ACI 358.1R-92 - Analysys and Design of Reinforced Concrete Guideway Structures

ACI 358.1R-92

ANALYSIS AND DESIGN OF REINFORCEDAND PRESTRESSED-CONCRETE

GUIDEWAY STRUCTURES

Reported by ACI Committee 358

Hidayat N. Grouni Sami W. TabshChairman Secretary

T. Ivan CampbellMichael P. CollinsCharles W. DolanRoger A. DortonThomas T. C Hsu

Stephen J. KokkinsAndy MoucessianAndrzej S. NowakHenry G. Russell

These recommendations, prepared by Committee 358, pre-sent a procedure for the design and analysis of reinforced andprestressed-concrete guideway structures for public transit. Thedocument is specifically prepared to provide design guidance forelevated transit guideways. For items not covered in this docu-ment the engineer is referred to the appropriate highway and rail-way bridge design codes.

Limit states philosophy has been applied to develop the de-sign criteria. A reliability approach was used in deriving load andresistance factors and in defining load combinations. A target re-liability index of 4.0 and a service life of 75 years were taken asthe basis for safety analysis. The reliability index is higher than thevalue generally used for highway bridges, in order to provide alower probability of failure due to the higher consequences offailure of a guideway structure in a public tramit system The 75year service life is comparable with that adopted by AASHTO fortheir updated highway bridge design specifications.

KEYWORDS: Box beams; concrete construction; cracking (fracturing);deformation; fatigue (materials); guideways; loads (forces); monorailsystems: partial prestressing; precast concrete; prestressed concrete:prestress loss; rapid transit systems; reinforced concrete; serviceablity;shear properties: structural analysis; structural design: T-beams;torsion; vibration.

CONTENTSCHAPTER 1- Scope, Definitions, and Nota-tions, pg. 358.1R-2

1.1 Scope1.2 Definitions1.3 Notations1.4 SI Equivalents1.5 Abbreviations

Cl Committee Reports, Guides. Standard Practices, andommentaries are intended for guidance in designing, planning,

ting, or inspecting construction and in preparing specifications.

ocuments. If items found in these documents are desired to be part

358.1R

CHAPTER 2- General Design Considerations,pg. 358.1R-5

2.1 Scope2.2 Structural Considerations2.3 Functional Considerations2.4 Economic Considerations2.5 Urban Impact2.6 Transit Operations2.7 Structure/Vehicle Interaction2.8 Geometrics2.9 Construction Considerations2.10 Rails and Trackwork

CHAPTER 3 - Loads, pg. 358.1R-153.1 General3.2 Sustained Loads3.3 Transient Loads3.4 Loads due to Volumetric Changes3.5 Exceptional Loads3.6 Construction Loads

CHAPTER 4- Load Combinations and Loadand Strength Reduction Factors, pg. 358.1R-23

4.1 Scope4.2 Basic Assumptions4.3 Service Load Combinations4.4 Strength Load Combinations

CHAPTER 5- Serviceability Design, pg.358.1R-25

5.1 General5.2 Basic Assumptions5.3 Permissible Stresses5.4 Loss of Prestress5.5 Fatigue5.6 Vibration5.7 Deformation5.8 Crack Control

ACI 358.1R-92 supersedes ACI 358.1R-86, effective Sept. 1, 1992.Copyright 0 1992 American Concrete Institute.All rights reserved including rights of reproduction and use in any

form or by any means, including the making of copies by any photoprocess, or by any electronic or mechanical device. printed, written ororal or recording for sound or visual reproduction or for use in anyknowledge or retrieval system or device, unless permission in writing isobtained from the copyright proprietors.

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358.1R-2 MANUAL OF CONCRETE INSPECTION

CHAPTER 6 - Strength Design, pg. 356.1R-326.1 General Design and Analysis Considerations6.2 Design for Flexure and Axial Loads6.3 Shear and Torsion

CHAPTER 7- Reinforcement Details, pg.358.1R-34

CHAPTER 8 - References, pg. 358.1R-348.1 Recommended References

CHAPTER 1 - SCOPE, DEFINITIONSAND NOTATIONS

1.1- ScopeThese recommendations are intended to

provide public agencies, consultants, and otherinterested personnel with comprehensive criteriafor the design and analysis of concrete guidewaysfor public transit systems. They differ from thosegiven for bridge design in ACI 343R, AASHTObridge specifications, and the AREA manual ofstandard practice.

The design criteria specifically recognize theunique features of concrete transit guideways,namely, guideway/vehicle interaction, rail/structureinteraction, special fatigue requirements, andesthetic requirements in urban areas. The criteriaare based on current state-of-the-art practice formoderate-speed [up to 100 mph (160 km/h)]vehicles. The application of these criteria foradvanced technologies other than those discussedin this report, require an independent assessment.

ACI 343R is referenced for specific items notcovered in these recommendations. These refer-ences include materials, construction consider-ations, and segmental construction.

1.2-DefinitionsThe following terms are defined for general

use in this document. For a comprehensive list ofterms generally used in the design and analysis ofconcrete structures, the reader is referred toChapter 2 of ACI 318 and to ACI 116R. Theterminology used in this document conforms withthese references.

Broken rail - The fracture of a continuouslywelded rail.

Concrete, specified compressive strength of J$ -Compressive strength of concrete used in designand evaluated in accordance with Chapter 5 ofACI 318 is expressed in pounds per square inch(psi) [Megapascals (MPa)]; wherever this quantityis under a radical sign, the square root of thenumerical value only is intended and the resultantis in pounds per square inch (psi).

Concrete-A mixture of portland cement or anyother hydraulic cement, fine aggregate, coarseaggregate, and water, with or without admixtures.

Continuously welded rail - Running rails that actas a continuous structural element as a result offull penetration welding of individual lengths ofrail; continuously welded rails may be directlyfastened to the guideway, in which case theircombined load effects must be included in thedesign.

Dead load -The dead weight supported by amember, as defined in Chapter 3, without loadfactors.

Design load-All applicable loads and forces andtheir load effects such as, moments and shearsused to proportion members; for design accordingto Chapter 5, design load refers to load withoutload factors; for design according to Chapter 6,design load refers to loads multiplied by appro-priate load factors, as given in Chapter 4.

Flexural natural frequency- The first verticalfrequency of vibration of an unloaded guideway,based on the flexural stiffness and mass distri-bution of the superstructure.

Live load-The specified live load, without loadfactors.

Load factor-A factor by which the service load ismultiplied to obtain the design load.

Service load-The specified live and dead loads,without load factors.

Standard vehicle-The maximum weight of thevehicle used for design; the standard vehicleweight should allow for the maximum number ofseated and standing passengers and should allowfor any projected vehicle weight increases if largervehicles or trains are contemplated for future use.

1.3 - Notation

a = center-to-center distance of shorter dimen-sion of closed rectangular stirrups, in.(mm). Section 5.5.3

a1= side dimension of a square post-tensioning

anchor, or lesser dimension of a rectangularpost-tensioning anchor, or side dimension ofa square equivalent in area to a circularpost-tensioning anchor, in. (mm). Section5.8.2.1

a, = minimum distance between the center-lines*

GUIDEWAY STRUCTURES 358.1R-3

A =

A =

Abs =

Aoh =

Ar =As’ =

At =

Av =

b =

=

bb =

BR =Cd =CD =Ce =

:> zCL =CR =d =

dc =

D =DR =

of anchors, or twice the distance from thecenterline of the anchor to the nearestedge of concrete, whichever is less, in.(mm). Section 5.8.2.1effective tension area of concretesurrounding the main tension reinforcingbars and having the same centroid as thatreinforcement, divided by the number ofbars, in.2 (mm2); when the main rein-forcement consists of several bar sizes, thenumber of bars should be computed asthe total steel area divided by the area ofthe largest bar used. Section 5.8.1exposed area of a pier perpendicular tothe direction of stream flow, ft2 (m2).Section 3.3.4area of nonprestressed reinforcementlocated perpendicular to a potentialbursting crack, in.2 (mm2). Section 5.8.2.1Area enclosed by the centerline of closedtransverse torsion reinforcement, in.2(mm2). Section 5.5.3Cross-sectional area of a rail, in.2 (mm2).Area of compression reinforcement, in.2

(mm2).Area of one leg of a closed stirrup resis-ting torsion within a distance, in.2 (mm2).Area of shear reinforcement within a dis-tance, or area of shear reinforcement per-pendicular to main reinforcement withina distance for deep beams, in.2 (mm2).Width of compressive face of member, in.(mm).Center-to-center distance of longer dimen-sion of closed rectangular stirrup, in.(mm). Section 5.5.3Width of concrete in the plane of a poten-tial bursting crack, in. (mm). Section 5.8.2Broken rail forces.Horizontal wind drag coefficient.Flowing water drag coefficient.Wind exposure coefficient.Wind gust effect coefficient.Centrifugal force, kip (kN).Collision load, kip (kN).Forces due to creep in concrete, kip (kN).Distance from extreme compressive fiberto centroid of tension reinforcement, in.(mm).Thickness of concrete cover measuredfrom the extreme tensile fiber to thecenter of the bar located closest thereto,in. (mm).Dead load.Transit vehicle mishap load, due to vehiclederailment, kip (kN).Base of Napierian logarithms.Modulus of elasticity of concrete, psi (Pa).

Eci =

Es =

EI =

E Q ==

1=

fc =

fc' =

fci' =

kI

8 =c

ffr =

fm =

fpu =

fpy =

fr =

fs =

fsr =

fst =

fsv =

fy =

f1 =Fbs =

Fh =

Fr =

Fsj =

Fv =

FR =

Section 5.6.3Modulus of elasticity of concrete attransfer of stress, psi (MPa).Modulus of elasticity of reinforcement, psi(MPa)Flexural stiffness of compression mem-bers, k-in2 (kN-mm2).Earthquake force.Modulus of elasticity of rail, psi (MPa).Bursting stress behind a post-tensioninganchor, ksi (MPa).Extreme fiber compressive stress in con-crete at service loads, psi (MPa).Specified compressive strength of concreteat 28 days, psi (MPa).Compressive strength of concrete at timeof initial prestress, psi (MPa).Cracking stress of concrete, psi (MPa).Cracking stress of concrete at the time ofinitial prestress, psi (MPa).

Square root of specified compressivestrength of concrete, psi (MPa).Stress range in straight flexural reinforcingsteel, ksi (MPa).Algebraic minimum stress level, tensionpositive, compression negative, ksi (MPa).Ultimate strength of prestressing steel, psi(MPa).Specified yield strength of prestressingtendons, psi (MPa).Axial stress in the continuously weldedrail, ksi (MPa). Section 3.4.3Tensile stress in reinforcement at serviceloads, psi (MPa).Stress range in shear reinforcement or inwelded reinforcing bars, ksi (MPa).Change in stress in torsion reinforcing dueto fatigue loadings, ksi (MPa).Change in stress in shear reinforcing dueto fatigue loadings, ksi (MPa).Specified yield stress, or design yield stressof non-prestressed reinforcement, psi(MPa).Flexural (natural) frequency, Hz.Total bursting force behind a post-tensioning anchor, kip (kN).Horizontal design pressure due to wind,psi (Pa).Axial force in the continuously weldedrail, kip (kN).Jacking force in a post-tensioning tendon,kip (kN).Vertical design pressure due to wind, psi(Pa).Radial force per unit length due tocurvature of continuously welded rail, k/in(Pa/mm).


g =

h =hf =

H =H =

HF =IICE==Icr =

Ie =

Ig =

jd =

kr =kt =kv =

PL 1LF =LFe =LFn =M =Ma =

Mcr =PS =q =

rv =

r/h =

R =s =

s =

S =

S F =SH =t =

Acceleration due to gravity = 32.2 ft/sec2

(9.807 m/sec2).Overall thickness of member, in. (mm).Compression flange thickness of I-andT-sections, in. (mm).Ambient relative humidity. Section 3.4.4Height from ground level to the top of thesuperstructure. Section 3.3.2Hunting force.Impact factor.Ice pressure.Moment of inertia of cracked sectiontransformed to concrete, in.4 (m4).Effective moment of inertia for compu-tation of deflections, neglecting thereinforcement, in.4 (m4). Chapter 5Moment of inertia of the gross concretesection about its centroidal axis neglectingreinforcement, in.4 (m4).Distance between tensile and compressionforces at a section based on an elasticanalysis, in. (mm).Average creep ratio.k,, as a function of time t.A function of rv for creep and shrinkagestrains.Span length, ft (m).Live load.Longitudinal force.Emergency longitudinal braking force.Normal longitudinal braking force.Mass per unit length, lb/in.-se&in. (kg/m).Maximum moment in member at stage forwhich deflection is being computed, lb-in.(N-mm).Cracking moment, lb-m (N-mm).Forces and effects due to prestressing.Dynamic wind pressure, psf (MPa).Chapter 3.Volume-to-surface-area ratio, (volume perunit length of a concrete section dividedby the area in contact with freely movingair), in. (mm).Ratio of base radius to height of trans-verse deformations of reinforcing bars;when actual value is not known, use 0.3.Radius of curvature, ft (m). Chapter 3Shear or torsion reinforcement spacing ina direction parallel to the longitudinalreinforcement, in. (mm).Spacing of reinforcement, in. (mm),Section 5.8.2Service load combinations. Chapters 4 and5.Stream flow load, lb (N). Chapter 3.Forces due to shrinkage in concrete.Time, days.

