Railway Bridge

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CHAPTER 17

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TABLE OF CONTENTS RAILROAD BRIDGES NOTATION 17.0

INTRODUCTION

17.1

TYPICAL PRODUCTS AND DETAILS 17.1.1 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 CONSIDERATIONS 17.2.1 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-WAY ASSOCIATION 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 PRACTICE 17.4.1 New Bridges 17.4.2 Replacement Bridges 17.4.3 Simple Span Bridges 17.4.4 Skew Bridges

17.5

CASE 17.5.1 17.5.2 17.5.3 17.5.4 17.5.5 17.5.6

STUDY NO. 1—TRUSS BRIDGE REPLACEMENT Existing Bridge New Piles New Intermediate Piers New Superstructure for Approach Spans Truss Removal New Superstructure for Truss Spans

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TABLE OF CONTENTS RAILROAD BRIDGES 17.6

CASE 17.6.1 17.6.2 17.6.3 17.6.4

STUDY NO. 2—TIMBER TRESTLE REPLACEMENT Existing Bridge New Superstructure Substructure Construction Superstructure Construction

17.7

DESIGN EXAMPLE—DOUBLE-CELL BOX BEAM, SINGLE SPAN, NONCOMPOSITE, DESIGNED IN ACCORDANCE WITH AREMA SPECIFICATIONS 17.7.1 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 17.7.5.4 Load Combinations 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

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TABLE OF CONTENTS RAILROAD BRIDGES 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

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NOTATION RAILROAD BRIDGES A Ac Aps Aps Av Avh a B b be bv bw CF D DF d E Ec Eci Es Es EQ e ec F fb f ´c fcds f ´ci fcr fd flc fle flr fls fpc fpe

fps

= area of cross-section of precast beam = total transformed area of composite section = area of one pretensioning strand or post-tensioning bar = area of strands in the tensile zone = area of shear reinforcement = area of web reinforcement per unit length required for horizontal shear = compression block depth = buoyancy = width of compression face of member = top flange width of precast beam = width of cross section at the contact surface being investigated for horizontal shear = width of web of a flanged member = centrifugal force = dead load = live load distribution factor = distance from extreme compressive fiber to centroid of the prestressing force = earth pressure = modulus of elasticity of concrete at 28 days = modulus of elasticity of concrete at transfer = modulus of elasticity of pretensioning steel = modulus of elasticity of non-pretensioned reinforcement = earthquake (seismic) = eccentricity of strands at transfer length = eccentricity of strands at midspan = longitudinal force due to friction or shear resistance at expansion bearings = concrete stress at the bottom fiber of the beam = specified concrete strength at 28 days = concrete stress at the centroid of the pretensioning steel due to all dead loads except the dead load present at the time the pretensioning force is applied = specified concrete strength at transfer = stress in the concrete at the centroid of the pretensioning steel = stress due to unfactored dead load, at extreme fiber of section where tensile stress is caused by externally applied loads = loss of prestress due to creep of concrete = loss of prestress due to elastic shortening = loss of prestress due to relaxation of pretensioning steel = loss of prestress due to concrete shrinkage = compressive stress in concrete (after allowance for all prestress losses) at the centroid of cross section resisting externally applied loads = compressive stress in concrete due to effective pretensioning forces only (after allowance for all pretension losses) at the extreme fiber of section where tensile stress is caused by externally applied loads = stress in the pretensioning steel at nominal strength SEPT 01

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NOTATION RAILROAD BRIDGES fpu fse ft ftc fy h hc I I ICE Ic L L LF M Mcr MD Md Mg MLL+I Mmax Mn MSDL Mu Mx n OF Peff Pse Psi R Sb Sbc St Stc Stg SF s V Vc

= ultimate tensile strength of pretensioning steel = effective stress in pretensioning steel after losses = concrete stress at the top fiber of the precast beam = concrete stress at top of fiber of the slab for the composite section = specified yield strength of non-prestressed reinforcement = overall depth of precast beam = total height of composite section = moment of inertia about the centroid of the non-composite precast beam = the percentage of the live load for impact = ice pressure = moment of inertia of composite section = span length = live load = longitudinal force from live load = maximum service load design moment = moment causing flexural cracking at section due to externally applied loads = unfactored bending moment due to total dead load = unfactored bending moment due to composite beam dead load = unfactored bending moment due to precast beam self-weight = unfactored bending moment due to live load + impact = maximum factored moment at the section due to externally applied loads = nominal moment strength of a section = unfactored bending moment due to superimposed dead load = factored bending moment at the section = bending moment at a distance x from the support = modular ratio of elasticity between slab and beam materials = other forces (rib shortening, shrinkage, temperature and/or settlement of supports) = effective post-tensioning force = effective pretension force after allowing for all losses = total pretensioning force immediately after transfer = relative humidity = non-composite section modulus of the extreme bottom fiber of the precast beam = composite section modulus for extreme bottom fiber of the precast beam = non-composite section modulus of the extreme top fiber of the precast beam = composite section modulus for extreme top fiber of the slab = composite section modulus for top fiber of the precast beam = stream flow = spacing of the shear reinforcement in direction parallel to the longitudinal reinforcement = service load shear force = nominal shear strength provided by concrete

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NOTATION RAILROAD BRIDGES Vci Vcw VD Vd Vg Vi VLL+I Vp Vs VSDL Vu Vx vdh W WL w wc wequ x yb ybc ybs yt ytc ytg D f rp y

= nominal shear strength provided by concrete when diagonal cracking results from combined shear and moment = nominal shear strength provided by concrete when diagonal cracking results from excessive principal tensile stress in web = unfactored shear force at section due to total dead load = unfactored shear force due to composite beam dead load = unfactored shear force due to precast beam self-weight = factored shear force at section due to externally applied loads occurring simultaneously with Mmax = unfactored shear force at section due to live load plus impact = component of pretensioning force in the direction of the applied shear = nominal shear strength provided by shear reinforcement = unfactored shear force due to superimposed dead loads = factored shear force at the section = shear force at a distance x from the support = horizontal shear stress = wind load on structure = wind load on live load = weight per foot = unit weight of concrete = equivalent uniform load = distance from the support = distance from centroid to extreme bottom fiber of the non-composite precast beam = distance from the centroid of the composite section to extreme bottom fiber of the precast beam = distance from the center of gravity of strands to the bottom fiber of the beam = distance from centroid to extreme top fiber of the non-composite precast beam = distance from the centroid of the composite section to the extreme top fiber of the slab = distance from the centroid of the composite section to extreme top fiber of the precast beam = deflection = strength reduction factor = ratio of pretensioning reinforcement = angle of harped pretensioned reinforcement

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Railroad Bridges

17.0 INTRODUCTION

Precast concrete is playing an increasingly important role in railroad bridge structures. The economy, durability and speed of construction make precast concrete the material of choice for new and replacement railroad bridges. The focus of this chapter is on the specific requirements and guidelines for railroad bridges. Typical products and details, construction considerations, and identification of applicable AREMA (American Railway Engineering and Maintenance-of-Way Association, formerly AREA) provisions are also discussed. Two case studies and a railroad superstructure design example are presented.

