railway bridge

NOTATION

17.0 INTRODUCTION

17.1 TYPICAL PRODUCTS AND DETAILS17.1.1 Piles

17.1.2 Pile Caps and Abutments

17.1.3 Superstructures

17.1.3.1 Slab Beams and Box Beams

17.1.3.2 Other Products

17.1.3.3 Connection Details

17.2 CONSTRUCTION CONSIDERATIONS17.2.1 Advantages

17.2.2 Standard Designs

17.2.3 Train Operations

17.2.4 Construction Methods

17.2.5 Substructures

17.3 THE AMERICAN RAILWAY ENGINEERING AND MAINTENANCE-OF-WAYASSOCIATION LOAD PROVISIONS 17.3.1 AREMA Manual

17.3.2 AREMA Loads

17.3.2.1 Live Load

17.3.2.2 Impact Load

17.3.2.3 Other Loads

17.3.2.4 Load Combinations

17.4 CURRENT DESIGN PRACTICE17.4.1 New Bridges

17.4.2 Replacement Bridges

17.4.3 Simple Span Bridges

17.4.4 Skew Bridges

17.5 CASE STUDY NO. 1—TRUSS BRIDGE REPLACEMENT17.5.1 Existing Bridge

17.5.2 New Piles

17.5.3 New Intermediate Piers

17.5.4 New Superstructure for Approach Spans

17.5.5 Truss Removal

17.5.6 New Superstructure for Truss Spans

PCI BRIDGE DESIGN MANUAL CHAPTER 17

SEPT 01

TABLE OF CONTENTSRAILROAD BRIDGES

5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM


SEPT 01

17.6 CASE STUDY NO. 2—TIMBER TRESTLE REPLACEMENT 17.6.1 Existing Bridge

17.6.2 New Superstructure

17.6.3 Substructure Construction

17.6.4 Superstructure Construction

17.7 DESIGN EXAMPLE—DOUBLE-CELL BOX BEAM, SINGLE SPAN, NON-COMPOSITE, DESIGNED IN ACCORDANCE WITH AREMA SPECIFICATIONS17.7.1 Background

17.7.2 Introduction

17.7.2.1 Geometrics

17.7.2.2 Sign Convention

17.7.2.3 Level of Accuracy

17.7.3 Material Properties

17.7.3.1 Concrete

17.7.3.2 Pretensioning Strands

17.7.3.3 Reinforcing Bars

17.7.4 Cross-Section Properties for a Single Beam

17.7.5 Shear Forces and Bending Moments

17.7.5.1 Shear Forces and Bending Moments Due to Dead Load

17.7.5.2 Shear Forces and Bending Moments Due to Superimposed Dead Load

17.7.5.3 Shear Forces and Bending Moments Due to Live Loads


17.7.6 Permissible Stresses in Concrete at Service Loads

17.7.7 Estimate Required Prestressing Force

17.7.8 Determine Prestress Losses

17.7.8.1 Prestress Losses at Service Loads

17.7.8.1.1 Elastic Shortening of Concrete

17.7.8.1.2 Creep of Concrete

17.7.8.1.3 Shrinkage of Concrete

17.7.8.1.4 Relaxation of Prestressing Steel

17.7.8.1.5 Total Losses at Service Loads

17.7.8.2 Prestress Losses at Transfer

17.7.9 Concrete Stresses

17.7.9.1 Stresses at Transfer at Midspan

17.7.9.2 Stresses at Transfer at End

17.7.9.3 Stresses at Service Load at Midspan

17.7.9.4 Stresses at Service Load at End

17.7.10 Flexural Strength

17.7.10.1 Stresses in Strands at Flexural Strength

17.7.10.2 Limits for Reinforcement





SEPT 01

17.7.10.3 Design Moment Strength

17.7.10.4 Minimum Reinforcement

17.7.10.5 Final Strand Pattern

17.7.11 Shear Design

17.7.11.1 Required Shear Strength

17.7.11.2 Shear Strength Provided by Concrete

17.7.11.2.1 Simplified Approach

17.7.11.2.2 Calculate Vci

17.7.11.2.3 Calculate Vcw

17.7.11.2.4 Calculate Vc

17.7.11.3 Calculate Vs and Shear Reinforcement

17.7.11.3.1 Calculate Vs

17.7.11.3.2 Determine Stirrup Spacing

17.7.11.3.3 Check Vs Limit

17.7.11.3.4 Check Stirrup Spacing Limits

17.7.12 Deflections

17.7.12.1 Camber Due to Prestressing at Transfer

17.7.12.2 Deflection Due to Beam Self-Weight at Transfer

17.7.12.3 Deflection Due to Superimposed Dead Load

17.7.12.4 Long-Term Deflection

17.7.12.5 Deflection Due to Live Load

17.8 REFERENCES



NOTATIONRAILROAD BRIDGES

A = area of cross-section of precast beam

Ac = total transformed area of composite section

Aps = area of one pretensioning strand or post-tensioning bar

Aps = area of strands in the tensile zone

Av = area of shear reinforcement

Avh = area of web reinforcement per unit length required for horizontal shear

a = compression block depth

B = buoyancy

b = width of compression face of member

be = top flange width of precast beam

bv = width of cross section at the contact surface being investigated for horizontal shear

bw = width of web of a flanged member

CF = centrifugal force

D = dead load

DF = live load distribution factor

d = distance from extreme compressive fiber to centroid of the prestressing force

E = earth pressure

Ec = modulus of elasticity of concrete at 28 days

Eci = modulus of elasticity of concrete at transfer

Es = modulus of elasticity of pretensioning steel

Es = modulus of elasticity of non-pretensioned reinforcement

EQ = earthquake (seismic)

e = eccentricity of strands at transfer length

ec = eccentricity of strands at midspan

F = longitudinal force due to friction or shear resistance at expansion bearings

fb = concrete stress at the bottom fiber of the beam

f c = specified concrete strength at 28 days

fcds = concrete stress at the centroid of the pretensioning steel due to all dead loads exceptthe dead load present at the time the pretensioning force is applied

f ci = specified concrete strength at transfer

fcr = stress in the concrete at the centroid of the pretensioning steel

fd = stress due to unfactored dead load, at extreme fiber of section where tensile stress iscaused by externally applied loads

flc = loss of prestress due to creep of concrete

fle = loss of prestress due to elastic shortening

flr = loss of prestress due to relaxation of pretensioning steel

fls = loss of prestress due to concrete shrinkage

fpc = compressive stress in concrete (after allowance for all prestress losses) at the centroidof cross section resisting externally applied loads

fpe = compressive stress in concrete due to effective pretensioning forces only (afterallowance for all pretension losses) at the extreme fiber of section where tensile stressis caused by externally applied loads

fps = stress in the pretensioning steel at nominal strength

SEPT 01

5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 5

fpu = ultimate tensile strength of pretensioning steel

fse = effective stress in pretensioning steel after losses

ft = concrete stress at the top fiber of the precast beam

ftc = concrete stress at top of fiber of the slab for the composite section

fy = specified yield strength of non-prestressed reinforcement

h = overall depth of precast beam

hc = total height of composite section

I = moment of inertia about the centroid of the non-composite precast beam

I = the percentage of the live load for impact

ICE = ice pressure

Ic = moment of inertia of composite section

L = span length

L = live load

LF = longitudinal force from live load

M = maximum service load design moment

Mcr = moment causing flexural cracking at section due to externally applied loads

MD = unfactored bending moment due to total dead load

Md = unfactored bending moment due to composite beam dead load

Mg = unfactored bending moment due to precast beam self-weight

MLL+I = unfactored bending moment due to live load + impact

Mmax = maximum factored moment at the section due to externally applied loads

Mn = nominal moment strength of a section

MSDL = unfactored bending moment due to superimposed dead load

Mu = factored bending moment at the section

Mx = bending moment at a distance x from the support

n = modular ratio of elasticity between slab and beam materials

OF = other forces (rib shortening, shrinkage, temperature and/or settlement of supports)

Peff = effective post-tensioning force

Pse = effective pretension force after allowing for all losses

Psi = total pretensioning force immediately after transfer

R = relative humidity

Sb = non-composite section modulus of the extreme bottom fiber of the precast beam

Sbc = composite section modulus for extreme bottom fiber of the precast beam

St = non-composite section modulus of the extreme top fiber of the precast beam

Stc = composite section modulus for extreme top fiber of the slab

Stg = composite section modulus for top fiber of the precast beam

SF = stream flow

s = spacing of the shear reinforcement in direction parallel to the longitudinal reinforcement

V = service load shear force

Vc = nominal shear strength provided by concrete


SEPT 01




SEPT 01


Vci = nominal shear strength provided by concrete when diagonal cracking results fromcombined shear and moment

Vcw = nominal shear strength provided by concrete when diagonal cracking results fromexcessive principal tensile stress in web

VD = unfactored shear force at section due to total dead load

Vd = unfactored shear force due to composite beam dead load

Vg = unfactored shear force due to precast beam self-weight

Vi = factored shear force at section due to externally applied loads occurring simultaneouslywith Mmax

VLL+I = unfactored shear force at section due to live load plus impact

Vp = component of pretensioning force in the direction of the applied shear

Vs = nominal shear strength provided by shear reinforcement

VSDL = unfactored shear force due to superimposed dead loads

Vu = factored shear force at the section

Vx = shear force at a distance x from the support

vdh = horizontal shear stress

W = wind load on structure

WL = wind load on live load

w = weight per foot

wc = unit weight of concrete

wequ = equivalent uniform load

x = distance from the support

yb = distance from centroid to extreme bottom fiber of the non-composite precast beam

ybc = distance from the centroid of the composite section to extreme bottom fiber of theprecast beam

ybs = distance from the center of gravity of strands to the bottom fiber of the beam

yt = distance from centroid to extreme top fiber of the non-composite precast beam

ytc = distance from the centroid of the composite section to the extreme top fiber of theslab

ytg = distance from the centroid of the composite section to extreme top fiber of the precast beam

D = deflection

f = strength reduction factor

rp = ratio of pretensioning reinforcement

y = angle of harped pretensioned reinforcement


Precast concrete is playing an increasingly important role in railroad bridge struc-tures. The economy, durability and speed of construction make precast concrete thematerial of choice for new and replacement railroad bridges. The focus of this chapter ison the specific requirements and guidelines for railroad bridges. Typical products anddetails, construction considerations, and identification of applicable AREMA(American Railway Engineering and Maintenance-of-Way Association, formerlyAREA) provisions are also discussed. Two case studies and a railroad superstructuredesign example are presented.

