23609507 17-bridge-engineering

17Thomas A. Ostrom Steven L. Mellon

ChiefOffice of Structures-North

California Department of TransportationSacramento, California

Senior Bridge Design EngineerQuincy Engineering, Inc.Sacramento, California

BRIDGE ENGINEERING

Bridge engineering covers the planning,design, construction, operation, andmaintenance of structures that carryfacilities for movement of humans, ani-

mals, or materials over natural or created obstacles.Most of the diagrams used in this section were

taken from the “Manual of Bridge Design Practice,”State of California Department of Transportationand “Standard Specifications for HighwayBridges,” American Association of State Highwayand Transportation Officials. The authors expresstheir appreciation for permission to use theseillustrations from this comprehensive and author-itative publication.

General Design Considerations

17.1 Bridge Types

Bridges are of two general types: fixed and mov-able. They also can be grouped according to thefollowing characteristics:

Supported facilities: Highway or railway bridgesand viaducts, canal bridges and aqueducts, pedes-trian or cattle crossings, material-handling bridges,pipeline bridges.

Bridge-over facilities or natural features: Bridgesover highways and over railways; river bridges;bay, lake, slough and valley crossings.

Basic geometry: In plan—straight or curved,square or skewed bridges; in elevation—low-levelbridges, including causeways and trestles, or high-level bridges.

Structural systems: Single-span or continuous-beam bridges, single- or multiple-arch bridges,suspension bridges, frame-type bridges.

Construction materials: Timber, masonry, con-crete, and steel bridges.

17.2 Design Specifications

Designs of highway and railway bridges of con-crete or steel often are based on the latest editionsof the “Standard Specifications for HighwayBridges” or the “Load and Resistance FactorDesign Specifications” (LRFD) of the AmericanAssociation of State Highway and TransportationOfficials (AASHTO) and the “Manual for Rail-way Engineering” of the American Railway En-gineering and Maintenance-of-Way Association(AREMA). Also useful are standard plans issuedby various highway administrations and railwaycompanies.

Length, width, elevation, alignment, and angleof intersection of a bridge must satisfy thefunctional requirements of the supported facilitiesand the geometric or hydraulic requirements ofthe bridged-over facilities or natural features.Figure 17.1 shows typical highway clearancediagrams.

Selection of the structural system and of theconstruction material and detail dimensions isgoverned by requirements of structural safety;economy of fabrication, erection, operation, andmaintenance; and aesthetic considerations.

Highway bridge decks should offer comfort-able, well-drained riding surfaces. Longitudinalgrades and cross sections are subject to standardssimilar to those for open highways (Sec. 16).Provisions for roadway lighting and emergencyservices should be made on long bridges.

Barrier railings should keep vehicles within theroadways and, if necessary, separate vehicular

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Source: Standard Handbook for Civil Engineers

lanes from pedestrians and bicyclists. Utilitiescarried on or under bridges should be adequatelyprotected and equipped to accommodate expan-sion or contraction of the structures.

Most railroads require that the ballast bed becontinuous across bridges to facilitate vertical trackadjustments. Long bridges should be equippedwith service walkways.

17.3 Design Loads for Bridges

Bridges must support the following loads withoutexceeding permissible stresses and deflections:

Dead load D, including permanent utilities

Live load L and impact I

Longitudinal forces due to acceleration or decel-eration LF and friction F

Centrifugal forces CF

Wind pressure acting on the structure W and themoving load WL

Earthquake forces EQ

Earth E, water and ice pressure ICE, stream flow SF,and uplift B acting on the substructure

Forces resulting from elastic deformations, includ-ing rib shortening R

Forces resulting from thermal deformations T,including shrinkage S, and secondary prestressingeffects

17.3.1 Highway Bridge Loads

Vehicular live load of highway bridges is expressedin terms of design lanes and lane loadings. Thenumber of design lanes depends on the width ofthe roadway.

Fig. 17.1 Minimum clearances for highway structures. (a) Elevation of a highway bridge showingminimum vertical clearances below it. (b) Typical bridge cross sections indicating minimum horizontalclearances. Long-span bridges may have different details and requirements.

17.2 n Section Seventeen



BRIDGE ENGINEERING

In the standard specifications, each lane load isrepresented by a standard truck with trailer(Fig. 17.3) or, alternatively, as a 10-ft-wide uniformload in combination with a concentrated load(Fig. 17.2). As indicated in Fig. 17.3, there are twoclasses of loading: HS20 and HS15, which representa truck and trailer with three loaded axles. Theseloading designations are followed by a 44, whichindicates that the loading standard was adopted in1944. The LRFD HL-93 vehicular live load consistsof a combination of the HS20-44 design truckdepicted in Fig. 17.3, or the LRFD design tandem,and the LRFD live load. The LRFD design tandemis defined as a pair of 25 kip axles spaced 4.0 ftapart. The LRFD live load consists of 0.64 k/lfapplied uniformly in the longitudinal and trans-verse direction.

When proportioning any member, all lane loadsshould be assumed to occupy, within their res-pective lanes, the positions that produce maximumstress in that member. Table 17.1 gives maximummoments, shears, and reactions for one loadedlane. Effects resulting from the simultaneousloading of more than two lanes may be reduced

by a loading factor, which is 0.90 for three lanes and0.75 for four lanes.

In design of steel grid and timber floors for HS20loading, one axle load of 24 kips or two axle loadsof 16 kips each, spaced 4 ft apart, may be used,whichever produces the greater stress, instead ofthe 32-kip axle shown in Fig. 17.3. For slab design,the centerline of the wheel should be assumed to be1 ft from the face of the curb.

Wind forces generally are considered as mov-ing loads that may act horizontally in any direc-tion. They apply pressure to the exposed area of thesuperstructure, as seen in side elevation; to trafficon the bridge, with the center of gravity 6 ft abovethe deck; and to the exposed areas of the sub-structure, as seen in lateral or front elevation. Windloads in Tables 17.2 and 17.3 were taken from“Standard Specifications for Highway Bridges,”American Association of State Highway andTransportation Officials. They are based on 100-mi/h wind velocity. They should be multiplied by(V/100)2 for other design velocities except forGroup III loading (Art. 17.4).

In investigation of overturning, add to horizon-tal wind forces acting normal to the longitudinalbridge axis an upward force of 20 lb/ft2 for thestructure without live load or 6 lb/ft2 when thestructure carries live load. This force should beapplied to the deck and sidewalk area in planat the windward quarter point of the transversesuperstructure width.

Impact is expressed as a fraction of live-loadstress and determined by the formula:

I ¼ 50

125þ l30% maximum (17:1)

where l ¼ span, ft; or for truck loads on cantilevers,length from moment center to farthermost axle; orfor shear due to truck load, length of loaded por-tion of span. For negative moments in continuousspans, use the average of two adjacent loadedspans. For cantilever shear, use I ¼ 30%. Impact isnot figured for abutments, retaining walls, piers,piles (except for steel and concrete piles aboveground rigidly framed into the superstructure),foundation pressures and footings, and sidewalkloads.

Longitudinal forces on highway bridgesshould be assumed at 5% of the lane load plusconcentrated load for moment headed in one

Fig. 17.2 HS loadings for simply supportedspans. For maximum negative moment in continu-ous spans, an additional concentrated load of equalweight should be placed in one other span for max-imum effect. For maximum positive moment, onlyone concentrated load should be used per lane, butcombined with as many spans loaded uniformlyas required for maximum effect.

Bridge Engineering n 17.3



BRIDGE ENGINEERING

direction, plus forces resulting from friction inbridge expansion bearings.

Centrifugal forces should be computed as apercentage of design live load

C ¼ 6:68S2

R(17:2)

where S ¼ design speed, mi/h

R ¼ radius of curvature, ft

These forces are assumed to act horizontally 6 ftabove deck level and perpendicular to the bridgecenterline.

Restraint forces, generated by preventingrotations of deformations, must be considered indesign.

Thermal forces, in particular, from restraint,may cause overstress, buckling, or cracking.Provision should be made for expansion andcontraction due to temperature variations, and

Fig. 17.3 Standard truck loading. HS trucks:W ¼ combined weight on the first two axles, which is thesame weight as for H trucks. V indicates a variable spacing from 14 to 30 ft that should be selected toproduce maximum stress.




BRIDGE ENGINEERING

Table 17.1 MaximumMoments, Shears, and Reactions for Truck Loads on One Lane, Simple Spans*

H15 H20 HS15 HS20

Span, ft Moment†End shearand endreaction‡

Moment†End shearand endreaction‡



10 60.0§ 24.0§ 80.0§ 32.0§ 60.0§ 24.0§ 80.0§ 32.0§

20 120.0§ 25.8§ 160.0§ 34.4§ 120.0§ 32.2§ 160.0§ 41.6§

30 185.0§ 27.2§ 246.6§ 36.3§ 211.6§ 37.2§ 282.1§ 49.6§

40 259.5§ 29.1 346.0§ 38.8 337.4§ 41.4§ 449.8§ 55.2§

50 334.2§ 31.5 445.6§ 42.0 470.9§ 43.9§ 627.9§ 58.5§

60 418.5 33.9 558.0 45.2 604.9§ 45.6§ 806.5§ 60.8§

70 530.3 36.3 707.0 48.4 739.2§ 46.8§ 985.6§ 62.4§

80 654.0 38.7 872.0 51.6 873.7§ 47.7§ 1164.9§ 63.6§

90 789.8 41.1 1053.0 54.8 1008.3§ 48.4§ 1344.4§ 64.5§

100 937.5 43.5 1250.0 58.0 1143.0§ 49.0§ 1524.0§ 65.3§

110 1097.3 45.9 1463.0 61.2 1277.7§ 49.4§ 1703.6§ 65.9§

120 1269.0 48.3 1692.0 64.4 1412.5§ 49.8§ 1883.3§ 66.4§

130 1452.8 50.7 1937.0 67.6 1547.3§ 50.7 2063.1§ 67.6140 1648.5 53.1 2198.0 70.8 1682.1§ 53.1 2242.8§ 70.8150 1856.3 55.5 2475.0 74.0 1856.3 55.5 2475.1 74.0160 2076.0 57.9 2768.0 77.2 2076.0 57.9 2768.0 77.2170 2307.8 60.3 3077.0 80.4 2307.8 60.3 3077.0 80.4180 2551.5 62.7 3402.0 83.6 2551.5 62.7 3402.0 83.6190 2807.3 65.1 3743.0 86.8 2807.3 65.1 3743.0 86.8200 3075.0 67.5 4100.0 90.0 3075.0 67.5 4100.0 90.0220 3646.5 72.3 4862.0 96.4 3646.5 72.3 4862.0 96.4240 4266.0 77.1 5688.0 102.8 4266.0 77.1 5688.0 102.8260 4933.5 81.9 6578.0 109.2 4933.5 81.9 6578.0 109.2280 5649.0 86.7 7532.0 115.6 5649.0 86.7 7532.0 115.6300 6412.5 91.5 8550.0 122.0 6412.5 91.5 8550.0 122.0

* Based on “Standard Specifications for Highway Bridges,” American Association of State Highway and Transportation Officials.Impact not included.

† Moments in thousands of ft-lb (ft-kips).‡ Shear and reaction in kips. Concentrated load is considered placed at the support. Loads used are those stipulated for shear.§ Maximum value determined by standard truck loading. Otherwise, standard lane loading governs.

Table 17.2 Wind Loads for Superstructure Design

Trusses and arches Beams and girders Live Load

Wind load 75 lb/ft2 50 lb/ft2 100 lb/lin ft

Minimums:On loaded chord 300 lb/lin ftOn unloaded chord 150 lb/lin ftOn girders 300 lb/lin ft




BRIDGE ENGINEERING

on concrete structures, also for shrinkage. For thecontinental United States, Table 17.4 covers tem-perature ranges of most locations and includes theeffect of shrinkage on ordinary beam-type concretestructures. The coefficient of thermal expansion forboth concrete and steel per 8Fahrenheit is 0.0000065(approximately 1⁄150,000). The shrinkage coefficientfor concrete arches and rigid frames should beassumed as 0.002, equivalent to a temperature dropof 31 8F.

Stream-flow pressure on a pier should be com-puted from

P ¼ KV2 (17:3)

where P ¼ pressure, lb/ft2

V ¼ velocity of water, ft/s

K ¼ 4⁄3 for square ends, 1⁄2 for angle endswhen angle is 308 or less, and 2⁄3 forcircular piers

Ice pressure should be assumed as 400 psi. Thedesign thickness should be determined locally.

Earth pressure on piers and abutments shouldbe computed by recognized soil-mechanics for-mulas, but the equivalent fluid pressure should beat least 36 lb/ft3 when it increases stresses and notmore than 27 lb/ft3 when it decreases stresses.

Sidewalks and their direct supports shouldbe designed for a uniform live load of 85 lb/ft2.

Table 17.3 Wind Loads for Substructure Design

a. Loads transmitted by superstructure to substructure slab and girder bridges (up to 125-ft span)

Transverse Longitudinal

Wind on superstructure when not carrying live load, lb/ft2 50 12Wind on superstructure when carrying live load, lb/ft2 15 4Wind on live load, lb/lin ft* 100 40

Major and unusual structures

No live load on bridge Live load on bridge

Skew

Wind ontrusses, lb/ft2

Wind ongirders, lb/ft2

Wind ontrusses, lb/ft2

Wind ongirders, lb/ft2

Wind onlive load,lb/lin ft*

angle, orwind,deg

Lat-eralload

Longi-tudinalload

Lat-eralload

Longi-tudinalload

Lat-eralload

Longi-tudinalload

Lat-eralload

Longi-tudinalload

Lat-eralload

Longi-tudinalload

0 75 0 50 0 22.5 0 15 0 100 015 70 12 44 6 21 3.6 13.2 1.8 88 1230 65 28 41 12 19.5 8.4 12.3 3.6 82 2445 47 41 33 16 14.1 12.3 9.9 4.8 66 3260 25 50 17 19 7.5 15 5.1 5.7 34 38

b. Loads from wind acting directly on the substructure†

Horizontal wind—no live load on bridge, lb/ft2 40Horizontal wind—live load on bridge, lb/ft2 12

* Acting 6 ft above deck.† Resolve wind forces acting at a skew into components perpendicular to side and front elevations of the substructure and apply at

centers of gravity of exposed areas. These loads act simultaneously with wind loads from superstructure.




BRIDGE ENGINEERING

The effect of sidewalk live loading on main bridgemembers should be computed from

P ¼ 30þ 3000

l

� �55� w

50� 60 lb=ft2 (17:4)

where P ¼ sidewalk live load, lb/ft2

l ¼ loaded length of sidewalk, ft

w ¼ sidewalk width, ft

Curbs should resist a force of 500 lb/lin ft acting10 in above the floor. For design loads for railings,see Fig. 17.4.

17.3.2 Railway Bridge Loads

Live load is specified by axle-load diagrams or bythe E number of a “Cooper’s train,” consisting oftwo locomotives and an indefinite number offreight cars. Figure 17.5 shows the typical axlespacing and axle loads for E80 loading.

Members receiving load from more than onetrack should be assumed to be carrying the fol-lowing proportions of live load: For two tracks, fulllive load; for three tracks, full live load from twotracks and half from the third track; for four tracks,full live load from two, half from one, and one-fourth from the remaining one.

Impact loads, as a percentage of railroad liveloads, may be computed from Table 17.5.

Longitudinal forces should be computed forbraking and traction and centrifugal forces shouldbe computed corresponding to each axle. See theAREMA ‘‘Manual for Railway Engineering’’ formore information (www.arema.org).

17.3.3 Proportioning of BridgeMembers and Sections

The following groups represent various combi-nations of loads and forces to which a structuremay be subjected. Each component of the structure,or the foundation on which it rests, should beproportioned to withstand safely all group combi-nations of these forces that are applicable to theparticular site or type. Group loading combinationsfor service load design and load factor design aregiven by

Group (N) ¼ g[bDDþ bL(Lþ I)þ bCCF

þ bEEþ bBBþ bSSFþ bWW

þ bWLWLþ bLLF

þ bR(Rþ Sþ T)þ bEQEQþ bICEICE]

(17:5)

Table 17.4 Expansion and Contraction of Structures*

Steel Concrete†

Air temp rangeTemp riseand fall, 8F

Movement perunit length

Temp riseand fall, 8F

Movement perunit length

Extreme:120 8F, certain mountain 60 0.00039 40 0.00024and desert locations

Moderate:100 8F, interior valleys and 50 0.00033 35 0.00021most mountain locations

Mild:80 8F, coastal areas, Los 40 0.00026 30 0.00018Angeles, and San FranciscoBay area

* This table was developed for California. For other parts of the United States, the temperature limits given by AASHTO “StandardSpecifications for Highway Bridges” should be used.

† Includes shrinkage.




BRIDGE ENGINEERING

Fig. 17.4 Service loads for railings: P ¼ 10 kips, L ¼ post spacing,w ¼ 50 lb/ft. Rail loads are shown onthe left, post loads on the right. (Rail shapes are for illustrative purposes only.)




BRIDGE ENGINEERING

where N ¼ group number, or number assigned to aspecific combination of loads

g ¼ capacity reduction factor to provide forsmall adverse variations in materials,workmanship, and dimensions withinacceptable tolerances

b ¼ load factor (subscript indicates appli-cable type of load)

See Table 17.6 for appropriate coefficients. See alsoArt. 17.3.1 and Secs. 8 and 9.

AASHTO LRFD associates load combinationswith various limit states according to design ob-jectives. The sum of the factored loads must be lessthan the sum of the factored resistance:X

higiQi � wRn (17:6)

where hi ¼ loadmodifier relating toductility, redun-dancy, and operational importance

gi ¼ load factor, a statistically based multi-plier reflecting certainty in the value forforce effect

Qi ¼ force effect i

w ¼ resistance factor, a statistically basedmultiplier reflecting certainty in valuefor particular material property

See Table 17.7 and 17.8 for design objectives, limitstate load combinations and load factors. Resist-ance factors vary according to material and char-acteristic such as bending, shear, bearing, torsion,etc., and are not shown. In LRFD, both the g’s andw’s have been calibrated to achieve a uniform levelof safety throughout the structure.