17.1 TYPICAL PRODUCTS AND DETAILS

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

17.1.1 Piles

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

17.1.2 Pile Caps and Abutments

Precast concrete pile caps are widely used throughout the country. Typically, these are fabricated with an embedded plate running along the bottom of the cap. This allows welding of steel piles to the bottom of the cap. Concrete pile caps are sometimes used to support steel or timber beams, as well as concrete beams. Some railroads are now beginning to use precast concrete caps with precast concrete piles. The caps are cast with a socket for the pile to fit into. Grouting is used to tie the components together after installation. Bridge abutments can also be prefabricated. The bases of these abutments are similar to the pile caps and serve the same function of supporting the superstructure. Abutment backwalls and wingwalls can be precast in sections and bolted or welded together in the field.

17.1.3 Superstructures

Railroads use a wide variety of superstructure elements. Spans typically range from 12 ft to over 80 ft. Since many precast concrete spans are installed to replace timber trestles, standard span lengths for a given railroad are frequently multiples of their standard timber stringer span lengths (typically 14 to 16 ft). For spans of 12 ft to 20 ft, 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 Ibeams are occasionally used. For spans over 30 ft, box beams are dominant. Spans up to 50 ft typically use two box beams per track. Generally, these are double celled with through-voids. Through-voids allow fabricators to use removable and reusable void forms in casting the beams. This helps reduce costs. Spans over 50 ft generally use four single-void box beams per track. The shift from two beams per track on shorter spans to four on longer spans is dictated by the lifting restrictions associated with the SEPT 01

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heavier weight of the longer beams. Shear keys and transverse post-tensioned steel tie rods are frequently used to tie the box beams together with diaphragms provided at the location of the tie rods. For spans greater than 70 to 80 ft, beams with composite cast-in-place concrete decks are frequently used. 17.1.3.1 Slab Beams and Box Beams

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

Figure 17.1.3.1-1 Typical Precast Concrete Superstructure Shapes

7'-0" Varies from 1'-2" to 1'-8" Slab Beam Spans 12' to 20' 3'-6"

7'-0" Varies from 2'-6" to 4'-0"

Varies from 2'-6" to 7'-0" Single Cell Box Spans 20' to 80' 17.1.3.2 Other Products

Double Cell Box Spans 20' to 50'

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

Figure 17.1.3.2-1 Tee Beam (Intermediate and Long Spans)

Tee Beam (Intermediate Span)

Super Tee (Long Span)

Precast Cap

Steel Piling w/Welded Plate Connection to Pile Cap

The solid single tee beam is used for spans of 20 to 34 ft, and the voided super tee for spans up to 55 ft in length. Both beams are set on a precast concrete cap that has a welded plate connection to the piles as needed. SEPT 01

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Figure 17.1.3.2-2 Box Beam (Intermediate Spans)

Optional Curb

Closed Ended Voided Box Beam

Open Ended Voided Box Beam

Precast Cap

Steel Piling w/Welded Plate Connection to Pile Cap

24" Octagonal Prestressed Piling w/C.I.P. Cap

Voided box beams are used on 20- to 50-ft long spans, with optional diaphragms and curbs. Boxes may be set on precast or cast-in-place concrete caps with piling. Figure 17.1.3.2-3 Low Profile Slab (Short Spans)

Optional Curb

Concrete Keeper

Low Profile Slabs Steel Keeper Precast Cap

Steel Piling w/Welded Plate Connection to Pile Cap

Precast Prestressed Cap

Timber Piling

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

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RAILROAD BRIDGES 17.1.3.2 Other Products/17.1.3.3 Connection Details

Figure 17.1.3.2-4 Ballast Deck (With Steel Beams)

Integral Walkway

Precast Ballast Deck on Steel Beam Steel Beams

Precast Cap

Steel Piling w/Welded Plate Connection to Pile Cap

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 ballast curbs and with integral walkways to further speed up construction of the bridge. 17.1.3.3 Connection Details

Figure 17.1.3.3-1 Steel Tee between Box Beams

Structural steel tees or plates are frequently used to cover the longitudinal joint in slab beams and double-cell box beams as shown in Figure 17.1.3.3-1. Transverse posttensioned steel tie rods, as shown in Figure 17.1.3.3-2, are generally provided in multiple 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 of the caps to limit lateral movement, as shown in Figure 17.1.3.3-3. Designers should contact the specific railroad to determine their standards and preferred connection details.

Steel Tee

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Figure 17.1.3.3-2 Post-Tensioned Steel Tie Rod

Post-Tensioned Steel Tie Rod

Diaphragm

Bearing Plate

Figure 17.1.3.3-3 Concrete and Steel Keeper Details

Concrete Keeper

Steel Keeper

Pile Cap

17.2 CONSTRUCTION CONSIDERATIONS 17.2.1 Advantages

Precast concrete offers many advantages in the construction of railroad bridges. These include: • Speed of construction—Precast concrete structures can usually be constructed faster than bridges comprised of alternative materials. • Fabrication time—In addition to saving construction time, the lead time for fabricating elements is shorter than for competing materials such as steel.

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RAILROAD BRIDGES 17.2.1 Advantages/17.2.5 Substructures

• Durability—Compared with many older structures that require frequent inspections and maintenance, railroad engineers find the low maintenance requirements of precast concrete attractive. Use of concrete with low permeability and strict quality control in the casting plant help assure durable bridge components. • Quality—The higher quality control of workmanship and materials available in casting plants compared to cast-in-place construction is another plus. Railroads can work with precast suppliers to ensure that members are cast to their satisfaction. • Site constraints—The remote locations of many railroad bridges make the “precast” aspect of precast construction very useful. When the nearest ready-mix plant is many miles away from the site, cast-in-place construction within a railroad’s time constraints is virtually impossible. • Emergency response—Precast concrete bridge elements provide components for rapid repair of bridges as a result of damage caused by derailments or timber trestle fires. Several railroads keep entire precast bridges stockpiled for rapid emergency replacement. Concrete bridges are less vulnerable to damage from fire compared to steel or timber bridges. 17.2.2 Standard Designs

Most railroads have standard precast concrete trestle bridge designs that incorporate repetition of modular precast units. These standard designs are used for replacement of existing bridges, as well as construction of new bridges. Railroads and contractors familiar with railroad bridge construction have developed low-cost methods of trestle bridge construction. These methods minimize the time that railroad operations must be suspended. 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.

17.2.3 Train Operations

For construction of bridges, railroads normally only permit train operations to be suspended 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 railroad and using the other railroad’s personnel. Use of either option is dependent upon the type and density of train traffic and the availability of alternate routes.