T = Loads due to temperature or thermalgradient in the structure exclusive of railforces. Chapter 4.

T = Time-dependent factor for sustained load.Section 5.7.2

_̂ T = Change in torsion at section due tofatigue loadings. Section 5.5.3

T0 = Stress-free temperature of rail.T1

= Final temperature in the continuouslywelded rail.

U = Ultimate load combinations._̂ V = Change in shear at section due to fatigueloadings, kip (kN). Section 5.5.3.

V = Velocity of water, wind, or vehicle, ft/sec(m/sec). Chapter 3.

VCF = Vehicle crossing frequency, Hz. Section3.3.1.

wc= Unit weight of concrete, lb/ft3 (kg/m3).

W = Wind load. Chapter 3.WL = Wind load on live load. Chapters 3 and 4.WS = Wind load on structure. Chapters 3 and 4.xm

= Location of maximum bursting stress,measured from the loaded face of the endblock, in. (mm).

yt = Distance from the centroidal axis of crosssection, neglecting the reinforcement, tothe extreme fiber in tension, in. (mm).

Z = A quantity limiting distribution of flexuralreinforcement.

a = Coefficient of thermal expansion. Chapter3.

Y = Mass density of water, lb/ft3 (kg/m3).‘i = Initial elastic strain.cC, = Concrete creep strain at time t.%k = Concrete shrinkage strain at time t.csku = Concrete shrinkage strain at t = 00.8 = Angle in degrees between the wind force

and a line normal to the guideway center-line.

a = Multiplier for additional long-timedeflection as defined in Section 5.7.2.

P = Density of air in Section 3.3.2pbs = Ratio of nonprestressed reinforcement

located perpendicular to a potentialbursting crack in Section 5.8.2.

P’ = Compression reinforcement ratio =A,‘lbd.

4 = Strength reduction factor.11 = A parameter used to evaluate end block

stresses. Section 5.8.2.1.

1.4- SI EquivalentsThe equations contained in the following

chapters are all written in the U.S. inch-poundsystem of measurements. In most cases, theequivalent SI (metric) equation is also given;however, some equations do not have definitive SI


equivalents. The reader is referred to ACI 318Mfor a consistent metric or SI presentation. Ineither case, the engineer must verify that the unitsare consistent in a particular equation.

1.5-AbbreviationsThe following abbreviations are used in this

report:

AASHTO American Association of StateHighway and TransportationOfficials

ACI American Concrete InstituteAREA American Railway Engineering

AssociationASTM American Society for Testing and

MaterialsAWS American Welding SocietyCRSI Concrete Reinforcing Steel

InstituteFRA Federal Railway Administration,

U.S. Department of Transportation

CHAPTER 2 - GENERAL DESIGNCONSIDERATIONS

2.1- Scope2.1.1- General

Transit structures carry frequent loads throughurban areas. Demands for esthetics, performance,cost, efficiency and minimum urban disruptionduring construction and operation are greater thanfor most bridge structures. The design of transitstructures requires an understanding of transittechnology, constraints and impacts in an urbanenvironment, the operation of the transit systemand the structural options available.

The guideway becomes a permanent feature ofthe urban scene. Therefore, materials and featuresshould be efficiently utilized and built into theguideway to produce a structure which willsupport an operating transit system as well as fitthe environment.

These guidelines provide an overview of thekey issues to be considered in guideway design.They are intended to be a minimum set of re-quirements for materials, workmanship, technicalfeatures, design, and construction which will pro-duce a guideway that will perform satisfactorily.Serviceability and strength considerations are givenin this report. Sound engineering judgment mustbe used in implementing these recommendations.

2.1.2 - Guideway StructuresThe guideway structure must support the tran-

sit vehicle, guide it through the alignment andrestrain stray vehicles. Guidance of transit vehicles

includes the ability to switch vehicles betweenguideways. The guideway must generally satisfyadditional requirements, such as providingemergency evacuation, supporting wayside powerdistribution services and housing automatic traincontrol cables.

Within a modern transit guideway, there is ahigh degree of repeatability and nearly an equalmix of tangent and curved alignment. Guidewaysoften consist of post-tensioned concrete members.Post-tensioning may provide principal rein-forcement for simple-span structures and con-tinuity reinforcement for continuous structures.Bonded post-tensioned tendons are recommendedfor all primary load-carrying applications and theiruse is assumed in this report. However, unbondedtendons may be used where approved, especiallyfor strengthening or expanding existing structures.

2.13-VehiclesTransit vehicles have a wide variety of physical

configurations, propulsion, and suspensionsystems. The most common transit vehicles aresteel-wheeled vehicles running on steel rails,powered by conventional guidance systems. Tran-sit vehicles also include rubber-tired vehicles, andvehicles with more advanced suspension orguidance systems, such as air-cushioned or mag-netically levitated vehicles. Transit vehicles may beconfigured as individual units or combined intotrains.

2.2- Structural Considerations2.2.1-GeneralTransit systems are constructed in four types of

right-of-way: exclusive, shared-use rail corridor,shared-use highway corridor, and urban arterial.The constraints of the right-of-way affect the typeof structural system which can be deployed for aparticular transit operation. Constraints resultingfrom the type of right-of-way may include limitedconstruction access, restricted working hours,limits on environmental factors such as noise, dust,foundation and structure placement, and avail-ability of skilled labor and equipment.

Three types of concrete girders are used fortransit superstructures. Namely, precast, cast-in-place, and composite girders. The types ofguideway employed by various transit systems arelisted in the Committee 358 State-of-the-ArtReport on Concrete Guideways.2.1

2.2.2-Precast Girder ConstructionWhen site conditions are suitable, entire beam

elements are prefabricated and transported to thesite. Frequently, box girder sections are used fortheir torsional stiffness, especially for short-radiuscurves. Some transit systems having long-radius


horizontal curves have used double-tee beams forthe structure.

Continuous structures are frequently used.Precast beams are made continuous by developingcontinuity at the supports. A continuous structurehas less depth than a simple-span structure andincreased structural redundancy. Rail systemsusing continuously welded rail are typically limitedto simple-span or two-span continuous structuresto accommodate thermal movements between therails and the structure. Longer lengths of con-tinuous construction are used more readily insystems with rubber tired vehicles.

Segmental construction techniques may beused for major structures, such as river crossingsor where schedule or access to the site favorsdelivery of segmental units. The use of segmentalconstruction is discussed in ACI 343R.

2.2.3 - Cast-in-place StructuresCast-in-place construction is used when site

limitations preclude delivery of large precastelements. Cast-in-place construction has not beenused extensively in modern transit structures.

2.2.4 - Composite StructuresTransit structures can be constructed in a

similar manner to highway bridges, using precastconcrete or steel girders with a cast-in-placecomposite concrete deck. Composite constructionis especially common for special structures, such asswitches, turnouts and long spans where theweight of an individual precast element limits itsshipping to the site. The girder provides a work-ing surface which allows accurate placement oftransit hardware on the cast-in-place deck.

2.3- Functional Considerations2.3.1- General

The functions of the structure are to supportpresent and future transit applications, satisfyserviceability requirements, and provide for safetyof passengers. The transit structure may also bedesigned to support other loads, such as automo-tive or pedestrian traffic. Mixed use applicationsare not included in the loading requirements ofChapters 3 and 4.

2.3.2 - Safety ConsiderationsConsiderations for a transit structure must

include transit technology, human safety andexternal safety, in accordance with the require-ments of NFPA 130, “Fixed Guideway TransitSystems.“2.3

Transit technology considerations include bothnormal and extreme longitudinal, lateral, and ver-tical loads of the vehicle, as well as passingclearances for normal and disabled vehicles,

vehicle speeds, environmental factors, transitoperations, collision conditions, and vehicleretention.

Human safety addresses emergency evacuationand access, structural maintenance, fire controland other related subjects. Transit operationsrequire facilities for evacuating passengers fromstalled or disabled vehicles. These facilities shouldalso enable emergency personnel to access suchvehicles. In most cases, emergency evacuation isaccomplished by a walkway, which may be adja-cent to the guideway or incorporated into theguideway structure. The exact details of theemergency access and evacuation methods on theguideway should be resolved among the transitoperator, the transit vehicle supplier, and theengineer. The National Fire Protection Associ-ation (NFPA) Code, Particularly NFPA - 130,gives detailed requirements for safety provisionson fixed guideway transit systems.

External safety considerations include safetyprecautions during construction, prevention oflocal street traffic collision with the transitstructure, and avoidance of navigational hazardswhen transit structures pass over navigablewaterways.

2.3.3-LightingThe requirements for lighting of transit struc-

tures should be in accordance with the provisionsof the authority having jurisdiction. Such pro-visions may require that lighting be provided foremergency use only, or for properties adjacent tothe guideway structure, or, alternatively, be de-leted altogether.

2.3.4-DrainageTo prevent accumulation of water within the

track area, transit structures should be designed sothat surface runoff is drained to either the edge orthe center of the superstructure, whereupon thewater is carried longitudinally.

Longitudinal drainage of transit structures isusually accomplished by providing a longitudinalslope to the structure; a minimum slope of 0.5percent is preferred. Scuppers or inlets, of a sizeand number that adequately drain the structureshould be provided. Downspouts, where required,should be of a rigid, corrosion-resistant materialnot less than 4 in. (100 mm) and preferably 6 in.(150 mm) in the least dimension; they should beprovided with cleanouts. The details of thedownspout and its deck inlet and outlet should besuch as to prevent the discharge of water againstany portion of the structure and should preventerosion at ground level. Slopes should be arrangedso that run-off drains away from stations.Longitudinal grades to assure drainage should be


coordinated with the natural topography of thesite to avoid an unusual appearance of thestructure.

Architectural treatment of exposed downspoutsis important. When such treatment becomes com-plicated, the use of internal or embedded down-spouts, becomes preferable. For internal orexternal downspouts, consideration must be givento the prevention of ice accumulation in cold-weather climates. This may require localizedheating of the drain area and the downspout itself.All overhanging portions of the concrete deckshould be provided with a drip bead or notch.

2.3.5 -Expansion Joints and BearingsExpansion joints should be provided at span

ends; this allows the beam ends to accommodatemovements due to volumetric changes in thestructure. Joints should be designed to reducenoise transmission and to prevent moisture fromseeping to the bearings. Adequate detailing shouldbe provided to facilitate maintenance of bearingsand their replacement, when needed, during the

life of the structure.Aprons or finger plates, when used, should be

designed to span the joint and to prevent theaccumulation of debris on the bearing seats.When a waterproof membrane is used, the detailshould be such that penetration of water into theexpansion joint and the bearing seat is prevented.

2.3.6 - DurabilityIn order to satisfy the design life of 75 years or

more, details affecting the durability of the struc-ture should be given adequate consideration; theseshould include materials selection, structural de-tailing, and construction quality control.

Materials selection includes the ingredients ofconcrete and its mix design, allowing for a lowwater-cement ratio and air entrainment in areassubject to freeze-thaw action. Epoxy-coated rein-forcement and chloride-inhibitor sealers may bebeneficial if chloride use is anticipated as part ofthe winter snow-clearing operations or if theguideway may be exposed to chloride-laden sprayfrom a coastal environment or to adjacent high-ways treated with deicing chemicals.

In structural detailing, both the reinforcementplacement and methods to prevent deleteriousconditions from occurring should be considered.Reinforcement should be distributed in the sectionso as to control crack distribution and size. Thecover should provide adequate protection to thereinforcement.

Incidental and accidental loadings should beaccounted for and adequate reinforcement shouldbe provided to intersect potential cracks. Straycurrents, which could precipitate galvanic corro-

sion, should be accounted for in the design ofelectrical hardware and appurtenances and theirgrounding.

Construction quality control is essential toensure that the design intent and the durabilityconsiderations are properly implemented. Suchquality-control should follow a pre-establishedformal plan with inspections performed as speci-fied in the contract documents.

To satisfy a 75-year service life, regularinspection and maintenance programs to ensureintegrity of structural components should be in-stituted. These programs may include periodicplacement of coatings, sealers or chemicalneutralizers.

2.4 - Economic ConsiderationsThe economy of a concrete guideway is

measured by the annual maintenance cost andcapitalized cost for its service life. It is particularlyimportant that the design process give considera-tion to the cost of operations and maintenanceand minimize them. Therefore, consideration mustbe given to the full service life cost of theguideway structure. The owners should providedirection for the establishment of cost analyses.Economy is considered by comparative studies ofreinforced, prestressed, and partially prestressed-concrete construction. Trade-offs should be con-sidered for using higher grade materials for sensi-tive areas during the initial construction againstthe impact of system disruption at a later date ifthe transit system must be upgraded. For ex-ample, higher quality aggregates may be selectedfor the traction surface where local aggregateshave a tendency to polish with continuous wear.