A wide variety of precast products is used for railroad bridge construction. From theground up, these include concrete piles, pile caps, abutments and superstructure beams.Over the years, many railroads have developed standards for precast concrete, includingconcrete mixes, member design, member detailing and quality control.

Several railroads use precast, prestressed concrete piles, but their use may be limited by thecapacity of track-mounted pile drivers. Concrete piles are preferred for use in marine envi-ronments. In highly corrosive locations, precast concrete pile extensions are spliced to steelpipe piles. This permits the embedment of the steel into the anaerobic soil zone and pro-vides a more durable prestressed concrete pile in the more corrosive environment.

Precast concrete pile caps are widely used throughout the country. Typically, these arefabricated with an embedded plate running along the bottom of the cap. This allowswelding of steel piles to the bottom of the cap. Concrete pile caps are sometimes usedto support steel or timber beams, as well as concrete beams. Some railroads are nowbeginning to use precast concrete caps with precast concrete piles. The caps are castwith a socket for the pile to fit into. Grouting is used to tie the components togeth-er after installation. Bridge abutments can also be prefabricated. The bases of theseabutments are similar to the pile caps and serve the same function of supporting thesuperstructure. Abutment backwalls and wingwalls can be precast in sections andbolted or welded together in the field.

Railroads use a wide variety of superstructure elements. Spans typically range from12 ft to over 80 ft. Since many precast concrete spans are installed to replace timbertrestles, standard span lengths for a given railroad are frequently multiples of theirstandard timber stringer span lengths (typically 14 to 16 ft). For spans of 12 ft to 20ft, precast slab beams are frequently used. For spans in the 20- to 30-ft range, precast,prestressed concrete box beams are the most common although tee-beams and I-beams are occasionally used. For spans over 30 ft, box beams are dominant. Spans upto 50 ft typically use two box beams per track. Generally, these are double celled withthrough-voids. Through-voids allow fabricators to use removable and reusable voidforms in casting the beams. This helps reduce costs. Spans over 50 ft generally usefour single-void box beams per track. The shift from two beams per track on shorterspans to four on longer spans is dictated by the lifting restrictions associated with the


SEPT 01

Railroad Bridges

17.0 INTRODUCTION

17.1.1 Piles

17.1.2 Pile Caps and Abutments

17.1.3 Superstructures

17.1 TYPICAL PRODUCTS

AND DETAILS


heavier weight of the longer beams. Shear keys and transverse post-tensioned steel tierods are frequently used to tie the box beams together with diaphragms provided atthe location of the tie rods. For spans greater than 70 to 80 ft, beams with compos-ite cast-in-place concrete decks are frequently used.

A variety of shapes with depth and width variations are available throughout thecountry. Designers should contact the manufacturers and the specific railroad todetermine the properties and dimensions of products available for a proposed pro-ject. Typical superstructure shapes and span ranges applicable to railroad bridges areshown in Figure 17.1.3.1-1.

There are a few other precast products used for different span ranges. Brief descrip-tions of these products are given in Figures 17.1.3.2-1 through 17.1.3.2-4.

The solid single tee beam is used for spans of 20 to 34 ft, and the voided super teefor spans up to 55 ft in length. Both beams are set on a precast concrete cap that hasa welded plate connection to the piles as needed.


RAILROAD BRIDGES17.1.3 Superstructures/17.1.3.2 Other Products

SEPT 01

17.1.3.1 Slab Beams and Box Beams

17.1.3.2 Other Products

Figure 17.1.3.1-1 Typical Precast Concrete

Superstructure Shapes

7'-0"

3'-6" 7'-0"

Varies from1'-2" to 1'-8"

Varies from2'-6"

to 7'-0"

Varies from2'-6"

to 4'-0"

Slab BeamSpans 12' to 20'

Single Cell BoxSpans 20' to 80'

Double Cell BoxSpans 20' to 50'

Figure 17.1.3.2-1 Tee Beam

(Intermediate and Long Spans)

Tee Beam(Intermediate

Span)

Precast Cap

Super Tee(Long Span)

Steel Pilingw/Welded PlateConnection to

Pile Cap


Voided box beams are used on 20- to 50-ft long spans, with optional diaphragms andcurbs. Boxes may be set on precast or cast-in-place concrete caps with piling.

Short span bridges up to 24 ft in length with limited headroom require the use of lowprofile slabs. These slabs may be set on precast caps that are either prestressed or non-prestressed.


RAILROAD BRIDGES17.1.3.2 Other Products

SEPT 01

Figure 17.1.3.2-2 Box Beam

(Intermediate Spans)

OptionalCurb

Precast Cap


Pile Cap

24" OctagonalPrestressed Piling

w/C.I.P. Cap

Closed EndedVoided

Box Beam

Open Ended VoidedBox Beam

Figure 17.1.3.2-3 Low Profile Slab

(Short Spans)Optional

Curb

ConcreteKeeper

SteelKeeper

Low ProfileSlabs

Precast Cap Precast Prestressed Cap


Pile Cap

TimberPiling


Precast, prestressed concrete deck slabs are used in a variety of lengths and widths;with new or existing steel beams. These slabs can be cast with single and double bal-last curbs and with integral walkways to further speed up construction of the bridge.

Structural steel tees or plates are frequently used to cover the longitudinal joint in slabbeams and double-cell box beams as shown in Figure 17.1.3.3-1. Transverse post-tensioned steel tie rods, as shown in Figure 17.1.3.3-2, are generally provided inmultiple single-cell box beam superstructures to help the group act as a unit.Concrete or structural steel “keepers” or retainers are usually provided at the ends ofthe caps to limit lateral movement, as shown in Figure 17.1.3.3-3. Designers shouldcontact the specific railroad to determine their standards and preferred connectiondetails.


RAILROAD BRIDGES17.1.3.2 Other Products/17.1.3.3 Connection Details

SEPT 01

Figure 17.1.3.2-4 Ballast Deck

(With Steel Beams)


Pile Cap

Precast Cap

Steel Beams

Precast Ballast Deck on Steel Beam

Integral Walkway

17.1.3.3 Connection Details

Figure 17.1.3.3-1 Steel Tee between Box Beams Steel Tee


Precast concrete offers many advantages in the construction of railroad bridges. Theseinclude:

• Speed of construction—Precast concrete structures can usually be constructedfaster than bridges comprised of alternative materials.

• Fabrication time—In addition to saving construction time, the lead time forfabricating elements is shorter than for competing materials such as steel.


RAILROAD BRIDGES17.1.3.3 Connection Details /17.2.1 Advantages

SEPT 01

Figure 17.1.3.3-2 Post-Tensioned Steel Tie Rod Post-Tensioned

Steel Tie Rod

Diaphragm

BearingPlate

Figure 17.1.3.3-3 Concrete and Steel

Keeper Details

ConcreteKeeper Steel

Keeper

Pile Cap

17.2 CONSTRUCTION

CONSIDERATIONS

17.2.1 Advantages


• Durability—Compared with many older structures that require frequent inspec-tions and maintenance, railroad engineers find the low maintenance requirementsof precast concrete attractive. Use of concrete with low permeability and strictquality control in the casting plant help assure durable bridge components.

• Quality—The higher quality control of workmanship and materials available incasting plants compared to cast-in-place construction is another plus. Railroads canwork with precast suppliers to ensure that members are cast to their satisfaction.

• Site constraints—The remote locations of many railroad bridges make the “pre-cast” aspect of precast construction very useful. When the nearest ready-mixplant is many miles away from the site, cast-in-place construction within a rail-road’s time constraints is virtually impossible.

• Emergency response—Precast concrete bridge elements provide componentsfor rapid repair of bridges as a result of damage caused by derailments or tim-ber trestle fires. Several railroads keep entire precast bridges stockpiled for rapidemergency replacement. Concrete bridges are less vulnerable to damage fromfire compared to steel or timber bridges.

Most railroads have standard precast concrete trestle bridge designs that incorporate rep-etition of modular precast units. These standard designs are used for replacement ofexisting bridges, as well as construction of new bridges. Railroads and contractors famil-iar with railroad bridge construction have developed low-cost methods of trestle bridgeconstruction. These methods minimize the time that railroad operations must be sus-pended. In addition, precast concrete bridge components are often shipped by rail,which, in many cases, is the only way to deliver components to remote locations.

For construction of bridges, railroads normally only permit train operations to besuspended from two to eight hours at any one time depending on the day and time.If an alternate route is available, 12 to 72 hours are the normal acceptable range.Additional costs of rerouting include obtaining operating rights on another railroadand using the other railroad’s personnel. Use of either option is dependent upon thetype and density of train traffic and the availability of alternate routes.