17.2.4 Construction Methods

The various methods used to construct railroad bridges to support existing trackage while 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 the amount of time that would be required to construct the new bridge piece by piece in its permanent location.

17.2.5 Substructures

In many bridges, the existing substructure is reused and, if necessary, modified for replacement of the superstructure. Sometimes, the bridge may require new substructure elements. In both cases, the substructure work is performed beneath the existing SEPT 01

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track and superstructure so that the track is out of service for only very limited periods while driving piles or placing temporary supports. For replacement of existing bridges utilizing this method, ballast removal, as well as relocating the decks and beams 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 construction due to reduced load carrying capacity resulting from relocating the decks and beams. Precast concrete beams are usually installed using pick and set methods. This method requires access to the bridge construction site for cranes that have adequate capacity to lift the beams. A typical bridge replacement procedure is illustrated in Figure 17.2.5-1. Figure 17.2.5-1 Typical Bridge Replacement Construction Sequence

SUSPEND 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

REMOVE EXISTING SUPERSTRUCTURE

INSTALL NEW PRECAST CONCRETE SUPERSTRUCTURE ON BENT CAPS

RECONNECT TRACK

SURFACE AND ALIGN TRACK

RESUME TRAIN OPERATIONS

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RAILROAD BRIDGES 17.3 The American Railway Engineering And Maintenance-of-Way Association Load Provisions/17.3.2.1 Live Load

17.3 THE AMERICAN RAILWAY ENGINEERING AND MAINTENANCEOF-WAY ASSOCIATION LOAD PROVISIONS

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

17.3.1 AREMA Manual

The AREMA Manual provides the recommended practice for railroads and others concerned with the engineering, design and construction of railroad fixed properties, allied services and facilities. Prior to starting the design of a project, design engineers should discuss specific loadings, forces, standards and procedures with the appropriate railroad.

17.3.2 AREMA Loads

The AREMA Manual Chapter 8, Concrete Structures and Foundations, specifically addresses reinforced concrete and prestressed concrete structures. Article 2.2.3 covers the design loads and forces to be considered in the design of railroad structures supporting tracks, including bridges. Briefly, design loads include: D L I CF E B W WL LF

17.3.2.1 Live Load

= Dead Load = Live Load = Impact = Centrifugal Force = Earth Pressure = Buoyancy = Wind Load on Structure = Wind Load on Live Load = Longitudinal Force from Live Load

= 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/or Settlement of Supports) F

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

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

52,000 52,000 52,000 52,000

80,000 80,000 80,000 80,000

40,000

52,000 52,000 52,000 52,000

80,000 80,000 80,000 80,000

Figure 17.3.2.1-1 Cooper E 80 Load

40,000

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 track is the Cooper E 80 load, which is shown in Figure 17.3.2.1-1. Table 17.3.2.1-1 provides a table for live load bending moments, shear forces and reactions for simple span bridges. Values for span lengths not shown are generally computed by interpolation. (2) The Engineer (the Railroad’s Chief Engineer) shall specify the Cooper live load to be used, and such load shall be proportional to the recommended load, with the same axle spacing. (3) For bridges on curves, provisions shall be made for the increased proportion carried by any truss, beam or stringer due to the eccentricity of the load and centrifugal force.

8,000 lb per lin ft

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(4) For members receiving load from more than one track, the design live load on the tracks 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 onequarter 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 critical design 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) All values are for one rail (one-half track load)

Span Length ft

Maximum Bending Moment ft-kips

Maximum Bending Moment at Quarter Point ft-kips

End

5 6 7 8 9 10 11 12 13 14 16 18 20 24 28 32 36 40 45 50 55 60 70 80 90 100

50.00 60.00 70.00 80.00 93.89 112.50 131.36 160.00 190.00 220.00 280.00 340.00 412.50 570.42 730.98 910.85 1,097.30 1,311.30 1,601.20 1,901.80 2,233.10 2,597.80 3,415.00 4,318.90 5,339.10 6,446.30

37.50 45.00 55.00 70.00 85.00 100.00 115.00 130.00 145.00 165.00 210.00 255.00 300.00 420.00 555.00 692.50 851.50 1,010.50 1,233.60 1,473.00 1,732.30 2,010.00 2,608.20 3,298.00 4,158.00 5,060.50

40.00 46.67 51.43 55.00 57.58 60.00 65.45 70.00 73.84 77.14 85.00 93.33 100.00 110.83 120.86 131.44 141.12 150.80 163.38 174.40 185.31 196.00 221.04 248.40 274.46 300.00

Maximum Shear Forces kips Quarter Point 30.00 30.00 31.43 35.00 37.78 40.00 41.82 43.33 44.61 47.14 52.50 56.67 60.00 70.00 77.14 83.12 88.90 93.55 100.27 106.94 113.58 120.21 131.89 143.41 157.47 173.12

Midspan

20.00 20.00 20.00 20.00 20.00 20.00 21.82 23.33 24.61 25.71 27.50 28.89 28.70(1) 31.75 34.29 37.50 41.10 44.00 45.90 49.73 52.74 55.69 61.45 67.41 73.48 78.72

Maximum Pier Reaction kips

40.00 53.33 62.86 70.00 75.76 80.00 87.28 93.33 98.46 104.29 113.74 121.33 131.10 147.92 164.58 181.94 199.06 215.90 237.25 257.52 280.67 306.42 354.08 397.70 437.15 474.24

(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.

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RAILROAD BRIDGES 17.3.2.2 Impact Load/17.3.2.4 Load Combinations

17.3.2.2 Impact Load

For reinforced concrete (precast and cast-in-place), the impact load is a percentage of the live load based on the ratio of live load to live load plus dead load: 100L [AREMA Eq. 2-1] L +D The impact load shall not exceed 60% for diesel engines and 80% for steam engines. I=

For prestressed concrete, the impact load is a percentage of the live load based on span 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 17.3.2.3 Other Loads

All other loads and forces are defined similarly to highway bridges although the magnitudes are different. The design engineer should refer to the AREMA Manual for additional information.

17.3.2.4 Load Combinations

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

Table 17.3.2.4-1 Group Loading Combinations— Service Load Design

Table 17.3.2.4-2 Group Loading Combinations— Load Factor Design

Group

Item

I II III IV V VI VII VIII IX

D + L + I + CF + E + B + SF D + E + B + SF + W Group I + 0.5W + WL + LF + F Group I + OF Group II + OF Group III + OF D + E + B + SF + EQ Group I + ICE Group II + ICE

Allowable Percentage of Basic Unit Stress 100 125 125 125 140 140 133 140 150

Group

Item

I IA II III IV V VI VII VIII IX

1.4 (D + 5/3(L + I) + CF + E + B + SF) 1.8 (D + L + I + CF + E + B + SF) 1.4 (D + E + B + SF + W) 1.4 (D + L + I + CF + E + B + SF + 0.5W + WL + LF + F) 1.4 (D + L + I + CF + E + B + SF + OF) Group II + 1.4 (OF) Group III + 1.4 (OF) 1.4 (D + E + B + SF + EQ) 1.4 (D + L + I + E + B + SF + ICE) 1.2 (D + E + B + SF + W + ICE) SEPT 01

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RAILROAD BRIDGES 17.4 Current Design Practice/17.4.3 Simple Span Bridges

17.4 CURRENT DESIGN PRACTICE

As with all engineering design practices, railroad industry practice continues to change as experience and research is incorporated into the AREMA Manual and individual railroad company standards and procedures. This section will discuss current railroad industry practice relative to overall railroad bridge design philosophy, skew limitations and superstructure continuity. Designers should discuss philosophies, standards and procedures with the specific railroad as applicable to the project.