17.4 Seismic Design

Seismic forces are an important loading consider-ation that often controls the design of bridges inseismically active regions. All bridges should bedesigned to insure life safety under the demandsimparted by theMaximumConsidered Earthquake(MCE). Higher levels of performance may berequired by the bridge owner to provide postearthquake access to emergency facilities or whenthe time required to restore service after anearthquake would create a major economic impact.

Fig. 17.5 Axle Spacing and Axle Loads for E80 loading




BRIDGE ENGINEERING

All bridges should have a clearly identifiablesystem to resist forces and deformations imposedby seismic events. Experimental research and pastperformance has demonstrated that simple bridgefeatures lead to more predictable seismic response.Irregular features lead to complex and lesspredictable seismic response and should beavoided in high seismic region whenever possible(See Table 17.9). Every effort should be made tobalance the effective lateral stiffness betweenadjacent bents within a frame, adjacent columnswithin a bent, and adjacent frames. If irregularfeatures or significant variations in lateral stiffnessare unavoidable, they should be assessed withmore rigorous analysis and designed for a higherlevel of seismic performance.

Seismic effects for box culverts and buriedstructures need not be considered, except whenthey cross active faults.

17.4.1 Seismic DesignApproach

Ordinarily bridges are not designed to remainelastic during the MCE because of economic con-straints and the uncertainties in predicting seismicdemands. Design codes permit the designer to takeadvantage of ductility and post elastic strength aslong as the expected deformations do not exceedthe bridge’s lateral displacement capacity. Ductile

Table 17.5 Railroad Impact Factors

Structure type Impact percent*

Prestressed concrete:

L , 60 35� L2

500

60 , L , 135800

L� 2þ 14

L � 135 20%

Reinforced concrete:100LL

LLþDL(80% max. for steam engines)(60% max. for diesel engines)

Steel:**

Non-hammerblow engine equipmentL , 80 RE þ 40 � 3L2

1600

L � 80 RE þ 16 þ 600

L� 30Steam engine equipment with hammerblowL , 100 RE þ 60 � L2

500

L � 100 RE þ 10 þ 1800

L� 40

Truss spans RE þ 15 þ 4000

Lþ 25

* For ballasted decks use 90% of calculated impact (steel bridges only)L ¼ span, ft; S ¼ longitudinal beam spacing, ft; DL ¼ applicable dead load; LL ¼ applicable live load.RE ¼ the rocking effect consisting of the percentage of downward on one rail and upward on the other

rail, increasing and decreasing, respectively, the loads otherwise specified. RE shall be expressed as apercentage; either 10% of the axle load or 20% of the wheel load.

** Impact is reduced for L . 175 ft or when load is received from more than two tracks.




BRIDGE ENGINEERING

Table 17.6 Capacity-Reduction and Load Factors

Load factor b for*

Group g D (L þ I)n (L þ I)P CF E B SF W WL LF R þ S þ T EQ ICE % of basicunit stresses

Service-Load Design†

I 1.0 1 1 0 1 bE 1 1 0 0 0 0 0 0 100IA 1.0 1 2 0 0 0 0 0 0 0 0 0 0 0 150IB 1.0 1 0 1 1 bE 1 1 0 0 0 0 0 0 ‡

II 1.0 1 0 0 0 1 1 1 1 0 0 0 0 0 125III 1.0 1 1 0 1 bE 1 1 0.3 1 1 0 0 0 125IV 1.0 1 1 0 1 bE 1 1 0 0 0 1 0 0 125V 1.0 1 0 0 0 1 1 1 1 0 0 1 0 0 140VI 1.0 1 1 0 1 bE 1 1 0.3 1 1 1 0 0 140VII 1.0 1 0 0 0 1 1 1 0 0 0 0 1 0 133VIII 1.0 1 1 0 1 1 1 1 0 0 0 0 0 1 140IX 1.0 1 0 0 0 1 1 1 1 0 0 0 0 1 150

Load-Factor Design§

I 1.3 bD 1.67} 0 1.0 bE 1 1 0 0 0 0 0 0IA 1.3 bD 2.20 0 0 0 0 0 0 0 0 0 0 0IB 1.3 bD 0 1 1.0 bE 1 1 0 0 0 0 0 0II 1.3 bD 0 0 0 bE 1 1 1 0 0 0 0 0III 1.3 bD 1 0 1 bE 1 1 0.3 1 1 0 0 0IV 1.3 bD 1 0 1 bE 1 1 0 0 0 1 0 0V 1.25 bD 0 0 0 bE 1 1 1 0 0 1 0 0VI 1.25 bD 1 0 1 bE 1 1 0.3 1 1 1 0 0VII 1.3 bD 0 0 0 bE 1 1 0 0 0 0 1 0VIII 1.3 bD 1 0 1 bE 1 1 0 0 0 0 0 1IX 1.20 bD 0 0 0 bE 1 1 1 0 0 0 0 1

* D ¼ dead load LF ¼ longitudinal force from live load T ¼ temperature

L ¼ live load (L þ I)n ¼ live load plus impact for AASHTO EQ ¼ earthquake

I ¼ live-load impact highway loading SF ¼ stream flow pressure

E ¼ earth pressure CF ¼ centrifugal force ICE ¼ ice pressure

B ¼ buoyancy F ¼ longitudinal force due to friction (L þ I)P ¼ live load plus impact consistent

W ¼ wind load on structure R ¼ rib shortening with the overload criteria of the

WL ¼ wind load on live load S ¼ shrinkage operating agency† For service-load design: No increase in allowable unit stresses is permitted for members or connections carrying wind loads only.

bE ¼ 1.0 for lateral loads on rigid frames subjected to full earth pressure

¼ 0.5 when positive moment in beams and slabs is reduced by half the earth-pressure moment

Check both loadings to see which one governs.

‡ % ¼ Maximum unit stress(operating rating)Allowable basic unit stress

� 100

§ For load factor design:

bE ¼ 1.3 for lateral earth pressure for rigid frames excluding rigid culverts

¼ 0.5 for lateral earth pressure when checking positive moments in rigid frames

¼ 1.0 for vertical earth pressure

bD ¼ 0.75 when checking member for minimum axial load and maximum moment or maximum eccentricity and column design

¼ 1.0 when checking member for maximum axial load and minimum moment and column design

¼ 1.0 for flexural and tension members} bD ¼ 1.25 for design of outer roadway beam for combination of sidewalk and roadway live load plus impact, if it governs the design,

but section capacity should be at least that required for bD ¼ 1.67 for roadway live load alone

¼ 1.00 for deck-slab design for D þ L þ I




BRIDGE ENGINEERING

Table

17.7

AASHTO

LRFD

Load

Combinationsan

dLoad

Factor

Designobjective

Load

combination

Lim

itstate

DC

DD

DW

EH

EV

ES

EL

LL

IM CE

BR

PL

LS

WA

WS

WL

FR

TU

CR

SH

TG

SE

Use

oneof

theseat

atime

EQ

ICCT

CV

Tohav

estructural

integrity

forall

statistically

significantload

s

STRENGTH

IgP

1.75

1.00

––

1.00

0.50

/1.20

gTG

gSE

––

––

STRENGTH

IIgP

1.35

1.00

––

1.00

0.50

/1.20

gTG

gSE

––

––

STRENGTH

III

gP

–1.00

1.40

–1.00

0.50

/1.20

gTG

gSE

––

––

STRENGTH

IVgP

–1.00

––

1.00

0.50

/1.20

––

––

––

STRENGTH

VgP

1.35

1.00

0.40

1.0

1.00

0.50

/1.20

gTG

gSE

––

––

Tosu

rvivewithout

collap

singduringa

flood,collision,or

earthquak

e

EXTREME

EVENTI

gP

gEQ

1.00

––

1.00

––

–1.00

––

–

EXTREME

EVENTII

gP

0.50

1.00

––

1.00

––

––

1.00

1.00

1.00

Tolast

75years

SERVIC

E-I

1.00

1.00

1.00

0.30

1.0

1.00

1.00

/1.20

gTG

gSE

––

––

SERVIC

E-II

1.00

1.30

1.00

––

1.00

1.00

/1.20

––

––

––

SERVIC

E-III

1.00

0.80

1.00

––

1.00

1.00

/1.20

gTG

gSE

––

––

Towithstan

dcyclic

load

ing,

especiallyat

connections

FATIG

UE

–0.75

––

––

––

––

––

–




BRIDGE ENGINEERING

response in bridge systems is typically achievedthrough sustained hysteric force-deformationcycles that dissipate energy. This dissipation occursinternally, within the structural members, by theformation of flexural plastic hinges, or externallywith isolation bearings or external dampers.

Inelastic behavior should be limited to pre-determined locations within the bridge that can beeasily inspected and repaired following an earth-quake. Preferable locations for inelastic behavioron most bridges include columns, pier walls, andabutment backwalls and wingwalls. Inelastic res-

Table 17.8 Load Factors for Permanent Loads gp

Load factor

Type of load Maximum Minimum

DC: Component and Attachments 1.25 0.90

DD: Downdrag 1.80 0.45

DW: Wearing Surfaces and Utilities 1.50 0.65

EH: Horizontal Earth Pressure† Active 1.50 0.90† At-Rest 1.35 0.90

EL: Locked in Erection Stresses 1.0 1.0

EV: Vertical Earth Pressure† Retaining Walls and Abutments 1.35 1.00† Rigid Buried Structure 1.30 0.90† Rigid Frames 1.35 0.90† Flexible Buried Structures other thanMetal Box Culverts 1.95 0.90† Flexible Metal Box Culverts 1.50 0.90

ES: Earth Surcharge 1.50 0.75

Table 17.9 Examples of Irregular Bridge Features

Geometry† Multiple superstructure levels† Variable width, bifurcating, or highly curved superstructures† Significant in-plane curvature† Highly skewed supports

Framing† Outrigger or C-bent supports† Unbalanced mass and/or stiffness distribution† Multiple superstructure types

Geologic Conditions† Soft soil† Moderate to high liquefaction potential† Proximity to an earthquake fault




BRIDGE ENGINEERING

ponse in the superstructure is not desirable becauseit is difficult to inspect and repair and may preventthe bridge from being restored to a serviceablecondition.

Members not participating in the primaryenergy dissipating system (i.e. column shear, joints,cap beams and foundations) should be capacityprotected. This is achieved by ensuring that themaximum moment and shear from plastic hinges,isolation bearings and dampers can be dependablyresisted by the adjoining elements.

17.4.2 Seismic Demands

The uniform load method can be used to determinethe seismic loading for bridges that will respondprincipally in their fundamental mode of vibration.Equivalent static earthquake loads are calculatedby multiplying the tributary permanent load by aresponse spectra coefficient:

Pe ¼ CsmW

L(17:7)

where pe ¼ Equivalent uniform static seismic loadper unit length of bridge

Csm ¼ Elastic response coefficient seeequation 17.8

W ¼ Dead load of the bridge superstructureand tributary substructure

L ¼ Total length of bridge in ft

Csm ¼ 1:2AS

T2=3m

� 2:5A (17:8)

where Tm ¼ Period of vibration of the mth mode(seconds)

A ¼ Acceleration coefficient from nationalground motion maps.

S ¼ Site coefficient specified in Table 17.10

Tm ¼ 2p

ffiffiffiffiffiffiW

gK

s(17:9)

where g ¼ Acceleration of gravity

K ¼ Bridge lateral stiffness

Single span bridges do not require seismicanalysis. The minimum design force at the con-nections between the superstructure and substruc-ture shall not be less than the product of the sitecoefficient S, the acceleration coefficient A, and thetributary permanent load.

The multimode spectral mode analysis methodshould be used if coupling between the longitudi-nal, transverse and/or vertical response is expec-ted. A three dimensional linear dynamic modelshould be used to represent the bridge. The elasticseismic forces and displacement generated frommultiple mode shapes are combined using accep-table methods such as the root-mean-squaremethod or the complete quadratic combinationmethod. The number of modes in the model shouldbe at least three times the number of spans beingmodeled. Site-specific response spectra are oftendeveloped for multi-modal analysis that incorpor-ates the seismic source, ground attenuation, andnear fault phenomena.

When response spectra analysis is used, amaximum single seismic force is calculated bycombiningtwohorizontalorthogonalgroundmotioncomponents. These components are applied along a

Table 17.10 Soil Coefficients

Soil profiletype

Sitecoefficient S Description

I 1.0 Rock of any description (shale-like or crystalline) or stiff soils (sands,gravels, stiff clays) less than 200 ft in depth overlying rock

II 1.2 Stiff cohesive or deep cohesionless soils more than 200 ft in depthoverlying rock

III 1.5 Soft to medium-stiff clays and sands characterized by 30 ft or more ofclay with or without intervening layers of sand.

IV 2.0 Soft clays or silts greater than 40 ft of depth.




BRIDGE ENGINEERING

longitudinal axis defined by a chord intersecting thecenterline of the bridge at the abutments and anormal transverse axis (See Fig. 17.7).

It is uneconomical to design bridges to resistlarge earthquakes elastically. Columns are assumedto deform inelastically where seismic forces exceeddesign levels established by dividing the elasticallycomputed moments by the appropriate responsemodification factors, R. (See Tables 17.11 and 17.12)

The AASHTO Bridge Design Specificationdefines three levels of response modification

factors for critical bridges, essential bridgesand other bridges. The bridge owner mustdetermine the performance level required consi-dering social/survival and security/defenserequirements.

More rigorous analysis such as inelastic timehistory analysis should be used on geometricallycomplex bridges, critical bridges and bridgeswithinclose proximity of earthquake faults. The nonlinearanalysis provides forces and deformations as afunction of time for a specified earthquake motion.

Fig. 17.6 Equivalent static earthquake loads.

Fig. 17.7 Orthogonal bridge axis definition.




BRIDGE ENGINEERING

A minimum of three ground motions representingthe design event should be used.

Nonlinear static analysis, commonly known aspushover analysis has recently been adopted byCaltrans. The inelastic displacement capacity of thepiers is compared to the displacements from anelastic demand analysis that considers the bridge’scracked flexural stiffness. The inelastic deformationcapacity of the earthquake resisting members iscalculated using moment curvature analysis utiliz-ing expected material properties and dependablematerials strain limits. Displacement capacities are

also limited by degradation of strength and P-Deffects that occur under large inelastic defor-mations. If the P-D moments are less than 20% ofthe plastic moment capacity of the member, theyare typically ignored.

17.4.3 Seismic Design ofConcrete BridgeColumns

Cross sectional column dimensions should belimited to the depth of the superstructures or bentcap to reduce the potential for inelastic damagemigrating into the superstructure. The longitudinalreinforcement for compression members shouldnot exceed 4% of the columns gross cross sectionalarea to insure adequate ductility, avoid congestionand to permit adequate anchorage of the longi-tudinal reinforcement. Conversely not less than 1%of the columns gross cross sectional area to insurea reasonable level of strength. In the column po-tential plastic hinge regions, the transverse rein-forcement rs for circular columns shall not be lessthan:

rs ¼ 0:12f 0cfy

(17:10)

f 0c ¼ specified compressive strength of con-crete at 28 days (ksi)

fy ¼ yield strength of reinforcing bars (ksi)

Table 17.11 AASHTO Substructure Response Modification Factors

SubstructureImportance Category

Critical Essential other

Wall-type piers—larger dimension 1.5 1.5 2.0

Reinforced concrete pile bents† Vertical piles only 1.5 2.0 3.0† With batter piles 1.5 1.5 2.0

Single Columns 1.5 2.0 3.0

Steel or composite steel and concrete pile bents† Vertical pile only 1.5 3.5 5.0† With batter piles 1.5 2.0 3.0

Multiple column bents 1.5 3.5 5.0

Table 17.12 AASHTO Connection ResponseModification Factors

Connection All ImportanceCategories

Superstructure to abutment 0.8

Expansion joints within aspan of the superstructure

0.8

Column, piers, or piles bent tocap beam or superstructure

1.0

Column or piers tofoundations

1.0




BRIDGE ENGINEERING

For rectangular sections the total gross sectionalarea of rectangular hoop reinforcement shall not beless than either:

Ash ¼ 0:30shcf 0cfy

Ag

Ac� 1

� �or Ash ¼ 0:12shc

f 0cfy

(17:11)

where:

s ¼ vertical spacing of hoops not to exceed4.0 inches (in)

Ac ¼ area of column core (in2)

Ag ¼ gross area of column (in2)

Ash ¼ total cross sectional area of tie reinforce-ment, including supplementary cross tieshaving a vertical spacing “s” and crosssection having core diameter of hc (in

2)

hc ¼ core dimension of tied column in thedirection under consideration (in2)

The potential plastic hinge region is defined asthe larger of 1.5 times the cross sectional dimensionin the direction of bending or the region of columnwhere the moment exceeds 75% of the maximumplastic moment.

The column design shear force should becalculated considering the flexural overstrength

developed at the most probable location within thecolumn with a rational combination of the mostadverse end moments. The shear resisting mech-anism is provided by a combination of truss action(Vs), concrete tensile contribution (Vc) and arch orstrut action (Vp).

Vu , Vs þ Vp þ Vc (17:12)

The concrete contribution is significantly dimin-ished under high ductilities and cyclic loading andis often ignored in the plastic moment regions. Theflexural reinforcement in continuous or cantilevermembers needs to detailed to provide continuity ofreinforcement at intersections with other membersto develop nominal moment resistance of the jointcan be developed to resist the shear depicted in Fig.17.8. Several shear design models defining theshear resisting mechanisms for columns and jointscan be found in the AASHTODesign Specificationsor the Caltrans Seismic Design Criteria.