2.5 - Urban Impact2.5.1 - GeneralThe guideway affects an urban environment in

three general areas: visual impact, physical im-pact, and access of public safety equipment. Visu-al impact includes both the appearance of theguideway from surrounding area and the appear-ance of the surrounding area from the guideway.Physical impacts include placement of columnsand beams and the dissipation of, noise, vibration,and electromagnetic radiation. Electromagneticradiation is usually a specific design considerationof the vehicle supplier. Public safety requiresprovision for fire, police, and emergency serviceaccess and emergency evacuation of passengers.

2.5.2 -Physical AppearanceA guideway constructed in any built-up

environment should meet high standards ofesthetics for physical appearance. The size andconfiguration of the guideway elements should en-


sure compatibility with its surroundings. While therange of sizes and shapes is unlimited in theselection of guideway components the followingshould be considered:

a. View disruptionb. Shade and shelter created by the guidewayc. Blockage of pedestrian waysd. Blockage of streets and the effect on traffic

and parkinge. Impairment of sight distances for traffic belowf. Guideway mass as it relates to adjacent

structuresg. Construction in an urban environmenth. Methods of delivery of prefabricated

components and cast-in-place constructioni. Interaction with roadway and transit vehiclesj. Visual continuity

Attention to final detailing is important. Itemsto be considered should include:

a. Surface finishb. Colorc. Joint detailingd. Provision to alleviate damage from water

dripping from the structuree. Control and dissipation of surface water runofff. Differences in texture and color between

cast-in-place and precast elements

2.5.3 -SightlinessIn the design of a guideway the view of the

surroundings from the transit system itself shouldbe considered. The engineer should be aware thatpatrons riding on the transit system will have aview of the surroundings which is quite differentfrom that seen by pedestrians at street level. Assuch, the guideway placement and sightlinessshould reflect a sensitivity to intrusion on privateproperties and adjacent buildings. In some cases,the use of noise barriers and dust screens shouldbe considered.

The view of the guideway from a higher van-tage point has some importance. The interior ofthe guideway should present a clean, orderly ap-pearance to transit patrons and adjacent observers.Any supplemental cost associated with obtainingan acceptable view must be evaluated.

2.5.4 -Noise SuppressionA transit system will add to the ambient

background noise. Specifications for new con-struction generally require that the wayside noise50 ft. (15 m) from the guideway not exceed arange of 65 to 75 dBA. This noise is generatedfrom on-board vehicle equipment such as propul-sion and air-conditioning units, as well as from

vehicle/track interaction, especially when jointedrail is used.

It is normally the responsibility of the vehicledesigner to control noise emanating from the ve-hicle. Parapets and other hardware on the guide-way structure should be designed to meet generalor specific noise suppression criteria. Determina-tion of these criteria is made on a case-by-casebasis, frequently in conjunction with the vehiclesupplier.

2.5.5- VibrationTransit vehicles on a guideway generate vibra-

tions which may be transmitted to adjacent struc-tures. For most rubber tired transit systems, thisgroundborne vibration is negligible. In many railtransit systems, especially those systems withjointed rails, the noise and the vibration can behighly perceptible. In these situations, vibrationisolation of the structure is necessary.

2.5.6 -Emergency Services AccessA key concern in an urban area is the accessi-

bility to buildings adjacent to a guideway by fire orother emergency equipment. Within the confinedright-of-way of an urban street, space limitationsmake this a particularly sensitive concern. In mostcases a clearance of about 15 ft. (5 m) betweenthe face of a structure and a guideway providesadequate access. Access over the top of a guide-way may not represent a safe option.

2.6- Transit Operations2.6.1 - GeneralOnce a transit system is opened for service, the

public depends on its availability and reliability.Shutdowns to permit maintenance, operation, orexpansion of the system can affect the availabilityand reliability of the transit system. These con-cerns often lead to long-term economic, opera-tional, and planning analyses of the design andconstruction of the transit system.

In most transit operations, a shutdown periodbetween the hours of 1:00 a.m. and 5:00 a.m.(0100 and 0500) can be tolerated; slightly longershutdowns are possible in certain locations and onholidays. It is during this shutdown period thatroutine maintenance work is performed.

Many transit systems also perform maintenanceduring normal operating hours. This practice tendsto compromise work productivity and guidewayaccess rules and operations in order to provide asafe working space. The transit operators shouldprovide the engineer with guidelines regardingcapital cost objectives and their operation andmaintenance plans.

2.6.2 -Special Vehicles


Transit systems frequently employ specialvehicles for special tasks, such as, retrievingdisabled vehicles and repairing support or steeringsurfaces. While the design may not be predicatedon the use of special vehicles, their frequency ofuse, weights, and sizes must be considered in thedesign.

2.6.3 -Expansion of SystemExpansion of a transit system can result in

substantial disruption and delay to the transitoperation while equipment, such as switches, arebeing installed. In the initial design and layout ofa transit system, consideration should be given tofuture expansion possibilities. When expansion iscontemplated within the foreseeable future afterconstruction and the probable expansion pointsare known, provisions should be incorporated inthe initial design and construction phases.

2.7- Structure/Vehicle Interaction2.7.1- General

Vehicle interaction with the guideway canaffect its performance as related to support,steering, power distribution and traction com-ponents of the system. It is usually considered indesign through specification of serviceability re-quirements for the structure. In the final designstage close coordination with the vehicle supplieris imperative.

2.7.2- Ride Quality2.7.2.1- GeneralRide quality is influenced to a great degree by

the quality of the guideway surface. System speci-fications usually present ride quality criteria aslateral, vertical and longitudinal accelerations andjerk rates (change in rate of acceleration) asmeasured inside the vehicle. These specificationsmust be translated into physical dimensions andsurface qualities on the guideway and in the sus-pension of the vehicle. The two elements thatmost immediately affect transit vehicle perform-ance are the support surface and steering surface.

2.7.2.2 - Support SurfaceThe support surface is basically the horizontal

surface of the guideway which supports the transitvehicle against the forces of gravity. It influencesthe vehicle performance by the introduction ofrandom deviations from a theoretically perfectalignment. These deviations are input to thevehicle suspension system. The influence of thesupport surface on the vehicle is a function of thetype of the suspension system, the supportmedium (e.g., steel wheels or rubber tire), and thespeed of the vehicle.

There are three general components of sup-

port surfaces which must be considered. Namely,local roughness, misalignment, and camber. Localroughness is the amount of distortion on the sur-face from a theoretically true surface. In mosttransit applications, the criterion of a l/8-inch (3mm) maximum deviation from a 10 ft. (3 m)straightedge, as given in ACI 117, is used.

With steel rails, a Federal Railway Admini-stration (FRA) Class 62.2 tolerance is acceptable.The FRA provision include provisions for longi-tudinal and transverse (roll) tolerances. Thesetolerances are consistent with operating speeds ofup to 50 mph (80 km/h). Above these speeds,stricter tolerance requirements have to be applied.

Vertical misalignment most often occurs whenadjacent beam ends meet at a column or otherconnection. There are two types of misalignmentwhich must be considered. The first, is a physicaldisplacement of adjacent surfaces. This occurswhen one beam is installed slightly lower or higherthan the adjacent beam. These types of misalign-ment should be limited to l/16 in. (1.5 mm) asspecified by ACI 117.

The second type of vertical misalignmentoccurs when there is angular displacement be-tween beams. Such an angular displacement mayresult from excessive deflection, sag, or camber.Excessive camber or sag creates a discontinuitywhich imparts a noticeable input to the vehiclesuspension system.

In the design and construction of the beams theeffects of service load deflection, initial camberand long-time deflections should be considered.There is no clear definition on the amount ofangular discontinuity that can be tolerated at abeam joint. However, designs which tend to mini-mize angular discontinuity generally provide asuperior ride. Continuous guideways are particu-larly beneficial in controlling such misalignment.

Camber or sag in the beam can also affect ridequality. Consistent upward camber in structureswith similar span lengths can create a harmonic vi-bration in the vehicle resulting in a dynamicamplification, especially in continuous structures.When there are no specific deflection or cambercriteria cited for a project, the designer shouldaccount for these dynamic effects by analytical orsimulation techniques. The deflection compati-bility requirements between structural elementsand station platform edges should be accountedfor.

2.7.2.3- Steering SurfaceThe steering surface provides a horizontal input

to the vehicle. The steering surfaces may be eitherthe running rails for a flanged steel-wheel-railsystem or the concrete or steel vertical sur-faces that are integrated into the guideway struc-


ture, for a rubber tired system. The condition ofthe steering surface is particularly important sincefew vehicles have sophisticated lateral suspensionsystems. In most existing guideways, the toleranceof a l/8 in. (3 mm) deviation from a 10 ft. (3 m)straightedge, specified by ACI-117, corrected forhorizontal curvature, has proven to be adequatefor rubber tired vehicles operating at 35 mph (56

km/h) or less. In steel-rail systems, an FRA Class62.2 rail tolerance has generally proven to besatisfactory for speeds up to 70 mph (112 km/h).Other tolerance limits are given in Table 2.7.2.3.

Table 2.7.2.3 Track Construction Tolerances

Type and Class of Track

-Dimensions are-H=Horizontal. Sup.=Superelevation-Total Deviation between the theoretical and the actual alignments at any point along

-Variations from theoretical gage, cross level and superelevation are not to exceed l/8 in. (3 mm)per 15’ -6 (4.7 m) of track.-The total Deviation in platform areas should be zero towards the platform and l/4 in (6 mm) awayfrom the platform.

There is a particular interaction between thesteering surface and the support surface, which istechnology dependent and requires specific consid-eration by the engineer. This interaction resultsfrom a coupling effect which occurs when a ve-hicle rolls on the primary suspension system, caus-ing the steering mechanism to move up and down(Fig. 2.7.2.3). The degree of this up and down

NORMAL CONFlGURATIONSTEERING WHEELS

CENTERED IN THE GUIDEWAY

ROLLED COFIGURATiONRIGHT STEERING WHEEL COMPRESSED AGAINSTTHE GUIDEWAY GENERATlNG A SPURIOUS STEERING IMPUT.

Fig. 2.7.2.3- Interaction between support andsteering

movement is dependent on the steering mechan-ism which is typically an integral part of thevehicle truck (bogie) system, and the stiffness ofthe primary suspension which is also within thetruck assembly.

Depending upon the relationship between thesupport and the steering surfaces, and the supportand guidance mechanisms of the vehicle (primary,in the case of rubber tired system) a couple can becreated between the two, which causes a spurioussteering input into the vehicle. There are nogeneral specifications for this condition. Theengineer should be aware that this condition canexist and, if there is a significant distanceseparating the horizontal and vertical contactsurfaces, additional tolerance requirements for thefinished surfaces have to be imposed. This is inorder to reduce the considerable steering input,which can cause over or under steering, whichleads to an accelerated wear of components anddegraded ride comfort.


2.7.3 -Traction SurfacesTransit vehicles derive their traction from the

physical contact of the wheels with the concrete orrunning rail or through an electromagnetic force.In those systems where traction occurs throughphysical contact with the guideway, specificattention must be given to the traction surface.

In automated transit, the traction between thewheel and the reaction surface is essential to en-sure a consistent acceleration and a safe stoppingdistance between vehicles. It is also important forautomatic control functions. The engineer shoulddetermine the minimum traction required for thespecific technology being employed. If the trac-tion surface is concrete, appropriate aggregatesshould be provided in the mix design to maintainminimum traction for the working life of thestructure.

Operation in freezing rain or snow may alsoaffect traction on the guideway. The engineershould determine the degree of traction mainten-ance required under all operating conditions. Iffull maintenance is required, then the engineershould examine methods to mitigate the effects ofsnow or freezing rain. These mitigating effects mayinclude heating the guideway, enclosing theguideway, or both.

If deicing chemicals are contemplated, propermaterial selection and protection must be con-sidered. Corrosion protection may require consid-eration of additional concrete cover, sealants,epoxy-coated reinforcing steel, and special con-crete mixes.

2.7.4 -Electrical Power DistributionThere are two components to electrical power

distribution: the wayside transmission of power tothe vehicle and the primary power distribution tothe guideway. The wayside power distribution tothe vehicle is normally done through power railsor through an overhead catenary. Provision mustbe made on the guideway for the mounting ofsupport equipment for the installation of thiswayside power.

For systems using steel running rails, wherethe running rail is used for return current, pro-visions must also be made to control any strayelectrical currents which may cause corrosion inthe guideway reinforcement or generate otherstray currents in adjacent structures or utilities.

The primary power distribution network asso-ciated with a guideway may require several sub-stations along the transit route. Power must betransmitted to the power rails on the guidewaystructure at various intervals. This is usually donethrough conduits mounted on or embedded in theguideway structure.

Internal conduits are an acceptable means of

transmitting power; they may be used to routepower from the substation to the guideway. How-ever, access to internal conduits is difficult todetail and construct. Sufficient space must beprovided within the column-beam connection andwithin the beam section for the conduit turns;space must also be provided for safe electricalconnections. Exterior conduits can detract fromthe guideway appearance and can cause increasedmaintenance requirements.

2.7.5 - Special EquipmentA guideway normally carries several pieces of

special transit equipment. This equipment mayconsist of switches, signaling, command and con-trol wiring, or supplemental traction and powerdevices. The specialty transit supplier shouldprovide the engineer with explicit specifications ofspecial equipments and their spatial restrictions.For example, the placement of signaling cableswithin a certain distance of the wayside powerrails or reinforcing steel may be restricted.

