be a straight reach of There should be a straight reach of stream at bridge sitestream at bridge site

4.4. Site should have firm, permanent, Site should have firm, permanent, straight and high banksstraight and high banks

5.5. Flow of water at bridge site should Flow of water at bridge site should be steady regime conditions, it be steady regime conditions, it should be free from whirls and should be free from whirls and cross currentscross currents

Ideal Bridge SiteIdeal Bridge SiteCharacteristicsCharacteristics

6.6. It is feasible to have straight It is feasible to have straight approach roads and square approach roads and square alignmentalignment

7.7. Site providing the adequate vertical Site providing the adequate vertical height available underneath for height available underneath for navigationnavigation

8.8. There should be no adverse There should be no adverse environmental inputenvironmental input

9.9. Construction facilities availableConstruction facilities available

10.10.Time ConsiderationsTime Considerations

Types of BridgesTypes of Bridges

1.1. W.r.t Materials of ConstructionW.r.t Materials of Construction

1.1. R.C.C BridgesR.C.C Bridges

2.2. Pre- Stressed BridgesPre- Stressed Bridges

3.3. Steel BridgesSteel Bridges

4.4. Wooden BridgesWooden Bridges

5.5. Hanging Cable BridgesHanging Cable Bridges


2.2. W.r.t ConstructionW.r.t Construction

1.1. Pre- cast BridgesPre- cast Bridges

2.2. Cast Insitu BridgesCast Insitu Bridges

3.3. W.r.t Load Carrying ConditionsW.r.t Load Carrying Conditions

1.1. Compression Bridges (Arch Type)Compression Bridges (Arch Type)

2.2. Tension Bridges ( Suspension Tension Bridges ( Suspension Type)Type)

3.3. Flexural bridges ( Deck-Girder Flexural bridges ( Deck-Girder Type)Type)


4.4. W.r.t X-Section ConditionsW.r.t X-Section Conditions1.1. Solid Slab BridgeSolid Slab Bridge2.2. Hollow BridgeHollow Bridge3.3. Box- Girder BridgeBox- Girder Bridge

5.5. W.r.t Design ConditionsW.r.t Design Conditions1.1. Slab BridgeSlab Bridge2.2. Deck- Girder BridgeDeck- Girder Bridge


1.1. Slab BridgeSlab Bridge Slab is Supported by Abutments & Slab is Supported by Abutments &

Slab is designed as one-way slab Slab is designed as one-way slab supported at edges. The main supported at edges. The main reinforcement is parallel to the reinforcement is parallel to the flow of trafficflow of traffic

2.2. Deck- Girder BridgeDeck- Girder Bridge The main reinforcement is The main reinforcement is

perpendicular to the flow of perpendicular to the flow of traffic, slab is supported on traffic, slab is supported on girders (interior, exterior)girders (interior, exterior)

Slab Bridge

Deck – Girder Bridge

AASHTO AASHTO Design ConditionsDesign Conditions

1.1. Design is based on Elastic- Design is based on Elastic- Theory Theory

2.2. AASHTO Stress limitationsAASHTO Stress limitations1.1. ffcc = = 0.40.4 f fcc//

2.2. ffs = 0.5 s = 0.5 ffy y

3.3. Span length Span length

1.1. C/C distance between supportsC/C distance between supports

2.2. Clear Span + Slab ThicknessClear Span + Slab Thickness(Which ever is larger)(Which ever is larger)


4.4. Dead LoadDead Load1.1. (h / 12)*150 = Slab Weight(h / 12)*150 = Slab Weight

2.2. Weight of Wearing Surface =Weight of Wearing Surface =15 to 30 15 to 30 psfpsf

3.3. Self weight of (a) Girder (b) Edge Self weight of (a) Girder (b) Edge beambeam

5.5. Live LoadLive Load

1.1. HS- 20 TruckHS- 20 Truck

2.2. HS- 15 TruckHS- 15 Truck

3.3. Equivalent Lane LoadEquivalent Lane Load

HS- Truck LoadingHS- Truck Loading

14 /

6 /

16000 lbs16000 lbs4000 lbs

2 /

2 /

14 /

6 /

12000 lbs12000 lbs3000 lbs

2 /

2 /

HS-20 Loading

HS-15 Loading

EquivalentEquivalentLane LoadingLane Loading

PCPC

ww

PCPC = 18000 lbs 26000 18000 lbs 26000 lbslbs

W W = 640 lbs/ft640 lbs/ft

For HS-20 Loading

For HS-15 Loading Take 3/4 th Take 3/4 th

Moment Shear

LoadingLoading

Lane Loading / Standard Truck Lane Loading / Standard Truck loading shall be assumed to loading shall be assumed to occupy a width of 10 ftoccupy a width of 10 ft