The unseating of girders and abutments must beavoided in all circumstances. The seat width needsto accommodate thermal movement, prestressshortening, creep, shrinkage and anticipated earth-quake displacements. The seat width should not beless then 1.5 times the elastic seismic displacement

Fig. 17.8 Joint shear stresses in T-joints.




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of the superstructure at the seat or:

N ¼ (8þ 0:02Lþ 0:08H) 1þ S2

8000

� �� (17:13)

N ¼ Support width normal to the centerline ofbearing

L ¼ Length of the bridge deck to the adjacentexpansion joint, or the endof thebridge (ft)

H ¼ Average height of the columns support-ing the bridge deck to the next expansionjoint (ft) (H ¼ 0 for single span bridges)

S ¼ Skew of the support measured from linenormal to span (deg)

(MCEER, “Recommended LRFD Guidelines for theSeismic Design of Highway Bridges,” CaltransSeismic Design Criteria, vol. 1.1 (www.dot.ca.gov);AASHTO LRFD Bridge Design Specification(www.aashto.org).)

Steel Bridges

Steel is competitive as a construction material formedium and long-span bridges for the followingreasons: It has high strength in tension and com-pression. It behaves as a nearly perfect elasticmaterial within the usual working ranges. It hasstrength reserves beyond the yield point. The highstandards of the fabricating industry guaranteeusers uniformity of the controlling propertieswithin narrow tolerances. Connection methods arereliable, and workers skilled in their applicationare available.

The principal disadvantage of steel in bridgeconstruction, its susceptibility to corrosion, is beingincreasingly overcome by chemical additives orimproved protective coatings.

17.5 Systems Used for SteelBridges

The following are typical components of steelbridges. Each may be applied to any of thefunctional types and structural systems listed inArt. 17.1.

Main support: Rolled beams, plate girders, boxgirders, or trusses.

Connections: (See also Art. 17.7.) High-strength-bolted, welded, or combinations.

Materials for traffic-carrying deck: Timber string-ers and planking, reinforced concrete slab or pre-stressed concrete slab, stiffened steel plate(orthotropic deck), or steel grid.

Timber decks are restricted to bridges on roadsof minor importance. Plates of corrosion resistantsteel should be used as ballast supports on throughplate-girder bridges for railways. For roadwaydecks of stiffened steel plates, see Art. 17.13.

Deck framing: Deck resting directly on mainmembers or supported by grids of stringers andfloor beams.

Location of deck: On top of main members: deckspans (Fig. 17.9a); between main members, theunderside of the deck framing being flush with thatof the main members: through spans (Fig. 17.9b).

17.6 Grades and DesignCriteria for Steel forBridges

Preferred steel grades, permissible stresses, andstandards of details, materials, and quality of workfor steel bridges are covered in the AREMA andAASHTO specifications. Properties of the variousgrades of steel and the testing methods to be usedto control them are regulated by specifications ofASTM. Properties of the structural steels presentlypreferred in bridge construction are Tabulated inTable 17.13.

Dimensions and geometric properties of com-mercially available rolled plates and shapes aretabulated in the “Steel Construction Manual,” forallowable stress design and for load-and-resistance-factor design of the American Institute of SteelConstruction (AISC), and in manuals issued by themajor steel producers.

All members, connections, and parts of steelbridges should be designed by the load-factordesign method, and then checked for fatigue atservice-level loads. The fatigue check should assurethat all connections are within allowable stressranges (FSR).

The design strength of a beam or girder is basedon the dimensional properties of the section andthe spacing of compression flange bracing. Thethree types of member sections are (1) compact, (2)braced noncompact, and (3) partially braced. TheAASHTO Flexural design formulas for the threetypes of I-Girder sections are shown in Table 17.14.




BRIDGE ENGINEERING

Design Limitations on Depth Ratios,Slenderness Ratios, Deflections n AASHTOspecifications restrict the depth-to-span ratios D/Lof bridge structures and the slenderness ratios l/rof individual truss or bracing members to thevalues in Table 17.15.

where D ¼ depth of construction, ft

L ¼ span, ft, c to c bearings for simple spansor distance between points of contra-flexure for continuous spans

l ¼ unsupported length of member, in

r ¼ radius of gyration, in

These are minimum values; preferred values arehigher.

Fig. 17.9 Two-lane deck-girder highway bridge




BRIDGE ENGINEERING

Both specifications limit the elastic deflections ofbridges under design live load plus impact to 1⁄800 ofthe span, measured c to c bearings, except that1⁄1000may be used for bridges used by pedestrians;1⁄300 of the length of cantilever arms. Deflectioncalculations should be based on the gross sectionsof girders or truss members. Anticipated dead-loaddeflections must be compensated by adequatecamber in the fabrication of steel structures.

Splices n Shop, assembly yard, or erectionsplices must be provided for units whoseoverall length exceeds available rolled lengths ofplates and shapes or the clearances of availableshipping facilities. Splices also must be providedwhen total weight exceeds the capacity of availableerection equipment.

Accessibility n All parts should be accessibleand adequately spaced for fabrication, assembly,and maintenance. Closed box girders and box-typesections should be equipped with handholes ormanholes.

On long and high bridges, installation of per-manent maintenance travelers may be justified.

17.7 Steel Connections inBridges

Connections of steel members to other steelmembers are usually made with high-strengthbolts, welds, or pins. In composite construction,steel beams are joined to concrete decks by steelstuds or channels welded to the top flange of thebeams.

17.7.1 Connections withHigh-Strength Bolts

The parts may be clamped together by bolts ofquenched and tempered steel, ASTM A325. Thenuts are tightened to 70% of their specified tensilestrength.

Details and quality of work are covered by the“Specifications for Structural Joints Using ASTMA325 and A490 Bolts,” approved by the ResearchCouncil on Structural Connections of the Engin-eering Foundation. Maximum stresses for bearingtype connections are given in Table 17.11.

Tensioned ASTM A325 bolts are the preferredbolt for all steel bridge connections. The nuts on

Table 17.13 Minimum Mechanical Properties of Structural Steel

Property Structuralsteel

High-strengthlow-alloy

steel

Quenchedand tempered

low-alloysteel

High-yield-strength, quenched

and temperedalloy steel

AASHTOdesignation

M270Grade 36

M270Grade 50

M270Grade 50W

M270Grade 70W

M270 Grades100/100W

EquivalentASTMdesignations

A709Grade 36

A709Grade 50

A709Grade 50W

A709Grade 70W

A709 Grades100/100W

Thickness ofplates, in

Up to 4incl.

Up to 4incl.

Up to 4incl.

Up to 4incl.

Up to 2.5incl.

Over 2.5to 4 incl.

Shapes Allgroups

Allgroups

Allgroups

Notapplicable

Notapplicable

Notapplicable

Minimumtensilestrength, Fu, ksi 58 65 70 90 110 100

Minimum yieldpoint or yieldstrength, Fy, ksi 36 50 50 70 100 90




BRIDGE ENGINEERING

Table 17.14 ASSHTO Flexural Design Formulas for I-Girders

Sectiondescription

Compressionflange

slenderness

Webslenderness

Lateral Bracingof compression

flange

Mu

Compactb

t� 4100ffiffiffiffiffi

Fyp D

tw� 19,230ffiffiffiffiffi

Fyp

Lbry

�3:6� 2:2

Ml

Mu

� �Fy

2664

3775� 106

FyZ

When b=t and D=tw exceeds 75% of the abovelimits, the following interaction equation shallapply

D

twþ 4:68

b

t

� �� 33,650ffiffiffiffiffiffiffi

Fyfp

BracedNon-Compact

b

t� 24 With transverse stiffeners only:

D


Fyp

With transverse stiffeners and onelongitudinal stiffeners:

D


Fyp

Lb � 20,000,000

FydLessor of:

Fy Sxt orFcr Sxc Rb

PartiallyBraced

No Max.Requirements

No Max.Requirements

No Max.Requirements

See AASHTOStandardSpecificationsfor HighwayBridges

Af ¼ flange area (sq in2)

b ¼ compression flange width

D ¼ clear distance between flanges

d ¼ depth of beam or girder

f ¼ the lesser of ( fb/Rb) Fy (psi)

fb ¼ factored bending stress in the compression flange (psi)

fcr ¼ critical stress of the compression flange (psi)

Fy ¼ specified minimum field strength of the steel being used (psi)

Fyf ¼ specified minimum field strength of the compression flange (psi)

Lb ¼ distance between points of bracing of the compression flange (in)

Ml ¼ smaller moment at the end of the unbraced length of the member (lb-in)

Mu ¼ design strength equal Fy*Z at the other end of the unbraced length:

(Ml/Mu) is positive when moments cause single curvature between brace points

(Ml/Mu) is negative when moments cause reverse curvature between brace points (lb-in)

Rb ¼ Bending Capacity Reduction Factor, See AASHTO Standard Specifications for Highway Bridges

ry ¼ radius of gyration of the steel section with respect to the Y-Y axis (in)

Sxc ¼ elastic section modulas with respect to compression flange (in3)

Sxt ¼ elastic section modulas with respect to tension flange (in3)

t ¼ flange thickness (in)

tw ¼ web thickness (in)

Z ¼ plastic section modulas (in3)




BRIDGE ENGINEERING

tensioned A325 and A490 bolts will not loosenunder vibrations associated with bridge loadings.If ASTM A307 bolts or non tensioned high strengthbolts are used, provisions should be made toprevent nut loosing by the use of thread lockingadhesive, self-locking nuts, or double nuts. Boltedconnections subject to tension, or combined tensionand shear, or stress reversal, or severe vibration, orheavy impact loads, or any other condition wherejoint slippage would be detrimental, shall use ten-sioned High-Strength bolts and be designed as aslip-critical connection.

Slip-critical connections are designed to preventslip at a specified overload condition in addition tomeeting the strength requirements in bearing. Theoverload condition at which the connection isrequired work as a friction connection (no slip) isequal to Dead load þ 1.67(Live load þ Impact). Theslip strength of the connection is based on thenumber of slip plains, the friction coefficient of thecontact surfaces, the typeofhole, and thebolt tensionstress. The AASHTO specifications provide equa-tions for determining the slip strength of connec-tions.

17.7.2 Welded Connections

In welding, the parts to be connected are fused athigh temperatures, usually with addition of suit-able metallic material. The “Structural WeldingCode,” AWS D1.5, American Welding Society,regulates application of the various types and sizesof welds, permissible stresses in the weld and

parent metal, permissible edge configurations,kinds and sizes of electrodes, details of quality ofwork, and qualification of welding procedures andwelders. (For Maximum welding stresses, seeTable 17.16.)

Many designers favor the combination of shopweldingwithhigh-strength-boltedfield connections.

17.7.3 Pin Connections

Hinges between members subject to relativerotation are usually formed with pins, machinedsteel cylinders. They are held in either semicircularmachined recesses or smoothly fitting holes in theconnected members.

For fixation of the direction of the pin axis, pinsup to 10-in diameter have threaded ends for recessednuts, which bear against the connected members.Pins over 10-in diameter are held by recessed caps.These in turn are held by either tap bolts or a rod thatruns axially through a hole in the pin itself and isthreaded and secured by nuts at its ends.

Pins are designed for bending and shear andfor bearing against the connected members. (Forstresses, see Art. 9.6.)

17.8 Rolled-Beam Bridges

The simplest steel bridges consist of rolled wide-flange beams and a traffic-carrying deck. Rolledbeams serve also as floor beams and stringers fordecks of plate-girder and truss bridges.

Reductions in steel weight may be obtained, butwith greater labor costs, by adding cover plates in

Table 17.15 Dimensional Limitations for BridgeMembers

AASHTO

Min depth-span ratios:For noncomposite beams or girders 1/25For simple span composite girders* 1/22For continuous composite girders* 1/25For trusses 1/10

Max slenderness ratios:For main members in compression 120For bracing members in compression 140For main members in tension 200For bracing members in tension 240

* For composite girders the depth shall include the concrete slab.




BRIDGE ENGINEERING

the area of maximum moments, by providingcontinuity over several spans, by utilizing the deckin composite action, or by a combination of thesemeasures. The principles of design and detailsare essentially identical with those of plate girders(Art. 17.9).

17.9 Plate-Girder Bridges

The term plate girder applies to structural elementsof I-shaped cross section that are welded from

plates. Plate girders are used as primary support-ing elements in many structural systems: as simplebeams on abutments or, with overhanging ends, onpiers; as continuous or hinged multispan beams;as stiffening girders of arches and suspensionbridges, and in frame-type bridges. They also serveas floor beams and stringers on these other bridgesystems.

Their prevalent application on highway andrailway bridges is in the form of deck-plate girdersin combination with concrete decks (Fig. 17.9). (Fordesign of concrete deck slabs, see Art. 17.20. For

Table 17.16 Design Strength of Connectors

Type of fastener Strength (fF)

Groove welda 1.00FyFillet weldb 0.45Fu

Low-carbon steel bolts ASTM A307Tensiong 30 ksiShear on Bolt with threads in shear plane 18 ksi

Power-driven rivets ASTM A502Shear—Grade 1 25 ksiShear—Grade 2 30 ksi

High-Strength BoltsAASHTO M 164 (ASTM A325)

Applied Static Tensionc,g 68 ksiShear on bolt with threads in shear planec,d,e 35 ksi

AASHTO M 253 (ASTM A490)Applied Static Tensiong 85 ksiShear on bolt with threads in shear planed,e 43 ksi

Bolt bearing on connected material f 0.9LctFu � 1.8dtFuaFy ¼ yield point of connected materialbFu ¼ minimum strength of the welding rod metal but not greater than the tensile strength of the

connected parts.cThe tensile strength of M 164 (A 325) bolts decreases for diameters greater than 1 inch.The design values listed are for bolts up to 1 inch diameter. The design values shall be multiplied

by 0.875 for diameters greater than 1 inch.dTabulated values shall be reduced by 20 percent in bearing-type connections whose length

between extreme fasteners in each of the spliced parts measured parallel to the line of axial forceexceeds 50 inches.

eIf material thickness or joint details preclude threads in the shear plane, multiply values by 1.25fBearing on connected material in standard oversized short slotted holes loaded in any direction or

long slotted holes parallel to the applied bearing force. For long slotted holes perpendicular to theapplied bearing force calculated values shall be reduced 20 percent. Lc is clear distance between theholes or between the hole and the edge of the material in the direction of the applied bearing force(in); d is the diameter of the bolt (in), t is thickness of connected material (in) and Fu is the specifiedminimum tensile strength of the connected part given in Table 17.9.

gFor combined tension and shear when fv/Fv . 0.33 the design tensile strength, Ft (in table) shall bereduced to F0t where:

F0t ¼ Ft

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ( fv=Fy)

2q

fv ¼ calculated bolt stress in shearFv ¼ design shear strength of bolt (in table)




BRIDGE ENGINEERING

girders with steel decks (orthotropic decks), see Art17.13. Girders with track ties mounted directly onthe top flanges, open-deck girders, are used onbranch railways and industrial spurs. Throughplate girders (Fig. 17.9b) are now practicallyrestricted to railway bridges where allowablestructure depth is limited.

The two or more girders supporting each spanmust be braced against each other to providestability against overturning and flange buckling,to resist transverse forces (wind, earthquake,centrifugal), and to distribute concentrated heavyloads. On deck girders, this is done by transversebracing in vertical planes. Transverse bracingshould be installed over each bearing and atintermediate locations not over 25 ft apart. Thisbracing may consist either of full-depth crossframes or of solid diaphragms with depth at leasthalf the web depth for rolled beams and preferablythree-quarters the web depth for plate girders.End cross frames or diaphragms should be pro-portioned to transfer fully all vertical and lateralloads to the bearings. On through-girder spans,since top lateral and transverse bracing systemscannot be installed, the top flanges of the girdersmust be braced against the floor system. For thepurpose, heavy gusset plates or knee braces may beused (Fig. 17.9b).

The most commonly used type of steel bridgegirder is the welded plate girder. It is typicallylaterally braced, noncompact, and unsymmetrical,with top and bottom flanges of different sizes.Figure 17.10b shows a typical welded plate girder.

Variations in moment resistance are obtained byusing flange plates of different thicknesses, widths,or steel grades, butt-welded to each other in suc-cession. Web thickness too may be varied. Girderwebs should be protected against buckling bytransverse and, in the case of deep webs, longitu-dinal stiffeners. Transverse bearing stiffeners arerequired to transfer end reactions from the web intothe bearings and to introduce concentrated loadsinto the web. Intermediate and longitudinal stiff-eners are required if the girder depth-to-thicknessratios exceed critical values (see Art. 9.13.4).

Stiffeners may be plain plates, angles, or Tsections. Transverse stiffeners can be in pairs orsingle elements. The AASHTO Specifications con-tain restrictions on width-to-thickness ratios andminimum widths of plate stiffeners (Art. 9.13.4).

Web-to-flange connections should be capable ofcarrying the stress flow from web to flange at every

section of the girder. At an unloaded point, the stressflow equals the horizontal shear per linear inch.Where a wheel load may act, for example, at upperflange-to-web connections of deck girders, the stressflow is the vectorial sum of the horizontal shear perinch and thewheel load (assumed distributed over aweb length equal to twice the deck thickness).Weldsconnecting bearing stiffeners to the web must bedesigned for the full bearing reaction.

Space restrictions in the shop, clearance restric-tions in transportation, and erection considerationsmay require dividing long girders into shortersections, which are then joined (spliced) in thefield. Individual segments, plates or angles, mustbe spliced either in the shop or in the field if theyexceed in length the sizes produced by the rollingmills or if shapes are changed in thickness to meetstress requirements.