The various methods used to construct railroad bridges to support existing trackagewhile minimizing disruptions to train operations include the following:

• rolling spans on runways

• floating spans on barges

• pick and set

• temporary rail line change

• permanent rail line change

• trestle bridge construction

These methods are utilized because train operations cannot be suspended for theamount of time that would be required to construct the new bridge piece by piece inits permanent location.

In many bridges, the existing substructure is reused and, if necessary, modified forreplacement of the superstructure. Sometimes, the bridge may require new substruc-ture elements. In both cases, the substructure work is performed beneath the existing


RAILROAD BRIDGES17.2.1 Advantages/17.2.5 Substructures

SEPT 01

17.2.2 Standard Designs

17.2.3 Train Operations

17.2.4 Construction Methods

17.2.5 Substructures


track and superstructure so that the track is out of service for only very limited peri-ods while driving piles or placing temporary supports. For replacement of existingbridges utilizing this method, ballast removal, as well as relocating the decks andbeams of the existing bridge, may be required to allow pile driving for the new bridge.It is often necessary to reduce the speed of traffic over existing bridges during con-struction due to reduced load carrying capacity resulting from relocating the decksand beams.

Precast concrete beams are usually installed using pick and set methods. This methodrequires access to the bridge construction site for cranes that have adequate capacity tolift the beams. A typical bridge replacement procedure is illustrated in Figure 17.2.5-1.


RAILROAD BRIDGES17.2.5 Substructures

SEPT 01

Figure 17.2.5-1 Typical Bridge Replacement

Construction SequenceSUSPEND TRAIN OPERATIONS

INTERMITTENTLY AS REQUIRED TO INSTALL PILES OR SHAFTS

CONSTRUCT BENT CAPS

SUSPEND TRAIN OPERATIONS

DISCONNECT TRACK AT EACH END OF BRIDGE OR SPAN TO BE REPLACED

RESUME TRAIN OPERATIONS

INSTALL NEW PRECAST CONCRETE SUPERSTRUCTURE ON BENT CAPS

REMOVE EXISTING SUPERSTRUCTURE

RECONNECT TRACK

SURFACE AND ALIGN TRACK


This section briefly discusses the types of loads on railroad bridges. The emphasis ison those loads that are different from highway bridge loads covered in Chapter 7.Provisions of the American Railway Engineering and Maintenance-of-WayAssociation (AREMA) Manual for Railway Engineering are introduced relative todesign loads and load combinations. In addition, applicable portions of the manualare referenced.

The AREMA Manual provides the recommended practice for railroads and others con-cerned with the engineering, design and construction of railroad fixed properties, alliedservices and facilities. Prior to starting the design of a project, design engineers shoulddiscuss specific loadings, forces, standards and procedures with the appropriate railroad.

The AREMA Manual Chapter 8, Concrete Structures and Foundations, specificallyaddresses reinforced concrete and prestressed concrete structures. Article 2.2.3 coversthe design loads and forces to be considered in the design of railroad structures sup-porting tracks, including bridges. Briefly, design loads include:

Design engineers familiar with highway bridge design will recognize the loads andforces listed above. The magnitude of the loads and forces are explained in detail inthe AREMA Manual. Loads that are different from highway bridges are described inthe following sections.

The following description of live load is based on the AREMA Manual:

(1) The recommended live load in pounds per axle and uniform trailing load for each trackis the Cooper E 80 load, which is shown in Figure 17.3.2.1-1. Table 17.3.2.1-1 pro-vides a table for live load bending moments, shear forces and reactions for simple spanbridges. Values for span lengths not shown are generally computed by interpolation.

(2) The Engineer (the Railroad’s Chief Engineer) shall specify the Cooper live loadto be used, and such load shall be proportional to the recommended load, withthe same axle spacing.

(3) For bridges on curves, provisions shall be made for the increased proportion carried byany truss, beam or stringer due to the eccentricity of the load and centrifugal force.

D = Dead Load

L = Live Load

I = Impact

CF = Centrifugal Force

E = Earth Pressure

B = Buoyancy

W = Wind Load on Structure

WL = Wind Load on Live Load

LF = Longitudinal Force from Live Load

F = Longitudinal Force due to Friction or Shear Resistance at Expansion Bearings

EQ = Earthquake (Seismic)

SF = Stream Flow Pressure

ICE = Ice Pressure

OF = Other Forces (Rib Shortening,Shrinkage, Temperature and/orSettlement of Supports)

Figure 17.3.2.1-1 Cooper E 80 Load

8'

40,0

00

80,0

0080

,000

80,0

0080

,000

52,0

0052

,000

52,0

0052

,000

40,0

00

80,0

0080

,000

80,0

0080

,000

52,0

0052

,000

52,0

0052

,000

8,000 lb perlin ft

8' 8'5' 5' 5' 5' 5' 5' 5' 5' 5'6'5'5' 6'9' 9'


RAILROAD BRIDGES17.3 The American Railway Engineering And Maintenance-of-Way

Association Load Provisions/17.3.2.1 Live Load

SEPT 01

17.3 THE AMERICAN

RAILWAY ENGINEERINGAND MAINTENANCE-

OF-WAY ASSOCIATIONLOAD PROVISIONS

17.3.1 AREMA Manual

17.3.2 AREMA Loads

17.3.2.1 Live Load


(4) For members receiving load from more than one track, the design live load on thetracks shall be as follows:

• For two tracks, full live load on two tracks

• For three tracks, full live load on two tracks and one-half on the other track

• For four tracks, full live load on two tracks, one-half on one track, and one-quarter on the remaining track

• For more than four tracks, as specified by the Engineer

The selection of the tracks for these loads shall be that which produces the most criticaldesign condition in the member being designed.

Table 17.3.2.1-1 Maximum Bending Moments, Shear Forces and Pier Reactions for Cooper E 80 Live Load (Based on AREMA Manual Table 1-17)

SpanLength

ft

567891011121314161820242832364045505560708090

100

MaximumBendingMomentft-kips

50.0060.0070.0080.0093.89112.50131.36160.00190.00220.00280.00340.00412.50570.42730.98910.85

1,097.301,311.301,601.201,901.802,233.102,597.803,415.004,318.905,339.106,446.30

MaximumBending

Moment atQuarter Point

ft-kips

37.5045.0055.0070.0085.00100.00115.00130.00145.00165.00210.00255.00300.00420.00555.00692.50851.50

1,010.501,233.601,473.001,732.302,010.002,608.203,298.004,158.005,060.50

End

40.0046.6751.4355.0057.5860.0065.4570.0073.8477.1485.0093.33100.00110.83120.86131.44141.12150.80163.38174.40185.31196.00221.04248.40274.46300.00

QuarterPoint30.0030.0031.4335.0037.7840.0041.8243.3344.6147.1452.5056.6760.0070.0077.1483.1288.9093.55100.27106.94113.58120.21131.89143.41157.47173.12

Maximum Shear Forceskips

Midspan

20.0020.0020.0020.0020.0020.0021.8223.3324.6125.7127.5028.8928.70(1)

31.7534.2937.5041.1044.0045.9049.7352.7455.6961.4567.4173.4878.72

MaximumPier

Reactionkips

40.0053.3362.8670.0075.7680.0087.2893.3398.46104.29113.74121.33131.10147.92164.58181.94199.06215.90237.25257.52280.67306.42354.08397.70437.15474.24

All values are for one rail (one-half track load)

(1) AREMA table does not include a value for Cooper E 80 live load. A value of 28.70 kips is provided for alternative live load.


RAILROAD BRIDGES17.3.2.1 Live Load

SEPT 01


For reinforced concrete (precast and cast-in-place), the impact load is a percentage ofthe live load based on the ratio of live load to live load plus dead load:

I = [AREMA Eq. 2-1]

The impact load shall not exceed 60% for diesel engines and 80% for steam engines.

For prestressed concrete, the impact load is a percentage of the live load based onspan length in ft:

L ≤ 60 ft, I = 35 - L2/500 [AREMA Eq. 17-1]

60 < L ≤ 135 ft, I = 14 + 800/(L - 2)

L > 135 ft, I = 20%

where L = span length of member in ft

All other loads and forces are defined similarly to highway bridges although the mag-nitudes are different. The design engineer should refer to the AREMA Manual foradditional information.

The various combinations of loads and forces to which a structure may be subjected aregrouped in a similar manner as highway bridges. Each component of the structure or foun-dation upon which it rests, shall be proportioned for the group of loads that produces themost critical design condition. The group loading combinations for service load design andload factor design are as shown in Table 17.3.2.4-1 and Table 17.3.2.4-2, respectively, andare reproduced from AREMA Article 2.2.4.

100LL D+

Table 17.3.2.4-1 Group Loading Combinations—

Service Load DesignItemGroup

AllowablePercentage of

Basic Unit StressI 100II 125III Group I + 0.5W + WL + LF + F

D + L + I + CF + E + B + SFD + E + B + SF + W

125IV Group I + OF 125V Group II + OF 140VI Group III + OF 140VII D + E + B + SF + EQ 133VIII Group I + ICE 140IX Group II + ICE 150

Table 17.3.2.4-2 Group Loading Combinations—

Load Factor DesignGroup Item

IIA

1.4 (D + 5/3(L + I) + CF + E + B + SF)1.8 (D + L + I + CF + E + B + SF)

II 1.4 (D + E + B + SF + W)III 1.4 (D + L + I + CF + E + B + SF + 0.5W + WL + LF + F)IV 1.4 (D + L + I + CF + E + B + SF + OF)V Group II + 1.4 (OF)VI Group III + 1.4 (OF)VII 1.4 (D + E + B + SF + EQ)VIII 1.4 (D + L + I + E + B + SF + ICE)IX 1.2 (D + E + B + SF + W + ICE)


RAILROAD BRIDGES17.3.2.2 Impact Load/17.3.2.4 Load Combinations

SEPT 01

17.3.2.2 Impact Load

17.3.2.3 Other Loads



As with all engineering design practices, railroad industry practice continues tochange as experience and research is incorporated into the AREMA Manual and indi-vidual railroad company standards and procedures. This section will discuss currentrailroad industry practice relative to overall railroad bridge design philosophy, skewlimitations and superstructure continuity. Designers should discuss philosophies,standards and procedures with the specific railroad as applicable to the project.