These loads shall be placed in 12 These loads shall be placed in 12 ft wide traffic lanes spaced across ft wide traffic lanes spaced across the entire bridge road waythe entire bridge road way

A 20 to 24 feet wide road shall A 20 to 24 feet wide road shall have two design lanes each equal have two design lanes each equal to half of width of road wayto half of width of road way

LoadingLoading

Each 10 feet lane loading or single Each 10 feet lane loading or single standard truck shall be considered standard truck shall be considered as a unit, and fractional load lane or as a unit, and fractional load lane or fractional trucks shall not be usedfractional trucks shall not be used

Where maximum stresses are caused Where maximum stresses are caused in any member by loading any in any member by loading any number of traffic lanes number of traffic lanes simultaneously, following % age of simultaneously, following % age of resultant live load stresses shall be resultant live load stresses shall be usedused One or Two lanesOne or Two lanes 100 %100 % Three LanesThree Lanes 90 % 90 % More Than 3 lanesMore Than 3 lanes 75 % 75 %


6.6. Impact LoadImpact Load

II = 50 / S+125 = 50 / S+125

* S = Span length* S = Span length

I I > 30 % of Live Load> 30 % of Live Load

Design ofDesign ofSlab BridgeSlab Bridge

Design of SlabDesign of Slab Design of Edge BeamDesign of Edge Beam

Dead Load Moment = Dead Load Moment = w lw l 22 / 8 / 8 Live LoadLive Load Moment = Moment = HS-20 / HS-15 HS-20 / HS-15

Live Load Moment = Live Load Moment = 900 *S for S <= 50’900 *S for S <= 50’Live Load Moment = Live Load Moment = 1300*S – 20,000 lb-ft1300*S – 20,000 lb-ft

for S > 50’for S > 50’or or

= = 16000 / E – w16000 / E – wE= Equivalent Lane LoadingE= Equivalent Lane LoadingE= 4 +0.06 * S <=7’E= 4 +0.06 * S <=7’

(S+2)/32 * P20 ft-lb per foot width (S+2)/32 * P20 ft-lb per foot width of slabof slab

(S+2)/32 * P15(S+2)/32 * P15

for HS-20 P = 16,000 lbsfor HS-20 P = 16,000 lbs

for HS-15 P = 12,000 lbsfor HS-15 P = 12,000 lbs

Design ofDeck Girder Bridge

Design ofDesign ofSlab BridgeSlab Bridge

Total Moment =Total Moment =D.L Moment + L.L Moment + Impact D.L Moment + L.L Moment + Impact Load moment Load moment

M = 1 /2 * fc * kd * bjdM = 1 /2 * fc * kd * bjd K= n / (n+r)K= n / (n+r)

n = ES /EC = 29* 10n = ES /EC = 29* 106 6 / 57000 / 57000 √ √ fc’fc’ j =1 – (k /3)j =1 – (k /3) r = fs / fcr = fs / fc Cover = 1.5 “ totalCover = 1.5 “ total AAss = M / (fs*j*d) = M / (fs*j*d) Distribution Steel = 100 / Distribution Steel = 100 / √ √ S % age of main steelS % age of main steel Distribution Steel =220/Distribution Steel =220/ √ √ S % age of main steel S % age of main steel

(Deck –Girder Bridge)(Deck –Girder Bridge)

Design ofDesign ofEdge BeamEdge Beam

Dead Load of edge beamDead Load of edge beam Dead load moment = wlDead load moment = wl22 /8 /8 Live Load moment = 0.1 pc*SLive Load moment = 0.1 pc*S

Where Pc is wheel load Where Pc is wheel load

for HS-20 Pc = 16,000 lbsfor HS-20 Pc = 16,000 lbs

for HS-15 Pc = 12,000 lbsfor HS-15 Pc = 12,000 lbs

ExampleExample

Design a slab bridge having clear span of 15 Design a slab bridge having clear span of 15 // a clear a clear width of 26 width of 26 / / . Live load HS-20 Truck & wearing . Live load HS-20 Truck & wearing surface load is 30 psf. Concrete strength fc’ = 3,000 surface load is 30 psf. Concrete strength fc’ = 3,000 psi and fy = 40,000 psipsi and fy = 40,000 psi

SolutionSolution S = 15 ’S = 15 ’ Clear width = 26 ‘Clear width = 26 ‘ Live load = HS-20 Live load = HS-20 fc’ = 3,000 psifc’ = 3,000 psi fy = 40,000 psi fy = 40,000 psi Wearing surface = 30psfWearing surface = 30psf