The transit supplier should also provide theengineer with the forces and fatigue requirementsof any special equipment so that proper connec-tions to the structure can be designed and in-stalled. An example of connection requirementswould be linear induction motor reaction railattachments.

When no system supplier has been selected, theengineer must provide for the anticipated servicesand equipment. In this instance, a survey of theneeds of potential suppliers for the specific appli-cation may be required prior to design.

2.8- Geometries

2.8.1 - GeneralThe geometric alignment of the transit line can

have a substantial impact on the cost of thesystem. Standardization of the guideway compo-nents can lead to cost savings. During the plan-ning and design stages of the transit system, thebenefits of standardizing the structural elements,in terms of ease and time of construction andmaintenance, should be examined and the effec-tive options implemented.

2.8.2 -StandardizationStraight guideway can be produced at a lower

cost than curved guideway. Geometric alignmentsand column locations that yield a large number ofstraight beams tend to be cost-effective. Physicalconstraints at the ground influence column loca-tions. However, when choices are available, theplacement of columns to generate straight beams,as opposed to those with a slight horizontal orvertical curvature, will usually prove to be more


cost effective.Standardization and coordination of the in-

ternal components and fixtures of the guidewayalso tends to reduce overall cost. These includeinserts for power equipment, switches, or othersupport elements. Methods to achieve this arediscussed in Section 2.9.3.

2.8.3 -Horizontal GeometryThe horizontal geometry of a guideway align-

ment consists of circular curves connected totangent elements with spiral transitions. Mosttypes of cubic spirals are satisfactory for thetransition spiral. The vehicle manufacturer mayprovide additional constraints on the selection ofa spiral geometry to match the dynamic character-istics of the vehicle.

2.8.4 -Vertical GeometryThe vertical geometry consists of tangent

sections connected by parabolic curves. In mostcases, the radius of curvature of the paraboliccurves is sufficiently long that a transition betweenthe tangent section and the parabolic section isnot required.

2.8.5 - SuperelevationSuperelevation is applied to horizontal curves

in order to partially offset the effect of lateralacceleration on passengers. To accomplish the re-quired superelevation, the running surface awayform the curve center is raised increasingly relativeto that closer to the curve center. This results inthe outer rail or wheel track being raised while theinner rail or wheel track being kept at the profileelevation. The amount of superelevation is afunction of the vehicle speed and the degree ofcurvature. It is usually limited to a maximum valueof 10 percent.

2.9- Construction Considerations2.9.1- General

Construction of the guideway in an urbanenvironment has an impact on the residents,pedestrians, road traffic, and merchants along theroute. Consideration should be given to the costand length of disruption, in terms of street closureand construction details.

2.9.2 - Street Closures and DisruptionsThe amount of time that streets are closed and

neighborhoods are disrupted should be kept to aminimum. Coordination with the public shouldbegin at the planning stage. The selection ofprecast or cast-in-place concrete components andmethods of construction depend on the availabilityof construction time and on the ease of stockpilingequipment and finished products at the proximity

of the site. Construction systems which allow forrapid placement of footings and columns and forreopening of the street prior to the installation ofbeams, may have an advantage in the maintenanceof local traffic.

2.9.3 - Guideway Beam ConstructionGuideway beams may be cast-in-place or

precast. In order to ascertain the preferredconstruction technique, the following items needto be considered early in the design process:typical section and alignment, span composition(uniform or variable), structure types, span-depthratios, and major site constraints.

Cast-in-place construction offers considerabledesign and construction flexibility, however, it alsorequires a greater amount of support equipmenton the site. This equipment, especially shoring andfalsework, has to remain in place while theconcrete cures.

Precast concrete beam construction offers thepotential for reduced construction time on site andallows better quality control and assurance.Advantages of precast concrete are best realizedwhen the geometry and the production methodsare standardized.

Two types of guideway beam standardizationappear to offer substantial cost benefits. Namely,modular construction and adjustable form con-struction.

Modular construction utilizes a limited numberof beam and column types to make up the guide-way. Thus, like a model train set, these beams areinterwoven to provide a complete transit guideway.Final placement of steering surfaces and othersystem hardware on the modular elements pro-vides the precise geometry necessary for transitoperation. Modules may be complete beams.Segmental construction also typifies this con-struction technique.

An adjustable form allows the fabrication ofcurved beams to precisely match the geometric re-quirements at the site. For alignments where asubstantial amount of variation in geometry is dic-tated by the site, this solution provides a highdegree of productivity at a reasonable cost.

2.9.4 - Shipping and DeliveryPrior to the completion of final design, the

engineer should be aware of limitations which maybe placed upon the delivery of large precast ele-ments. Weight limitations imposed by local depart-ments of transportation, as well as dimensionallimitations on turnoff radii, width, and length ofbeam elements, may play an important role in thefinal guideway design. The deployment of largecranes and other construction equipment along thesite is also a consideration.


2.9.5- Approval ConsiderationsThese recommendations for transit guideways

are intended to provide procedures based on thelatest developments in serviceability and strengthdesign. Other pertinent regulations issued by state,federal, and local agencies should be considered.

Specific consideration should be given to thefollowing:

- Alternative designs- Environmental impact statements- Air, noise, and water pollution statutes- Historic and park preservation requirements- Permits- Life-safety requirements- Construction safety requirements

2.9.6 -Engineering DocumentsThe engineering documents should define the

work clearly. The project drawings should show alldimensions of the finished structure in sufficientdetail to facilitate the preparation of an accurateestimate of the quantities of materials and costsand to permit the full realization of the design.

The contract documents should define test andinspection methods, as well as the allowable pro-cedures and tolerances to ensure good workman-ship, quality control, and application of unit costs,when required in the contract. The contractor’sresponsibilities should be clearly defined. Wherenew or innovative structures are employed, sug-gested construction procedures to clarify theengineer’s intent should also be provided. Com-puter graphics or integrated data bases can assistin this definition.

2.10- Rails and Trackwork

2.10.1- GeneralGuideways for transit systems which utilize

vehicles with steel wheels operating on steel railsrequire particular design and construction con-siderations, which include, rail string assembly, useof continuous structures, and attachment of therails to the structure.

Two options exist for assembling the rails:They may be jointed with bolted connections instandard 39 ft. (11.9 m) lengths, or welded intocontinuous strings. The rails may be fasteneddirectly to the structure or installed on tie-and-ballast.

2.10.2- Jointed RailThe traditional method of joining rail is by

bolted connections. Sufficient longitudinal railmovement can develop in these connections toprevent the accumulation of the thermal stressesalong the length of the rails.

The space between the rail ends presents adiscontinuity to the vehicle support and steeringsystems. Vehicle wheels hitting this discontinuitycause progressive deterioration of the joints, gen-erate loud noise, reduce ride comfort, and in-crease the dynamic forces on the structure.

Because of these limitations, most modern tran-sit systems use continuously welded rail. However,jointed rail conditions will exist in switch areas,maintenance yards and other locations wherephysical discontinuities are required. However,even in these areas, discontinuities can be reducedgreatly by the use of bonded rail joints.

2.10.3 -Continuously Welded Rail

2.10.3.1 -GeneralTo improve the ride quality and decrease track

maintenance, individual rails are welded into con-tinuous strings. There is no theoretical limit to thelength of continuously welded rail if a minimumrestraint is provided.Minimum rail restraintconsists of prevention of horizontal or verticalbuckling of rails and anchorage at the end of acontinuous rail to prevent excessive rail gaps fromforming at low temperatures, if accidental breaksin the rail should occur.

Continuously welded rail (CWR) has becomethe standard of the transit industry over the pastseveral decades. The use of CWR requires par-ticular attention to several design details, whichinclude, thermal forces in the rails, rail break gapand forces, welding of CWR, and fastening ofCWR to the structure. The principal variablesused in the evaluation of rail forces are rail size interms of its cross-sectional area, the characteristicsof the rail fastener, the stiffness of the structuralelements, rail geometry, and operational environ-ment, in terms of temperature range.

In cases where accumulation of the thermaleffects would produce conditions too severe forthe structure, slip joints can be used. Slip jointsallow limited movement between rail strings. Theygenerally cause additional noise and require in-creased maintenance. Their use therefore is notdesirable. Location of rail anchors and rail expan-sion joints will affect the design of the structure.

2.10.3.2 -Thermal ForcesChanges in temperature of continuously welded

rails will develop stresses in the rail and in thestructure. Rails are typically installed at a designstress-free ambient temperature, to reduce the riskof rail buckling at high temperatures and railbreaks at low temperatures. Depending upon themethod of attachment of the rails to the structure,the structure should be designed for:- Horizontal forces resulting from a rail break


- Radial forces resulting from thermal changesin the rails on horizontal or vertical curves

- End anchorage forces

2.10.3.3 -Rail BreaksContinuously welded rails will, on occasion,

fail in tension. This situation occurs because of railwear, low temperature, defects in the rail, defectsin a welded joint, fatigue or some combination ofthese effects. The structure should be designed toaccommodate horizontal thrust associated with thebreak.

2.10.3.4 -Rail WeldingContinuous welded rail is accomplished by

either the them-rite welding process or the electricflash butt welding process. Proper weld proce-dures should ensure that:

- Adjacent rail heads are accurately aligned- Rails are welded at the predetermined stress-

free ambient temperature- Rail joint is clean of debris- The finished weld is free of intrusions- Weld is allowed to cool prior to tightening

the fasteners.

Ultrasonic or x-ray inspection of the welds atrandom locations is suggested.

2.10.4 -Rail Installation2.10.4.1 -GeneralRails are attached to either cross ties on

ballast or directly to the guideway structure. Thepreference in recent years has become direct railfixation as a means of improving ride quality,maintaining rail tolerances, reducing maintenancecosts, and reducing structure size.

2.10.4.2 -Tie and BallastTie and ballast construction is the conven-

tional method of installing rails at grade andoccasionally on elevated structures. Ties are usedto align and anchor the rails. Ballast provides anintermediate cushion between the rails and thestructure, stabilizes the tracks, and preventsthermal forces to be transmitted from the rails tothe structure.

Ballast substantially increases the structuredead load. Tie-and-ballast installations makecontrol of rail break gaps difficult since the tiesare not directly fastened to the primary structure.Rail breaks can develop horizontal, vertical, andangular displacements of the rail relative to thestructure.

2.10.4.3 -Direct FixationDirect fixation of the rail to the structure is

accomplished by means of mechanical rail fas-tener. Elastomeric pads are incorporated in thefastener to provide the required vertical andhorizontal flex and provisions for adjust-ment between adjacent fasteners and the struc-ture. The elastomeric pads also assist in the re-duction of noise, vibration, and impact.

Important design and construction consider-ations for the direct fixation fasteners include:

- Method of attachment to the structure- Vertical stiffness- Allowance for horizontal and vertical

adjustment- Ability to restrain the rail against rollover- Longitudinal restraint

Direct fixation fasteners are one of the mostimportant elements in the design of the track-work. They are subjected to a high number ofcyclic loads and there are thousands of fastenersin place in any one project. Progressive failuredoes not generally create catastrophic results, butleads to a substantial maintenance effort andpossible operational disruptions.

No industry wide specifications exist for thedefinition or procurement of direct fixation fas-teners. A thorough examination of the charac-teristics and past performance of available fas-teners, and the characteristics of the proposedtransit vehicle should be undertaken prior to fas-tener selection for any specific installation.

2.10.4.4 -Continuous StructureDirect fixation of continuous rail to a con-

tinuous structure creates a strain discontinuity ateach expansion joint in the structure. Fastenersmust be designed to provide adequate slip at thesejoints while still being able to limit the rail-gapsize in the event of a rail break. In climates withextreme ranges in temperature [- 40 F to +90 F(- 40 C to + 30 C)], structural continuity isgenerally limited to 200 to 300 ft. (60 to 90 m)lengths. In more moderate climates, longer runs ofcontinuous structure may be possible.

REFERENCES*

2.1 ACI Committee 358, “State-of-the-Art Report onConcrete Guideways,” Concrete Intenational, V. 2, No. 7, July1980, pp. 11-32.

2.2 Code of Federal Regulations, 49, Transportation, Parts200-999, Subpart C, Track Geometry, Federal Railroad Admin-istration, Washington, D.C., Section 213.51-213.63.

2.3 National Fire Codes, Publication NFPA - 130, 1983,Standard on Fixed Guideway Systems, National Fire Protec-tion Association, Battery March Park, Quincy, MA 02269.


*For recommended references, see Chapter 8.