17.4.1 New Bridges

New railroad bridges are constructed to support railroad tracks over existing waterways, roadways, and other railroads. In addition, new railroad bridges are built to replace 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

17.4.2 Replacement Bridges

The large majority of railroad bridge projects usually involve existing trackage. Consequently, one of the most important considerations for the railroad bridge designer is to design the bridge such that construction will have minimal disruption to train operations. This affects design details, construction methods and project costs. Much of today’s rail traffic is under contract with the customer and the contract often includes a guarantee of service between origin and destination. Penalties and possible loss of a contract can result if unreasonable delays in the agreed upon schedule are experienced. Taking a track out of service or reducing the speed of rail traffic for an extended period of time for bridge construction can have a detrimental economic effect on the railroad. The project must be properly planned and coordinated with the operating and marketing departments of the railroad during the design and construction phases. The use of standardized precast components speeds both the design and construction of bridges. Replacement spans can be specified by length alone, and railroad bridge workers are familiar with the sections and construction procedures. Since the vast majority of precast concrete bridges have all the superstructure below track level, vertical and horizontal clearance is not limited by these structures. This allows wide cargo or double stack containers to be shipped without clearance concerns and reduces the threat of bridge damage caused by shifted loads.

17.4.3 Simple Span Bridges

Many railroads prefer simple span bridges to continuous structures, finding them easier to install and maintain. Since they are structurally determinate, simple spans are better able to handle problems such as support settlement and thermal effects than some continuous bridges. Precast concrete elements are particularly suited to simplespan construction. Additional reasons many railroads prefer simply supported bridges to continuous span bridges include the following: • If repair or replacement of superstructure elements is necessary, less interruption to train traffic is incurred with a simple span bridge than with a continuous span bridge. • Installation of simple spans can be accomplished more quickly than continuous spans. SEPT 01

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RAILROAD BRIDGES 17.4.3 Simple Span Bridges/17.5.3 New Intermediate Piers

• If a bridge experiences substructure problems such as settlement, a continuous span bridge may require immediate and more extensive work, thereby resulting in greater interruptions to train traffic. • Simple span bridges have a proven history of performing well. 17.4.4 Skew Bridges

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

Figure 17.4.4-1 Layouts for Skewed Bridges

Skew ≤ 30°

Skew > 30° 17.5 CASE STUDY NO. 1— TRUSS BRIDGE REPLACEMENT 17.5.1 Existing Bridge

This case study describes a Southern Pacific railroad truss bridge replacement (Marianos, 1991). This project illustrates the use of precast concrete elements to replace a structure without serious interruption to rail traffic. The existing structure consisted of a 90-ft long timber trestle approach, two 154-ft long through-truss spans and a 30-ft long plate-girder approach span. The truss spans were nearly 90 years old and were at the end of their useful service lives due to joint wear. Since the truss spans required replacement, the railroad decided to replace the entire bridge with precast concrete.

17.5.2 New Piles

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

17.5.3 New Intermediate Piers

Since the truss spans crossed a creek subject to high flood flows, it was essential to minimize obstruction of the waterway. For this reason, new intermediate piers with four 79-ft long precast, prestressed box beams replaced the two 154-ft long truss spans. The 79-ft long beams were beyond the span range of the railroad standards and required a new design. SEPT 01

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RAILROAD BRIDGES 17.5.3 New Intermediate Piers/17.5.5 Truss Removal

Railroad crews built intermediate piers at midspan of each truss by driving piles through the existing truss floor systems, and the 79-ft long box beams were ordered and fabricated. 17.5.4 New Superstructure for Approach Spans

When the substructure was completed, superstructure replacement began. The 90-ft long 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 each span. Each box beam has two through-voids and an integral ballast retaining sidewall and walkway cast on the outside edge. A shear key between the box beams helped ensure load distribution between the two beams. The box beams were placed using a track-mounted crane. A similar 30-ft long box beam span was used to replace the steel plate-girder span on the approach opposite the timber trestle. Precast concrete bolster blocks were used on top of the existing masonry piers to obtain the proper elevation because the new structure was shallower than the existing one.

Figure 17.5.4-1 Precast 30-ft Approach Span on Precast Bolster Blocks

17.5.5 Truss Removal

After the approach spans were completed, preparation began for replacing the truss spans. An area under the truss spans was filled with ballast and leveled. Railroad track panels were laid perpendicular to the bridge on the fill below the structure. Steel frames mounted on rail trucks were placed on these tracks and used to support the trusses for removal. With these preparations for truss replacement complete, a carefully orchestrated construction effort began.

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RAILROAD BRIDGES 17.5.5 Truss Removal/17.5.6 New Superstructure for Truss Spans

First, the truss ends were jacked up to lift them off the pier. The truss was then secured to the steel frames and rolled laterally clear of the work area, as shown in Figure 17.5.5-1. The construction crew then finished preparations on the pier top for placing the precast, prestressed concrete box beams. This work included removing the remaining truss attachments and placing elastomeric bearing pads. Figure 17.5.5-1 Roll-Out of Truss Span to be Replaced

17.5.6 New Superstructure for Truss Spans

Each 154-ft long steel truss was replaced by two spans of precast box beams. When the pier preparation was completed, the four box beams of the first span were lifted into position using truck cranes. While workmen epoxied the longitudinal joints and shear keys between these beams, the box beams for the second span were being placed. After the joints of both spans were epoxied and handrail cables strung along the walkways, prefabricated panels of railroad track were placed on the spans. This allowed 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 rail traffic. 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 and economical replacement of the structure, using the railroad’s own work force.

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RAILROAD BRIDGES 17.5.6 New Superstructure for Truss Spans/17.6.2 New Superstructure

Figure 17.5.6-1 Completed Structure

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

This case study discusses a timber trestle bridge replacement on the Union Pacific Railroad system. Bridge 177.81 is located approximately 1.59 miles west of Marysville, 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 steel plate-girder span over the Yuba River. The plate-girder was to remain in place and the timber trestle portion of the bridge was to be replaced.

Figure 17.6.1-1 Existing Plate-Girder and Timber Trestle Spans.