ExampleExample

AASHTO allowable StressesAASHTO allowable Stresses fc = 0.4 fc ‘ = 0.4 * 3000 = 1200 psifc = 0.4 fc ‘ = 0.4 * 3000 = 1200 psi fs = 0.5 fy = 0.5 *40,000 =20,000 psifs = 0.5 fy = 0.5 *40,000 =20,000 psi

Load CalculationsLoad Calculations Assuming thickness of slab = 12”Assuming thickness of slab = 12” Dead load of slab = (12 / 12 )* 150 = 150 psfDead load of slab = (12 / 12 )* 150 = 150 psf Total Dead load = 150 + 30 = 180 psfTotal Dead load = 150 + 30 = 180 psf Total Dead load moment = wlTotal Dead load moment = wl22 /8 /8

= 180 (16)= 180 (16)2 2 / 8 = 5760 / 8 = 5760 lb-ftlb-ft

ExampleExample

Moment CalculationsMoment Calculations Live load moment = 900 * S = 900 * 16 = Live load moment = 900 * S = 900 * 16 =

14400 lb-ft14400 lb-ft Impact moment = Impact moment = II = 50 / (S+125) = 50 / (S+125)

=50 / (16+125) = 0.3570=50 / (16+125) = 0.3570

So we will use 0.3So we will use 0.3

Impact moment = Impact moment = II = 0.3 Live load moment = 0.3 Live load moment

= 0.3 * 14400 = 4320 lb-ft= 0.3 * 14400 = 4320 lb-ft TotalTotal Moment calculationMoment calculation

M = 5760 +14400+4320 = 24480 lb-ftM = 5760 +14400+4320 = 24480 lb-ft

ExampleExample Using Elastic TheoryUsing Elastic Theory

k =n / (n+r) k =n / (n+r) n = Es/ Ec = 29*10n = Es/ Ec = 29*1066 / 57000 / 57000√√3000 = 9.33000 = 9.3 r = fs / fc = 20000/1200 = 16.67r = fs / fc = 20000/1200 = 16.67 k = n / (n+r) = 0.358k = n / (n+r) = 0.358 j = 1- (k /3) = 1- 0.358/3 = 0.881j = 1- (k /3) = 1- 0.358/3 = 0.881 M = ½ fc bkd * jdM = ½ fc bkd * jd 24480*12=1/2* 1200*12*0.358*0.881*d24480*12=1/2* 1200*12*0.358*0.881*d22 d=11.4”d=11.4” h=d + Cover +0.5 “ = 11.4 +0.75+0.5 = h=d + Cover +0.5 “ = 11.4 +0.75+0.5 =

12.6”12.6” > 12 “> 12 “

ExampleExample Using Elastic TheoryUsing Elastic Theory

Lets assume h = 14 “Lets assume h = 14 “ Dead load = (14 / 12 ) * 150 = 175 psfDead load = (14 / 12 ) * 150 = 175 psf W.S load = 30 psfW.S load = 30 psf Total Dead Load = 175 + 30 = 205 psfTotal Dead Load = 175 + 30 = 205 psf Total Dead load moment = wlTotal Dead load moment = wl22 /8 /8

= 205 (16)= 205 (16)2 2 / 8 = 6560 lb-ft/ 8 = 6560 lb-ft Live load moment = 900 * S = 900 * 16 = 14400 lb-ftLive load moment = 900 * S = 900 * 16 = 14400 lb-ft

Impact moment = Impact moment = II = 0.3 Live load moment = 0.3 Live load moment

= 0.3 * 14400 = 4320 = 0.3 * 14400 = 4320 lb-ftlb-ft

M = 6560 +14400+4320 = M = 6560 +14400+4320 = 25280 lb-ft25280 lb-ft

ExampleExample Calculation of Steel AreaCalculation of Steel Area

AAss = M / (fs*j*d) = M / (fs*j*d) = (25280*12)/ (20000*0.881*12.75)= (25280*12)/ (20000*0.881*12.75)

d= 14-1.25d= 14-1.25** = 12.75 = 12.75 **(0.5+0.75) (0.5+0.75)

AAss = 1.44 in = 1.44 in22

# 7 @ 5” c/c# 7 @ 5” c/c

Distribution Steel = 100 / Distribution Steel = 100 / √ √ S % age of main steelS % age of main steel

= 100 / = 100 / √√16 = 25 % of main steel = 16 = 25 % of main steel = 0.3375 in0.3375 in22