CHAPTER 3 -LOADS

3.1 -GeneralThe engineer should investigate all special,

unusual, and standard loadings that may occur inthe guideway being designed. Special or unusualloads may include emergency, maintenance, orevacuation equipment or conditions. The fol-lowing loads commonly occur and are consideredwhen assessing load effects on elevated guidewaystructures.3.1

a. Sustained loads- Dead load- Earth pressure- External restraint forces- Differential settlement effects- Buoyancy

b. Transient loads- Live load and its derivatives- Wind- Loads due to ice- Loads due to stream current

c. Loads due to volumetric changes- Temperature- Rail-structure interaction- Shrinkage- Creep

d. Exceptional loads- Earthquake- Derailment- Broken rail- Collision loads at street level

e. Construction Loads- Dead Loads- Live Loads

3.2 - Sustained loads3.2.1 -Dead Loads, D

Four components of dead load are considered:

- Weight of factory-produced elements- Weight of cast-in-place elements. Weight of trackwork and appurtenances which

includes running and power rails, second-pourplinths and fasteners, barrier walls, and noise-suppression panels

. Weight of other ancillary components

3.2.2 -Other Sustained LoadsLoads from differential settlement, earth

pressure, effects of prestress forces (PS) or ex-ternal structural restraints should be included inthe design, as they occur. The beneficial effects ofbuoyancy may only be included when its existenceis ensured. References 3.2 and 3.11 may be usedas guides to evaluate the effects of these sustainedloads.

3.3 - Transient Loads3.3.1- Live Load and its Derivatives3.3.1.1- Vertical Standard Vehicle Loads, LThe vertical live load should consist of the

weight of one or more standard vehicles posi-tioned to produce a maximum load effect in theelement under consideration. The weight andconfiguration of the maintenance vehicle are to beconsidered in the design. The weight of pas-sengers should be computed on the basis of 175 lb(780 N) each and should comprise those oc-cupying all the seats (the seated ones) and thosewho are standing in the rest of the space that doesnot have seats (standees). The number of standeesshall be based on one passenger per 1.5 ft.2 (0.14m’).

For torsion-sensitive structures, such asmonorails, the possibility of passengers beingcrowded on one side of the vehicle should beconsidered in the design.

3.3.1.2 -Impact Factor, IThe minimum dynamic load allowance3.2.3.3

shown in Table 3.3.1.2 should be applied to thevertical vehicle loads, unless alternative valuesbased on tests or dynamic analysis are approved.

Definition of terms in the Table follow:

vehicle speed, ft/sec (m/sec)VCF = (3-l)

span length, ft (m)

fi = first mode flexural (natural) frequency3.4

of the guideway where,

(3-2)

where

e = span length, center-to-center ofsupports, in. (m)

M = mass per unit length of the guideway,which includes all the sustained loadsthe beam carries including its own mass,lb/in.-sec2/in. (kg/m)


Table 3.3.1.2 Dynamic Load Allowance (Impact)I

Structure Types Rubber-tired andContinuously Welded Rail

Jointed rail

Simple-span structures,

I - VCF- - - 0 . 14

>_ 0.10 >_ 0.30

Continuous-span structures,

I - VCF- - -0.124

10.10 >_ 0.30

EC = modulus of elasticity of the guideway,psi (Pa)

Ig= moment of inertia of uncrackedsection of the guideway, in.4 (m4)

VCF = Vehicle Crossing Frequency, Hz

The dynamic load allowance should not beapplied to footings and piles.

3.3.1.3 -Centrifugal Force, CFThe centrifugal force, CF, acting radially

through the center of gravity of the vehicle at acurved track may be computed from,

where,

CF = f L, WN) (3-3) I

R = radius of curvature, ft (m)g = acceleration due to gravity, 32.2 ft/sec/sec

(9.82 m/s2)V = maximum operating speed of the vehicle,

ft/sec (m/s2) and,L = the standard vehicle load, kips (kN)

The load, L, should be applied simultaneouslywith other load combinations (Chapter 4) in orderto produce the maximum force effect on thestructure.

3.3.1.4 -Hunting Force, HFThe hunting (or “nosing”) force, HF, is caused

by the lateral interaction of the vehicle and theguideway. It should be applied laterally on theguideway at the point of wheel-rail contact, as afraction of the standard vehicle load, L, as follows:

Bogie type Hunting force

Nonsteerable 0.08LSteerable 0.06L

When centrifugal and hunting forces can actsimultaneously, only the larger force need beconsidered.

For rail and structure design, the huntingforce would be applied laterally by a steel wheel tothe top of the rail at the lead axle of a transittrain. it need not be applied for rubber tiredsystems; typically, LIM propelled vehicles run onsteel-wheel-and-rail and, hence require consider-ation of hunting effects.

3.3.1.5 - Longitudinal Force, LFThe longitudinal force acts simultaneously

with the vertical live load of a standard vehicle onall wheels. It may be applied in either direction:forward in braking or deceleration or reverse inacceleration. The longitudinal force should beapplied as follows:

Emergency braking, LFe = 0.30LNormal braking, LFn = 0.15L

Continuously welded rail trackwork candistribute longitudinal forces to adjacent com-ponents of guideway structures. This distributionmay be considered in design. Use of slip jointsmay prevent transfer and distribution oflongitudinal forces.

3.3.1.6 - Service Walkway LoadsLive load on service or emergency walkways

shall be based on 85 psf (4.0 kPa) of area. Thisload should be used together with empty vehicleson the guideway, since the walkway load is theresult of vehicles being evacuated.


3.3.1.7-Loads on Safety RailingThe lateral load from pedestrian traffic on

railings should be 100 lb/ft (1.5 kN/m) applied atthe top rail.

3.3.2 -Wind Loads, W3.3.2.1 -GeneralThis section provides design wind loads for

elevated guideways and special structures. Windloads, based on the reference wind pressure, shallbe treated as equivalent static loads as defined inSection 3.5.3.

Wind forces are applied to the structure andto the vehicles in accordance with the load com-binations in Chapter 4. WL is used to designatewind loads applied to vehicle, while WS indicateswind loads applied to the structure only.

The net exposed area is defined as the netarea of a body, member, or combination of mem-bers as seen in elevation. For a straight super-structure, the exposed frontal area is the sum ofthe areas of all members, including the railingsand deck systems, as seen in elevation at 90degrees to the longitudinal axis. For a structurecurved in plan, the exposed frontal area is takennormal to the beam centerline and is computed ina similar manner to tangent structures.

The exposed plan area is defined as the netarea of an element as seen in plan from above orbelow. In the case of a superstructure, the ex-posed plan area is the plan area of the deck andthat of any laterally protruding railings, membersor attachments.

The gust effect coefficient is defined as theratio of the peak wind-induced response of astructure, including both static and dynamic action,to the static wind-induced response.

Buildings and other adjacent structures canaffect the wind forces. Wind tunnel tests may beconsidered as a method to improve wind forcepredictions or to validate design coefficients in thealternative design approach provided in Section3.5.3.

3.3.2.2 - Design for WindThe guideway superstructure should be de-

signed for wind-induced horizontal, Fh and verti-cal, Fv drag loads acting simultaneously. The windshould be considered to act on a structure curvedin plan, in a direction such that the resulting forceeffects are maximized. For a structure that isstraight in plan, the wind direction should betaken perpendicular to the longitudinal axis of thestructure.

The following uniformly distributed load in-tensities may be used for design:

Fh = the greater of 50 lb/ft2 (2.4 kPa) or 300lb/ft (4.4 kN/m)

and

Fv = 15 lb/ft2 (0.7 kPa)

The wind loads, Fh and Fv, should be appliedto the exposed areas of the structure and vehiclein accordance with the provisions of sections 4.3and 4.4.

These loads and provisions are consistent withthe recommendations of the AASHTO StandardSpecifications for Highway Bridges3.11 derivedfrom wind velocities of 100 mph (160 km/h). Windloads may be reduced or increased in the ratio ofthe square of the design wind velocity to thesquare of the base wind velocity, provided that themaximum probable wind velocity can be ascer-tained with reasonable accuracy, or provided thatthere are permanent features of the terrain thatmake such changes safe and are viable.

The substructure should be designed forwind-induced loads transmitted from the super-structure and wind loads acting directly on thesubstructure. Loads for wind directions both nor-mal to and skewed to the longitudinal centerlineof the superstructure should be considered.

3.3.2.3 -Alternative Wind LoadThe alternative wind load method may be

used in lieu of that given in Section 3.3.2.1.Alternative wind loads are suggested for projectsinvolving unusual height guideways, unusual gustconditions, or guideway structures that are, in thejudgment of the engineer, more streamlined thanhighway structures.3.7.3.8

The wind load per unit exposed frontal areaof the superstructure, WS, and of the vehicle, WL,applied horizontally, may be taken as:

Fh = qCeCgCd (3-4)

Similarly, the wind load per unit exposed plandeck or soffit area applied vertically, upwards ordownwards, shall be taken as:

Fv = qCeCgCdqc,cgcd (3-5)

Where, Cd = 1.0 and Ce, Cg, and q are defined inSection 3.3.2.4. The maximum vertical windvelocity may be limited to 30 mph (50 km/h).

In the application of Fv, as a uniformlydistributed load over the plan area of the struc-ture, the effects of a possible eccentricity shouldbe considered. For this purpose, the same totalload should be applied as an equivalent vertical


line load at the windward quarter point of thesuperstructure.

3.3.2.4 -Reference Wind PressureThe reference wind pressures at a specific site

should be based on the hourly mean wind velocityof a 75-year return period. A l0-year returnperiod may be used for structures under con-struction.

The reference wind pressure, q, may bederived from the following expression:

where

V = mean hourly velocity of wind, ft/sec (m/s)P = density of air at sea level at 32 F (0 C)

= 0.0765 lb/ft3 (1.226 kg/m3)g = 32.2 ft/sec2 (9.807 m/s2)

For structures that are not sensitive to wind-induced dynamics, which include elevated guide-ways and special structures up to a span length of400 ft (122m), the gust effect coefficient Cg mayvary between 1.25 and 1.50. For design purposes,a factor of 1.33 may be used for Cg. For struc-tures that are sensitive to wind action, Cg shouldbe determined by an approved method of dynamicanalysis or by model testing in a wind tunnel. Forguideway appurtenances, such as sign posts, light-ing poles, and flexible noise barriers, Cg may betaken as 1.75.

The exposure coefficient or height factor, Ce,may be computed from:

Ce= l/2’@, 2 l.O,forIiinfl

=5/8’@, 2 l.O,forHinm (3-7)

(3-6)

H is the height from ground level to the top of thesuperstructure. It should be measured from thefoot of cliffs, hills, or escarpments when thestructure is located on uneven terrain, or from thelow water level when the structure is located overbodies of water. Where excessive funneling may becaused by the topography at the site, Ce should beincreased by 20 percent.

The drag coefficient or shape factor, Cd, is afunction of many variables, the most important ofwhich are the skew angle (horizontal angle ofwind), and aspect ratio (ratio of length to width ofstructure). For box or I-girder superstructures andsolid-shaft piers with wind acting at zero skew andpitch angles, Cd may vary between 1.2 and 2.0. A

factor of 1.50 for Cd may be used for design pur-poses. For unusual exposure shapes, the drag co-efficient, Cd, should be determined from wind-tunnel tests.

Where wind effects are considered at a skewangle of B degrees measured from a line perpendi-cular to the longitudinal axis of a structure, thenCd should be multiplied by 0.0078 for the longitu-dinal wind load component and by (1 - 0.0001813~)for the transverse or perpendicular load compo-nent.

3.3.2.5- Wind Load on Slender Elements andAppurtenances

Slender elements, such as light and signsupports, should be designed for horizontal windloads provided for in Sections 3.3.2.3 and 3.3.2.4,as well as lateral and crosswind load effects causedby vortex shedding. Both serviceability andstrength considerations should be investigated.Details that may cause stress concentrations dueto fatigue or resonance should be avoided. 3.9

The wind drag coefficient, Cd, for sign andbarrier panels with aspect ratios of up to 1.0, of1.0 to 10.0, or more than 10.0, should be 1.1, 1.2,or 1.3, respectively.

For light fixtures and sign supports withrounded surfaces, octagonal sections with sharpcomers, or rectangular flat surfaces, the values ofCd should be 0.5, 1.2, or 1.4, respectively. A Valueof 1.2 for Cd should be used for suspended signalunits.

When ice accretion is expected on the surfaceof slender components, the total frontal areashould include the thickness of ice.

The dynamic effects of vortex shedding shouldbe analyzed and the stress limits for 2 x l06 cyclesof loading shall be applied.

3.3.3 -Loads Due to Ice Pressure, ICEFloating ice forces on piers and exposed pier

caps should be evaluated according to the localconditions at the site. Consideration should begiven to the following types of ice action on pierserected in bodies of water:

Dynamic ice pressure due to ice sheets andice floes in motion caused by stream orcurrent flow and enhanced by wind action,Static ice pressure caused by thermal actionon continuous stationary ice sheets over largebodies of water,Static pressure resulting from ice jams at aguideway site,Static uplift or vertical loads due to ice sheetsin water bodies of fluctuating level.

Ice loads resulting from freezing rain or con-


solidation of compact snow on the guidewaysuperstructure and vehicle should be included, asappropriate.

