pc bridge design manual
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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 Page 1
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
17.7.5.4 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
TABLE OF CONTENTSRAILROAD BRIDGES
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 2
PCI BRIDGE DESIGN MANUAL CHAPTER 17
TABLE OF CONTENTSRAILROAD BRIDGES
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 3
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
PCI BRIDGE DESIGN MANUAL CHAPTER 17
SEPT 01
NOTATIONRAILROAD BRIDGES
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 6
PCI BRIDGE DESIGN MANUAL CHAPTER 17
SEPT 01
NOTATIONRAILROAD BRIDGES
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 7
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
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 9
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 10
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
RAILROAD BRIDGES17.1.3.2 Other Products
SEPT 01
Figure 17.1.3.2-2 Box Beam
(Intermediate Spans)
OptionalCurb
Precast Cap
Steel Pilingw/Welded PlateConnection to
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
Steel Pilingw/Welded PlateConnection to
Pile Cap
TimberPiling
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 11
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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)
Steel Pilingw/Welded PlateConnection to
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 12
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 13
• 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
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 14
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 15
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'
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 16
(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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
RAILROAD BRIDGES17.3.2.1 Live Load
SEPT 01
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 17
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)
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
17.3.2.4 Load Combinations
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 18
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 19
• 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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 20
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 21
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
17.5.6 New Superstructure
for Truss Spans
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 22
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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.
17.6.2 New Superstructure
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 23
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 24
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
RAILROAD BRIDGES17.6.4 Superstructure Construction
SEPT 01
17.6.4 Superstructure
Construction
Figure 17.6.4-1 Completed Bridge Structure
5844 Bridge Manual Ch 17.0-17.6 9/24/01 1:28 PM Page 25
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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)
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 2
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
.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 3
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, ( ), ( )
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 4
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
−
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 5
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( )
. %
PCI BRIDGE DESIGN MANUAL CHAPTER 17
RAILROAD BRIDGES17.7.5.3 Shear Forces and Bending Moments Due to Live Load/
17.7.7 Estimate Required Prestressing Force
SEPT 01
17.7.5.4 Load Combinations
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 6
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
( . . , . ),
PCI BRIDGE DESIGN MANUAL CHAPTER 17
RAILROAD BRIDGES17.7.7 Estimate Required Prestressing Force /17.7.8 Determine Prestress Losses
SEPT 01
17.7.8 Determine
Prestress Losses
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 7
[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 =
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 8
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..
. %
=
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 9
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
= − ++ + +
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 10
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
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 11
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.
. ( . ). ( )( )
.′ = =
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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"
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 12
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
′ + +
PCI BRIDGE DESIGN MANUAL CHAPTER 17
RAILROAD BRIDGES17.7.11.2.1 Simplified Approach/17.7.11.2.2 Calculate Vci
SEPT 01
17.7.11.2.2 Calculate Vci
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 14
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′ = =
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 15
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. ( )( . )
.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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"
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 16
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, . ( . ) ( )
( , )( , )
PCI BRIDGE DESIGN MANUAL CHAPTER 17
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)
↑
↑
↓↑
↑
↓↓
↑
↑
↓↓
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 17
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.
PCI BRIDGE DESIGN MANUAL CHAPTER 17
RAILROAD BRIDGES17.8 References
DEC 00
17.8 REFERENCES
5844 Bridge Manual Ch 17.7 9/24/01 1:37 PM Page 19
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