New railroad bridges are constructed to support railroad tracks over existing water-ways, roadways, and other railroads. In addition, new railroad bridges are built toreplace existing bridges due to:

• unsatisfactory capacity to support current or future loadings

• unsafe condition resulting from deterioration and/or poor maintenance

• damage as a result of an accident or natural disaster

• inadequate waterway opening

• highway or railroad grade separation projects

• navigation, drainage and flood control projects

The large majority of railroad bridge projects usually involve existing trackage.Consequently, one of the most important considerations for the railroad bridgedesigner is to design the bridge such that construction will have minimal disruptionto train operations. This affects design details, construction methods and projectcosts. Much of today’s rail traffic is under contract with the customer and the con-tract often includes a guarantee of service between origin and destination. Penaltiesand possible loss of a contract can result if unreasonable delays in the agreed uponschedule are experienced. Taking a track out of service or reducing the speed of railtraffic for an extended period of time for bridge construction can have a detrimentaleconomic effect on the railroad. The project must be properly planned and coordi-nated with the operating and marketing departments of the railroad during thedesign and construction phases.

The use of standardized precast components speeds both the design and constructionof bridges. Replacement spans can be specified by length alone, and railroad bridgeworkers are familiar with the sections and construction procedures. Since the vastmajority of precast concrete bridges have all the superstructure below track level, ver-tical and horizontal clearance is not limited by these structures. This allows widecargo or double stack containers to be shipped without clearance concerns andreduces the threat of bridge damage caused by shifted loads.

Many railroads prefer simple span bridges to continuous structures, finding them eas-ier to install and maintain. Since they are structurally determinate, simple spans arebetter able to handle problems such as support settlement and thermal effects thansome continuous bridges. Precast concrete elements are particularly suited to simple-span construction. Additional reasons many railroads prefer simply supported bridgesto continuous span bridges include the following:

• If repair or replacement of superstructure elements is necessary, less interrup-tion to train traffic is incurred with a simple span bridge than with a continu-ous span bridge.

• Installation of simple spans can be accomplished more quickly than continuousspans.


RAILROAD BRIDGES17.4 Current Design Practice/17.4.3 Simple Span Bridges

SEPT 01

17.4 CURRENT DESIGN

PRACTICE

17.4.1 New Bridges

17.4.2 Replacement Bridges

17.4.3 Simple Span Bridges


• If a bridge experiences substructure problems such as settlement, a continuousspan bridge may require immediate and more extensive work, thereby resultingin greater interruptions to train traffic.

• Simple span bridges have a proven history of performing well.

It is desirable to limit the end skew of railroad bridge precast beams to less than 30degrees for constructibility and placement of reinforcing steel in the beam. When thebridge skew relative to the substructure exceeds 30 degrees, staggered precast ele-ments as shown in Figure 17.4.4-1 should be considered.

This case study describes a Southern Pacific railroad truss bridge replacement(Marianos, 1991). This project illustrates the use of precast concrete elements toreplace a structure without serious interruption to rail traffic. The existing structureconsisted of a 90-ft long timber trestle approach, two 154-ft long through-truss spansand a 30-ft long plate-girder approach span.

The truss spans were nearly 90 years old and were at the end of their useful servicelives due to joint wear. Since the truss spans required replacement, the railroad decid-ed to replace the entire bridge with precast concrete.

Using a track-mounted pile driver, steel H-piles were driven through the track on thetimber trestle. The pile bents were spaced to give 30-ft replacement span lengths inthe trestle area. After the piles were cut off at the required elevation, precast concretebent caps were placed and the piles welded to steel plates embedded in the bottom ofthe caps.

Since the truss spans crossed a creek subject to high flood flows, it was essential tominimize obstruction of the waterway. For this reason, new intermediate piers withfour 79-ft long precast, prestressed box beams replaced the two 154-ft long trussspans. The 79-ft long beams were beyond the span range of the railroad standardsand required a new design.


RAILROAD BRIDGES17.4.3 Simple Span Bridges/17.5.3 New Intermediate Piers

SEPT 01

17.4.4 Skew Bridges

17.5.1 Existing Bridge

17.5.2 New Piles

17.5.3 New Intermediate Piers

Figure 17.4.4-1 Layouts for Skewed Bridges

Skew ≤ 30°

Skew > 30°

17.5 CASE STUDY NO. 1—

TRUSS BRIDGEREPLACEMENT


Railroad crews built intermediate piers at midspan of each truss by driving pilesthrough the existing truss floor systems, and the 79-ft long box beams were orderedand fabricated.

When the substructure was completed, superstructure replacement began. The 90-ftlong timber trestle was replaced by 30-ft long spans of precast, prestressed box beams,as shown in Figure 17.5.4-1. Two box beams placed side by side were used for eachspan. Each box beam has two through-voids and an integral ballast retaining sidewalland walkway cast on the outside edge. A shear key between the box beams helpedensure load distribution between the two beams. The box beams were placed using atrack-mounted crane.

A similar 30-ft long box beam span was used to replace the steel plate-girder span onthe approach opposite the timber trestle. Precast concrete bolster blocks were used ontop of the existing masonry piers to obtain the proper elevation because the newstructure was shallower than the existing one.

After the approach spans were completed, preparation began for replacing the trussspans. An area under the truss spans was filled with ballast and leveled. Railroad trackpanels were laid perpendicular to the bridge on the fill below the structure. Steelframes mounted on rail trucks were placed on these tracks and used to support thetrusses for removal. With these preparations for truss replacement complete, a care-fully orchestrated construction effort began.


RAILROAD BRIDGES17.5.3 New Intermediate Piers/17.5.5 Truss Removal

SEPT 01

17.5.4 New Superstructure for

Approach Spans

17.5.5 Truss Removal

Figure 17.5.4-1 Precast 30-ft Approach Span

on Precast Bolster Blocks


First, the truss ends were jacked up to lift them off the pier. The truss was thensecured to the steel frames and rolled laterally clear of the work area, as shown inFigure 17.5.5-1. The construction crew then finished preparations on the pier topfor placing the precast, prestressed concrete box beams. This work included remov-ing the remaining truss attachments and placing elastomeric bearing pads.

Each 154-ft long steel truss was replaced by two spans of precast box beams. Whenthe pier preparation was completed, the four box beams of the first span were liftedinto position using truck cranes. While workmen epoxied the longitudinal joints andshear keys between these beams, the box beams for the second span were beingplaced. After the joints of both spans were epoxied and handrail cables strung alongthe walkways, prefabricated panels of railroad track were placed on the spans. Thisallowed a hopper car to be moved out on the track to dump ballast on the new spans.

After the ballast was tamped and the track reconnected, the new spans were ready for railtraffic. Replacing a 154-ft long truss span was completed in a 12-hour track closure.Several weeks later, the second truss span was replaced, completing the reconstruction.

The use of precast elements, as shown in Figure 17.5.6-1, allowed the speedy andeconomical replacement of the structure, using the railroad’s own work force.


RAILROAD BRIDGES17.5.5 Truss Removal/17.5.6 New Superstructure for Truss Spans

SEPT 01

Figure 17.5.5-1 Roll-Out of Truss Span

to be Replaced


for Truss Spans


This case study discusses a timber trestle bridge replacement on the Union PacificRailroad system. Bridge 177.81 is located approximately 1.59 miles west ofMarysville, CA on Union Pacific Railroad’s Canyon Subdivision. The existing bridge,shown in Figure 17.6.1-1, consisted of numerous timber trestle spans and a steelplate-girder span over the Yuba River. The plate-girder was to remain in place and thetimber trestle portion of the bridge was to be replaced.

Due to the volume of rail traffic and importance of on-time delivery by the UnionPacific Railroad, minimal disruption to train operations was mandatory. Substructureconstruction was to be performed without interference or downtime to the railroad.Superstructure change-out would be performed during “windows” approved by therailroad. A precast, prestressed concrete superstructure system was selected based oneconomics, speed of erection and the ability to meet the construction constraintsassociated with the need for minimal disruption to train operations.


RAILROAD BRIDGES17.5.6 New Superstructure for Truss Spans/17.6.2 New Superstructure

SEPT 01

Figure 17.5.6-1 Completed Structure

17.6 CASE STUDY NO. 2—

TIMBER TRESTLEREPLACEMENT

17.6.1 Existing Bridge

Figure 17.6.1-1 Existing Plate-Girder and

Timber Trestle Spans.



The existing timber trestle spans varied in length with an average span of slightly lessthan 15 ft. Based on a field survey of the timber bent locations, new bent locationswere selected to minimize interference with existing timber pile bents and optimizebeam spans. A span length of 44 ft was selected for the new superstructure. For thisspan length, 45-in. deep double-cell, prestressed concrete box beams were deter-mined to be the most economical structural system.

Based on field conditions, prevalent construction practice in the area and construc-tion constraints governed by railroad operations, cast-in-place reinforced concretebents were selected for the substructure. The bents consisted of 100-ft long, 4-ftdiameter drilled shafts, 4-ft diameter cast-in-place reinforced concrete column exten-sions and cap beams. All structural components were designed in accordance with theAREMA Manual and Union Pacific Railroad standards and procedures.