3.3.4- Loads due to Stream Current, SF3.3.4.1 -Longitudinal LoadsThe load acting on the longitudinal axis of a

pier due to flowing water may be computed by thefollowing expression.3.5

SF = ‘h CDAV2y (3-8)

where

A = Exposed area of the pier perpendicular tothe direction of stream flow, ft2 (m2)

Y = Mass density of water, 62.4 lb/ft3 (1000kg/m3)

V = Speed of stream flow, ft/sec (m/set)CD

= 0.7 for semicircular-nosed piers= 0.8 for wedge-nosed piers= 1.4 for squared-ended piers and against

drift lodged on the pier

3.3.4.2 -Transverse LoadsThe lateral load on a pier shaft due to stream

flow and drift should be resolved from the maindirection of flow. The appropriate componentshould be applied as a uniformly distributed loadon the exposed area of the pier, below the highwater level, in the direction under consideration.

3.4 -Loads due to Volumetric Changes3.4.1- General

Provisions should be made for all movementsand forces that can occur in the structure as aresult of shrinkage, creep, and variations in tem-perature. Load effects that may be induced by arestraint to these movements should be includedin the analysis. These restraints include thoseimposed during construction on a temporary basisand those imposed by the rail-fastener interactionon an on-going basis. Effects due to thermal gra-dients within the section should also be con-sidered.3.5

3.4.3 -Temperature, T3.4.2.1. -Temperature RangeThe minimum and maximum mean daily

temperatures should be based on local meteoro-logical data for a 50-year return period. The rangeof effective temperature for computing thermalmovements of the concrete structure should be thedifference between the warmest maximum and thecoldest minimum effective temperatures, whichmay be considered to be 5 F (2.5 C) above orbelow the mean daily minimum and maximumtemperatures. If local temperature data are not

available, the structure may be designed for aminimum temperature rise of 30 F (17 C) and aminimum temperature drop of 40 F (23 C) fromthe installation temperature.

3.4.2.2 -Effective Construction TemperatureIf the guideway is to be designed to accom-

modate continuously welded rails, an effectiveconstruction temperature should be selected. Thistemperature, which should be based on the meandaily temperature prevalent for the locality underconsideration, is used to establish the baseline railforce.

3.4.2.3 -Thermal Gradient EffectsCurvature caused by a temperature gradient

should be considered in the design of the struc-ture.

The temperature differential between topand bottom surfaces varies nonlinearly accordingto the depth and exposure of the structuralelements and their locality. A winter differential of15 F (8 C) and a summer differential of 25 F (14C) between the top of the deck and the soffit ofthe structure may be used. The temperaturedifferential should be increased in regions withhigh solar radiation; NCHRP 267 document maybe used as a guide in this respect.3.12

3.4.2.4 -Coefficient of Thermal ExpansionIn lieu of a more precise value, the coef-

ficient of linear thermal expansion for normalweight concrete may be taken as 6.5 x l0-6/deg F(12 x 10-6/deg C).

3.4.3-Rail-Structure Interaction FR and FrContinuously welded rail directly fastened to

the guideway, induces an axial force in the struc-ture through the fastener restraint when the struc-ture expands or contracts due to variations in tem-perature. Continuously welded rail is assumed tobe installed in a zero stress condition at an effec-tive installation temperature, T0. If the CWR isinstalled at a temperature that is different fromthe effective installation temperature, then the railis physically stressed to be compatible with thezero stress condition for which it is designed at theinstallation temperature.3.6

3.4.3.1 -Thermal Rail ForcesAxial rail stress fr due to a change in the

temperature after installation, is expressed by

fr = Er a (T1 - T0) (3-9)

CK = coefficient of thermal expansionTo = the installation temperature (zero-stress

condition)


r, = the final rail temperatureE, = modulus of elasticity of rail steel, given in

Section 5.6.3

For a temperature decrease, T1 may be takenas the minimum effective temperature described inSection 3.4.2.1. For a temperature rise, T1 may betaken as the maximum effective temperature plus20 F (12 C). The corresponding rail force, Fr, isexpressed by:

Fr =SId;=BA&a(Tl-To) (3-10)

where Z implies that the forces in all rails shouldbe summed up. The movement of the structurethrough the fasteners induces either a tensile orcompressive axial force on the rail, depending onwhether the temperature rises or drops, respec-tively, from that at installation.

A vertically or horizontally curved structureexperiences a radial force resulting from thethermal rail forces. This radial force per unitlength of rail is expressed as

where R is the radius of curvature. FR alwaysoccurs in combination with Fr.

The preceding expressions apply where thereis no motion of the rail relative to the structure.Where rail motion may occur, the relaxation ofthe rail must be analyzed to determine its effecton the structure. Rail motion may occur when:

- Rail expansion joints are present or,- Radial or tangential movements of rail and

guideway structure at curves occur, or- A rail break takes place, or- Continuous rails cross structural joints, or- Creep and shrinkage strains in prestressed

concrete elements continue to take place.

3.4.3.2 -Broken Rail ForcesAt very low temperatures, the probability of a

rail break increases. The most likely place for arail break to take place is at an expansion joint inthe structure. A rail break at this location gener-ally creates the largest forces in the structure.

When the rail breaks, it slips through thefasteners on both sides of the break until thetensile force in the rail before the break iscounteracted by the reversed fastener restraintforces. The unbalanced force from the broken railis resisted by both the unbroken rails and theguideway support system in proportion to their

relative stiffnesses. The probability that more thanone rail will break at the same time is small, andis generally not considered in the design.

3.4.3.3 - Rail GapThe relative stiffness of the system should be

proportioned so that the magnitude of the gap be-tween broken rail ends be equal to the maximumallowable in order to prevent vehicle derailment.Typically acceptable rail gaps are in the range of2 in. (50 mm) for a 16-in. (0.4-m) diameter wheeland up to 4 in. (100 mm) for larger wheels. Railgap is controlled by the spacing and stiffness ofthe fasteners.

3.4.4 -Shrinkage in Concrete, SHShrinkage is a function of number variables,

the most significant of which are the charac-teristics of the aggregates, the water-cement ratioof the mix, the type and the duration of curing,surface-to-volume ratio of the member, the am-bient temperature and relative humidity at thetime of placing the concrete. For a major transitproject, shrinkage and creep behavior of the con-crete mix should be validated as part of the designprocess. For precast members, only the portion ofshrinkage or creep remaining after the element isintegrated into the structure needs to be con-sidered.

In the absence of more accurate data ormethod of analysis, shrinkage strain r-days aftercasting of normal weight concrete may becomputed from the following expression:3.2

‘sh =k&tEshu (3-12)

where the ultimate shrinkage strain, E&,,, isexpressed as:

E* = 55o l - iii6[ ( IIH 2 xl04 (3-13)

For 0 I r I 12 in. (300 mm),

k, = 1-S[ T

+ 0.5, (3-14)

where rv is in inches,

i T1 ‘,-300

+ 0.5,

where rv is in mm.


For rv z= 12 in. (300 mm)

kv= 0.5

where rv ,= volume-to-surface-area ratio, t is thetime in days after the end of curing, and H is therelative ambient humidity, in percent.

k = 1 - e-O.‘ti (3-15)*

3.4.5-Creep in Concrete, CRCreep is a function of relative humidity,

volume-surface ratio and of time t after appli-cation of load. Creep is also affected by theamount of reinforcement in the section, themagnitude of sustained prestress force, the age ofthe concrete when the force is applied, and theproperties of the concrete mix. If the design issensitive to volumetric change, then an ex-perimental validation of creep behavior, based onthe ingredients to be used, may be necessary.

In the absence of more accurate data andprocedure, creep at r-days after application of loadmay be expressed in terms of the initial elasticstrain, 6 from:3.2

6CT = flak

where,

kr = 4.250 - 0.025H

For 0 4 rv I 10 in. (250 mm)

(3-16)

+ 0.7, (3-17)

where rv is in inches,

I= 1-z[ T250

+ 0.7,

where rv is in mm

For rv > 10 in. (250 mm)

k = 0.7

where t is the time in days after application ofload or prestress, and,

k = 1 - e-0.w (3-18)f

3.5 - Exceptional Loads3.5.1 - Earthquake Effects, EQ

In regions designated as earthquake zones,structures should be designed to resist seismicmotions by considering the relationship of the siteto active faults, the seismic response of the soils atthe site, and the dynamic response characteristicsof the total structure in accordance with the latestedition of AASHTO “Standard Specifications forHighway Bridges."3.11 Certain local jurisdictionshave Zone 4 high seismic risk requirements foranalysis and design. For structures in this zone, adynamic analysis is recommended.

3.5.2 -Derailment Load, DRDerailment may occur when the vehicle

steering mechanism fails to respond on curves orwhen the wheels jump the rails at too large apull-apart gap, which may be the result of a breakin a continuously welded rail. Derailment may alsobe caused by intervehicle collision. For the designof the top slab and the barrier wall of theguideway, both the vertical and horizontalderailment loads may be considered to act si-multaneously.

The force effects caused by a single derailedstandard vehicle should be considered in the de-sign of the guideway structure components. Theseeffects, whether local or global, should in-cludeflexure, shear, torsion, axial tension orcompression, and punching shear through thedeck. The derailed vehicle should be assumed tocome to rest as close to the barrier wall asphysically possible to produce the largest forceeffect. In the design of the deck slab, a dynamicload allowance of 1.0 should be included in thewheel loads.

The magnitude and line of action of a hori-zontal derailment load on a barrier wall is afunction of a number of variables. These includethe distance of the tracks from the barrier wall,the vehicle weight and speed at derailment, theflexibility of the wall, and the frictional resistancebetween the vehicle and the wall. In lieu of adetailed analysis, the barrier wall should bedesigned to resist a lateral force equivalent to 50percent of a standard vehicle weight distributedover a length of 15 ft (5 m) along the wall andacting at the axle height. This force is equivalentto a deceleration rate of 0.5 g.

Collision forces between vehicles result fromthe derailment of a vehicle and its subsequentresting position against the guideway sidewall.


This eccentric load on the guideway causes tor-sional effects, which should be accounted for inthe design. The magnitude and eccentricity of thisvertical collision load is a function of the distanceof the guideway center line from the side wall, theaxle width and the relative position of the centerlines of the car body and the truck after thecollision.

3.5.3 -Broken Rail Forces, BRForces on the guideway support elements due

to a broken rail are discussed in Section 3.4.3,under Rail-Structure Interaction.

3.5.4 - Collision Load, CLPiers or other guideway support elements that

are situated less than 10 ft (3 m) from the edge ofan adjacent street or highway should be designedto withstand a horizontal static force of 225 kips(1000 kN), unless protected by suitable barriers.The force is to be applied on the support element,or the protection barrier, at an angle of 10 degfrom the direction of the road traffic and at aheight of 4 ft (1.20 m) above ground level. TheCollision Load need not be applied concurrentlywith loads other than the dead load of thestructure.

The possibility of overheight vehicles collidingwith the guideway beam should be considered forguideways with less than 16.5ft (5.0m) clearanceover existing roadways.

3.6 - Construction Loads3.6.1 -General

Loads due to construction equipment andmaterials that may be imposed on the guidewaystructure during construction should be accountedfor. Additionally, transient load effects duringconstruction due to wind, ice, stream flow andearthquakes should be considered with returnperiods and probabilities of single or multipleoccurrences commensurate with the expected lifeof the temporary structure or the duration of aparticular construction stage.

3.6.2 - Dead LoadsDead loads on the structure during con-

struction should include the weights of formwork,falsework, fixed appendages and stored materials.The dead weights of mobile equipment that maybe fixed at a stationary location on the guidewayfor long durations shall also be considered. Suchequipment includes lifting and launching devices.

3.6.3 -Live LoadsLive loads on the structure during construc-

tion should include the weight of workers and allmobile equipment, such as vehicles, hoists, cranes,and structural components used during the processof erection. It is recommended that constructionlive load limits be identified on the contractdocuments.

REFERENCES

3.1 “GOALRT (Government of Ontario Advanced LightRail Transit) System Standards - Design Criteria for theGOALRT Elevated Guideway and Special Structures,GOALRT Program, Downsview, Part 3, Loads, and Part 4,Design Methods.

3.2 “OHBD (Ontario Highway Bridge Design) Code,” 3rdEdition, Ministry of Transportation, Downsview, Ontario 1991,V. 1 and V. 2.

3.3 Ravera, R.J., and Anders, J.R., “Analysis andSimulation of Vehicle/Guideway Interactions with Applicationto a Tracked Air Cushion Vehicle,” MITRE Technical ReportMTR-6839, The MITRE Corporation, McLean, VA 22101,Feb. 1975 pp. 95.

3.4 Billing, J.R., “Estimation of the Natural Frequenciesof Continuous Multi-Span Bridges: Report No. RR.219,Ministry of Transportation, Downsview, Jan. 1979, 20 pp.

3.5 Priestly, M.J.N., and Buckle, I.G., “Ambient ThermalResponse of Concrete Bridges” Bridge Seminar, RoadResearch Unit, National Roads Board, Wellington, 1978, V. 2.

3.6 Grouni, H., and Sadler. C.. “Thermal InteractionBetween Continuously Welded Rail and Elevated TransitGuideway," Proceedings, International Conference on Short andMedium Span Bridges, Aug. 17-21, 1986, Ottawa, Ont. Canada.

3.7 “National Building Code of Canada” (NRCC 23174),National Research Council of Canada, Ottawa, 1977, Part 4,pp. 151-180.

3.8 “Design of Highway Bridges,” (CAN 3-S6), CanadianStandards Association, Rexdale, 1974.