Specifications require splices to be designed forthe average between the stress due to design loadsand the capacity of the unspliced segment, but fornot less than 75% of the latter. In bolted design,material may have to be added at each splice tosatisfy this requirement. Each splice elementmust beconnected by a sufficient number of bolts to developits full strength. Whenever it is possible to do so,splices of individual segments should be staggered.No splices should be located in the vicinity of thehighest-stressed parts of the girder, for example, atmidspan of simple-beam spans, or over the bearingson continuous beams. Figure 17.10a presents adesign flow chart for welded plate girders.

(F. S. Merritt and R. L. Brockenbrough, “Struc-tural SteelDesigners’Handbook,” 2nd ed.,McGraw-Hill Inc., New York (books-mcgraw-hill.com).)

17.10 Composite-GirderBridges

Installation of appropriately designed shear con-nectors between the top flange of girders or beamsand the concrete deck allows use of the deck as partof the top flange (equivalent cover plate). Theresulting increase in effective depth of the totalsection and possible reductions of the top-flangesteel usually allow some savings in steel comparedwith the noncomposite steel section. The overalleconomy depends on the cost of the shear connec-tors and any other additions to the girder or the deckthat may be required and on possible limitations ineffectiveness of the composite section as such.




BRIDGE ENGINEERING

In areas of negative moment, composite effectmay be assumed only if the calculated tensilestresses in the deck are either taken up fully byreinforcing steel or compensated by prestressing.The latter method requires special precautions toassure slipping of the deck on the girder during the

prestressing operation but rigidity of connectionafter completion.

If the steel girder is not shored up while thedeck concrete is placed, computation of dead-load stresses must be based on the steel sectionalone.

Fig. 17.10 Welded plate girder. (a) Flow chart gives steps in load-factor design. (b) Typical plategirder—stiffened, braced, and noncompact.




BRIDGE ENGINEERING

The effective flange width of the concrete slabthat is used as a T-beam flange of a compositegirder is the lesser of the following:

1. One-fourth of the span length of the girder

2. The center to center distance between adjacentgirders

3. Twelve times the least thickness of the slab

Shear connectors should be capable of resistingall forces tending to separate the abutting concreteand steel surfaces, both horizontally and vertically.Connectors should not obstruct placement andthorough compaction of the concrete. Their instal-lation should not harm the structural steel.

The types of shear connectors presently pre-ferred are channels, or welded studs. Channelsshould be placed on beam flanges normal to theweb and with the channel flanges pointing towardthe girder bearings.

The modular ratio recommended for stressanalysis of composite girders under live loads isgiven in Table 17.17.

For composite action under dead loads, theconcrete section may be assumed to be subjectedto constant compressive stress. This will cause theconcrete to undergo plastic flow and thus willreduce its capacity to resist stress. This is taken intoaccount in design of a composite girder for deadloads bymultiplying by 3 the modular ratio n givenin Table 17.17. Most composite girders, however,are designed for composite action only for liveloads and dead loads (usually, curbs, railings, andutilities) that are added after the concrete deck hasattained sufficient strength to support them.

Example—Stress Calculations for a CompositeGirder: The following illustrates the procedure fordetermining flexural stresses in a composite weldedgirder for factored loads. The girder is assumed tobe fabricated of M270, Grade 50, steel, with yieldpoint Fy ¼ 50 ksi. It will not be shored duringplacement of the concrete deck. For the concrete,the 28-day compressive strength is assumed to bef 0c ¼ 3:25ksi, n ¼ 10 for live loads, n ¼ 30 for deadloads. Dimensions, section properties, and bendingmoments are given in the following:

The section properties of the steel girder aloneare determined first. For the purpose, the momentof inertia I1-1 of the steel section (Fig. 17.11a) iscalculated with respect to the bottom of the girder.Then, the moment of inertia INAwith respect to theneutral axis is computed. Next, the section prop-erties of the composite section (Fig. 17.11b) arecalculated. Stresses in the concrete are small, sincethe steel girder carries the weight of the deck.

Table 17.17 Modular Ratio for CompositeGirders with Live Loads

Specified minimumcompressive strengthof concrete deck f 0c , psi

Modularratio n ¼ Es=E

�c

2000–2400 152500–2900 123000–3900 104000–4900 8

5000 or more 6

*Es ¼ elastic modulus of the steelEc ¼ elastic modulus of the concrete

Fig. 17.11 Sections of composite plate girder:(a) steel section alone; (b) composite section.




BRIDGE ENGINEERING

17.11 Fatigue Design ofBridge Members

All members and connections should be designedso that maximum stresses induced by loads are lessthan allowable stresses and also so that the range ofstresses induced by variations in service loads isless than the allowable fatigue stress range. If amember is entirely in compression and never issubjected to tensile stresses, a fatigue check is notrequired.

Fatigue is an important consideration in designof all bridge components but may be especiallycritical for welded girders. Welding leaves residualstresses in welded regions due to heat input duringthe welding process and subsequent differentialcooling.

The types of connections that are most com-monly used with welded plate girders and thatshould be checked for fatigue are illustrated inFig. 17.12, and the stress category assigned for eachtype is given in Table 17.18a. Table 17.19 gives theallowable stress ranges for various stress categ-ories. Table 17.20 lists allowable stress cycles forvarious types of roads and bridge members.

(“Economical and Fatigue-Resistant SteelBridge Details,” FHWA-HI-90-043, Federal High-way Administration; “Guide Specifications forFatigue Critical Non-Redundant Steel Bridges,”American Association of State Highway andTransportation Officials (www.aashto.org).)

17.12 Orthotropic-DeckBridges

An orthotropic deck is, essentially, a continuous,flat steel plate, with stiffeners (ribs) welded to itsunderside in a parallel or rectangular pattern. Theterm orthotropic is shortened from orthogonalanisotropic, referring to the mathematical theoryused for the flexural analysis of such decks.

When used on steel bridges, orthotropic decksare usually joined quasi-monolithically, by weldingor high-strength bolting, to the main girders andfloor beams. They then have a dual function asroadway and as structural top flange.

The combination of plate or box girders withorthotropic decks allows the design of bridges ofconsiderable slenderness and of nearly twice thespan reached by girders with concrete decks. The

Steel Section for Slab and Girder Loads (Fig. 17.11a)

Material Size, in Area y Ay Ay2

�1 Top flange 12�5⁄8 7.50 95.31 715 68,130

�2 Web 94�5⁄16 29.38 48.00 1410 67,680

�3 Bottom flange 14 � 1 14.00 0.50 7 4

SA ¼ 50.88 SAy ¼ 2132 135,814

Moment of inertia of web ¼ þ21,629

yb ¼ SAy

SA¼ 41:9 I1-1 ¼ 157,443

�y2bSA ¼ 289,325

yt ¼ 95.6 2 41.9 ¼ 53.7 INA ¼ 68,118

Section for Curb Loads, Railing, Utilities (Composite) (Fig. 17.11b)

Material Area y Ay Ay2

Steel section 50.88 2132 135,814

�4 Concrete: A/n, n ¼ 30 51.57 103.6 5342 553,463

102.45 7474 689,277

Moment of inertia of girder web ¼ þ21,629

yb ¼ 7474

102:45¼ 72:9 I1-1 ¼ 710,906

�y2bSA ¼ 2544,461

yt ¼ 95.6 2 72.9 ¼ 22.7 INA ¼ 166,445

Section for Live Loads (Composite) (Fig. 17.11b)

Material Area y Ay Ay2

Steel section 50.88 2132 135,814

�4 Concrete: A/n, n ¼ 10 154.70 103.6 16,027 1,660,389

205.58 18,159 1,796,203

Moment of inertia of girder web ¼ þ21,629

yb ¼ 18:159

205:58¼ 88:3 I1-1 ¼ 1,817,832

�y2bSA ¼ 21,603,995

yt ¼ 95.6 2 88.3 ¼ 7.3 INA ¼ 213,837

Moments

For slab and girder loads ¼ 1825kips-ft

For curb loads ¼ 347kips-ft

For live loads ¼ 6295kips-ft

Stresses in Steel Girder

Type of Load Bottom fs Top fs

Slab and girder

loads

1825�12

68,118�41:9 ¼ 13:5

1825�12

68,118�53:7 ¼ 17:3

Curb loads347�12

166,445�72:9 ¼ 1:8

347�12

166,445�22:7 ¼ 0:6

Live loads6295�12

213,937�88:3 ¼ 31:2

6295�12

213,937�7:3 ¼ 2:6

Bottom fs ¼ 46.5kips/in2 Top fs ¼ 20.5kips/in2




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most widespread application of orthotropic decksis on continuous, two- to five-span girders on low-level river crossings in metropolitan areas, whereapproaches must be kept short and grades low.This construction has been used for main spans upto 1100 ft in cable-stayed bridges and up to 856 ftwithout cable stays. There also are some spectacu-lar high-level orthotropic girder bridges and somearch and suspension bridges with orthotropic stiff-ening girders. On some of the latter, girders anddeck have been combined in a single lens-shapedbox section that has great stiffness and low aero-dynamic resistance.

17.12.1 Box Girders

Single-web or box girders may be used fororthotropic bridges. Box girders are preferred ifstructure depth is restricted. Their inherent stiff-ness makes it possible to reduce, or to omit,unsightly transverse bracing systems. In crosssection, they usually are rectangular, occasionallytrapezoidal. Minimum dimensions of box girdersare controlled by considerations of accessibilityand ease of fabrication.

Wide decks are supported by either single boxgirders or twin boxes. Wide single boxes have beenbuilt with multiple webs or secondary interiortrusses. Overhanging floor beams sometimes aresupported by diagonal struts.

17.12.2 Depth-Span Ratios

Girder soffits are parallel to the deck, tapered, orcurved. Parallel flanges, sometimes with taperedside spans, generally are used on unbraced girderswith depth-to-main-span ratios as low as 1 :70.Parallel-flange unbraced girders are practicallyrestricted to high-level structures with unrestrictedclearance. Unbraced low-level girders usually aredesigned with curved soffits with minimum depth-to-main-span ratios of about 1 :25 over the mainpiers and 1:50 at the shallowest section.

17.12.3 Cable-SuspendedSystems withOrthotropic Decks

Main spans of bridges may have girders suspendedfrom or directly supported by cables that are hungfrom towers, or pylons. The cables are curved if the

Fig. 17.12 Fatigue stress categories for some commonly used connections (see Table 17.13). In (c),category C applies also to transverse loading.




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girders are suspended at each floor beam (suspen-sion bridges); otherwise they are straight (cable-stayed bridges). In cable-stayed bridges, the cablesmay extend from the pylons to the connectionswith the girders in tiers, parallel to each other(harped), or in a bundle pattern (radiating from thepylons). See Fig. 17.24.

Each cable stay adds one degree of statical in-determinancy to a system. To make the actual con-ditions conform to design assumptions, the cablelength must be adjustable either at the anchoragesto the girders or at the saddles on the towers. (Seealso Art. 17.16.)

17.12.4 Steel Grades

The steel commonly used for orthotropic plates isweldable high-strength, low-alloy structural steel

M270, Grade 50. Minimum thickness is seldom lessthan 7⁄16 in (10 mm), to avoid excessive deflectionsunder heavy wheel loads. The maximum thicknessseldom exceeds 3⁄4 in because of the decrease inpermissible working stresses of high-strength low-alloy steel and the increase of fillet- and butt-weldsizes for plates of greater thickness.

17.12.5 Floor Beams

If, as in most practical cases, the deck spanstransversely between main girders, transverse ribsare replaced by the floor beams, which are thenbuilt up of inverted T sections, with the deck plateacting as top flange. Floor-beam spacings arepreferably kept constant on any given structure.They range from less than 5 ft to over 15 ft. Longerspacings have been suggested for greater economy.

Table 17.18 Fatigue Stress Categories for Bridge Members

(a) Stress Categories for Typical Connections

Type of connection Figure No. Stress Category

Toe of transverse stiffeners 17.13a Tension or reversal CButt weld at flanges 17.13b Tension or reversal BGusset for lateral bracing(assumed groove weld,R � 24 in)

17.13c Tension or reversal B

Flange to web 17.13d Shear F

(b) Stress Categories for Weld Conditions in Fig. 17.13c

Weld condition* Category

Unequal thickness; reinforcement in place EUnequal thickness; reinforcement removed DEqual thickness; reinforcement in place CEqual thickness; reinforcement removed B

(c) Stress Categories for Radii R in Fig. 17.13c

Category for welds

R, in† Fillet Groove

24 or more D BFrom 6 to 24 D CFrom 2 to 6 D D2 or less E E

* For transverse loading, check transition radius for possible assignment of lower category.† Also applies to transverse loading.




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17.12.6 Ribs

These are either open (Fig. 17.13a) or closed(Fig. 17.13b). The spacing of open ribs is seldomless than 12 in or more than 15 in. The lower limitis determined by accessibility for fabrication andmaintenance, the upper by considerations ofdeck-plate stiffness. To reduce deformations ofthe surfacing material under concentrated trafficloads, some specifications require the platethickness to be not less than 1⁄25 of the spacingbetween open ribs or between the weld lines ofclosed ribs.

Usually, the longitudinal ribs are made continu-ous through slots or cutouts in the floor-beamwebsto avoid a multitude of butt welds. Rib splices canthen be coordinated with the transverse decksplices.

Closed ribs, because of their greater torsionalrigidity, give better load distribution and, otherthings being equal, require less steel and lessweld-ing than open ribs. Disadvantages of closed ribsare their inaccessibility for inspection and main-tenance and more complicated splicing details.There have also been some difficulties in definingthe weld between closed ribs and deck plate.

Table 17.19 Allowable Fatigue Stress Range FSR*, ksi, for Bridge Members

For Structures with Redundant Load Paths†

Category For 100,000Cycles

For 500,000Cycles

For 2,000,000Cycles

For over2,000,000 Cycles

A 63S 37S 24S 24SB 49 29 18 16C 35.5 21 13 10

12‡

D 28 16 10 7E 22 13 8 4.5F 16 9.2 5.8 2.6G 15 12 9 8

Nonredundant-Load-Path Structures

Category For 100,000Cycles

For 500,000Cycles

For 2,000,000Cycles

For over2,000,000 Cycles

A 50S 29S 24S 24SB 39 23 16 16C 28 16 10 9

12‡ 11‡

D 22 13 8 5Ex 17 10 6 2.3F 12 9 7 6

* The range of stress is defined as the algebraic difference between the maximum stress and the minimum stress. Tension stress isconsidered to have the opposite algebraic sign from compression stress.

† Structure types with multiload paths where a single fracture in a member cannot lead to the collapse. For example, a simplesupported single-span multibeam bridge or a multielement eyebar truss member has redundant load path.

‡ For transverse stiffener welds on girder webs or flanges.x Partial-length welded cover plates should not be used on flanges more than 0.8 in thick for nonredundant-load path structures.

S For unpainted weathering steel, A709, the category ‘A’ allowable FSR values are less then values shown, see AASHTOSpecifications.




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17.12.7 Fabrication

Orthotropic decks are fabricated in the shop inpanels as large as transportation and erection faci-lities permit. Deck-plate panels are fabricated bybutt-welding available rolled plates. Ribs and floorbeams are fillet-welded to the deck plate in upside-down position. Then, the deck is welded to thegirder webs.

It is important to schedule all welding se-quences to minimize distortion and locked-upstresses. The most effective method has been to fitup all components of a panel—deck plate, ribs, andfloor beams—before starting any welding, then toplace the fillet welds from rib to rib and from floorbeam to floor beam, starting from the panel centerand uniformly proceeding toward the edges. Sincethis sequence practically requires manual welding

throughout, American fabricators prefer to join theribs to the deck by automatic fillet welding beforeassembly with the floor beams. After slipping thefloor-beam webs over the ribs, the fabricators weldmanually only the beam webs to the deck. Thismethod requires careful preevaluation of ribdistortions, wider floor-beam slots, and conse-quently more substantial or only one-sided rib-to-floor-beam welds.

17.12.8 Analysis

Stresses in orthotropic decks are considered asresulting from a superposition of four staticsystems:

System I consists of the deck plate considered asan isotropic plate elastically supported by the ribs

Table 17.20 Allowable Stress Cycles for Bridge Members

Main (longitudinal) load-carrying members

Type of road Case ADTT* Truck loading Lane loading†

Freeways, expressways,major highways,and streets

I 2500 or more 2,000,000‡ 500,000


II less than 2500 500,000 100,000

Other highwaysand streets not includedin case I or II

III 100,000 100,000

Transverse members and details subjected to wheel loads

Type of road Case ADTT* Truck loading


I 2500 or more over 2,000,000


II less than 2500 2,000,000

Other highwaysand streets

III 500,000

* Average daily truck traffic (one direction).† Longitudinal members should also be checked for truck loading.‡ Members should also be investigated for fatigue when over 2 million stress cycles are produced by a single truck on the bridge with

load distributed to the girders as designated for traffic lane loading.




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(Fig. 17.14a). The deck is subject to bending fromwheel loads between the ribs.

System II combines the deck plate, as transverseelement, and the ribs, as longitudinal elements.The ribs are continuous over, and elasticallysupported by, the floor beams (Fig. 17.14b). Theorthotropic analysis furnishes the distribution ofconcentrated (wheel) loads to the ribs, their flexuraland torsional stresses, and thereby the axial andtorsional stresses of the deck plate as their topflange.

System III combines the ribs with the floor beamsand is treated either as an orthotropic system or asa grid (Fig. 17.14c). Analysis of this systemfurnishes the flexural stresses of the floor beams,

Fig. 17.13 Rib shapes used in orthotropic-platedecks.

Fig. 17.14 Orthotropic-plate deck may be considered to consist of four systems: (a) Deck platesupported on ribs; (b) rib-deck T beams spanning between floor beams; (c) floor beam with deck plate astop flange, supported on girders; (d) girder with deck plate as top flange.




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including the stresses the deck plate receives astheir top flange.