17.6.2 New Superstructure

Due to the volume of rail traffic and importance of on-time delivery by the Union Pacific Railroad, minimal disruption to train operations was mandatory. Substructure construction was to be performed without interference or downtime to the railroad. Superstructure change-out would be performed during “windows” approved by the railroad. A precast, prestressed concrete superstructure system was selected based on economics, speed of erection and the ability to meet the construction constraints associated with the need for minimal disruption to train operations. SEPT 01

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RAILROAD BRIDGES 17.6.2 New Superstructure/17.6.3 Substructure Construction

The existing timber trestle spans varied in length with an average span of slightly less than 15 ft. Based on a field survey of the timber bent locations, new bent locations were selected to minimize interference with existing timber pile bents and optimize beam spans. A span length of 44 ft was selected for the new superstructure. For this span length, 45-in. deep double-cell, prestressed concrete box beams were determined to be the most economical structural system. 17.6.3 Substructure Construction

Based on field conditions, prevalent construction practice in the area and construction constraints governed by railroad operations, cast-in-place reinforced concrete bents were selected for the substructure. The bents consisted of 100-ft long, 4-ft diameter drilled shafts, 4-ft diameter cast-in-place reinforced concrete column extensions and cap beams. All structural components were designed in accordance with the AREMA 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 facilitate drilled shaft installation. The drilled shafts were spaced at 15-ft centers perpendicular to the track to allow installation of the drilled shafts without interference to railroad operations. Continuous train operations were maintained throughout the entire construction of the substructure. Due to foundation conditions, steel pipe casing was necessary for drilled shaft installation. The pipe casing was installed using a vibratory hammer. Reinforcing steel cages were set and the holes were filled with 4,000 psi compressive strength concrete. Drilled shaft column extensions, bent cap beams and the abutment were constructed under the existing timber superstructure. Due to the depth of the new concrete beams, the bent and abutment construction were completed without interfering with the existing timber superstructure, as shown in Figure 17.6.3-1.

Figure 17.6.3-1 Completed Concrete Bents under Existing Timber Trestle

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RAILROAD BRIDGES 17.6.4 Superstructure Construction

17.6.4 Superstructure Construction

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

Figure 17.6.4-1 Completed Bridge Structure

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RAILROAD BRIDGES 17.7 Design Example—Double-Cell Box Beam, Single Span, Non-Composite, Designed in Accordance with AREMA Specifications/17.7.2 Introduction

17.7 DESIGN EXAMPLE— DOUBLE-CELL BOX BEAM, SINGLE SPAN, NONCOMPOSITE, DESIGNED IN ACCORDANCE WITH AREMA SPECIFICATIONS 17.7.1 Background

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

17.7.2 Introduction

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. The beams are assumed to be fully prestressed under service load conditions. The dead load consists of the self-weight of the beam including diaphragms. The superimposed dead loads consist of ballast, ties, rails, concrete curbs and handrails, as shown in Figures 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 Concrete Design, Article 2.2.3. The prestressed concrete beams are designed using the AREMA Manual, Chapter 8, Part 17, Prestressed Concrete Design Specifications for Design of Prestressed Concrete Members. The beams in this example are checked for both serviceability and strength requirements.

Figure 17.7.2-1 Bridge Cross-Section

C L Track & Bridge 8'-0" Min. Clear

Timber ties

Ballast

3'-10 7/8"

8'-0" Min. Clear Handrail post (Typ.)

Precast curb and walkway

30" Prestressed concrete box beam

8" Min. 1/2" Gap 7'-0"

7'-0"

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

Steel tee (Typ.)

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RAILROAD BRIDGES 17.7.2 Introduction/ 17.7.2.2 Sign Convention

Figure 17.7.2-2 Bridge Elevation

30'-1" Face to face of backwalls

Well compacted granular fill Cast-in-place abutment CL Abutment No.1 17.7.2.1 Geometrics

17.7.2.2 Sign Convention

30" prestressed concrete box beam Flow line

Cast-in-place abutment CL Abutment No.2

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)

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RAILROAD BRIDGES 17.7.2.3 Level of Precision/17.7.3.2 Pretensioning Strands

17.7.2.3 Level of Precision

Item Concrete Stress Steel Stress Prestress Force Moments Shears For the Beam: Cross-Section Dimensions Section Properties Length Area of Prestressing Steel Area of Mild Reinforcement

Units ksi ksi kips ft-kips kips in. in. ft in.2 in.2

Precision 1/1000 1/10 1/10 1/10 1/10 1/100 1 1/100 1/1000 1/100

Some calculations are carried out to a higher number of significant figures than common practice with hand calculation. Depending on available computation resources and designer preferences, other levels of precision may be used. 17.7.3 Material Properties 17.7.3.1 Concrete

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 Ec = wc 33 f c′ , psi 1.5

[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: E ci = (150) (33) 4, 000 / 1, 000 = 3, 834 ksi 1.5

Modulus of elasticity of concrete at 28 days, using f ´c = 7,000 psi, is: E c = (150) (33) 7 , 000 / 1, 000 = 5, 072 ksi 1.5

17.7.3.2 Pretensioning Strands

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

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RAILROAD BRIDGES 17.7.3.3 Reinforcing Bars/ 17.7.5.1 Shear Forces and Bending Moments Due to Dead Load 17.7.3.3 Reinforcing Bars

17.7.4 Cross-Section Properties for a Single Beam

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 that the depth varies from 30 in. to 31 in. to provide drainage

Figure 17.7.4-1 Box Beam Cross-Section

Relative vertical position of prestressing strand to mild steel

(24)#6 Bars (place as shownadjust as required to clear prestressing strands) 7"

6" 1 1/2" 2'-0" Clr. (Typ.)

3x3" Fillet 1'-5 1/2" (Typ.) #4 Stirrups

5"

2'-8 3/4"

#4 Bars 1'-5 1/2"

8 1/2"

2'-7"

6 1/2" 2'-8 3/4"

5"

7'-0" 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. Reinforcement in curbs and walkway not shown for clarity 17.7.5 Shear Forces and Bending Moments 17.7.5.1 Shear Forces and Bending Moments Due to Dead Load

Self-weight of beam =

1, 452(150) = 1.513 kip/ft 1, 000(144)

Weight of end diaphragm = 1.7 kips

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RAILROAD BRIDGES 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

The equations for shear force (Vx) and moment (Mx) for uniform loads on a simple span (L) are given by: L  Vx = w  − x 2  Mx =

(Eq. 17.7.5.1-1)

wx − (L − x) 2

(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. Table 17.7.5.1-1 Shear Forces and Bending Moments

x, ft V g , kip Mg , ft-kips V SDL , kip MSDL , ft-kip V LL+I , kip MLL+I , kip

1.27** 20.0

4.0 15.9

6.0 12.8

0.0

26.6

75.7

104.4

20.1 0.0

18.4 24.5

14.6 69.5

164.6 0.0

150.7 194.5

0.0* 21.9

7.25 10.9

10.0 6.8

14.5 0.0

119.3

143.7

159.1

11.8 95.8

10.1 109.5

6.3 132.0

0.0 146.0

—

—

—

—

104.8 785.7

86.8 892.0

46.8 1,033.0

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

Diaphragm Load: Since distance between the centerline of the bearing and center of gravity of the diaphragm is less than the effective depth, ignore the effect of the diaphragm load in this example. 17.7.5.2 Shear Forces and Bending Moments Due to Superimposed Dead Load