The sequence of construction was as follows:

The existing bridge footwalk and handrail were removed as required to facilitatedrilled shaft installation. The drilled shafts were spaced at 15-ft centers perpendicu-lar to the track to allow installation of the drilled shafts without interference to rail-road operations. Continuous train operations were maintained throughout the entireconstruction of the substructure. Due to foundation conditions, steel pipe casing wasnecessary for drilled shaft installation. The pipe casing was installed using a vibrato-ry hammer. Reinforcing steel cages were set and the holes were filled with 4,000 psicompressive strength concrete. Drilled shaft column extensions, bent cap beams andthe abutment were constructed under the existing timber superstructure. Due to thedepth of the new concrete beams, the bent and abutment construction were com-pleted without interfering with the existing timber superstructure, as shown inFigure 17.6.3-1.


RAILROAD BRIDGES17.6.2 New Superstructure/17.6.3 Substructure Construction

SEPT 01

17.6.3 Substructure Construction

Figure 17.6.3-1 Completed Concrete Bents

under Existing Timber Trestle


Working within railroad approved construction “windows,” the timber structure wasremoved and precast beams were set. In a continuous, well-planned procedure, theballast, ties and rail were placed and train operations were resumed. The use of pre-cast concrete allowed the Union Pacific Railroad to replace a timber trestle with astronger, more durable structural system with minimal disruption to railroad service.The completed bridge is shown in Figure 17.6.4-1.


RAILROAD BRIDGES17.6.4 Superstructure Construction

SEPT 01

17.6.4 Superstructure

Construction

Figure 17.6.4-1 Completed Bridge Structure



RAILROAD BRIDGES17.7 Design Example—Double-Cell Box Beam, Single Span, Non-Composite, Designed

in Accordance with AREMA Specifications/17.7.2 Introduction

SEPT 01

Prestressed concrete double-cell box beams and solid slab beams are commonly usedin the railroad industry. Solid slab beams are used for spans up to 20 ft, especiallywhen superstructure depth has to be minimized. Prestressed concrete double-cell boxbeams are used for spans up to 50 ft in length. Prestressed concrete single-cell boxbeams are more economical for spans longer than 40 ft and are used for span lengthsup to 80 ft. When span lengths exceed 80 ft, prestressed concrete I-beams with acomposite deck become more feasible from a design, economic and constructionpoint of view. This example illustrates the design of a non-composite, prestressedconcrete, double-cell box beam.

In non-composite design, the beam acts as the main structural element. Therefore,the beam has to carry all the dead loads, superimposed dead loads and live load. Thebeams are assumed to be fully prestressed under service load conditions. The deadload consists of the self-weight of the beam including diaphragms. The superimposeddead loads consist of ballast, ties, rails, concrete curbs and handrails, as shown inFigures 17.7.2-1 and 17.7.2-2. The live load used for this bridge is Cooper E 80,which is described in the AREMA Manual, Chapter 8, Part 2, Reinforced ConcreteDesign, Article 2.2.3. The prestressed concrete beams are designed using the AREMAManual, Chapter 8, Part 17, Prestressed Concrete Design Specifications for Design ofPrestressed Concrete Members. The beams in this example are checked for both service-ability and strength requirements.

17.7 DESIGN EXAMPLE—

DOUBLE-CELL BOX BEAM,SINGLE SPAN, NON-

COMPOSITE, DESIGNEDIN ACCORDANCE WITH

AREMA SPECIFICATIONS17.7.1

Background

17.7.2 Introduction

Figure 17.7.2-1 Bridge Cross-Section

Ballast

Handrail post (Typ.)

30" Prestressed concrete box beam

Precast curband walkway

Void drain, typ.1 ea. end, ea. cell

Timber ties

LC Track & Bridge

8'-0" Min. Clear

8" Min.

1/2" Gap7'-0"7'-0"

8'-0" Min. Clear

3'-10 7/8"

Steel tee (Typ.)

5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 1

For design, the bridge has the following dimensions:

Beam length = 30.0 ft

Beam width = 7.0 ft

Center-to-center distance between bearings = 29.0 ft

Bearing width (measured longitudinally) = 8 in.

Bearing length (measured transversely) = 6.67 ft

Depth of ballast = 15 in.

Timber ties: length = 9 ft; width = 9 in.; depth = 7 in.

Rail section = 132 RE (Bethlehem Steel Co.)

No. of tracks = one

For concrete:

Compression positive (+ve)

Tension negative (-ve)

For steel:

Compression negative (-ve)

Tension positive (+ve)

Distance from center of gravity:

Downward positive (+ve)

Upward negative (-ve)


RAILROAD BRIDGES17.7.2 Introduction/ 17.7.2.2 Sign Convention

SEPT 01

Figure 17.7.2-2 Bridge Elevation 30'-1" Face to face of backwalls

LC Abutment No.1

LC Abutment No.2

abutmentCast-in-place

abutmentCast-in-place

Flow line

box beam30" prestressed concrete

granular fill

Well compacted

17.7.2.1 Geometrics

17.7.2.2 Sign Convention


Some calculations are carried out to a higher number of significant figures than com-mon practice with hand calculation. Depending on available computation resourcesand designer preferences, other levels of precision may be used.

Concrete strength at transfer, f ci = 4,000 psi

Concrete strength at 28 days, f c = 7,000 psi

Concrete unit weight, wc = 150 pcf

Modulus of elasticity of prestressed concrete, Ec

, psi [AREMA Art. 2.23.4]

where

wc = unit weight of concrete, pcf

f c = specified strength of concrete, psi

Modulus of elasticity of concrete at transfer, using f ci = 4,000 psi, is:

Modulus of elasticity of concrete at 28 days, using f c = 7,000 psi, is:

1/2-in. diameter, seven wire, low-relaxation strands

Area of one strand, Aps = 0.153 in.2

Ultimate tensile strength, fpu = 270.0 ksi

Modulus of elasticity, Es = 28,000 ksi

E ksic = ( ) =150 33 7 000 1 000 5 0721 5.

( ) , / , ,

E ksici = ( ) =150 33 4 000 1 000 3 8341 5.

( ) , / , ,

E w fc c c= ′1 533

.


RAILROAD BRIDGES17.7.2.3 Level of Precision/17.7.3.2 Pretensioning Strands

SEPT 01

17.7.2.3 Level of Precision

Item Units PrecisionConcrete Stress 1/1000Steel Stress 1/10Prestress Force 1/10Moments 1/10Shears 1/10For the Beam:Cross-Section Dimensions 1/100Section Properties 1Length 1/100Area of Prestressing Steel 1/1000Area of Mild Reinforcement 1/100

ksiksi

kips

kips

in.in.

in.2

in.2

ft

ft-kips

17.7.3 Material Properties

17.7.3.1 Concrete

17.7.3.2 Pretensioning Strands


Yield strength, fy = 60,000 psi

Modulus of elasticity, Es = 29,000 ksi

For cross-sectional dimensions of a single box beam, see Figure 17.7.4-1. Note thatthe depth varies from 30 in. to 31 in. to provide drainage

A = area of cross-section of precast beam = 1,452 in.2

h = average depth of the precast beam = (0.5)(31 + 30) = 30.5 in.

I = moment of inertia about the centroid of the precast beam = 171,535 in.4

yb = distance from centroid to extreme bottom fiber of the precast beam = 15.25 in.

yt = distance from centroid to extreme top fiber of the precast beam = 15.25 in.

Sb = section modulus for the extreme bottom fiber of the precast beam = 11,248 in.2

St = section modulus for the extreme top fiber of the precast beam = 11,248 in.3

NOTE: Section properties do not include precast curbs and walkway. Reinforcementin curbs and walkway not shown for clarity

Self-weight of beam = = 1.513 kip/ft

Weight of end diaphragm = 1.7 kips

1 452 1501 000 144, ( ), ( )


RAILROAD BRIDGES17.7.3.3 Reinforcing Bars/

17.7.5.1 Shear Forces and Bending Moments Due to Dead Load

SEPT 01

17.7.3.3 Reinforcing Bars

17.7.4 Cross-Section Properties

for a Single Beam

Figure 17.7.4-1 Box Beam Cross-Section

mild steelof prestressing strand to Relative vertical position

#4 Bars

#4 Stirrups

3x3" Fillet (Typ.)

prestressing strands)adjust as required to clear(24)#6 Bars (place as shown-

5"

1'-5 1/2"

(Typ.)

1 1/2" Clr.

2'-8 3/4"8 1/2"

2'-8 3/4"5"7'-0"

2'-7"

7"

1'-5 1/2"

6 1/2"

6"

2'-0"

17.7.5 Shear Forces and

Bending Moments

17.7.5.1 Shear Forces and Bending

Moments Due to Dead Load


The equations for shear force (Vx) and moment (Mx) for uniform loads on a simplespan (L) are given by:

Vx = (Eq. 17.7.5.1-1)

Mx = (Eq. 17.7.5.1-2)

where

w = weight/ft = 1.513 kip/ft

L = span length, ft

x = distance from the support, ft

Using the above equations, values of shear forces (Vg) and bending moments (Mg)are computed and given in Table 17.7.5.1-1.

Diaphragm Load: Since distance between the centerline of the bearing and center ofgravity of the diaphragm is less than the effective depth, ignore the effect of thediaphragm load in this example.

Superimposed dead loads consist of ballast, ties, rails, curbs and handrails.