System IV comprises the main girders with theorthotropic deck as top flange (Fig. 17.14d). Axialstresses in the deck plate and ribs and shearstresses in the deck plate are obtained from theflexural and torsional analysis of the main girdersby conventional methods.

Theoretically, the deck plate should be designedfor the maximum principal stresses that may resultfrom the simultaneous effect of all four systems.Practically, because of the rare coincidence of themaxima from all systems and in view of the greatinherent strength reserve of the deck as a mem-brane (second-order stresses), a design is generallysatisfactory if the stresses from any one system donot exceed 100% of the ordinarily permissibleworking stresses and 125% from a combination ofany two systems.

In the design of long-span girder bridges,special attention must be given to buckling stabilityof deep webs and of the deck. Also, considerationshould be given to conditions that may arise atintermediate stages of construction.

17.12.9 Steel-Deck Surfacing

All traffic-carrying steel decks require a covering ofsome nonmetallic material to protect them fromaccidental damage, distribute wheel loads, com-pensate for surface irregularities, and provide anonskid, plane riding surface. To be effective, thesurfacing must adhere firmly to the base and resistwear and distortion from traffic under all con-ditions. Problems arise because of the elastic andthermal properties of the steel plate, its sensitivityto corrosion, the presence of bolted deck splices,and the difficulties of replacement or repair undertraffic.

The surfacing material usually is asphaltic.Strength is provided by the asphalt itself (mastic-type pavements) or by mineral aggregate (asphalt-concrete pavement). The usefulness of mastic-typepavements is restricted to a limited temperaturerange, below which they become brittle andabove which they may flow. The effectiveness ofthe mineral aggregate of asphalt concrete dependson careful grading and adequate compaction,which on steel decks sometimes is difficult toobtain. Asphalt properties may be improved byadmixtures of highly adhesive or ductile chemicalsof various plastics families.

(“Design Manual for Orthotropic Steel PlateDeck Bridges,” American Institute of SteelConstruction, Chicago, Ill.; F. S. Merritt and R. L.Brockenbrough, “Structural Steel Designers’ Hand-book,” 2nd ed., McGraw-Hill, Inc., New York.)

17.13 Truss Bridges

Trusses are lattices formed of straight membersin triangular patterns. Although truss-type con-struction is applicable to practically every staticsystem, the term is restricted here to beam-typestructures: simple spans and continuous andhinged (cantilever) structures. For typical single-span bridge truss configurations, see Fig. 6.50. Forthe stress analysis of bridge trusses, see Arts. 6.46through 6.50.

Truss bridges require more field labor thancomparable plate girders. Also, trusses are morecostly to maintain because of the more complicatedmakeup of members and poor accessibility of theexposed steel surfaces. For these reasons, and as aresult of changing aesthetic preferences, use oftrusses is increasingly restricted to long-spanbridges for which the relatively low weight andconsequent easier handling of the individualmembers are decisive advantages.

The superstructure of a typical truss bridge iscomposed of two main trusses, the floor system, atop lateral system, a bottom lateral system, crossframes, and bearing assemblies.

Decks for highway truss bridges are usuallyconcrete slabs on steel framing. On long-spanrailway bridges, the tracks are sometimes mounteddirectly on steel stringers, although continuity ofthe track ballast across the deck is usually pre-ferred. Orthotropic decks are rarely used on trussbridges.

Most truss bridges have the deck locatedbetween the main trusses, with the floor beamsframed into the truss posts. As an alternative, thedeck framing may be stacked on top of the topchord.Deck trusses have the deck at or above top-chord level (Fig. 17.15); through trusses, near thebottom chord (Fig. 17.16). Through trusses whosedepth is insufficient for the installation of a toplateral system are referred to as half throughtrusses or pony trusses.

Figure 17.16 illustrates a typical cantilever trussbridge. The main span comprises a suspended




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span and two cantilever arms. The side, or anchor,arms counterbalance the cantilever arms.

Sections of truss members are selected to en-sure effective use of material, simple details forconnections, and accessibility in fabrication, erec-tion, and maintenance. Preferably, they should besymmetrical.

In bolted design, the members are formed ofchannels or angles and plates, which are combinedinto open or half-open sections. Open sides arebraced by lacing bars, stay plates, or perforatedcover plates. Welded truss members are formed ofplates. Figure 17.17 shows typical truss-membersections. For slenderness restrictions of trussmembers, see Art. 17.7.

The design strength of tensile members iscontrolled by their net section, that is, by thesection area that remains after deduction of rivet

or bolt holes. In shop-welded field-bolted con-struction, it is sometimes economical to build uptensile members by butt-welding three sectionsof different thickness or steel grades. Thickerplates or higher-strength steel is used for the endsections to compensate for the section loss at theholes.

The permissible stress of compression membersdepends on the slenderness ratio (see Art. 9.11).Design specifications also impose restrictions onthe width-to-thickness ratios of webs and coverplates to prevent local buckling.

The magnitude of stress variation is restrictedfor members subject to stress reversal duringpassage of a moving load (Art. 9.20).

All built-up members must be stiffened bydiaphragms in strategic locations to secure theirsquareness. Accessibility of all members and con-

Fig. 17.15 Deck truss bridge.




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nections for fabrication and maintenance should bea primary design consideration.

Whenever possible, each web member shouldbe fabricated in one piece reaching from the top tothe bottom chord. The shop length of chord mem-bers may extend over several panels. Chord splicesshould be located near joints and may be in-corporated into the gusset plates of a joint.

In most trusses, members are joined by boltingor welding with gusset plates. Pin connections,which were used frequently in earlier truss bridges,are now the exception. As a rule, the centerlines orcenter-of-gravity lines of all members convergingat a joint intersect in a single point (Fig. 17.19).

Stresses in truss members and connections aredivided into primary and secondary stresses. Pri-mary stresses are the axial stresses in the membersof an idealized truss, all of whose joints are madewith frictionless pins and all of whose loads areapplied at pin centers. Secondary stresses are thestresses resulting from the incorrectness of theseassumptions. Somewhat higher stresses are al-lowed when secondary stresses are considered.

(Some specifications require computation of theflexural stresses in compression members causedby their own weight as primary stresses.) Underordinary conditions, secondary stresses must becomputed only for members whose depth is morethan one-tenth of their length.

(F. S. Merritt and R. L. Brockenbrough,“Structural Steel Designers’ Handbook,” 2nd ed.,McGraw-Hill, Inc., New York (books.mcgraw-hill.com).)

17.14 Suspension Bridges

These are generally preferred for spans over1800 ft, and they compete with other systems onshorter spans.

The basic structural system consists of flexiblemain cables and, suspended from them, stiffeninggirders or trusses (collectively referred to as“stiffening beams”), which carry the deck framing.The vehicular traffic lanes are as a rule accom-modated between the main supporting systems.

Fig. 17.16 Typical cantilever truss bridge.




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Sidewalks may lie between the main systems orcantilever out on both sides.

17.14.1 Stiffening Beams

Stiffening beams distribute concentrated loads,reduce local deflections, act as chords for the lateralsystem, and secure the aerodynamic stability of thestructure. Spacing of the stiffening beams is con-trolled by the roadway width but is seldom lessthan 1⁄50 the span.

Stiffening beams may be either plate girders,box girders, or trusses. On major bridges, theirdepth is at least 1⁄180 of the main span.

17.14.2 Anchorages

The main cables are anchored in massive concreteblocks or, where rock subgrade is capable of res-isting cable tension, in concrete-filled tunnels. Orthe main cables are connected to the ends of thestiffening girders, which then are subjected to

longitudinal compression equal to the horizontalcomponent of the cable tension.

17.14.3 Continuity

Single-span suspension bridges are rare in engin-eering projects. They may occur in crossings ofnarrow gorges where the rock on both sidesprovides a reliable foundation for high-level cableanchorages.

The overwhelming majority of suspensionbridges have main cables draped over two towers.Such bridges consist, thus, of a main span and twoside spans. Preferred ratios of side span to mainspan are 1:4 to 1 :2. Ratios of cable sag to main spanare preferably in the range of 1 :9 to 1 :11, seldomless than 1:12.

If the side spans are short enough, the maincables may drop directly from the tower tops tothe anchorages, in which case the deck is carried tothe abutments on independent, single-span plategirders or trusses. Otherwise, the suspensionsystem is extended over both side spans to the

Fig. 17.17 Typical sections used in steel bridge trusses.




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Fig.17.18

Boxgirder

stiffeningbeam—

Carquinez

Bridge.




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next piers. There, the cables are deflected to theanchorages. The first system allows the designersome latitude in alignment, for example, curvedroadways. The second requires straight side spans,in line with the main span. It is the common systemfor suspension bridges that are links in a chain ofmultiple-span crossings.

When side spans are not suspended, the stif-fening beam is of course restricted to the mainspan. When side spans are suspended, the stiffen-ing beams of the three spans may be continuous ordiscontinuous at the towers. The spans are typic-ally restrained to the tower at the ends. Continuityof stiffening beams is required in self-anchoredsuspension bridges, where the cable ends areanchored to the stiffening beams.

17.14.4 Cable Systems

The suspenders betweenmain cables and stiffeningbeams are usually equally spaced and vertical.

Main cables, suspenders, and stiffening beams(girders or trusses) are usually arranged in verticalplanes, symmetrical with the longitudinal bridgeaxis. Bridges with inward- or outward-slopingcables and suspenders and with offset stiffeningbeams are less common.

Three-dimensional stability is provided by topand bottom lateral systems and transverse frames,similar to those in ordinary girder and trussbridges. Rigid roadway decks may take the place ofeither or both lateral systems, especially in doubledecked trusses.

In the United States, the main cables are usuallymade up of 6-gage galvanized bridge wire of 220 to225 ksi ultimate and 82 to maximum 90 ksi workingstress. The wires are usually placed parallel butsometimes in strands and compacted and wrappedwith No. 9 wire. In Europe, strands containing elab-orately shaped heat-treated cast-steel wires aresometimes used. Strands must be prestretched.They have a lower and less reliable modulus ofelasticity than parallel wires. The heaviest cables,those of the Golden Gate Bridge, are about 36 in indiameter. Twin cables are used if larger sections arerequired.

Suspenders may be eyebars, rods, single steelropes, or pairs of ropes slung over the main cable.Connections to the main cable are made with cablebands. These are cast steel whose inner facesare molded to fit the main cable. The bands areclamped together with high-strength bolts.

17.14.5 Floor System

In the design of the floor system, reduction of deadload and resistance to vertical air currents shouldbe the governing considerations. The deck is usu-ally lightweight concrete or steel grating partlyfilled with concrete with the exception of boxsections which usually have a wearing surface.Expansion joints should be provided every 100 to120 ft to prevent mutual interference of deck andmain structure. Stringers should be made compo-site with the deck for greater strength and stiffness.Floor beams may be plate girders or trusses,depending on available clearance. With trusses,wind resistance is less.

17.14.6 Towers

The towers may be portal type, multistory, ordiagonally braced frames (Fig. 17.20). They may beof cellular construction, made of steel plates and

Fig. 17.19 Pin joint in the lower chord of abridge truss at a support.




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shapes, or steel lattices, or of reinforced concrete.The substructure below the “spray” line is con-crete. The base of steel towers is usually fixed, but itmay be hinged. (Hinged towers, however, offersome erection difficulties.) The cable saddles at thetop of fixed towers are sometimes placed on rollersto reduce the effect on the towers of unbalancedcable deflections. Cable bents can be considered asshort towers, either fixed or hinged, whose axiscoincides with the bisector of the angle formed bythe cable.

17.14.7 Analysis

For gravity loads, the three elements of a suspen-sion bridge in a vertical plane—the main cable or

chain, the suspenders, and the stiffening beam—are considered as a single system. The system ofdiscrete suspenders often is idealized as one ofcontinuous suspension.

The stiffening beam is assumed stresslessunder dead load, a condition approximated byappropriate methods of erection. Moments andshears are produced by that part of the live loadnot taken up by the main cable through thesuspenders. Also, moments and shears result fromchanges in cable length and sag due to tempera-ture variations or unbalanced loadings of adjacentspans. Deflections of the stiffening beam arestrictly elastic; that is, neglecting the effect ofshear, the curvature at any section of the elasticline of the loaded beam is proportional to the

Fig. 17.20 Types of towers used for long suspension bridges.




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bending moment divided by the moment ofinertia of that section.

The suspenders are subject to tension only. Theirelongation under live load is usually neglected inthe analysis.

The main cable typically is assumed to have noflexural stiffness and to be subject to axial tensiononly. Its shape is that of a funicular polygon of theapplied forces (which include the dead weight ofthe cable). The pole distance H, lb, which is thehorizontal component of the cable tension, isconstant for a given loading and a given sag. Theshape of the cable under given loads, that is, itsordinate y, ft, and slope tan a at any point withabscissa x, ft, can be expressed in terms of momentMo, ft-kips, and shear V, kips, that a simple beam ofthe same span L, ft, as the cable would have underthe same load (Fig. 17.21).

y ¼ Mo

Htana ¼ V

H(17:14)

In the special case of a uniform loadw, kips/lin ft,

H ¼ wL2

8f(17:15)

y ¼ wx(L� x)

2Hor y ¼ 4fx(L� x)

L2(17:16)

where f ¼ cable sag, ft.The shape of the cable under its own weight

without suspended load would be a catenary;under full dead load, the cable shape is usuallycloser to a parabola. The difference is small.

Concentrated or sectionally uniform live loadsuperimposed on the dead load subjects the cableto additional strain and causes it to adjust its shapeto the changed load configuration. The resultingdeformations are not exactly proportional to theadditional loading; their magnitude is influencedby the already existing dead-load stresses.

If Mo is the bending moment of the stiffeningbeam under the applied load but without cooper-ation of the cable, the beam moment M with co-operation of the cable will be

M ¼ Mo �Hy (17:17)

More specifically, using subscripts D and L, res-pectively, for dead and live load and consideringthat

yL ¼ yD þ Dy (17:18)

one gets the following expression for the dead- pluslive-load bending moment of the beam (seeFig. 17.21b):

M ¼MD þML ¼ MD0 þML, 0

� (HD þHL)(yD þ Dy) (17:19)

But, since MD ¼ MD0 2 HDyD ¼ 0, because thestiffening beam has no bending moment underdead load (ideally),

M ¼ ML0 � (HD þHL)Dy�HLyD (17:20)

This is the basic equation of the cable-beam system.In this equation, ML0, HD, and yD are given. HL

and Dy must be so determined that the conditionsof static equilibrium of all forces and geometric

Fig. 17.21 Stresses in cable and stiffening beamof a suspension bridge.




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compatibility of all deformations are satisfiedthroughout the system.

The mathematically exact solution of the prob-lem is known as the deflection theory. A less exact,older theory is known as the elastic theory. Besidesthese, there are several approximate methodsbased on observed regularities in the behavior ofsuspension bridges, which are sufficiently accurateto serve for preliminary design.

17.14.8 Wind Resistance

Wind acting on the main cables and on part of thesuspenders is carried to the towers by the cables.Wind acting on the deck, stiffening beams, and liveload is resistedmainly by the lateral bracing systemand slightly by the cables because of the gravitycomponent resulting from any elastic lateral de-flection of the main supporting system.

Oscillations of the structure may be generated bylive load, earthquake, or wind. Live-load vibrationsare insignificant in major bridges. (N. C. Raab andH. C. Wood, “Earthquake Stresses in the SanFrancisco–Oakland Bay Bridge,” Transactions of theAmerican Society of Civil Engineers, vol. 106, 1941).Oscillations due to wind, however, can becomedangerous if excessive amplitudes build up; that is,if the exciting impulses approach the naturalfrequency of the structure. Oscillating wind forcesare caused by eddies, which may be generatedoutside the structure or by the structure itself,especially on the lee side of large plates. Oscillationsof the structure may be purely flexural, purelytorsional, or coupled (flutter), the last two being themore dangerous.

Methods used to predict the aerodynamicbehavior of suspension bridges include:

Mathematical analysis of the natural frequency ofthe structure in flexure and torsion [F. Bleich, C. B.McCullogh, R. Rosecrans, and G. S. Vincent,“Mathematical Theory of Vibration in SuspensionBridges,” Government Printing Office, Washing-ton, D.C.: A. G. Pugsley, “Theory of SuspensionBridges,” Edward Arnold (Publishers) Ltd.,London].

Wind-tunnel tests on scale models of the entirestructure or of typical sections (“AerodynamicStability of Suspension Bridges with Special Ref-erence to the Tacoma Narrows Bridge,” Universityof Washington Engineering Experiment Station Bulle-tin 116).

Application of Steinman’s criteria (these arecontroversial) (D. B. Steinman, “Rigidity andAerodynamic Stability of Suspension Bridges,”with discussion, Transactions of the American Societyof Civil Engineers, vol. 110, 1945).

Tuned mass dampers and tuned liquid dampershave been used to decrease the amplitude of vortexoscillations.

17.14.9 Tower Stresses

The towers must resist the forces imposed on themby the main cables in addition to the gravity andwind loads acting directly.

The following forces must be considered: Thevertical components of the main cables in main andside spans under dead load, live load, temperaturechange, seismic, and wind acting on the maincables, both parallel and transverse to the bridgeaxis; reactions to longitudinal cable movementsdue to unbalanced loading. These reactions willdevelop unless the movements are taken up byhinges or friction-free roller nests. Theoretically, themagnitude of these movements will be affected bythe flexural resistance Q of the towers, but thiseffect, being comparatively small, is usually neg-lected.