• # 5 @ 10” c/c# 5 @ 10” c/c

ExampleExample

Design of Edge BeamDesign of Edge Beam Dead load of edge beam = ((24 “ * 24” )/144)*15Dead load of edge beam = ((24 “ * 24” )/144)*15

= 600 lb/ft= 600 lb/ft Dead load moment = 600 (16)Dead load moment = 600 (16)2 2 /8 = 19200 lb-/8 = 19200 lb-

ftft Live load moment = 0.1Pc*S = 0.1 (16000 Live load moment = 0.1Pc*S = 0.1 (16000

*16)*16)

= 25600 lb-ft= 25600 lb-ft Total Moment = 19200+25600 = 44800 lb-ftTotal Moment = 19200+25600 = 44800 lb-ft M= ½ fc bkd*jdM= ½ fc bkd*jd

44800*1244800*12 = ½ *1200-24”*0.357*0.881 d = ½ *1200-24”*0.357*0.881 d22

d= 10.9 “ d= 10.9 “

ExampleExample

Calculation of Steel AreaCalculation of Steel Area AAss = M / (fs*j*d) = M / (fs*j*d) AAs = s = (44800 *12 )/ (20000 (44800 *12 )/ (20000

*0.881*12.75)*0.881*12.75) AAs =s =2.39 in2.39 in22

Use 7 # 4 barsUse 7 # 4 bars

Draw the Sketches NeatlyDraw the Sketches Neatly

ExampleExample

Design a Deck-girder bridge having clear span of 48 Design a Deck-girder bridge having clear span of 48 // a clear width of 29 a clear width of 29 / / . Live load HS-20 Truck & wearing . Live load HS-20 Truck & wearing surface load is 30 psf. Concrete strength fc’ = 3,000 surface load is 30 psf. Concrete strength fc’ = 3,000 psi and fy = 40,000 psipsi and fy = 40,000 psi

SolutionSolution S = 4’- 4”S = 4’- 4” Clear width = 29‘Clear width = 29‘ Clear Span = 48’Clear Span = 48’ Live load = HS-20 Live load = HS-20 fc’ = 3,000 psifc’ = 3,000 psi fy = 40,000 psi fy = 40,000 psi Assume Wearing Surface = 15 psfAssume Wearing Surface = 15 psf

Load CalculationsLoad Calculations

Assuming thickness of slab = 6”Dead load of slab = (6 / 12 )* 150 = 75 psfTotal Dead load = 75 + 15 = 90 psfTotal (+ & - )Dead load moment = wlTotal (+ & - )Dead load moment = wl22 /10 /10

= 90 (4.333)= 90 (4.333)2 2 / 10 = / 10 = 169 169 lb-ftlb-ft

Live load moment = 0.80 Live load moment = 0.80 {(S+2)/32 }* P20 {(S+2)/32 }* P20 = 0.80 {(4.33+2)/32 }* 16000 ==2530 lb-ft 2530 lb-ft

Impact moment = Impact moment = II = 0.3 Live = 0.3 Live load moment load moment = 0.3 * 2530 = = 0.3 * 2530 = 760 lb-ft 760 lb-ft

Total Moment calculationM = 169 +2530+760 = 3459 lb-ft3459 lb-ft

M = ½ fc bkd * jd3459*12 =1/2*1200*12*0.375*0.875*d2

d = 4.19 in

h = 6.5” with 1” cover below # 6 bars assumed then d=4.37 in

As = M / (fs*j*d) = (3459*12)/ (20000*0.875*4.37) = 0.54 in2

# 6 @ 10” c/cDistribution Steel = 220 / √ S % age of main steel

= 220 / √4.33 = 105%of main steel = 0.56 7in2

5# 5 bars

Design of Interior GirderDesign of Interior GirderThe interior girders are T beams with flange width equal c/c of girders, the required stem dimensions governed by either Max. moment or max. shear

Assume bridges seats = 2ft

Effective Span length from center of bearings = 50 ft

Dead load from slab on plf of beam = {(6.5/12*150)+15}*5.5

= 528 plf

Assume Section below slab = 14”x 30” (437 plf )Total dead Load on Beam = 965 plf

Dead load moment = (965 x 502 )/8 = 302,000 lb-ft

The absolute Live load moment will occurs with HS 20 loading on the bridge in the position shown in the figure with distribution loads as specified by AASHTOEach interior girder must support 5.5/5 = 1.10 wheel load per wheel, therefore the load from rear wheel is 16000 x 1.1 = 17,600 lb and that from front wheel is 4000 x 1.1 = 4400 lb.

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