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

[AREMA Art. 2.2.3] 0.200 = 0.100 kip/ft 2

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 given in Table 17.7.5.1-1. SEPT 01

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RAILROAD BRIDGES 17.7.5.3 Shear Forces and Bending Moments Due to Live Load/ 17.7.7 Estimate Required Prestressing Force 17.7.5.3 Shear Forces and Bending Moments Due to Live Load

The actions caused by the Cooper E 80 live load can be determined by using the tables in the AREMA Manual, Chapter 15, Art. 1.15 Appendix or by using any commercially available computer program. A distribution factor (DF) equal to 0.5 is used, since there are two beams supporting one track. For span lengths less than 60 ft, the impact factor is:  L2   ( 29) 2  I =  35 − =  35 − = 33.32% of live load  500   500  

[AREMA Eq.17-1]

The values of shear forces (VLL+I) and bending moments (MLL+I) for live load plus impact for one beam were determined using a computer program and are given in Table 17.7.5.1-1. 17.7.5.4 Load Combinations

For Group I loading: Service Load Design = D + (L + I)(DF) Load Factor Design = 1.4(D + 5/3(L + I)(DF))

[AREMA Table 2-2] [AREMA Table 2-3]

Values of shear forces and bending moments for service load design and factored load design are determined from Table 17.7.5.1-1 and given in Table 17.7.5.4-1. Table 17.7.5.4-1 Shear Forces and Bending Moments for Design

Self Wt (g)

Dead (SDL)

Live + Impact (L+I)

Total Service Load

Total Factored Load

Max. Shear Force at 1.27 ft, kips

20.0

18.4

150.7

189.1

405.4

Max. Bending Moment at Midspan, ft-kips

159.1

1,46.0

1,033.0

1,338.1

2,837.5

The maximum value of shear occurs near the supports while the maximum value of bending moment occurs near midspan for a simply supported span. 17.7.6 Permissible Stresses in Concrete at Service Loads

17.7.7 Estimate Required Prestressing Force

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: 3 f ci′ without bonded reinforcement = 3 4, 000 = 0.190 ksi 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: fb =

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RAILROAD BRIDGES 17.7.7 Estimate Required Prestressing Force /17.7.8 Determine Prestress Losses

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 fb =

12(159.1 + 146.0 + 1, 033.0) = 1.428 ksi 11, 248

Since allowable tensile stress in bottom fiber at service load is zero, required precompression is 1.428 ksi. Bottom fiber stress due to prestress after all losses: P Pe f b = se + se c A Sb where Pse = effective pretension force after allowing for all losses Then 1.428 =

Pse P (12.75) + se 1, 452 11, 248

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 is the larger of 0.82fpy = (0.82)(0.9fpu) = 0.738 fpu or 0.75fpu 0.75 fpu = 0.75(270) = 202.5 ksi Number of strands required =

[AREMA Art. 17.6.5]

783.7 = 30.8 strands (1 − 0.18)(0.75 )(270)( 0.153)

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 =

32( 2.5) + 4(15.25) + 6( 27.50) = 7.29 in. 42

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 17.7.8 Determine Prestress Losses

To determine effective prestress, fse, allowance for losses of prestress due to elastic shortening of concrete, fle, creep of concrete, flc, shrinkage of concrete, fls, and relaxation of prestressing steel, flr, will be calculated.

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RAILROAD BRIDGES 17.7.8.1 Prestress Losses at Service Loads/ 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

f le =

Es f cr E ci

[AREMA Eq. 17-16]

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

Psi Psie c2 M g e c + − A I I

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

42(0.69)(0.153)( 270) 42(0.69)(0.153)(270)(7.96) 2 + 1, 452 171,535 −

f le =

17.7.8.1.2 Creep of Concrete

159.1(12)(7.96) = 0.824 + 0.442 − 0.089 = 1.177 ksi 171,535

28, 000 (1.177 ) = 8.6 ksi 3, 834

flc = 12fcr - 7fcds

[AREMA Eq. 17-18]

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

M SDL e c 146.0(12)(7.96) = = 0.081 ksi 171,535 I

fls = 12(1.177) - 7(0.081) = 13.6 ksi 17.7.8.1.3 Shrinkage of Concrete

Assume relative humidity, R = 70% (see also AREMA Fig. 17-1): fls = 17,000 - 150 R [AREMA Eq. 17-19] =

17 , 000 − 150(70)

= 6.5 ksi

1, 000 17.7.8.1.4 Relaxation of Prestressing Steel

For pretensioning tendons with 270 ksi low-relaxation strand: flr = 5,000 - 0.10fle - 0.05(fls + flc) [AREMA Eq. 17-21] =

5, 000 - 0.10(8.6) - 0.05(6.5 + 13.6) = 3.1 ksi 1, 000

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RAILROAD BRIDGES 17.7.8.1.5 Total Losses at Service Loads/17.7.9.1 Stresses at Transfer at Midspan

17.7.8.1.5 Total Losses at Service Loads

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  31.8  Percentage prestress losses =   100 = 15.7%  202.5 

17.7.8.2 Total Losses at Service Loads

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  8.6  Percentage initial prestress losses =   100 = 4.25%  202.5 

17.7.9 Concrete Stresses

Stresses need to be checked at several locations along the beam to ensure that the design 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, which will govern straight strand designs without debonding.

17.7.9.1 Stresses at Transfer at Midspan

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

Psi Psie c M g − + A St St

Mg is based on overall length of 30 ft Mg = wL2/8 = 1.513(30)2/8 = 170.2 ft-kips ft =

1, 246 (1, 246)(7.96) 170.2(12) − + 1, 452 11, 248 11, 248

= 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: fb = =

Psi Psie c M g − + A Sb Sb 1, 246 (1, 246)(7.96) 170.2(12) + − 1, 452 11, 248 11, 248

= 0.858 + 0.882 - 0.182 = 1.558 ksi Compare with permissible values: -0.190 ksi < 1.558 ksi < 2.400 ksi O.K.

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RAILROAD BRIDGES 17.7.9.2 Stresses at Transfer at End/ 17.7.10.1 Stress in Strands at Flexural Strength 17.7.9.2 Stresses at Transfer at End

Stresses should be checked at the end of the transfer length when designing a prestressed beam (see Section 9.1.8.2 for an example of this check). However, in this design example, a standard beam design is being checked. Therefore it is conservative to check the stresses at the very end of the member, assuming the full prestress force is effective at that location. Since the strands are straight and all strands are bonded for the full length of the beam, the concrete stresses at the end are simply the stresses at midspan without the stress due to dead load moment. f t = -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.