3.9 Davenport, A.G., and Isyumov, N., “Application of theBoundary Layer Wind Tunnel to the Prediction of WindLoading,” Proceedings, International Seminar on Wind Effectson Building and Structures (Ottawa, 1967). University ofToronto Press, 1968, pp. 201-230.

3.10 Davenport, A.G., “Response of Slender Line-LikeStructures to a Gusty Wind,” Proceedings, Institution of CivilEngineers (London), V. 23, Nov. 1962, pp. 389-408.

3.11 AASHTO, Standard Specification for HighwayBridges, American Association of State Highway andTransportation Officials, (Latest Edition).

3.12 NCHRP 267, National Cooperative HighwayResearch Program, Washington, D.C., (Latest Edition).


CHAPTER 4 - LOAD COMBINATIONS ANDLOAD AND STRENGTH REDUCTION

FACTORS

4.1 - ScopeThis chapter specifies load factors, strength

reduction factors, and load combinations to beused in serviceability and strength designs. Struc-tural safety is used as the acceptance criterion.The derivation of load and strength reduction fac-tors is based on probabilistic methods, usingavailable statistical data and making certain basicassumptions.4.2 - Basic Assumptions

The economic life of a transit guideway istaken as 75 years. Load and resistance modelswere developed accordingly.

Guideway structures should meet the require-ments for both serviceability and strength design.Serviceability design criteria were derived byelastic analysis; stresses and section resistanceswere determined accordingly. Strength design cri-teria were also derived by elastic analysis. How-ever, while stresses were determined accordingly,section resistances were determined by inelasticbehavior.

The load and resistance models used in thisstudy were based on available test data, analyticalresults, and engineering judgment.4.2,4.7

Live load is defined by a fully loaded standardvehicle. The weight of vehicles should include anallowance for potential weight growth. Resistancemodels take into account the degree of qualitycontrol during casting. Thus, the properties offactory-produced members are considered morereliable than those of cast-in-place members.Some requirements for concrete strength controlspecified by AASHTO are more stringent thanthose specified by ACI. However, ACI specifi-cations are generally assumed in this document.

Safety is measured in terms of the reliabilityindex. A higher reliability index, reflects a lowerprobability of failure. A target reliability index of4.0 is adopted for strength design. This impliesthat a transit structure would have a lower proba-bility of failure than a highway bridge, where a re-liability index of 3.5 is commonly used.4.8 The

higher target value is justified by the fact that theconsequences of failure of a transit guidewaywould be far greater than those of a highwaybridge. The target reliability index adopted forserviceability design, is 2.5 for cracking and 2.0 forfatigue.

The objective in deriving reliability-based loadfactors is to provide a uniform safety level to load-carrying components. The uncertainties in meth-ods of analysis, material properties and dimen-sional accuracies are taken into account in thederivation of strength reduction factors. Uncer-tainties to the magnitude of imposed loads andtheir mean-to-nominal ratios are accounted for inthe derivation of load factors. Because of the highfrequency of train passes on a guideway structure,environmental and emergency loads are combinedwith maximum live load. The dead load factor isset at 1.30 for both precast and cast-in-place com-ponents, consistent with the AASHTO bridge spe-cifications and ACI 343R. The derivation of loadand strength reduction factors for other load com-ponents is also based on reliability approach.

4.3 - Service Load CombinationsFour service load combinations, S1, S2, S3,

and S4 are listed in Table 4.3. When warranted,

Table 4.3 - Service load combinations

Sl = D + L + I +PS + LF, + (CF or HF or F()

S2 = Sl + [03 (WL + WS) or ICE or SF]

S3 = S2 + T + SH + CR

S4=PS+D+(WSorEQ)+T+SH+CR

more load combinations may be used on specificprojects. Load and strength reduction factors arenot used for serviceability design.

4.4 -Strength Load Combinations4.4.1 -General Requirements

For strength design, the factored strength ofa member should exceed the total factored loadeffect. The factored strength of a member or crosssection is obtained by taking the nominal memberstrength, calculated in accordance with Chapter 6,and multiplying it by the appropriate strengthreduction factor 4, given in Section 4.4.3. Thetotal factored load effect should be obtained fromrelevant strength combination, U, incorporatingthe appropriate load factors given in Table 4.4.

Simultaneous occurrence of loads is modeledby using available data. For the purposes of reli-ability analysis, loads are divided into categoriesaccording to their duration and the probability of


load combinations.

Load component U0 Ul U2 U3 U4 U5 U6

D 1.3* 1.3* 1.3* 1.3* 1.3* 1.3* 1.3*

L, I and either CF or HF 1.7 1.4 1.4 1.4 1.4 1.4**

SH and CR 1.0 1.0 1.0 1.0 1.0 1.0

PS 1.0 1.0 1.0 1.0 1.0 1.0 1.0

WL + WS 1.5 1.5

WS 1.0

ICE, T, SF, or EQ 1.5

LFe 1.4

BR (FR, FJ l.2

CL 1.3

DR 1A

l Use 0.9 when effect is more conservative.l * Use the weight of an empty train only.

their joint occurrence, as follows:

- Permanent loads: dead load, earth pressure,structural restraint

- Gradually varying loads: prestressing effects,creep and shrinkage, differential foundationsettlement, and temperature effects

- Transitory loads: live load (static anddynamic) and wind,

- Exceptional loads: earthquake, emergencybraking, broken rail, derailment, vehiclecollision

It is assumed that gradually varying loads actsimultaneously with permanent loads. ‘The formerare taken at their maximum or minimum level,whichever yield the worse case scenario for struc-tural performance, for the duration considered.

Transitory and exceptional loads are combinedaccording to Turkstra’s rule. 4.9 This rule stipulatesthat the maximum total load occurs when one ofthe load components is at its maximum value, si-multaneously with the other load componentstaken at their average values. Ail possible com-binations are considered in order to determine theone which maximizes the total effect. The loadfactors corresponding to the time-varying loadcombinations reflect the reduced likelihood ofsimultaneous occurrence of these loads.

4.4.2 -Load Combinations and Load FactorsLoad combinations, together with the corres-

ponding factors for strength design, are listed inTable 4.4. Values of load components are spe-cified in Chapter 3.

4.4.3 - Strength Reduction Factors, ol The capacity of a section should be reduced

by a strength reduction factor, 4, as follows:

- For flexure only, or flexure with ol = 0.95axial load in precast concrete

- For flexure only, or flexure with ol = 0.90axial load in cast-in-place concrete

- For shear and torsion ol = 0.75- For axial tension f#J = 0.85- For compression in members

with spiral reinforcement 4 = 0.75- For compression in other members 6 = 0.70

For low values of axial compression, 4 may beincreased linearly to 0.90 or 0.95 for cast-in-placeor precast concrete, respectively, as the axial loaddecreases from 0.10 f,’ Ag to zero.

The ol factors were computed with the as-sumption that precast concrete guideway compo-nents, with bonded post-tensioning tendons areused.


,

REFERENCES*

4.1 Corotis, B., “Probability-Based Design Codes,"Concrete International Design and Construction, V. 7, No. 4Apr. 1985, pp. 42-49.

4.2 Nowak, A.S., and Grouni, H., “ServiceabilityConsideration for Guideways and Bridges,” Canadian Journalof Civil Engineering, V. 15, No. 4, Aug. 1988, pp. 534-538.

4.3 Grouni, H.N., Nowak, A.S., Dorton, R.A., “DesignCriteria for Transit Guideways," Proceedings, 12th Congress,International Association for Bridge and StructuralEngineering, Zurich, 1984, pp. 539-546.

4.4 Nowak, A.S., and Grouni, H.N., “Development ofDesign Criteria for Transit Guideway," ACI JOURNAL,Proceedings V. 80, No. 5, Sept.-Oct. 1983, pp. 387-389.

4.5 Nowak, A.S. and Grouni, H.N., “Serviceability Criteriain Prestressed Concrete Bridges,” ACI JOURNAL, ProceedingsV. 83, No. 1, Jan.-Feb. 1966, pp. 43-49.

4.6 Thoft-Christensen, P., and Baker, MJ., StructuralReliability Theory and Its Applications, Springer-Verlag, NewYork, 1982, 267 pp.

4.7 Nowak, A.S., and Lind, NC, “Practical Bridge CodeCalibration,” Proceedings, ASCE, V. 105, STl2, Dec. 1979, pp.2497-2510.

4.8 “OHBD (Ontario Highway Bridge Design) Code,” 3rdEdition, Ministry of Transportation, Downsview, Ontario, 1991,V. 1 and V. 2.

4.9 Turkstra, C.J., “Theory of Structural DesignDecisions,” Study No. 2, Solid Mechanics Division, Universityof Waterloo, Ont., 1970, pp. 124.


CHAPTER 5- SERVICEABILITY DESIGN

5.1 - GeneralThis chapter covers the performance of

reinforced concrete guideways (both prestressedand non-prestressed) under service loadings.Serviceability requirements to be investigatedinclude stresses, fatigue, vibration, deformationand cracking.

Fatigue is included in serviceability designsince high cyclic loading influences the permissibledesign stresses. Load combinations for service-ability design are given in Section 4.3. Durabilityconsiderations are given in Section 2.3.6.

5.2 - Basic AssumptionsForce effects under service loads should be

determined by a linear elastic analysis. Forinvestigation of stresses at service conditions, thefollowing assumptions are made:

a. Strains are directly proportional to distance

from the neutral axisb. At cracked sections, concrete does not resist

tensionc. Stress is directly proportional to strain.

5.3 - Permissible Stresses5.3.1 - Non-prestressed Members

Fatigue and cracking are controlled by limit-ing the stress levels in the concrete and the non-prestressed reinforcement. The stress limitationsare discussed in Sections 5.5 and 5.8.

5.3.2 - Prestressed Members5.3.2.1 -ConcreteFlexural stresses in prestressed concrete mem-

bers should not exceed the following:

(a) At transfer:

Stresses before losses due to creep, shrinkageand relaxation and before redistribution of forceeffect take place, should not exceed the following:

- Compressionl pretensioned members:l post-tensioned members:

0.60fci’0.55fci'

- Tension in members without bondednonprestressed reinforcement in thetension zone: 0.4Of,

In the absence of more precise data, thecracking stress of concrete, f,., may be

taken as 7.5 ,& (psi) (0.6 & MPa).

- Tension in members with bonded non-prestressed reinforcement in the tensionzone: l.OOf,,

Where the calculated tensile stress isbetween 0.4Of, and l.Of=,+ reinforce-ment should be provided to resist thetotal tensile force in the concretecomputed on the basis of an uncrackedsection. The stress in the reinforcementshould not exceed 0.6Of or 30 ksi (200MPa), whichever is smaller.

- Tension at joints in segmental members:

0 Without bonded non-prestressedreinforcement passing through the joint inthe tension zone: 0.0


l With bonded non-prestressedreinforcement passing through the joint inthe tension zone: o.w?iWhere the calculated tensile stress is be-tween zero and 0.4Of, reinforcementshould be provided to resist the total tensileforce in the concrete computed on the basisof an uncracked section. The stress in thereinforcement should not exceed 0.60& or30 ksi (200 MPa), whichever is smaller.

(b) Service loads:

Stresses, after allowance for all losses due tocreep, shrinkage and relaxation and re-distribution of force effects, should not exceedthe following:

- Compression:l Load combination S1 or S2,

Precast members: 0.45f,'Cast-in-place members: 0.4Of,'

0 Load combination S3 or S4,Precast members: OhOf,Cast-in-place members: O.SSf,'

- Tension in precompressed tensile zones:l For severe exposure conditions, such as

coastal areas, members in axial tension,and load combination S1 (for combina-tion S3 and (S4) moderate caseapplies): 0.0

0 For moderate exposure conditions, andfor, load combination S2: 0.4OL

In the absence of more precise data

the cracking stress of concrete, f,’ may

be taken as 7.5 & (psi) (0.6 & MPa).

l Other cases and extreme operatingconditions at load combinations S3and S4: 0.8OLr

0 For segmental members withoutbonded prestressed reinforcementpassing through the joints: 0.0

l For design against fatigue: 0.0

l Tension in other areas should belimited by allowable stresses at transfer.

5.3.2.2 - SteelThe stress in prestressing steel should not

exceed the values given in Table 5.3.

Type of Steel

PrestressingStage

Stress-relieved strand Low relaxationand wire, strand and wire,fpu = 0.85 fP” f

pu= 0.90 fP”

High strengthbarfpu

= 0.80$,

At Jacking:PretensioningPost-tensioning

0.80 fp. 0.80 fp.0.80 $. 0.85 fp” 0.75 fP”

At transfer:PretensioningPost-tensioning

0.70 fP” 0.74 fP” 0.66 fpu0.70 $” 0.74 &” 0.66 fP”

The maximum stress at jacking should in nocase exceed 0.94f, or the maximum value recom-mended by the manufacturer of the prestressingtendons and anchorages, while that at transfershould in no case exceed 0.82f,. The maximumstress in the post-tensioning tendons, at anchor-ages and couplers, immediately after tendon an-chorage should not exceed 0.7Of, in accordancewith ACI 318R.