Ballast, including track ties at 120 pcf

= 15/12(7 + 0.04/2 gap)(0.120) = 1.053 kip/ft [AREMA Art. 2.2.3]

Track rails, inside guardrails and fastenings at 200 plf /track = = 0.100 kip/ft

For this example, assume concrete curb at 1.5 ft2 + handrail post at

5% = (1.5)(0.150)(1.05) = 0.236 kip/ft

Total superimposed dead load per beam per linear ft = 1.389 kip/ft

Using a uniform load of 1.389 kip/ft and Equations 17.7.5.1-1 and 17.7.5.1-2, values of shear forces (VSDL) and bending moments (MSDL) are computed and givenin Table 17.7.5.1-1.

0 2002

.

wx2

L x− −( )

wL

x2

−


RAILROAD BRIDGES17.7.5.1 Shear Forces and Bending Moments Due to Dead Load/

17.7.5.2 Shear Forces and Bending Moments Due to Superimposed Dead Load

SEPT 01

Table 17.7.5.1-1Shear Forces and

Bending Moments

x, ft 0.0*

21.9

0.0

20.10.0

0.0

164.6

10.0

6.8

143.7

6.3132.0

892.0

86.8

14.5

0.0

159.1

0.0146.0

1,033.0

46.8

7.25

10.9

119.3

10.1109.5

785.7

104.8

4.0

15.9

75.7

14.669.5

—

—

6.0

12.8

104.4

11.895.8

—

—

1.27**

20.0

26.6

18.424.5

194.5

150.7

Vg, kip

Mg, ft-kips

VSDL, kip

MSDL, ft-kip

VLL+I, kip

MLL+I, kip

* At the support** At the critical section for shear (See Section 17.7.11)

17.7.5.2 Shear Forces and Bending

Moments Due toSuperimposed Dead Load


The actions caused by the Cooper E 80 live load can be determined by using thetables in the AREMA Manual, Chapter 15, Art. 1.15 Appendix or by using any com-mercially available computer program. A distribution factor (DF) equal to 0.5 isused, since there are two beams supporting one track.

For span lengths less than 60 ft, the impact factor is:

[AREMA Eq.17-1]

The values of shear forces (VLL+I) and bending moments (MLL+I) for live load plusimpact for one beam were determined using a computer program and are given inTable 17.7.5.1-1.

For Group I loading:

Service Load Design = D + (L + I)(DF) [AREMA Table 2-2]

Load Factor Design = 1.4(D + 5/3(L + I)(DF)) [AREMA Table 2-3]

Values of shear forces and bending moments for service load design and factored loaddesign are determined from Table 17.7.5.1-1 and given in Table 17.7.5.4-1.

The maximum value of shear occurs near the supports while the maximum value ofbending moment occurs near midspan for a simply supported span.

At transfer (before time-dependent prestress losses): [AREMA Art. 17.6.4]

Compression: 0.60 f ci = 0.60(4,000) = 2.400 ksi

Tension: without bonded reinforcement =

At service loads (after allowance for all prestress losses): [AREMA Art. 17.6.4]

Compression: 0.40 f c = 0.40(7,000) = 2.800 ksi

Tension in precompressed tensile zone: 0 ksi

Try eccentricity of strands at midspan, ec = yb - 2.5 = 12.75 in.

Bottom tensile stress due to applied loads:

fM M M

Sbg SDL LL I

b

=+ + +

3 4 000, = 0.190 ksi3 fci′

IL

of live load= −

= −

=35

50035

29500

33 322 2( )

. %


RAILROAD BRIDGES17.7.5.3 Shear Forces and Bending Moments Due to Live Load/

17.7.7 Estimate Required Prestressing Force

SEPT 01


17.7.6 Permissible Stresses in

Concrete at Service Loads

17.7.7 Estimate RequiredPrestressing Force

Table 17.7.5.4-1 Shear Forces and Bending

Moments for DesignSelf Wt

(g)Dead

(SDL)

Live +Impact(L+I)

TotalService

Load

TotalFactored

LoadMax. Shear Force at 1.27 ft, kips 20.0 18.4 150.7 189.1 405.4

Max. BendingMoment at Midspan, ft-kips

159.1 1,46.0 1,033.0 1,338.1 2,837.5

17.7.5.3 Shear Forces and BendingMoments Due to Live Load


where

fb = concrete stress at the bottom fiber of the beam

Mg = unfactored bending moment due to precast beam self-weight, ft-kips

MSDL = unfactored bending moment due to superimposed dead load, ft-kips

MLL+I = unfactored bending moment due to live load plus impact, ft-kips

Since allowable tensile stress in bottom fiber at service load is zero, required precom-pression is 1.428 ksi.

Bottom fiber stress due to prestress after all losses:

where Pse = effective pretension force after allowing for all losses

Then 1.428 =

and Pse = 783.7 kips

Since losses are generally between 15 and 20%, assume 18% final prestress losses.

Allowable tensile stress in prestressing tendons immediately after prestress transfer isthe larger of 0.82fpy = (0.82)(0.9fpu) = 0.738 fpu or 0.75fpu

0.75 fpu = 0.75(270) = 202.5 ksi [AREMA Art. 17.6.5]

Number of strands required = = 30.8 strands

Try 32 strands at bottom, ybs = 2.5 in.

Plus 4 strands at mid-height, ybs = 15.25 in.

Plus 6 strands at top, ybs = 27.50 in.

Total No. of strands = 32 + 4 + 6 = 42 strands

Center of gravity of strands, ybs = = 7.29 in.

Eccentricity of strands, ec = yb - ybs = 15.25 - 7.29 = 7.96 in.

Total initial prestressing force before loss = 202.5(0.153)(42) = 1,301.3 kips

To determine effective prestress, fse, allowance for losses of prestress due to elasticshortening of concrete, fle, creep of concrete, flc, shrinkage of concrete, fls, and relax-ation of prestressing steel, flr, will be calculated.

32 2 5 4 15 25 6 27 5042

( . ) ( . ) ( . )+ +

783 71 0 18 0 75 270 0 153

.( . )( . )( )( . )−

P Pse se

1 45212 75

11 248,( . ),

+

f PA

P eSb

se se c

b

= +

f 1.428 ksib = + + =12 159 1 146 0 1 033 011 248

( . . , . ),


RAILROAD BRIDGES17.7.7 Estimate Required Prestressing Force /17.7.8 Determine Prestress Losses

SEPT 01

17.7.8 Determine

Prestress Losses


[AREMA Eq. 17-16]

where

fcr = stress in concrete at centroid of prestressing reinforcement immediately aftertransfer, due to total prestress force and dead load acting at time of transfer,and is calculated as follows:

=

where

Psi = pretension force after allowing for initial losses. Taken as 0.69 fpu

fcr =

flc = 12fcr - 7fcds [AREMA Eq. 17-18]

where

fcds = concrete stress at centroid of prestressing reinforcement, due to all deadloads not included in calculation of fcr

=

fls = 12(1.177) - 7(0.081) = 13.6 ksi

Assume relative humidity, R = 70% (see also AREMA Fig. 17-1):

fls = 17,000 - 150 R [AREMA Eq. 17-19]

= = 6.5 ksi

For pretensioning tendons with 270 ksi low-relaxation strand:

flr = 5,000 - 0.10fle - 0.05(fls + flc) [AREMA Eq. 17-21]

= - 0.10(8.6) - 0.05(6.5 + 13.6) = 3.1 ksi5 0001 000,,

17 000 150 70

1 000

,

,

− ( )

M eI

0.081 ksiSDL c = =146 0 12 7 96171 535. ( )( . )

,

f ksiel = ( ) =28 0003 834

1 177 8 6,

,. .

− = + − =159 1 12 7 96171 535. ( )( . )

,0.824 0.442 0.089 1.177 ksi

42 0 69 0 153 2701 452

42 0 69 0 153 270 7 96171 535

2( . )( . )( ),

( . )( . )( )( . ),

+

PA

P eI

M e

Isi si c

2g c+ −

fEE

fes

cicrl =


RAILROAD BRIDGES17.7.8.1 Prestress Losses at Service Loads/

17.7.8.1.4 Relaxation of Prestressing Steel

SEPT 01

17.7.8.1.2 Creep of Concrete

17.7.8.1.3 Shrinkage of Concrete

17.7.8.1.4 Relaxation of

Prestressing Steel

17.7.8.1 Prestress Losses at

Service Loads

17.7.8.1.1 Elastic Shortening

of Concrete


Total prestress losses = 8.6 + 13.6 + 6.5 + 3.1 = 31.8 ksi

Final prestressing force, Pse = (202.5 - 31.8)(0.153)(42) = 1,096.9 kips

Percentage prestress losses =

Losses due to elastic shortening, fle = 8.6 ksi

Total initial prestress losses = 8.6 ksi

Initial prestress force after loss, Psi = (202.5 - 8.6)(0.153)(42) = 1,246.0 kips

Percentage initial prestress losses = = 4.25%

Stresses need to be checked at several locations along the beam to ensure that thedesign satisfies permissible stresses at all locations at both transfer and service loads.For this design example, stresses will be checked at midspan and at the ends, whichwill govern straight strand designs without debonding.

Compute concrete stress at the top fiber of the beam, ft:

Mg is based on overall length of 30 ft

Mg = wL2/8 = 1.513(30)2/8 = 170.2 ft-kips

ft =

= 0.858 - 0.882 + 0.182 = 0.158 ksi

Compare with permissible values:

– 0.190 ksi < 0.158 ksi < 2.400 ksi O.K.

Compute concrete stress at the bottom fiber of the beam fb:

=

= 0.858 + 0.882 - 0.182 = 1.558 ksi

Compare with permissible values:

-0.190 ksi < 1.558 ksi < 2.400 ksi O.K.