17.7.9.3 Stresses at Service Load at Midspan

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

Pse Psee c M g + M SDL + M LL + I − + A St St 1, 096.9 (1, 096.9)(7.96) 1, 338.1(12) − + 1, 452 11, 248 11, 248

= 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: fb =

=

Pse Psee c M g + M SDL + M LL + I + − A Sb Sb 1, 096.9 (1, 096.9)(7.96) 1, 338.1(12) + − 1, 452 11, 248 11, 248

= 0.755 + 0.776 - 1.428 = 0.103 ksi > 0.0 ksi 17.7.9.4 Stresses at Service Load at End

O.K.

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

17.7.10 Flexural Strength 17.7.10.1 Stress in Strands at Flexural Strength

In lieu of a more accurate determination of stress in pretensioning strands at nominal strength, fps, based on strain compatibility, the following approximate value of fps is used:  f pu  f ps = f pu 1 − 0.5ρ p ′  , provided fse is greater than 0.5 fpu fc  

[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.

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RAILROAD BRIDGES 17.7.10.1 Stress in Strands at Flexural Strength/17.7.10.3 Design Moment Strength

rp =

A ps bd

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 32( 2.5) + 4(15.25) = 30.5 = 26.58 in. 36 Note: In many cases, strands near or above midheight are neglected when computing d for calculating the average stress in strands at flexural strength. This is because, at the flexural strength, the strands located higher in the cross-section will not reach a strain (and stress) as high as the bottom strands. However, for this standard beam design, the strands at midheight have been included as shown above. A strain compatibility analysis (described in Sections 8.2.2.5 and 8.2.2.6) can be used to compute the strain and stress in the strands at midheight. Such an analysis for this beam indicates that the strands at midheight would reach a stress of approximately 251 ksi, which is reasonable when compared with the stress, fps, computed below. The same analysis indicates that the strands in the bottom row would reach a stress of nearly 260 ksi. Therefore, in this case, incorporating the strands at midheight 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 =

A ps bd

=

5.508 = 0.00247 84( 26.58)

 270  fps = 2701 − (0.5)(0.00247 )  = 257.1 ksi  7.0  17.7.10.2 Limits for Reinforcement

Assuming a rectangular section, compute the reinforcement ratio as: ρp

f ps f c′

=

0.00247 ( 257.1) = 0.0907 < 0.30 7.0

O.K.

[AREMA Art. 17.5.4]

When the reinforcement ratio exceeds 0.30, design moment strength shall not be taken greater than the moment strength based on the compression portion of the moment couple. 17.7.10.3 Design Moment Strength

Assuming beam acts as a rectangular section::   f ps   fMn = f  A psf psd 1 − 0.6ρ p ′   f c       a  = f  A psf ps  d −    2  

[AREMA Eq. 17-3]

[AREMA Eq. 17-4]

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RAILROAD BRIDGES 17.7.10.3Design Moment Strength/17.7.10.5 Final Strand Pattern

where Mn = nominal moment strength of a section f = strength reduction factor for flexure = 0.95 a

=

A psf ps 0.85 f c′ b

=

[AREMA Art.17.5.2]

5.508( 257.1) = 2.83 in. 0.85(7 )(84)

[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:   2.83   1 fMn = 0.95 5.508( 257.1) 26.58 − = 2,821.2 ft-kips   2   12  Factored moment due to dead and live loads from Table 17.7.5.4-1 = 2,837.5 ft-kips. Percentage over =

17.7.10.4 Minimum Reinforcement

17.7.10.5 Final Strand Pattern

( 2, 837.5 − 2, 821.2) (100) = 0.58% (insignificant) say ok. 2, 821.2

The total amount of prestressed and non-prestressed reinforcement should be adequate to develop an ultimate moment at the critical section at least 1.2 times the cracking moment, Mcr: fMn ≥ 1.2Mcr. The calculation (not shown here but similar to 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

7'-0"

Figure 17.7.10.5-1 Strand Pattern

4" 3 1/2"

10"

1'-8"

1'-4"

1'-8"

10"

4" 2 1/2"

3'-3 3/4"

4 1/2"

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

6 Strands 2'-1" 4 Strands

Void Drains Drip 2 1/2" 3" 17 Spaces @ 2" = 2'-10" 10" 17 Spaces @ 2" = 2'-10"

2 1/2" 3" 32 Strands

Note: Curbs and warkway not shown

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RAILROAD BRIDGES 17.7.11 Shear Design /17.7.11.2.1 Simplified Approach

17.7.11 Shear Design 17.7.11.1 Required Shear Strength

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 a distance h/2 from face of support. In this design example, the critical section for shear is calculated from the centerline of the bearings since the pads are not rigid and have the potential to rotate. h/2 = 30.5/2 = 15.25 in. = 1.27 ft Vu = 405.4 kips (from Table 17.7.5.4-1)

17.7.11.2 Shear Strength Provided by Concrete 17.7.11.2.1 Simplified Approach

The shear strength provided by concrete, Vc, can be calculated by using AREMA Manual Eq. 17-9, provided that the effective prestress force is not less than 40% of the total tensile strength provided by the flexural reinforcement.  Vu d  ′ Vc =  0.6 f c + 700  b wd Mu   where Mu = factored bending moment at the section

[AREMA Eq. 17-9]

5   = 1.4  26.6 + 24.5 + (194.5) = 525.4 ft-kips   3 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. Vu d 405.4( 26.58) = = 1.71 > 1.0, use 1.0 525.4(12) Mu

(

[AREMA Art. 17.5.9c]

)

Vc = 0.6 7 , 000 + 700(1.0) 18.5( 26.58) / 1, 000 = 368.9 kips However, the maximum value of Vc is limited to: 5 f c′ b w d = 5 7 , 000 (18.5)( 26.58) / 1, 000 = 205.7 kips < Vc = 368.9

NO GOOD

AREMA Manual Art. 17.5.9c allows higher values of Vc if a more detailed calculation is made. According to this method, Vc is the lesser of Vci or Vcw. SEPT 01

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RAILROAD BRIDGES 17.7.11.2.1 Simplified Approach/17.7.11.2.2 Calculate Vci

where Vci = nominal shear strength provided by concrete when diagonal cracking results from combined shear and moment Vcw = nominal shear strength provided by concrete when diagonal cracking results from excessive principal tensile stress in web 17.7.11.2.2 Calculate Vci

′ Vci = 0.6 f c b w d + VD +

ViM cr M max

[AREMA Eq. 17-10]

but not less than 1.7 f c′ b w d where VD

= shear at section due to service dead load = Vg + VSDL = 20.0 + 18.4 = 38.4 kips = moment causing flexural cracking at section due to externally applied loads