Movement of the tower top generates bendingmoments. These increase from the top to thebottom at the rate of

Mx ¼ VyþQx (17:21)

where V ¼ vertical cable reaction

x ¼ distance below top

y ¼ horizontal deflection at x

Q ¼ horizontal resistance at top

The magnitude ofQ is such that the total deflectionequals the longitudinal cable movement. It is foundby solving the differential equation for the elasticcurve of the tower axis. Thus,

y ¼ A sin cxþ B cos cx�Q

Vx (17:22)

¼ Q

V

sin cx

c cos cL� x

� �

in which c ¼ ffiffiffiffiffiffiffiffiffiffiffiV=EI

p, I ¼ moment of inertia, and

E ¼ modulus of elasticity of tower, if the towers




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have constant cross sections. The bending momentat x is

Mx ¼ Q sin cx

c cos cL(17:23)

where L ¼ height of tower.If, as is usual, the tower cross section varies in

several steps, the coefficients A and B in Eq. (17.22)differ from section to section. They are found fromthe continuity conditions at each step.

Anchorages and footings should be designedfor adequate safety against uplift, tipping, andsliding under any possible combination of actingforces.

(S. Hardesty and H. E. Wessman, “PreliminaryDesign of Suspension Bridges,” Transactions of theAmerican Society of Civil Engineers, vol. 104, 1939;R. J. Atkinson and R. V. Southard, “On the Problemof Stiffened Suspension Bridges and Its Treatmentby Relaxation Methods,” Proceedings of the Instituteof Civil Engineers, 1939; C. D. Crosthwaite, “TheCorrected Theory of the Stiffened SuspensionBridge,” Proceedings of the Institute of Civil Engineers,1946; Ling-Hi Tsien, “A Simplified Method ofAnalyzing Suspension Bridges,” Transactions of theAmerican Society of Civil Engineers, vol. 114, 1947;F. S. Merritt and R. L. Brockenbrough, “StructuralSteel Designers’ Handbook,” 2nd ed., McGraw-Hill, Inc., New York (books.mcgraw-hill.com).)

17.15 Cable-Stayed Bridges*

The cable-stayed bridge, also called the stayed-girder (or truss), has come into wide use sinceabout 1950 for medium- and long-span bridgesbecause of its economy, stiffness, aesthetic qual-ities, and ease of erection without falsework.Design of cable-stayed bridges utilizes taut cablesconnecting pylons to a span to provide intermedi-ate support for the span. This principle has beenunderstood by bridge engineers for at least thelast two centuries, as indicated by the bridge inFig. 17.22. The Roeblings used cable stays assupplementary stiffening elements in the famousBrooklyn Bridge (1883). Many recently built andproposed suspension bridges also incorporate tautcable stays when dynamic (railroad) and long-span

effects have to be contended with, as in the SalazarBridge.

17.15.1 Characteristics ofCable-Stayed Bridges

The cable-stayed bridge offers a proper and eco-nomical solution for bridge spans intermediatebetween those suited for deck girders (usually upto 600 to 800 ft but requiring extreme depths, upto 33 ft) and the longer-span suspension bridges(over 1000 ft). The cable-stayed bridge thus findsapplication in the general range of 600- to 1600-ftspans but may be competitive in cost for spans aslong as 2900 ft.

A cable-stayed bridge has the advantage ofgreater stiffness over a suspension bridge. Use ofsingle or multiple box girders gains large torsionaland lateral rigidity. These factors make thestructure stable against wind and aerodynamiceffects.

The true action of a cable-stayed bridge(Fig. 17.23) is considerably different from that of asuspension bridge. As contrasted with the rela-tively flexible cable of the latter, the inclined, tautcables of the cable-stayed structure furnish rela-tively stable point supports in the main span.Deflections are thus reduced. The structure, ineffect, becomes a continuous girder over the piers,with additional intermediate, elastic (yet relativelystiff) supports in the span. As a result, the girdermay be shallow. Depths usually range from 1⁄60 to1⁄80 the main span, sometimes even as small as1⁄100 the span.

Cable forces are usually balanced between themain and flanking spans, and the structure isinternally anchored; that is, it requires no massivemasonry anchorages. Analogous to the self-anchored suspension bridge, second-order effectsof the type requiring analysis by a deflection theoryare of relatively minor importance. Thus, static

* Extracted with permission from F. S. Merritt and R. L.Brockenbrough, “Structural Steel Designers Handbook,”2nd ed., McGraw-Hill, Inc., New York.

Fig. 17.22 Cable-stayed chain bridge (Hatleysystem, 1840).




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analysis is simpler, and the structural behavior maybe more clearly understood.

The above remarks apply to the common, self-anchored type of cable-stayed bridges, character-ized by compression in the main bridge girders(Fig. 17.23a). It is possible to conceive of theopposite extreme of a fully anchored (earth-anchored) cable bridge in which the main girdersare in tension. This could be achieved by pinningthe girders to the abutments and providing slidingjoints in the side-span girders adjacent to thepylons (Fig. 17.23b). The fully anchored system isstiffer than the self-anchored system and may beadvantageously analyzed by second-order deflec-tion theory because (analogous to suspension

bridges) bending moments are reduced by thedeformations.

A further increase in stiffness of the fullyanchored system is possible by providing piers inthe side spans at the cable attachments (Fig. 17.24).This is advantageous if the side spans are not usedfor boat traffic below, and if, as is often the case, theside spans cross over low water or land (Knieb-rucke at Dusseldorf, Fig. 17.27i).

A partly anchored cable-stayed system (Fig.17.23c) has been proposed wherein some of thecables are self-anchored and some fully anchored.The axial forces in the girders are then partlycompression and partly tension, but their magni-tudes are considerably reduced.

Fig. 17.23 Axial forces in a cable-stayed girder of (a) self-anchored, (b) fully anchored, (c) partlyanchored cable-stayed bridges.

Fig. 17.24 Anchorage of side-span cables at piers and abutments increases stiffness of the center span.




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17.15.2 Classification ofCable-Stayed Bridges

The relatively small diameter of the cables and theabsolute minimum amount of overhead structurerequired are the principal features contributing tothe excellent architectural appearance of cable-stayed bridges. The functional character of thestructural design produces, as a by-product, agraceful and elegant solution for a bridge crossing.This is encouraged by the wide variety of possibletypes, using single or multiple cables, including thebundle, harp, fan, and star configurations, as seenin elevation (Fig. 17.25). These may be symmetricalor asymmetrical.

A wide latitude of choice of cross section of thebridge at the pylons is also possible (Fig. 17.26). The

most significant distinction occurs between thosewith twin pylons (individual, portal, or A frame)and those with single pylons in the center of theroadway. The single pylons usually require a largebox girder to resist the torsion of eccentric loadings,and the box is most frequently of steel with ananisotropic steel deck. The single-pylon type isadvantageous in allowing a clear unobstructedview from cars passing over the bridge. The pylonsmay (as with suspension-bridge towers) be eitherfixed or pinned at their bases. In the case of fixity,this may be either with the girders or directly withthe pier.

Some details of cable-stayed bridges areshown in the elevations and cross sections inFig. 17.27.

Fig. 17.25 Classification of cable-stayed bridges by arrangement of cables. (From A. Feige, “Evolution ofGerman Cable-Stayed Bridges: An Overall Survey,” Acier-Stahl-Steel, vol. 12, 1966.)

Fig. 17.26 Shapes of pylons used for cable-stayed bridges. (a) Portal-frame type with top crossmember; (b) pylon fixed to pier and without top cross member; (c) pylon fixed to superstructure andwithout top cross member; (d) axially located pylon fixed to the superstructure; (e) A-shaped pylon; ( f )laterally offset pylon fixed to a pier; (g) diamond-shaped pylon. (From A. Feige, “Evolution of German Cable-Stayed Bridges: An Overall Survey,” Acier-Stahl-Steel, vol. 12, 1966.)




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Fig. 17.27 Some cable-stayed bridges, with cross sections taken at pylons. (a) Buchenauer crossing atBruchsal, 1956; (b) Julicherstrasse crossing at Dusseldorf, 1964; (c) bridge over the Stromsund, Sweden,1955; (d) bridge over the Rhine near Maxau, 1966; (e) bridge on the elevated highway at Ludswigshafen,1969; ( f ) Severin Bridge, Cologne, 1959; (g) bridge over the Rhine near Levenkusen, 1965; (h) North Bridgeat Dusseldorf, 1958; (i) Kniebrucke at Dusseldorf, 1969; ( j) bridge over the Rhine at Rees, 1967.




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17.15.3 Cable-Stayed BridgeAnalysis

The static behavior of a cable-stayed girder can bestbe gaged from the simple, two-span example ofFig. 17.28. The girder is supported by one stay cablein each span, at E and F, and the pylon is fixed tothe girder at the center support B. The static systemhas two internal cable redundants and one externalsupport redundant.

If the cable and pylon were infinitely rigid, thestructure would behave as a continuous four-spanbeam AC on five rigid supports A, E, B, F, and C.The cables are elastic, however, and correspond tosprings. The pylon also is elastic but much stifferbecause of its large cross section. If cable stiffness isreduced to zero, the girder assumes the shape of adeflected two-span beam ABC.

Cable-stayed bridges of the nineteenth centurydiffered from those of the 1960s in that their tend-ons constituted relatively soft spring supports.Heavy and long, the tendons could not bestressed highly. Usually, the cables were installedwith significant slack or sag. Consequently, largedeflections occurred under live load as the sagwas diminished. Modern cables have high-strengthsteel, are relatively short and taut, and their weightis low. Their elastic action may therefore beconsidered linear, and an equivalent modulus ofelasticity may be used. The action of such cablesthen produces something more nearly like thefour-span beam for a structure like the one inFig. 17.28.

If the pylon were hinged at its base connectionwith the girder at B, the pylon would act as apendulum column. This would have an importanteffect on the stiffness of the system, for the springsupport at E would become more flexible. Inmagnitude, the effect might exceed that due to theelastic stretch of the cables. In contrast, the elasticshortening of the tower has no appreciable effect.

Relative girder stiffness plays a dominant rolein the structural action. The girder tends toapproach a beam on rigid supports A, E, B, F, Cas girder stiffness decreases toward zero. Withincreasing girder stiffness, however, the actionof the cables becomes minor and the bridgeapproaches a girder supported on its piers andabutments A, B, C.

In a three-span bridge, a side-span cableconnected to the abutment furnishes more rigidsupport to the main span than does a cableattached to some point in the side span. InFig. 17.28, for example, the support of the load Pin the position shown would be improved if thecable attachment at F were shifted to C. Thisexplains why cables from the pylon top to theabutment are structurally more efficient, althoughnot as aesthetically pleasing as other arrangements.

The stiffness of the system is also affected bywhether the cables are fixed at the towers (at D, forexample, in Fig. 17.28) or whether they run con-tinuously over (or through) the towers. Mostdesigns with more than one cable to a pylon fromthe main span require one of the cables to be fixedto the pylon and the others to be onmovable saddlesupports.

The curves of maximum-minimum girdermoments for all load variations usually show alarge range of stress. Designs providing for thecorresponding normal forces in the girder mayrequire large variation in cross sections. By pre-stressing the cables or by raising or lowering thesupport points, it is possible to achieve a moreuniform and economical moment capacity. Theamount of prestressing to use for this purpose maybe calculated by successively applying a unit forcein each cable and drawing the respective momentdiagrams. Then, by trial, the proper multiples ofeach force are determined so that when theirmoments are superimposed on the maximum-minimum moment diagrams, an optimum balanceresults.

17.15.4 Static Analysis—Elastic Theory

Cable-stayed bridges may be analyzed by thegeneral method of indeterminate analysis with theequations of virtual work.

The degree of internal redundancy of the sys-tem depends on the number of cables, types of

Fig. 17.28 Deflected positions (dash lines) of acable-stayed bridge.




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connections (fixed or movable) of cables with thepylons, and the nature of the pylon connection atits base with the girder or pier. The girder is usuallymade continuous over three spans. Figure 17.29shows the order of redundancy for various single-plane systems of cables.

If the bridge has two planes of cables, twogirders, and double pylons, it usually also must beprovided with a number of intermediate crossdiaphragms in the floor system, each of which iscapable of transmitting moment and shear. Thebridge may also have cross girders across the top ofthe pylons. Each cross member adds two redun-dants, to which must be added twice the internalredundancy of the single plane structure, and anyadditional reactions in excess of those needed forexternal equilibrium as a space structure. Theredundancy of the space structure is very high,usually of the order of 40 to 60. Therefore, the

methods of plane statics are normally used, exceptfor larger structures.

It is convenient to select as redundants thebending moments in the girder at those pointswhere the cables and pylons join the girder. Whenthese redundants are set equal to zero, anarticulated, statically determinate truss base sys-tem is obtained (Fig. 17.30). When the loads areapplied to this choice of base system, the stressesin the cables do not differ greatly from their finalvalues, so the cables may be dimensioned in apreliminary way.

Other approaches are also possible. One is touse the continuous girder itself as a statically in-determinate base system, with the cable forcesas redundants. But computation is generally in-creased.

A third method involves imposition of hinges,for example at a and b (Fig. 17.31), so placed as to

Fig. 17.29 Redundants in three-span cable-stayed bridges.




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form two coupled symmetrical base systems,each statically indeterminate to the fourth degree.The influence lines for the four indeterminatecable forces of each partial base system are atthe same time also the influence lines of the cableforces in the real system. The two redundantmoments Xa and Xb are treated as symmetricaland antisymmetrical group loads, Y ¼ Xa þ Xb,and Z ¼ Xa 2 Xb, to calculate influence lines forthe 10-degree-indeterminate structure shown. Kernmoments are plotted to determine maximumeffects of combined bending and axial forces.

Note that the bundle system in Fig. 17.29c and dgenerally has more favorable bending moments forlong spans than does the harp system of Fig. 17.29eand f. Cable stresses also are somewhat lower forthe bundle system because the steeper cables aremore effective. But the concentration of cable forcesat the top of the pylon introduces detailing andconstruction difficulties. When viewed at an angle,the bundle system presents aesthetic problemsbecause of the different intersection angles whenthe cables are in two planes. Furthermore, fixity ofthe cables at pylons with the bundle system inFig. 17.29c and d produces a wider range of stressthan does a movable arrangement. This caninfluence design for fatigue.

The secondary effect of creep of cables can beincorporated into the analysis. The analogy of abeam on elastic supports is changed thereby to abeam on linear viscoelastic supports.

17.15.5 Static Analysis—Deflection Theory

Distortion of the structural geometry of a cable-stayed bridge under action of loads is consider-ably less than in comparable suspension bridges.The influence on stresses of distortion is relativelysmall for cable-stayed bridges. In any case, theeffect of distortion is to increase stresses, as inarches, rather than the reverse, as in suspensionbridges. This effect for the Severin Bridge is 6%for the girder and less than 1% for the cables.Similarly for the Dusseldorf North Bridge, stressincrease due to distortion amounts to 12% for thegirders.

The calculations, therefore, most expeditiouslytake the form of a series of successive corrections toresults from first-order theory. The magnitude ofvertical and horizontal displacements of the girderand pylons can be calculated from the first-ordertheory results. If the cable stress is assumed con-stant, the vertical and horizontal cable componentsV and H change by magnitudes DV and DH byvirtue of the new deformed geometry. The firstapproximate correction determines the effects ofthese DVand DH forces on the deformed system, aswell as the effect of V and H due to the changedgeometry. This process is repeated until conver-gence, which is fairly rapid.

Fig. 17.30 Three-span cable-stayed bridge. (a) Girder is continuous over the three spans. (b) Insertionof hinges in the girder at cable-attachment points makes the structure statically determinate.

Fig. 17.31 Insertion of hinges at a and b in thecenter span of a three-span continuous girderreduces the degree of indeterminancy.




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17.15.6 Dynamic Analysis—AerodynamicStability

The aerodynamic action of cable-stayed bridges isless severe than that of suspension bridges becauseof increased stiffness due to the taut cables and thewidespread use of torsion box decks.

17.15.7 Preliminary Design ofCable-Stayed Bridges

In general, height of a pylon in a cable-stayedbridge is about 1⁄6 to

1⁄8 the span. Depth of girderranges from 1⁄60 to

1⁄80 the span and is usually 8 to14 ft averaging 11 ft.

Wide box girders are mandatory for single-plane systems to resist the torsion of eccentricloads. Box girders, even narrow ones, are also de-sirable for double-plane systems to enable cableconnections to be made without eccentricity.Single-web girders, however, are occasionallyused.

To achieve symmetry of cables at pylons theratio of side to main spans should be about 3 :7where three cables are used on each side of thepylons, and about 2:5 where two cables are used.A proper balance of side-span length to main-spanlength must be established if uplift at the abut-ments is to be avoided. Otherwise, movable (pen-dulum-type) tiedowns must be provided atthe abutments.

The usual range of live-load deflections is from1⁄400 to

1⁄500 the span.Since elastic-theory calculations are relatively

simple to program for a computer, a formal set isusually made for preliminary design after thegeneral structure and components have been pro-portioned.

17.15.8 Design Details forCable-Stayed Bridges

These structures differ from usual long-span girderbridges in only a few details.

Towers and Floor System n The towers arecomposed basically of two parts: the pier (belowthe deck) and the pylon (above the deck). Thepylons are frequently of steel box cross section,although concrete may also be used.

Bridge Deck n Although cable-stiffenedbridges usually incorporate an orthotropic steeldeck with steel box girders, to reduce the deadload, other types of construction also are in use.For the Lower Yarra River Bridge in Australia, aconcrete deck was specified to avoid site weldingand to reduce the amount of shop fabrication. TheMaracaibo Bridge likewise incorporates a concretedeck, and the Bridge of the Isles (Canada) has aconcrete-slab deck supported on longitudinal andtransverse steel box girders and steel floor beams.The Buchenauer Bridge also has a concrete deck.Use of a concrete deck in place of orthotropic-plateconstruction is largely a matter of local economics.The cost of structure to carry the added dead loadshould be compared with the lower cost per squarefoot of the concrete deck and other possibleadvantages, such as better durability and increasedstability against wind.