1 2461 452

1 246 7 9611 248

170 2 1211 248

,,

( , )( . ),

. ( ),

+ −

fPA

P eS

M

Sbsi si c

b

g

b

= − +

1 2461 452

1 246 7 9611 248

170 2 1211 248

,,

( , )( . ),

. ( ),

− +

fPA

P eS

M

Stsi si c

t

g

t

= − +

8 6202 5

100.

.

31 8202 5

100 15 7..

. %

=


RAILROAD BRIDGES17.7.8.1.5 Total Losses at Service Loads/17.7.9.1 Stresses at Transfer at Midspan

SEPT 01

17.7.9 Concrete Stresses

17.7.9.1 Stresses at Transfer

at Midspan

17.7.8.1.5 Total Losses at Service Loads

17.7.8.2Total Losses at Service Loads


Stresses should be checked at the end of the transfer length when designing a pre-stressed beam (see Section 9.1.8.2 for an example of this check). However, in thisdesign example, a standard beam design is being checked. Therefore it is conserva-tive to check the stresses at the very end of the member, assuming the full prestressforce is effective at that location. Since the strands are straight and all strands arebonded for the full length of the beam, the concrete stresses at the end are simply thestresses at midspan without the stress due to dead load moment.

ft = -0.023 ksi, which is within permissible values shown above O.K.

fb = 1.740 ksi, which is within permissible values shown above O.K.

Compute concrete stress at the top fiber of the beam, ft:

=

= 0.755 - 0.776 + 1.428 = 1.407 ksi < 2.800 ksi O.K.

Compute concrete stress at the bottom fiber of the beam, fb:

=

= 0.755 + 0.776 - 1.428 = 0.103 ksi > 0.0 ksi O.K.

The prestress force is at its maximum value at release and service loads do not affectstresses at the end of the beam. Therefore, stresses at release will govern at the end ofthe beam, so there is no need to check stresses at the end at service loads.

In lieu of a more accurate determination of stress in pretensioning strands at nominalstrength, fps, based on strain compatibility, the following approximate value of fps isused:

, provided fse is greater than 0.5 fpu [AREMA Eq. 17-2]

where

fse = effective stress in pretensioning steel after losses

= 202.5 - 31.8 = 170.7 ksi > 0.5(270) = 135.0 ksi O.K.

f ff

fps pu p

pu

c

= −

′1 0 5. ρ

1 096 91 452

1 096 9 7 9611 248

1 338 1 1211 248

, .,

( , . )( . ),

, . ( ),

+ −

fPA

P eS

M M M

Sbse se c

b

g SDL LL I

b

= + −+ + +

1 096 91 452

1 096 9 7 9611 248

1 338 1 1211 248

, .,

( , . )( . ),

, . ( ),

− +

fPA

P eS

M M M

Stse se c

t

g SDL LL I

t

= − ++ + +


RAILROAD BRIDGES17.7.9.2 Stresses at Transfer at End/

17.7.10.1 Stress in Strands at Flexural Strength

SEPT 01

17.7.10 Flexural Strength

17.7.10.1 Stress in Strands at

Flexural Strength

17.7.9.3Stresses at Service

Load at Midspan

17.7.9.4Stresses at Service

Load at End

17.7.9.2 Stresses at

Transfer at End


rp =

where

Aps = total area of pretensioning steel in tension zone

= 36 (0.153) = 5.508 in.2

b = effective flange width = 7(12) = 84.0 in.

d = distance from extreme compression fiber to centroid of pretensioning force

= 30.5 - = 26.58 in.

Note: In many cases, strands near or above midheight are neglected when com-puting d for calculating the average stress in strands at flexural strength. This isbecause, at the flexural strength, the strands located higher in the cross-section willnot reach a strain (and stress) as high as the bottom strands. However, for this stan-dard beam design, the strands at midheight have been included as shown above. Astrain compatibility analysis (described in Sections 8.2.2.5 and 8.2.2.6) can be usedto compute the strain and stress in the strands at midheight. Such an analysis forthis beam indicates that the strands at midheight would reach a stress of approxi-mately 251 ksi, which is reasonable when compared with the stress, fps, computedbelow. The same analysis indicates that the strands in the bottom row would reacha stress of nearly 260 ksi. Therefore, in this case, incorporating the strands at mid-height has provided a reasonable result. If the strands at midheight are neglected,the strength of the section at midspan would prove to be inadequate.

rp =

fps =

Assuming a rectangular section, compute the reinforcement ratio as:

O.K. [AREMA Art. 17.5.4]

When the reinforcement ratio exceeds 0.30, design moment strength shall not betaken greater than the moment strength based on the compression portion of themoment couple.

Assuming beam acts as a rectangular section::

fMn = f [AREMA Eq. 17-3]

= f [AREMA Eq. 17-4]A f da2ps ps −

A f df

fps ps p

ps

c

1 0 6−

′. ρ

ρpps

c

f

f0.0907 0.30 ′ = = <0 00247 257 1

7 0. ( . )

.

270 1 0 5 0 002472707 0

−

=( . )( . ).

257.1 ksi

A

bd0.00247ps = =5 508

84 26 58.

( . )

32 2 5 4 15 2536

( . ) ( . )+

A

bdps


RAILROAD BRIDGES17.7.10.1 Stress in Strands at Flexural Strength/17.7.10.3 Design Moment Strength

SEPT 01

17.7.10.2Limits for Reinforcement

17.7.10.3Design Moment Strength


where

Mn = nominal moment strength of a section

f = strength reduction factor for flexure = 0.95 [AREMA Art.17.5.2]

a = [AREMA Art.17.5.4d]

Average depth of top flange = 6.5 in. > 2.83 in.

Therefore, rectangular section assumption is appropriate.

Using AREMA Eq. 17-4:

fMn = 0.95 = 2,821.2 ft-kips

Factored moment due to dead and live loads from Table 17.7.5.4-1 = 2,837.5 ft-kips.

Percentage over = = 0.58% (insignificant) say ok.

The total amount of prestressed and non-prestressed reinforcement should be ade-quate to develop an ultimate moment at the critical section at least 1.2 times thecracking moment, Mcr: fMn ≥ 1.2Mcr. The calculation (not shown here but similarto the calculation in Section 9.1.10.2) yields 2,821.2 ft-kips > 2,427.3 ft-kips O.K.

Final strand locations are shown in Figure 17.7.10.5-1

( , . , . ), .

( )2 837 5 2 821 2

2 821 2100

−

5 508 257 1 26 582 83

21

12. ( . ) .

.−

A f

f bin.ps ps

c0 85

5 508 257 10 85 7 84

2 83.

. ( . ). ( )( )

.′ = =


RAILROAD BRIDGES17.7.10.3Design Moment Strength/17.7.10.5 Final Strand Pattern

SEPT 01

17.7.10.5Final Strand Pattern

17.7.10.4 Minimum Reinforcement

Figure 17.7.10.5-1 Strand Pattern

17 Spaces @ 2" = 2'-10"

2'-1"

2 1/2"

6 Strands

4 Strands

32 Strands

4 1/2"3'-3 3/4"

1'-3 1/4"

4"10"1'-8"1'-4"

7'-0"

1'-8"10"4"

2 1/2"

2 1/2"

3"10"17 Spaces @ 2" = 2'-10"

Void Drains Drip

Note: Curbs and warkway not shown

3"

2'-1"

3 1/2"


Prestressed concrete members subjected to shear are designed so that

Vu £ f (Vc + Vs) [AREMA Eq. 17-8]

where

Vu = factored shear force at section considered

Vc = nominal shear strength provided by concrete

Vs = nominal shear strength provided by shear reinforcement

f = strength reduction factor for shear = 0.90 [AREMA Art. 17.5.2]

Per the AREMA Manual, Article 17.5.9b, the critical section for shear is located at adistance h/2 from face of support. In this design example, the critical section for shearis calculated from the centerline of the bearings since the pads are not rigid and havethe potential to rotate.

h/2 = 30.5/2 = 15.25 in. = 1.27 ft

(from Table 17.7.5.4-1)

The shear strength provided by concrete, Vc, can be calculated by using AREMAManual Eq. 17-9, provided that the effective prestress force is not less than 40% ofthe total tensile strength provided by the flexural reinforcement.

Vc = [AREMA Eq. 17-9]

where

Mu = factored bending moment at the section

= 1.4 = 525.4 ft-kips

bw = total web width = 5 + 8.5 + 5 = 18.5 in.

d = 26.58 in. > 0.8h = (0.8)(30.5) = 24.4 in.

Therefore, use d = 26.58 in.

[AREMA Art. 17.5.9c]

However, the maximum value of Vc is limited to:

< Vc = 368.9 NO GOOD

AREMA Manual Art. 17.5.9c allows higher values of Vc if a more detailed calculationis made. According to this method, Vc is the lesser of Vci or Vcw.

5 5 7 000 18 5 26 58 1 000 205 7f b d kipsc w′ = =, ( . )( . ) / , .

V 368.9 kipsc = +( ) =0 6 7 000 700 1 0 18 5 26 58 1 000. , ( . ) . ( . ) / ,

V dM

1.71 1.0, use 1.0u

u

= = >405 4 26 58525 4 12

. ( . ). ( )

26 6 24 553

194 5. . .+ + ( )

0 6 700. fV dM

b dcu

uw

′ +

V kipsu = 405 4.