Mcr

= S b  6 f c′ + f pe − f d    where fpe= compressive stress in concrete due to effective prestress force only, at the extreme fiber of section where tensile stress is caused by externally applied loads fpe = =

Pse Pe + se c A Sb 1, 096.9 1, 096.9(7.96) + = 0.755 + 0.776 = 1.531 ksi 1, 452 11, 248

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

Mcr Vi Mmax

M g + M SDL Sb

(26.6 + 24.5)12 = 0.055 ksi 11, 248

 11, 248  6 7 , 000 =  = 1,854.0 ft-kips + 1.531 − 0.055  12  1, 000 = factored shear force at section due to externally applied loads occurring simultaneously with Mmax = Vu - VD = 405.4 - 38.4 = 367.0 kips = maximum factored moment at the section due to externally applied loads = Mu - Mg - MSDL = 525.4 - 26.6 - 24.5 = 474.3 ft-kips

′ Vci = 0.6 f c b w d + VD +

= 0.6

=

ViM cr M max

[AREMA Eq. 17-10]

7 , 000 367.0(1, 854.0) (18.5)(26.58) + 38.4 + = 1,497.7 kips 1, 000 474.3

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RAILROAD BRIDGES 17.7.11.2.2 Calculate Vci /17.7.11.3.2 Determine Stirrup Spacing

7 , 000 (18.5)(26.58) = 69.9 kips but not less than 1.7 f c′ b w d = 1.7 1, 000 Therefore, Vci = 1,497.7 kips 17.7.11.2.3 Calculate Vcw

Vcw =  3.5 f c′ + 0.3f pc  b w d + Vp

[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 the transfer length of the prestressing strands, a reduced pretensioning force will be considered when computing Vcw. [AREMA Art. 17.5.9c(2)(c)] Effective prestress force at distance h/2 from centerline of the bearing, Pse = fpc =

(15.25 + 6.00) (1, 096.9) = 932.4 kips 25

932.4 = 0.642 ksi 1, 452

Therefore,   3.5 7 , 000 + 0.3(0.642) (18.5)( 26.58) + 0 = 238.7 kips Vcw =    1, 000 17.7.11.2.4 Calculate Vc

17.7.11.3 Calculate Vs and Shear Reinforcement

Vc = lesser of Vci and Vcw Vc = Vcw = 238.7 kips Vs =

Vu 405.4 − Vc = − 238.7 = 211.7 kips φ 0.9

[AREMA Eq. 17-8]

17.7.11.3.1 Calculate Vs 17.7.11.3.2 Determine Stirrup Spacing

Required stirrup spacing is calculated as follows: Vs =

A vf yd s

[AREMA Eq. 17-14]

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RAILROAD BRIDGES 17.7.11.3.2 Determine Stirrup Spacing/17.7.11.3.4Check Stirrup Spacing Limits

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 of the top slab of the box beam. Calculations for the top slab flexural reinforcement are not provided in this example. A vf yd

Spacing required, s =

Vs

=

0.80(60)( 26.58) = 6.1 in. > 4 in. 210.4

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 =

17.7.11.3.3 Check Vs Limit

0.80(60)( 26.58) = 319.0 > 210.4 kips 4

O.K.

Allowable maximum shear strength provided by stirrups is: 8 f c′ b w d = 8 7 , 000 (18.5)( 26.58) / 1, 000 = 329.1 kips > Vs

17.7.11.3.4 Check Stirrup Spacing Limits

[AREMA Art. 17.5.9d(5)]

O.K.

Check for maximum spacing of stirrups 4 f c′ b w d = 4

7 , 000 (18.5)( 26.58) = 164.6 kips < Vs 1, 000

[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 Figure 17.7.11.3.4-1 Elevation Showing Non-Prestressed Reinforcement

#6 Bars 2 1/4"

#4 Bar

Note: #6 Bars at web not shown for clarity

#4 Stirrups

(4) #4 End bars (Typ.) 3 1/4"

11 Spaces @ 4" = 3'-8"

#6 Bars Spacing @ About 6" Centers CL Girder (Symm.) SEPT 01

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RAILROAD BRIDGES 17.7.12 Deflections/17.7.12.5 Deflection Due to Live Load

17.7.12 Deflections

Camber and deflection calculations are required to determine the bridge seat elevations and maintain the minimum ballast depth. They are also required for the design of the elastomeric bearings. 1, 219.7 (7.96)( 29(12)) P e L2 = - 0.223 in. ≠ ∆ = si c = − 8(3, 834)(171,535) 8E ciI 2

17.7.12.1 Camber Due to Prestressing at Transfer

5(1.513 / 12)( 29(12)) 5wL4 ∆= = = 0.037 in. Ø 384E ciI (384)(3, 834)(171,535) 4

17.7.12.2 Deflection Due to Beam Self-Weight at Transfer

5(1.389 / 12)( 29(12)) 5wL4 = 0.025 in Ø ∆= = 384E cI (384)(5, 072)(171,535) 4

17.7.12.3 Deflection Due to Superimposed Dead Load 17.7.12.4 Long-Term Deflection

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

Table 17.7.12.4-1 Calculated Deflection, in.

Prestress Self-Weight Dead Load Total

At Release (a) − 0.223 ↑ + 0.037 ↓ N/A − 0.186 ↑

Multiplier (b) 1.80 1.85

Erection (c) = (a)(b) − 0.401 ↑ + 0.068 ↓ + 0.025 ↓ − 0.308 ↑

Multiplier (d) 2.45 2.70 3.00

Final (e) = (a)(d) − 0.546 ↑ + 0.100 ↓ + 0.075* ↓ − 0.371 ↑

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

17.7.12.5 Deflection Due to Live Load

Live load deflection is generally calculated using influence lines. At this point, use of a computer program becomes very useful. However, for short span bridges, the designer can quickly calculate an approximate value for deflection by using the equivalent uniform load. The equivalent uniform live load, wequ, for a simply supported beam can be derived from the maximum moment at midspan, MLL + I = wequ =

D=

w equ L2 8

8M LL + I 8(1, 033.0)(12) = = 0.819 kip/in. 2 L2 (29(12)) 5(0.819)( 29(12))

4

384(5, 072)(171,535)

= 0.180 in. Ø

Maximum allowable deflection = =

29(12) = 0.544 in. > 0.180 in. 640

L 640 O.K.

[AREMA Art. 17.6.7a]

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RAILROAD BRIDGES 17.8 References

17.8 REFERENCES

AREMA Manual for Railway Engineering, 2000 Edition, American Railway Engineering and Maintenance-of-Way Association, Landover, MD, 2000 Marianos, W. N., Jr., “Railroad Use of Precast Concrete Bridge Structures,” ACI Concrete International, V. 13, No. 9, September 1991, pp. 30-35 PCI Design Handbood, Fifth Edition, Precast/Prestressed Concrete Institute, Chicago, IL, 1999, 690 pp.

DEC 00