(W. Podolny, Jr., and J. B. Scalzi, “Constructionand Design of Cable-Stayed Bridges,” 2nd ed., JohnWiley & Sons, Inc., New York (www.wiley.com);“Guidelines for Design of Cable-Stayed Bridges,”ASCE Committee on Cable-Stayed Bridges (www.asce.org).)

17.16 Steel Arch Bridges

A typical arch bridge consists of two or (rarely)more parallel arches or series of arches, plusnecessary lateral bracing and end bearings, andcolumns or hangers for supporting the deckframing. Types of arches correspond roughly topositions of the deck relative to the arch ribs.

Bridges with decks above the arches and clearspace underneath (Fig. 17.32a) are designed asopen spandrel arches on thrust-resisting abut-ments. Given enough underclearance and ade-quate foundations, this type is usually the mosteconomical. Often, it is competitive in cost withother bridge systems.

Bridges with decks near the level of the archbearings (Fig. 17.32b) are usually designed as tiedarches; that is, tie bars take the arch thrust. Endbearings and abutments are similar to those forgirder or truss bridges. Tied arches compete in costwith through trusses in locations where under-clearances are restricted. Arches sometimes arepreferred for aesthetic reasons. Unsightly overheadlaterals can be avoided by using arches with




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sufficiently high moment of inertia to resistbuckling.

Bridges with decks at an intermediate level(Fig. 17.32c) may be tied, may rest on thrust-resisting abutments, or may be combined structu-rally with side spans that alleviate the thrust ofthe main span on the main piers (Fig. 17.32d).Intermediate deck positions are used for long,high-rising spans on low piers.

Spans of multiple-arch bridges are usuallystructurally separated at the piers. But such bridgesmay also be designed as continuous structures.

17.16.1 Hinges

Whether or not hinges are required for arch bridgesdepends on foundation conditions. Abutmentmovements may sharply increase rib stresses.Fully restrained arches are more sensitive to smallabutment movements (and temperature variations)than hinged arches. Flat arches are more sensitivethan high arches. If foundations are not fully reli-able, hinged bearings should be used.

Complete independence from small abutmentmovements is achieved by installing a third hinge,usually at the crown. This hinge may be eitherpermanent or temporary during erection, to be

locked after all dead-load deformations have beenaccounted for.

17.16.2 Arch Analysis

The elementary analysis of steel arches is based onthe elastic, or first-order, theory, which assumesthat the geometric shape of the center line remainsconstant, irrespective of the imposed load. Thisassumption is never mathematically correct. Theeffects of deviations caused by overall flattening ofthe arch due to the elastic rib shortening, elastic orinelastic displacements of the abutment, and localdeformation due to live-load concentrations in-crease with initial flatness of the arch. An effort isusually made to eliminate the dead-load part of theeffect of rib shortening and abutment yieldingduring erection by jacking the legs of an archtoward each other or the crown section apart beforefinal closure. Arches subject to substantial defor-mation must be checked by the second-order, ordeflection, theory.

For heavy moving loads, it is sometimesadvantageous to assign the flexural resistance ofthe system to special stiffening girders or trusses,analogous to those of suspension bridges (Art.17.15). The arches themselves are then subject,essentially, to axial stresses only and can bedesigned as slender as buckling considerationspermit.

17.16.3 Arch Design

In general, steel arches must be designed forcombined stresses due to axial loads and bending.

The height-to-span ratio used for steel archesvaries within wide limits. Minimum values arearound 1:10 for tied arches, 1 :16 for open spandrelarches.

In cross section, steel arches may be I-shaped,box-shaped, or tubular. Or theymay be designed asspace trusses.

17.16.4 Deck Construction

The roadway deck of steel arch bridges is usually ofreinforced concrete, often of lightweight concrete,on a framing of steel floor beams and stringers. Toavoid undesirable cooperation with the primarysteel structure, concrete decks either are provided

Fig. 17.32 Basic types of steel arch bridges: (a)Open spandrel arch; (b) tied arch; (c) arch with deckat an intermediate level; (d) multiple-arch bridge.




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with appropriately spaced expansion joints orprestressed. Orthotropic decks that combine thefunctions of traffic deck, tie bar, stiffening girder,and lateral diaphragm have been used on somemajor arch bridges.

(F. S. Merritt and R. L. Brockenbrough,“Structural Steel Designers’ Handbook,” 2nd ed.,McGraw-Hill, Inc., New York (books.mcgraw-hill.com).)

17.17 Horizontally CurvedSteel Girders

For bridges with curved steel girders, the effects oftorsion must be taken into consideration by thedesigner. Also, careful attention should be given tocross frames—spacing, design, and connectiondetails. The effects of torsion decrease the stressesin the inside girders (those nearer the center ofcurvature). But there is a corresponding increase instresses in the outside girders. Although the dif-ferences are not large for multiple-girder systems,the differences in stress for two-girder systemswith short-radius curves and long spans can be ashigh as 50%. The torsional forces translate intovertical and horizontal forces, which must betransferred from the outside to inside girdersthrough the cross frames.

An approximate method for analysis of curvedgirder stresses is given in the U.S. Steel “HighwayStructures Design Handbook.” This approximatemethod has proven satisfactory for many struc-tures, but for complex structures (those with longspans, short-radius curves, or with only twogirders), it is recommended that a rigorous analysisusing a computer program be used. For thestructure in Fig. 17.33, the stress differentials inthe two girders are 50% and the cross framestransfer up to 70 kips of vertical and horizontalforces between girders. The center of the main spanrotated 4 in when the deck was placed. Suchrotations should be anticipated and the girderserected “out of plumb” so that the final webposition will be vertical.

Design of curved-girder bridges should con-sider the following:

1. Full-depth cross frames should be used totransfer the lateral forces from the flanges. (SeeFig. 17.34.)

2. The cross frames should be designed as primarystress-carrying members to transfer the loads.

3. Flange-plate width should be increased abovethe normal design minimums to provide sta-bility during handling and erection.

4. Cross-frame connections at the web plates arecritical. The web plate should be thickened toprovide bending resistance

Fig. 17.33 Curved girders of Tuolomne RiverBridge, California, were erected in pairs with theircross frames connected between them. (CaliforniaDepartment of Transportation.)

Fig. 17.34 Cross section of curved-girderbridge at cross frame, showing forces resultingfrom curvature.




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17.18 Bridge Bearings

Bearings are structural assemblies installed tosecure the safe transfer of all reactions from thesuperstructure to the substructure. They must ful-fill two basic requirements: They must spread thereactions over adequate areas of the substructure,and they must be capable of adapting to elastic,thermal, and other deformations of the super-structure without generating harmful restrainingforces.

Generally, bearings are classified as fixed,expansion, or elastomeric.

Fixed bearings adapt only to angular deflec-tions. They must be designed to resist both verticaland horizontal components of reactions.

Expansion bearings adapt to both angulardeflections and longitudinal movements of thesuperstructure. Except for friction, they resist onlythose components of the superstructure reactionsperpendicular to these movements.

In both types of bearings, provision must bemade for the safe transfer of all forces transverse tothe direction of the span.

Elastomeric bearings are a very efficientbearing for short to medium span bridges. Theyare relatively maintenance free and are one of thesafest bearings, under seismic loading. Elastomericbearings generally consist of laminated layers ofelastomer restrained at their surfaces by bondedlaminas. The elastomer is a Neoprene rubber; thelaminas consist of either glass-fiber fabrics or steelsheets. Steel-reinforced elastomeric bearings areusually used when anchor bolts are requiredthrough the bearing (Figs. 17.34 and 17.35).

The bearing pressure of elastomeric bearingsshould not exceed 800 psi under a service-load

combination of dead load and live load, notincluding impact. For steel-reinforced bearingpads, the pressure should not exceed 1000 psi. Theminimum pressure allowed on any pad due todead load only is 200 psi.

The capacity of an elastomeric bearing to absorbangular deflections and longitudinal movementsof the superstructure is a function of its thickness(or of the sum of the thicknesses of its rubberelements between steel laminas), its shape factor(area of the loaded face divided by the sum of theside areas free to bulge), and the properties of theelastomer.

AASHTO Specifications limit the overall thick-ness of a laminated bearing to one-third its lengthor width, whichever is smaller (or one-fourth of itsdiameter). The thickness should be at least twicethe horizontal movement.

An alternative is a pot bearing, which supportsthe structure on a hydraulic cylinder with anelastomer as the liquid medium.

Concrete Bridges

Reinforced concrete is used extensively in highwaybridges because of its economy in short andmedium spans, durability, low maintenance costs,and easy adaptability to horizontal and verticalcurvature. The principal types of cast-in-place sup-porting elements are the longitudinally reinforcedslab, T beam or girder, and cellular or box girder.Precast construction, usually prestressed, oftenemploys an I-beam or box-girder cross section. Inlong-span construction, posttensioned box girdersoften are used.

17.19 Slab Bridges

Concrete slab bridges, longitudinally reinforced,may be simply supported on piers and/or abut-ments, monolithic with wall supports, or continu-ous over intermediate supports.

17.19.1 Design Span

For simple spans, the design span is the distancecenter to center of supports but need not exceed theclear span plus slab thickness. For slabs monolithicwith walls (without haunches), use the clear span.For slabs on steel or timber stringers, use the clearspan plus half the stringer width.

Fig. 17.35 Steel-laminated elastomeric bear-ing pad.




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17.19.2 Load Distribution

In design, usually a 1-ft-wide longitudinal, typicalstrip is selected and its thickness and reinforcingdetermined for the appropriate HS loading. Wheelloads may be assumed distributed over a width, ft,

E ¼ 4þ 0:06S � 7 (17:24)

where S ¼ span, ft. Lane loads should be dis-tributed over a width of 2E.

For simple spans, the maximum live-loadmoment, ft-kips, per foot width of slab, withoutimpact, for HS20 loading is closely approxi-mated by

M ¼ 0:9S S � 50 ft (17:25a)

M ¼ 1:30S� 20 50 . S , 100 (17:25b)

For HS15 loading, use three-quarters of the valuegiven by Eqs. (17.25).

For longitudinally reinforced cantilever slabs,wheel loads should be distributed over a width, ft,

E ¼ 0:35X þ 3:25 � 7 ft (17:26)

whereX ¼ distance from load to point of support, ft.The moment, ft-kips per foot width of slab, is

M ¼ P

EX (17:27)

where P ¼ 16 kips for H20 loading and 12 kipsfor H15.

17.19.3 Reinforcement

Slabs should also be reinforced transversely todistribute the live loads laterally. The amount

Fig. 17.36 Example of an elastomeric bearing.




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should be at least the following percentage of themain reinforcing steel required for positive mo-ment: 100=

ffiffiffiS

p, but it need not exceed 50%.

The slab should be strengthened at all unsup-ported edges. In the longitudinal direction,strengthening may consist of a slab sectionadditionally reinforced, a beam integral with anddeeper than the slab, or an integral reinforcedsection of slab and curb. These should be designedto resist a live-load moment, ft-kips, of 1.6S forHS20 loading and 1.2S for HS15 loading on simplysupported spans. Values for continuous spansmay be reduced 20%. Greater reductions arepermissible if justified by more exact analysis.

At bridge ends and intermediate points wherecontinuity of the slabs is broken, the edges shouldbe supported by diaphragms or other suitablemeans. The diaphragms should be designed toresist the full moment and shear produced bywheel loads that can pass over them.

17.19.4 Design Procedure

The following procedure may be used for design ofa typical longitudinally reinforced concrete slabbridge (Fig. 17.37).

Step 1. Determine the live-load distribution(effective width). For the three-span, 90-ft-long

Fig. 17.37 Three-span concrete-slab bridge.




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bridge in Fig. 17.37, S ¼ 30 ft and

E ¼ 4þ 0:06� 30 ¼ 5:8 ft

The distributed load for a 4-kip front wheel then is4/5.8, or 0.69 kips, and for a 16-kip rear or trailerwheel load, 16/5.8, or 2.76 kips, per foot of slabwidth. For an alternative 12-kip wheel load, thedistributed load is 12/5.8, or 2.07 kips per foot ofslab width (see Fig. 17.38).

Step 2. Assume a slab depth.Step 3. Determine dead-load moments for the

assumed slab depth.Step 4. Determine live-load moment at point of

maximummoment. (This is done at this stage to geta check on the assumed slab depth.)

Step 5. Combine dead-load, live-load, andimpact moments at point of maximum moment.Compare the required slab depth with the assumeddepth.

Step 6. Adjust the slab depth, if necessary. If therequired depth differs from the assumed depth ofstep 2, the dead-load moments should be revisedand step 5 repeated. Usually, the second assump-tion is sufficient to yield the proper slab depth.Steps 2 through 6 follow conventional structuraltheory.

Step 7. Place live loads for maximum momentsat other points on the structure to obtain inter-mediate values for drawing envelope curves ofmaximum moment.

Step 8. Draw the envelope curves. Determinethe sizes and points of cutoff for reinforcing bars.

Step 9. Determine distribution steel.Step 10. Determine the number of piles required

at each bent.Figures 17.39 and 17.40 illustrate typical steel

reinforcement patterns for a single-span and a two-span concrete-slab bridge, respectively, similar toFig. 17.37, suitable for spans ranging from 16 to44 ft and carrying HS20 or alternate loading. Re-inforcement parallel to traffic in the single-spanbridge is mainly in the bottom of the slab (Fig.17.39b), rather than in the top (Fig. 17.39a). The two-span bridge has main steel reinforcement in the topof the slab (Fig. 17.40b) over the center bent, toresist negative moments and main steel reinforce-ment in the bottom of the slab (Fig. 17.40a) inpositive-moment regions. Reinforcement in multi-span bridges is arranged similarly. Transversedistribution steel is spaced typically at 11 to 12 in.The thickness of the concrete slab and reinforce-ment sizes depend on the specified 28-day concretecompressive strength f 0c and yield point of thereinforcement steel.

For skews up to 208, transverse reinforcementshould be placed parallel to the bent. For largerskews, transverse reinforcement should be placedperpendicular to the center line of the bridge.Skews exceeding 508 require special design.

(“Bridge Design Aids,” Division of Structures,California Department of Transportation, Sacra-mento, Calif. (www.dot.ca.gov).)

17.20 Concrete T-BeamBridges

Widely used in highway construction, this type ofbridge consists of a concrete slab supported on, andintegral with, girders (Fig. 17.41). It is especiallyeconomical in the 50- to 80-ft range. Wherefalsework is prohibited, because of traffic con-ditions or clearance limitations, precast construc-tion of reinforced or prestressed concrete may beused.

17.20.1 Design of TransverseSlabs

Since the girders are parallel to traffic, main rein-forcing in the slab is perpendicular to traffic. Forsimply supported slabs, the span should be thedistance center to center of supports but need notexceed the clear distance plus thickness of slabs.

Fig. 17.38 Wheel load per foot width of slab forbridge of Fig. 17.37.




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Fig. 17.40 Arrangement of slab reinforcement for a two-span bridge carrying HS20-44 or alternativeloading.

Fig. 17.39 Arrangement of slab reinforcement for a single-span bridge carrying HS20-44 or alternativeloading.




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For slabs continuous over more than two girders,the span may be taken as the clear distancebetween girders.

The live-load moment, ft-kips, for HS20 loadingon simply supported slab spans is given by

M ¼ 0:5(Sþ 2) (17:28)

where S ¼ span, ft.For slabs continuous over three or more

supports, multiply M in Eq. (17.28) by 0.8 for bothpositive and negative moment. For HS15 loading,multiply M by 3⁄4.

Reinforcement also should be placed in the slabparallel to traffic to distribute concentrated liveloads. The amount should be the following per-centage of the main reinforcing steel required forpositive moment: 220=

ffiffiffiS

p, but need not exceed

67%.Where a slab cantilevers over a girder, the wheel

load should be distributed over a distance, ft,parallel to the girder of

E ¼ 0:8X þ 3:75 (17:29)

Fig. 17.41 Four-span bridge with concrete T beams.




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where X ¼ distance, ft, from load to point ofsupport. The moment, ft-kips per foot of slabparallel to girder, is

M ¼ P

EX (17:30)

where P ¼ 16 kips for HS20 loading and 12 kips forHS15. Equations (17.28) to (17.30) apply also toconcrete slabs supported on steel girders, includingcomposite construction.

In design of the slabs, a l-ft-wide strip is selectedand its thickness and reinforcing determined.The dead-loadmoments, ft-kips, positive and nega-tive, can be assumed to be wS2/10, where w is thedead load, kips/ft2. Live-load moments are givenby Eq. (17.28) with a 20% reduction for continuity.Impact is a maximum of 30%. With these values,standard charts can be developed for design ofslabs on steel and concrete girders. Figure 17.42shows a typical slab-reinforcement layout.

17.20.2 T-Beam Design

The structure shown in Fig. 17.41 is a typical four-span grade-separation structure. The structuralframe assumed for analysis is shown in Fig. 17.43.Columns with a pinned base are less stiff than fixedcolumns which minimizes shrinkage and tempera-ture moments. In addition, foundation pressures in

pinned columns are considered fairly uniform,resulting in an economical footing size and design.

For concrete girder design, curves of maximummoments for dead load plus live load plus impactmay be developed to determine reinforcement.For live-load moments, truck loadings are movedacross the bridge. As they move, they generatechanging moments, shears, and reactions. It is nec-essary to accumulate maximum combinations ofmoments to provide an adequate design. For heavymoving loads, extensive investigation is necessaryto find the maximum stresses in continuous struc-tures.

Figure 17.44 shows curves ofmaximummomentsconsisting of dead load plus live load plus impactcombinations that are maximum along the span.From these curves, reinforcing steel amounts andlengthsmay be determined by plotting themomentsdeveloped. Figure 17.45 shows curves of maxi-mum shears. Figure 17.46 shows the girder steel

Fig. 17.42 Typical layout of reinforcement in the deck of a concrete T-beam bridge.