RAILROAD BRIDGES17.7.11 Shear Design /17.7.11.2.1 Simplified Approach

SEPT 01

17.7.11 Shear Design

17.7.11.1 Required Shear Strength

17.7.11.2 Shear Strength Provided

by Concrete

17.7.11.2.1Simplified Approach

5844 Bridge Manual Ch 17.7 10/8/01 11:43 AM Page 13

where

Vci = nominal shear strength provided by concrete when diagonal crackingresults from combined shear and moment

Vcw = nominal shear strength provided by concrete when diagonal crackingresults from excessive principal tensile stress in web

Vci = [AREMA Eq. 17-10]

but not less than

where

VD = shear at section due to service dead load = Vg + VSDL = 20.0 + 18.4= 38.4 kips

Mcr = moment causing flexural cracking at section due to externally applied loads

=

where

fpe= compressive stress in concrete due to effective prestress force only, at theextreme fiber of section where tensile stress is caused by externally appliedloads

fpe =

= = 0.755 + 0.776 = 1.531 ksi

fd = stress due to unfactored dead load at extreme fiber of section where ten-sile stress is caused by externally applied loads

fd =

Mcr =

Vi = factored shear force at section due to externally applied loads occurringsimultaneously with Mmax = Vu - VD = 405.4 - 38.4 = 367.0 kips

Mmax = maximum factored moment at the section due to externally appliedloads = Mu - Mg - MSDL = 525.4 - 26.6 - 24.5 = 474.3 ft-kips

Vci = [AREMA Eq. 17-10]

= = 1,497.7 kips0 67 000

1 00018 5 26 58 38 4

367 0 1 854 0474 3

.,

,( . )( . ) .

. ( , . ).

+ +

0 6. f b d VV MMc w D

i cr

max

′ + +

6 7 0001 000

1 531 0 05511 248

12,

,. .

,+ −

=1,854.0 ft-kips

M M

S0.055 ksig SDL

b

+=

+( )=

26 6 24 5 12

11 248

. .

,

1 096 91 452

1 096 9 7 9611 248

, .,

, . ( . ),

+

PA

P eS

se se c

b

+

S f f fb c pe d6 ′ + −

1 7. f b dc w′

0 6. f b d VV MMc w D

i cr

max

′ + +


RAILROAD BRIDGES17.7.11.2.1 Simplified Approach/17.7.11.2.2 Calculate Vci

SEPT 01

17.7.11.2.2 Calculate Vci


but not less than

Therefore,

Vci = 1,497.7 kips

Vcw = [AREMA Eq. 17-11]

where

fpc = compressive stress in the concrete (after allowance for all pretension losses)at the centroid of cross section resisting externally applied loads

Vp = vertical component of effective prestress force at section

= 0 for straight strands.

Transfer length of strands = 50 strand diameters = 50(0.5) = 25 in. from end of beam.

Since the distance h/2 = 15.25 in. is closer to end of member than the end of thetransfer length of the prestressing strands, a reduced pretensioning force will be con-sidered when computing Vcw. [AREMA Art. 17.5.9c(2)(c)]

Effective prestress force at distance h/2 from centerline of the bearing,

Pse =

fpc =

Therefore,

Vcw =

Vc = lesser of Vci and Vcw

Vc = Vcw = 238.7 kips

[AREMA Eq. 17-8]

Required stirrup spacing is calculated as follows:

[AREMA Eq. 17-14]

where Av = area of shear reinforcement within a spacing, s

VA f d

ssv y=

VV

V 211.7 kipssu

c= − = − =φ

405 40 9

238 7.

..

3 5 7 0001 000

0 3 0 642 18 5 26 58 0. ,

,. ( . ) ( . )( . )+

+ = 238.7 kips

932 41 452

.,

= 0.642 ksi

15 25 6 00

251 096 9

. .( , . )

+( )= 932.4 kips

3 5 0 3. .f f b d Vc pc w p′ +

+

1 7 1 77 000

1 00018 5 26 58 69 9. .

,,

( . )( . ) .f b d kipsc w′ = =


RAILROAD BRIDGES17.7.11.2.2 Calculate Vci /17.7.11.3.2 Determine Stirrup Spacing

SEPT 01

17.7.11.2.3 Calculate Vcw

17.7.11.2.4 Calculate Vc

17.7.11.3 Calculate Vs and

Shear Reinforcement

17.7.11.3.1 Calculate Vs

17.7.11.3.2Determine Stirrup Spacing


Try two closed stirrups, which provides (4) # 4 bars,

Av = 4(0.20) in.2 = 0.80 in.2

Stirrups are provided at 4 in. spacing to satisfy the minimum flexural requirements ofthe top slab of the box beam. Calculations for the top slab flexural reinforcement arenot provided in this example.

Spacing required, s = O.K.

Use # 4 stirrups (4 legs) at 4-in. centers.

Av provided = 4(0.20) = 0.80 in.2

Shear strength provided by stirrups,

Vs = O.K.

Allowable maximum shear strength provided by stirrups is:

[AREMA Art. 17.5.9d(5)]

= 329.1 kips > Vs O.K.

Check for maximum spacing of stirrups

[AREMA Art. 17.5.9d(3)]

Therefore, maximum spacing is lesser of 3/8h = 3/8(30.5) = 11.4 in. or 12 in.

Provide # 4 stirrups (4 legs) at 4-in. centers < 11.4 in. O.K.

Calculations for shear at other sections along the beam are not provided in this example.

For shear reinforcement details, see Figures 17.7.4-1 and 17.7.11.3.4-1

4 47 000

1 00018 5 26 58f b d 164.6 kips Vc w s

′ = = <,,

( . )( . )

8 8 7 000 18 5 26 58 1 000f b dc w′ = , ( . )( . ) / ,

0 80 60 26 584

. ( )( . ) = >319.0 210.4 kips

A f d

V6.1 in. in.v y

s

= = >0 80 60 26 58210 4

4. ( )( . )

.


RAILROAD BRIDGES17.7.11.3.2 Determine Stirrup Spacing/17.7.11.3.4Check Stirrup Spacing Limits

SEPT 01

17.7.11.3.4Check Stirrup

Spacing Limits

17.7.11.3.3 Check Vs Limit

Figure 17.7.11.3.4-1Elevation Showing

Non-Prestressed Reinforcement shown for clarity#6 Bars at web notNote:

#6 Bars#4 Stirrups#4 Bar

(4) #4 End bars

(Typ.)

#6 Bars

Girder(Symm.)

2 1/4"

Spacing @ About 6" Centers11 Spaces @ 3 1/4"

LC 4" = 3'-8"


Camber and deflection calculations are required to determine the bridge seat eleva-tions and maintain the minimum ballast depth. They are also required for the designof the elastomeric bearings.

= - 0.223 in. ≠

= 0.037 in. Ø

= 0.025 in Ø

According to PCI Design Handbook - 5th Edition, Table 4.8.2, long-term camber anddeflection of prestressed concrete members can be calculated by an approximate methodusing multipliers. Calculations are shown in Table 17.7.12.4-1.

Live load deflection is generally calculated using influence lines. At this point, use ofa computer program becomes very useful. However, for short span bridges, thedesigner can quickly calculate an approximate value for deflection by using the equiv-alent uniform load. The equivalent uniform live load, wequ, for a simply supportedbeam can be derived from the maximum moment at midspan,

MLL + I =

wequ =

D = Ø

Maximum allowable deflection =

= [AREMA Art. 17.6.7a]29 12640

( ) = 0.544 in. > 0.180 in. O.K.

L640

5 0 819 29 12

384 5 072 171 535

4( . ) ( )

( , )( , )

( )= 0.180 in.

8M

L0.819 kip/in.LL I

2+ =

( )=8 1 033 0 12

29 122

( , . )( )

( )

w L

8equ

2

∆ = =( )5wL

384E I

4

c

5 1 389 12 29 12

384 5 072 171 535

4( . / ) ( )

( )( , )( , )

∆ = =( )5wL

384E I

4

ci

5 1 513 12 29 12

384 3 834 171 535

4( . / ) ( )

( )( , )( , )

∆ = = −( )P e L

8E Isi c

2

ci

1 219 7 7 96 29 12

8 3 834 171 535

2, . ( . ) ( )

( , )( , )


RAILROAD BRIDGES17.7.12 Deflections/17.7.12.5 Deflection Due to Live Load

SEPT 01

17.7.12 Deflections

17.7.12.1 Camber Due to

Prestressing at Transfer

17.7.12.2 Deflection Due to Beam Self-Weight at Transfer

17.7.12.3 Deflection Due to

Superimposed Dead Load

17.7.12.5 Deflection Due to Live Load

17.7.12.4 Long-Term Deflection

Table 17.7.12.4-1Calculated Deflection, in.

At Release(a)

Multiplier(b)

Erection(c) = (a)(b)

Multiplier(d)

Final(e) = (a)(d)

Prestress − 0.223 1.80 − 0.401 2.45 − 0.546Self-Weight + 0.037 1.85 + 0.068 2.70 + 0.100Dead Load N/A + 0.025 3.00 + 0.075*Total − 0.186 − 0.308 − 0.371

* This is the result of multiplying the dead load deflection at erection (c) by multiplier (d)

↑

↑

↓↑

↑

↓↓

↑

↑

↓↓


AREMA Manual for Railway Engineering, 2000 Edition, American RailwayEngineering and Maintenance-of-Way Association, Landover, MD, 2000

Marianos, W. N., Jr., “Railroad Use of Precast Concrete Bridge Structures,” ACIConcrete International, V. 13, No. 9, September 1991, pp. 30-35

PCI Design Handbood, Fifth Edition, Precast/Prestressed Concrete Institute, Chicago,IL, 1999, 690 pp.


RAILROAD BRIDGES17.8 References

DEC 00

17.8 REFERENCES


railway bridge

Documents

cf

sf

american railway

american railway

unfactored

superimposed

extreme top

extreme bottom