Fig. 17.43 Assumed support conditions for thebridge in Fig. 17.41.




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reinforcement layout. Maximum-shear require-ments are derived theoretically by a point-to-pointstudy of variations. Usually, a straight line betweencenter line and end maximums is adequate.

Girder spacing ranges from about 7 to 9 ft.Usually, a deck slab overhang of about 2 ft 6 in iseconomical.

When the slab is made integral with the girder,its effective width of compression flange in designmay not exceed the distance center to center ofgirders, one-fourth the girder span, or girder web-width plus 12 times the least thickness of slab. Forexterior girders, however, effective overhang widthmay not exceed half the clear distance to the next

Fig. 17.44 Reinforcing for T beams of Fig. 17.41 is determined from curves of maximum bendingmoment. Numbers at the ends of the bars are distances, ft, from the center line of the span or bent.

Fig. 17.45 Curves of maximum shear for T beams of Fig. 17.41.




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girder, one-twelfth the girder span, or six times theslab thickness.

Ratios of beam depths to spans used in con-tinuous T-beam bridges generally range from 0.065to 0.075. An economical depth usually results whena small amount of compressive reinforcement isrequired at the interior supports.

Design of intermediate supports or bents varieswidely, according to the designer’s preference. Asimple two-column bent is shown in Fig. 17.41. Butconsiderable shape variations in column cross sec-tion and elevation are possible.

Abutments are usually seat type or a monolithicend diaphragm supported on piles.

(“Bridge Design Aids,” Division of Structures,California Department of Transportation, Sacra-mento, Calif. (www.dot.ca.gov).)

17.21 Concrete Box-GirderBridges

Box or hollow concrete girders (Fig. 17.47) arefavored by many designers because of the smoothplane of the bottom surface, uncluttered by lines ofindividual girders. Provision of space in the opencells for utilities is both a structural and an aestheticadvantage. Utilities are supported by the bottom

Fig. 17.46 Reinforcement layout for T beams of Fig. 17.41. Reinforcement is symmetrical about thecenter lines of the bridge and bent 3. Numbers at the ends of the bars indicate distances, ft, from the centerline of bent or span.




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slab, and access can be made available for inspec-tion and repair of utilities.

For sites where structure depth is not severelylimited, box girders and T beams have been aboutequal in price in the 80-ft span range. For shorterspans, T beams usually are cheaper, and for longerspans, box girders. These cost relations hold ingeneral, but box girders have, in some instances,been economical for spans as short as 50 ft whenstructure depth was restricted.

17.21.1 Girder Design

Structural analysis is usually based on two typicalsegments, interior and exterior girders (Fig. 17.48).An argument could be made for analyzing the

entire cross section as a unit because of its inherenttransverse stiffness. Requirements in “StandardSpecifications for Highway Bridges,” AmericanAssociation of State Highway and TransportationOfficials, however, are based on live-load distri-butions for individual girders, and so design usu-

Fig. 17.47 Three-span, reinforced concrete box-girder bridge. For more details, see Fig. 17.51.

Fig. 17.48 Typical design sections (cross-hatched) for a box-girder bridge.




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ally is based on the assumption that a box-girderbridge is composed of separate girders.

Effective width of slab as compression flange ofan interior girdermay be taken as the smallest of thedistance center to center of girders, one-fourth thegirder span, and girder-web width plus 12 timesthe least thickness of slab. Effective overhangwidth for an exterior girder may be taken as thesmallest of half the clear distance to the next girder,one-twelfth the girder span, and six times the leastthickness of the slab.

Usual depth-to-span ratio for continuous spansis 0.055. This may be reduced to about 0.048 withbalanced spans, at some sacrifice in economy andincrease in deflections. Simple spans usually re-quire a minimum depth-to-span ratio of 0.06.

A typical concrete box-girder highway bridge isillustrated in Fig. 17.47. Girder spacing is approxi-mately 11⁄2 times the structure depth. Minimumgirder web thickness is determined by shear butgenerally is at least 8 in. Changes should be grad-ual, spread over a distance at least 12 times the dif-ference in web thickness.

Top-slab design follows the procedure des-cribed for T-beam bridges in Art. 17.20. Bottom-slab thickness and secondary reinforcement areusually controlled by specification minimums.AASHTO Specifications require that slab thicknessbe at least one-sixteenth the clear distance betweengirders but not less than 6 in for the top slab and51⁄2in for the bottom slab. Fillets should be providedat the intersections of all surfaces within the cells.

Minimum flange reinforcement parallel to thegirder should be 0.6% of the flange area. This steelmay be distributed at top and bottom or placed in asingle layer at the center of the slab. Spacing shouldnot exceed 18 in. Minimum flange reinforcingnormal to the girder should be 0.5% and similarlydistributed. Bottom-flange bars should be bent upinto the exterior-girder webs and anchored using astandard 908 hook or equivalent. At least one-thirdof the top flange tension reinforcement shouldextend to the exterior face of the outside girder andshould be anchored with 908 bends or, where theflange projects beyond the girder sufficiently,extended far enough to develop bar strength inbond.

When the top slab is placed after the web wallshave set, at least 10% of the negative-moment rein-forcing should be placed in the web. The barsshould extend a distance of at least one-fourth thespan on each side of the intermediate supports of

continuous spans, one-fifth the span from the res-trained ends of continuous spans, and the entirelength of cantilevers. In any event, the web shouldhave reinforcing placed horizontally in both faces,to prevent temperature and shrinkage cracks. Thebars should be spaced not more than 12 inches c toc. Total area of this steel should be at least 10% ofthe area of flexural tension reinforcement.

Analysis of the structure in Fig. 17.47 for deadloads follows conventional moment-distributionprocedure. Assumed end conditions are shown inFig. 17.49a.

Fig. 17.49 Loading patterns for maximumstresses in a box-girder bridge.




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Live loads, positioned to produce maximumnegative moments in the girders over Pier 2, areshown in Fig. 17.49b to d. Similar loadings shouldbe applied to find maximum positive and negativemoments at other critical points. Moments shouldbe distributed and points plotted on a maximum-moment diagram (for dead load plus live load plusimpact), as shown in Fig. 17.50. Layout of maingirder reinforcement follows directly from thisdiagram. Figure 17.51 shows a typical layout.

(“Bridge Design Details,” Division of Structures,California Department of Transportation, Sacra-mento, Calif. (www.dot.ca.gov).)

17.22 Prestressed-ConcreteBridges

In prestressed-concrete construction, concrete issubjected to permanent compressive stresses ofsuch magnitude that little or no tension developswhen design loading is applied (Art. 8.42).

Prestressing allows considerably better utili-zation of concrete than conventional reinforcement.It results in an overall dead-load reduction, which

makes long spans possible with concrete, some-times competitive in cost with those of steel.Prestressed concrete, however, requires greatersophistication in design, higher quality of materials(both concrete and steel), and greater refinementand controls in fabrication than does reinforcedconcrete.

Depending on the methods and sequence offabrication, prestressed concrete may be precast,pretensioned; precast, posttensioned; cast-in-placeposttentioned; composite; or partly prestressed.

In precast-beam bridges, the primary structureconsists of precast-concrete units, usually I beams,channels, T beams, or box girders. They may beeither pretensioned or posttensioned. Precast slabsmay be solid or hollow. Precast I beams (Fig. 17.52)may be combined with fully or partly cast-in-placedecks. This construction has the advantage thatthe deck can be shaped closely to the desiredspecifications. Precast slabs, incorporated into thedeck, may be used in lieu of removable deck formswhere accessibility is poor, for example, on over-water trestles or causeways. Precast T beams(Fig. 17.53) offer no advantage over the easier tofabricate, more compact I sections. Alignment of

Fig. 17.50 Curves of maximum moment determine reinforcing for a box girder. Numbers at the endsof the bars indicate distances, ft, from the center line of piers or span.




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the flanges of T sections often is difficult. And aswith I beams, the flanges must be connected withcast-in-place concrete. Precast box sections may beplaced side by side to form a bridge span. Ifdesired, they may be posttensioned transversely.

Precast beams mainly are used for spans up toabout 90 ft where erection of conventional false-work is not feasible or desirable. Such beams areparticularly economical if conditions are favorablefor mass fabrication, for example, in multispanviaducts or causeways or in the vicinity ofcentralized fabrication plants. Longer spans are

possible but require increasingly heavy handlingequipment.

Standard designs for precast, prestressed gird-ers have been developed by the Federal HighwayAdministration and state highway departments.

Cast-in-place prestressed concrete often is usedfor low-level bridges, where ground conditionsfavor erection of conventional falsework. Typicalcross sections are essentially similar to those usedfor conventionally reinforced sections, except that,in general, prestressing permits structures withthinner depths.

Fig. 17.51 Reinforcing layout for the box-girder bridge Fig. 17.47 of and moment curves of Fig. 17.50.Design stresses for HS20 loading: f 0c ¼ 3500psi, fy ¼ 60 ksi.




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For fully cast-in-place single-span bridges, post-tensioning differs only quantitatively from that forprecast elements. In design of multispan continu-ous bridges, the following must be considered:Frictional prestress losses depend on the drapingpattern of the ducts. To reduce potential losses andincrease the reliability of effective prestress, avoidcontinuously waving tendon patterns. Instead, usediscontinuous simple patterns. Another method isto place tendons, usually bundles of cables, in thehollows of box girders and to bend the tendons atlubricated, accessible bearings.

Prestressed concrete is competitive with othermaterials for spans of 150 to 250 ft or more. Con-struction techniques and improvements in pre-stressing hardware, such as smooth, lightweightconduits, which reduce friction losses, havebrought prestressed concrete bridges into directcompetition with structural steel, once preeminentin medium and long spans.

Fig. 17.52 Typical precast, prestressed I beam used in highway bridges.

Fig. 17.53 Typical precast, prestressed T beamused in highway bridges.




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Segmental construction, both precast and cast-in-place, has eliminated the need for expensivefalsework, which previously made concrete brid-ges uneconomical in locations requiring long spansover navigation channels or deep canyons. The twotypes of segmental construction used most in theUnited States are the cast-in-place and precastbalanced cantilever types.

For cast-in-place construction, the movableformwork is supported by a structural framework,or traveler, which cantilevers from an adjacentcompleted section of the superstructure. As eachsection is cast, cured, and posttensioned, theframework is moved out and the process repeated.Figure 17.54 illustrates this type of construction.For precast construction the procedure is similar,except that the sections are prefabricated.

Other methods, such as full-span and incre-mental launching procedures, can be used to fit siteconditions. In all segmental construction, specialattention should be given in the erection plan tolimitation of temporary stresses and to mainte-nance of balance during erection and prior to spanclosing. Also important are an accurate predictionof creep and accurate calculation of deflections toensure attainment of the desired structure profileand deck grades in the completed structure.

Posttensioning makes possible widening orstrengthening or other remodeling of existingconcrete structures. For example, Fig. 17.55 showsa cross section through a double-deck viaduct. Therow of columns under the upper deck had to beremoved, and capacity had to be increased fromH15 to HS20 loading. No interference with upper-deck traffic and a minimum of interference withlower-deck traffic were permitted. This objectivewas accomplished by reinforcing each floor beamwith precast units incorporating preformed ductsfor tendons. Then the entire upper deck was pre-stressed transversely. This permitted the beams tospan the full width of the bridge and carry theheavier loading. Similar remodeling has been donewith cast-in-place concrete.

Determination of stresses in prestressed bridgesis similar to that for other structures. In analysis ofstatically indeterminate systems, however, thedeformations caused by prestressing must be takeninto account (see also Arts. 8.42 to 8.45).

[C. A. Ballinger and W. Podolny, Jr., “SegmentalBridge Construction in Western Europe,” Trans-portation Research Board, Record 665, 1978;A. Grand, “Incremental Launching of ConcreteStructures,” Journal of the American ConcreteInstitute, August 1975; W. Baur, “Bridge Erection

Fig. 17.54 Segmental cast-in-place concrete construction in progress for the Pine Valley Bridge,California. (California Department of Transportation.)




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by Launching Is Fast, Safe, and Efficient,” CivilEngineering, March 1977; F. Leonhardt, “NewTrends in Design and Construction of Long-Span Bridges and Viaducts (Skew, Flat Slabs,Torsion Box),” Eighth Congress, InternationalAssociation for Bridge and Structural Engineering,New York, Sept. 9 to 14, 1968.]

17.23 Concrete Bridge Piersand Abutments

Bridge piers are the intermediate supports of thesuperstructure of bridges with two or more open-ings. Abutments are the end supports and usually

have the additional function of retaining earth fillfor the bridge approaches.

The minimum height of piers and abutments isgoverned by requirements of accessibility formaintenance of the superstructure, including bear-ings; of protection against spray for bridges overwater; and of vertical clearance requirements forbridges over traveled ways. There is no upper limitfor pier heights, except that imposed by economicconsiderations. One of the piers of the EuropaBridge, which carries an international freeway inAustria, for instance, soars to 492 ft above theground surface of the valley.

The top surface of piers must have adequatelength and width to accommodate the bridge

Fig. 17.55 Double-deck viaduct strengthened by prestressing to permit removal of column andpassage of heavier trucks.




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bearings of the superstructure. On abutments,added width is required for the back wall (curtainwall or bulkhead), which retains approach fill andprotects the end section of the superstructure. Indesigning the aboveground sections of piers, res-trictions resulting from lateral-clearance require-ments of adjacent traveled ways and visibilityneeds may have to be taken into account. Lengthand width at the base level are controlled bystability, stress limitations in the pier shaft, andfoundation design.

For stress and stability analyses, the reactionsfrom loadings (dead and live, but not impact)acting on the superstructure should be combinedwith those acting directly on the substructure.Longitudinal reactions depend on the type ofbearing, whether fixed or expansion.

17.23.1 Piers

A number of basic pier shapes have been devel-oped to meet the widely varying requirements.Enumerated below are some of the more commontypes and their preferred uses.

Trestle-type piers are preferred on low-level“causeways” carried over shallow waters or seas-onally flooded land on concrete slab or beam-and-slab superstructures. Each pier or bent consists oftwo or more bearing piles, usually all driven in thesame plane, and a thick concrete deck or aprismatic cap into which the piles are framed(Fig. 17.37). Both cap and piles may be of timber or,for more permanent construction, of precastconventionally reinforced or prestressed concrete.

Wall-type concrete piers on spread footings aregenerally used as supports for two-lane over-crossings over divided highways. Given adequatelongitudinal support of the superstructure, thesepiers may be designed as pendulum walls, withjoints at top and bottom; otherwise, as cantileverwalls.

T-shaped piers on spread footings, with orwithout bearing piles, may be used to advantageas supports of twin girders. The girders are seatedon bearings at both tips of the cross beam atop thepier stem. T-shaped piers have been built eitherentirely of reinforced concrete or of reinforcedconcrete in various combinations with structuralsteel.

Single-column piers of rectangular or circularcross section on spread footings may be used to

support box girders, with built-in diaphragmsacting as cross beams (Fig. 17.47).

Portal frames may be used as piers under heavysteel girders, with bearings located directly overthe portal legs (columns). When more than twogirders are to be supported, the designer maychoose to strengthen the portal cap beam or to addmore columns. Preferably, all legs of each portalframe should rest on a common base plate. If,instead, separate footings are used, as, for instance,on separate pile clusters, adequate tie bars must beused to prevent unintended spreading.

Massive masonry piers have been built sinceantiquity for multiple-arch river bridges, high-levelaqueducts, and more recently, viaducts. In thetwentieth century, their place has been taken bymassive concrete construction, with or withoutnatural stone facing. Where reduction of dead loadis of the essence, hollow piers, often of heavilyreinforced concrete, may be used.

Steel towers on concrete pedestals may be used forhigh bridge piers. They may be designed either asthin-membered, special trellis or as closed box por-tals, or combinations of these (Figs. 17.20 and 17.26).

Very tall piers, when used, are usually con-structed of reinforced or prestressed concrete,either solid or cellular in design (Fig. 17.33).

Bridge abutments basically are piers withflanking (wing) walls. Abutments for short-spanconcrete bridges, such as T-beam or slab-typehighway overcrossings, are frequently simpleconcrete trestles built monolithically with thesuperstructure (see Figs. 17.37 and 17.47). Abut-ments for steel bridges and for long-span concretebridges that are subject to substantial end rotationand longitudinal movements should be designedas separate structures that provide a level area forthe bridge bearings (bridge seat) and a back wall(curtain wall or bulkhead). The wall (stem) belowthe bridge seat of such abutments may be of solidconcrete or thin-walled reinforced-concrete con-struction, with or without counterfort walls; but onrare occasions, masonry is used.

Sidewalls, which retain approach fill, shouldhave adequate length to prevent erosion andundesired spill of the backfill. They may be builteither monolithically with the abutment stem andbackwall in which case they are designed ascantilevers subject to two-way bending, or as self-supporting retaining walls on independent foot-ings. Sidewalls may be arranged in a straight linewith the abutment face, parallel to the bridge axis,




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or at any intermediate angle to the abutment facethat may suit local conditions. Given adequatefoundation conditions, the parallel-to-bridge-axisarrangement (U-shaped abutment) is often pre-ferred because of its inherent stability.

Abutments must be safe against overturningabout the toe of the footing, against sliding on thefooting, and against crushing of the underlying soilor overloading of piles. In earth-pressure compu-tations, the vehicular load on highways may betaken into account in the form of an equivalent

layer of soil 2 ft thick. Live loads from railroadsmay be assumed to be 0.5 kip/ft2 over a 14-ft-widestrip for each track.

In computations of internal stresses andstability, the weight of the fill material over aninclined or stepped rear face and over reinforcedconcrete spread footings should be considered asfully effective. No earth pressures however, shouldbe assumed from the earth prism in front of thewall. Buoyancy should be taken into account if itmay occur.




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