5.3.3 - Partial PrestressingThe preceding tensile strength limitations may

be waived if calculations, based on approved orexperimentally verified rational procedures, dem-onstrate adequate deflection, cracking and fatiguecontrol under specified loading combinations.


5.4 - Loss of PrestressIn determining the effective prestress, al-

lowance should be made for the following sourcesof prestress loss:

a. slip at the anchorageb. friction losses due to intended and unintended

(wobble) curvature in the tendonsc. elastic shortening of concreted. creep of concretee. shrinkage of concretef. relaxation of steel

The amount of prestress loss due to thesecauses depends on a number of factors that in-clude, properties of the materials used in thestructure, the environment, and the stress levels atvarious loading stages. Accurate estimates ofprestress loss require recognition that the indi-vidual losses resulting from the above sources areinterdependent.

The losses outlined above may be estimatedusing the methods outlined in the AASHTObridge specifications, ACI 343R, or References 5.1through 5.3.

For preliminary design of structures, usingnormal density concrete, the lump sum lossesshown in Table 5.4 may be used. Lump sum losses

Table 5.4- Lump Sum Losses for Preliminary Design5.12

PRETENSIONED POST-TENSIONED

Stress relieved Low relaxation Stress relieved Low relaxation

At transfer 29 19 4 4

After transfer

Total

Units are ksi (MPa).

(200) (130) (30) (30)

37 22 37 20(255) (150) (255) (135)

66 41 41 24(455) (280) (285) (165)

do not include anchorage and friction losses inpost-tensioned tendons. The losses are higher thanthose in the AASHTO bridge specifications due tothe higher jacking stresses.

For members constructed and prestressed inmultiple stages, or for segmental construction, thestress level at the commencement and termi-nation of each stage should be considered.

5.5 - Fatigue5.5.1 -GeneralA transit guideway may undergo six million or

more vehicle passes at various load levels duringits lifetime. This may be equivalent to three tofour million cycles at maximum live load level.Such high levels of cyclic loading render guidewaysprone to fatigue failure.

Areas of concern are the prestressing steeland the reinforcing bars located at sections wherea large number of stress cycles may occur atcracked sections.

5.5.2 - ConcreteUnder service load combination S1, the

flexural compressive stress in concrete, should notexceed 0.45f,' at sections where stress is cyclic andno tensile stresses are allowed.

5.5.3 - Non-prestressed ReinforcementUnder service load condition S1, the stress

range in straight flexural reinforcing bars ffr andfsr, in accordance with AASHTO bridge specifi-cations, should not exceed the following:

For straight bars:

ffr= (21 - 0.33fm + 8 r/h), ksi (5-l)

= (145 - 0.33fm + 55 r/h), MPa

where,

r/h = radius-to-height ratio of transversedeformations. When actual value is notknown, r/h = 0.3

fm = algebraic minimum stress, ksi (MPa)(tension, positive; compression, negative)

For bent flexural bars, stirrups and bars containingwelds conforming to requirements of AWS D1.4:

f sr = O.SOf, (5-2)

Bends and welds in principal reinforcement shouldnot be used in regions of high stress range.

For shear reinforcement, the change in stress,fsv, may be computed as follows:

/-=2, ksi (MPU) (5-3)


where

_̂ V = the range of the shear force at a section, k(N)

z4= spacing of shear reinforcement, in. (mm)

jd”= area of shear reinforcement, in.2 (mm’)= distance between tensile andcomprehensiveforces at a section based on an elastic analysis,in. (mm).

For torsion reinforcement, the change in stress,fst, may be computed for box sections or sectionswhere a/b < 0.6, as follows:

fst =_̂ Ts

(1.7A,A,)(5-4)

where,

_̂ T = the range of torsion at a section, k-in.(N-mm)

s = spacing of torsional reinforcement, in’(mm2)

At= area of torsional reinforcement, in2/mm2

Aoh = area enclosed by the centerline of closedtransverse torsional reinforcement, in2(mm2)

a,b = the shorter and longer center-to-centerdimensions of closed rectangular stirrups,respectively, in. (mm).

For combined effects of shear and torsion

fsv + fst < ffr (5-5)

5.5.4 - Prestressed ReinforcementIn prestressed concrete members, the change in

stress in the prestressing reinforcement for serviceload condition S1, or other appropriate load cases,using cracked or uncracked section analysis,should not exceed 0.04fpu. Recent experimentshave indicated that post-tensioned tendons aresusceptible to fatigue failures at locations wherethe tendon curves as found in ACI 215R. At theselocations the change in stress in the tendon due tocyclic loads should not exceed 0.025fpu.5.4

5.6 - Vibration5.6.1 -GeneralVibration of the guideway during the passage

of a transit vehicle induces motion of the vehiclethat result in a poor ride quality. Thus guidewaysmust be designed to provide an acceptable level ofpassenger comfort. This entails consideration ofthe vehicle-guideway interaction.

The most significant factor affecting ride qual-ity is the acceleration level experienced by the

passenger and, as a result, comfort criteria areusually expressed in terms of acceleration limits.

Maximum dynamic effects occur when the fre-quency of the vehicle is close to the natural fre-quency of the guideway, giving rise to a quasi-resonant condition. For a guideway structure, theonly natural frequency which usually needs to beconsidered is its lowest, or fundamental, naturalflexural frequency. A quasi-resonance conditionmay be avoided by ensuring that the structurefrequency is outside the frequency range of thevehicle, as provided by the manufacturer. Thus,natural frequencies of the guideway must be in-vestigated in the design process.

5.6.2 - Natural FrequencyThe expression for the fundamental flexural

frequency of a simply supported beam is given inSection 3.3.1.2.

The fundamental frequency of a continuousbeam, having a series of equal spans, is the sameas that of a simply supported beam of the samespan length. For a continuous beam, in which thespans are unequal, a reasonable estimate of thefundamental frequency may be obtained by assum-ing the longest span to be simply-supported. Amore accurate value of the fundamental frequencymay be obtained using the approaches in Refer-ences 5.5 and 5.6. Effects of the horizontalcurvature can be accounted for as shown in Ref-erence 5.7.

Continuous beams have frequencies of higherflexural modes which are closer to the funda-mental frequency than is the case for simplysupported beams. Consequently, care should betaken to ensure that one of these higher fre-quencies for a continuous beam does not coincidewith frequency of the vehicle.

Attention should be given to torsionalfrequencies of the guideway and the vehicle inguideway where not all supports can resist tor-sional effects. Methods for the computation oftorsional frequencies can be found in standardtextbooks on vibrations of structures.5.8

5.6.3 -Modulus of ElasticityThe modulus of elasticity, EC, for concrete

may be taken as Wc1.5 33 & in psi (wc’.’in MPa) for values of wc between 90 and 155(1500 and 2500 kg/m3).crete, Ec may be taken

The modulus of elasticity, Es, for non-prestressed reinforcement may be taken as29,000,000 psi (200,000 MPa).

The modulus of elasticity, Es, for prestressingtendons shall be determined by tests or suppliedby the manufacturer.


5.7 -Deformation5.7.1 -GeneralDeflections and rotations due to external

loading, prestress, and volume changes due totemperature, creep, and shrinkage, should be con-sidered in the design; excessive deformations canaffect the structure and the ride quality directly.Of particular importance is the angular disconti-nuity at the guideway surface at the ends of beamsat expansion joint.

Deformation in members under sustainedloading should be calculated as the sum of boththe immediate and the long-term deformations.Deflections, which occur immediately upon appli-cation of load, should be computed by the usualmethods for elastic deflections.

5.7.2 - Non-prestressed Members5.7.2.1 -Immediate DeflectionFor simple spans the effective moment of

inertia, Ie, should be taken as

Icr = moment of inertia of cracked sectiontransformed to concrete, in.4 (m4)

Ig= moment of inertia of gross concrete sectionabout the centroidal axis, neglecting thereinforcement, in.4 (m4)

Ma= maximum moment in member at stage forwhich deflection is being computed, lb - in. (N- mm)

2= cracking moment = fcrIg/yt= cracking stress in concrete, psi (MPa)

yt= distance from the centroidal axis of a cross-section (neglecting the reinforcement) to theextreme fiber in tension, in (mm).

For continuous spans, the effective moment ofinertia may be taken as the average of the valuesobtained using the preceding equation for thecritical positive and negative moment sections.

5.7.2.2 -Long-Term DeflectionIn lieu of a detailed analysis, the additional

long-term deflection resulting from creep andshrinkage for both normal weight and light-weightconcrete flexural members may be estimated bymultiplying the immediate deflection, caused bythe sustained load being considered, by the factor

A= T1 + 5op’

(5-7)

where,

PI = reinforcement ratio for non-prestressedcompressive reinforcement

T = time-dependent factor for sustained load,and may be taken as:

5 years or more, T = 2.012 months, T= 1.46 months, T= 1.43 months, T= 1.0

5.7.3 - Prestressed MembersThe effects induced by prestress should be

included in the computation of deformation.

5.7.3.1 -Immediate Camber/DeflectionThe moment of inertia should be taken as

that of the gross concrete section.

5.7.3.2 -Long-Term Camber/DeflectionIn lieu of a detailed analysis, long-term

camber and deflection, as a function of instan-taneous camber and deflection for members con-structed and prestressed in a single stage, may beestimated by multiplying the initial camber ordeflection by the factors shown in Table 5.7.5.9

It should be noted that these factors apply tosimple spans. For continuous spans, in the ab-sence of a detailed analysis, long-term deflectionsmay be estimated by applying two thirds of thefactors given in the table.

5.8 - Crack ControlCracking should be controlled in non-

prestressed reinforced members by suitable de-tailing and sizing of the reinforcement. Pre-stressed concrete members should contain non-prestressed reinforcement at the precompressedtensile zone.

Provisions should be made in design for posi-tive moments that may develop in the negativemoment regions of precast prestressed unitserected as simple span and made continuous forlive loads. The effects of loading in remote spans,as well as shrinkage, creep, and elastic shorteningof the piers should also be considered in thedesign.


At erection:

Deflection (downward) component -apply to the elastic deflectiondue to the member weight at release of prestress

Camber (upward) component -apply to the elastic camber due to prestress at the time ofrelease of prestress

Final:

Deflection (downward) component -apply to the elastic deflection due to the member weight atrelease of prestress

Camber (upward) component -apply to the elastic camber due to prestress at the time ofrelease of prestress

Deflection (downward) - apply to elastic deflection due tosuperimposed dead load only

Deflection (downward) - apply to elastic deflection caused by thecomposite topping

Without composite With compositetopping topping

1.85

1.80

2.70

2.45

3.00

1.85

1.80

2.40

2.20

3.00

2.30

5.8.l - Non-prestressed MembersTensile reinforcement should be distributed in

the tension zones so that the calculated stress inthe reinforcement would not exceed the following:

The quantity z should not exceed 130 kips/in.(23 kN/mm) for severe exposure and 170 kips/in(30kN/mm) for other conditions; where

dc= thickness of the concrete cover measuredfrom the extreme tensile fiber to the center ofthe bar located closest thereto.

A = effective tension area of concretesurrounding the main tension reinforcing barsand having the same centroid as that rein-forcement, divided by the number of bars.When the main reinforcement consists ofseveral bar sizes, the number of bars shouldbe computed as the total steel area divided bythe area of the largest bar used.

5.8.2 - Prestressed MembersReinforcement must be provided to control

two types of cracking, namely, bursting and spal-ling at the anchorage zones of post-tensionedmembers. Several methods of proportioning thereinforcement are available. The following ap-proach may be applied to the bursting componentof cracking; it is derived from expressions inReference 5.10, and presented in Reference 5.12as a representative approach.

5.8.2.1 -Post-Tensioned MembersThe maximum stress, fbs, causing bursting may

be computed from

fbs = 9 F,ila22y psi (5-9)

-%‘f =ca

and should not exceed 0.80fti + 20pbs,

where

(5-10)


AfrsPhc = -bbS

(5-11)

A bs = area of non-prestressed reinforcementlocated perpendicular to a potential burstingcrack, in.2 (mm2).

bb= width of concrete in the plane of apotential bursting crack, in. (mm).

S = spacing of reinforcement to resist burstingor pitch of spiral reinforcement, in. (mm).

fcri= cracking stress of concrete at time of initialprestress, psi (MPa)

For calculating fbs,, a symmetrically placedsquare anchor of side a1 acting on a square prismof side and depth a2 may be assumed. The dimen-sion a2 should be the minimum distance betweenthe centerline of anchors or two times the distancefrom the centerline of the anchor to the nearestedge of concrete, whichever is lesser [Fig.5.8.2(a)]. For circular anchors, aI should be takenas the side of a square with an area equal to thearea of the circular anchor.

The total force, Fbs, causing bursting in aplane perpendicular to the longitudinal axis of thetendon, may be computed from

Fbs = 0.70 Fsj 11 (5-12)

Reinforcement to resist the bursting forceshould be uniformly distributed from 0.52Xm to a distance equal to a2,, measured from the loaded face of the end block [Fig. 5.8.2(b)], where:

anchoragesf%*@;/~L-i--H s y m m e t r i c a l lLl-4 ’

QZR a2/2 a2f2prism am am

anchor spacing controls edge distance controls

t>, a2

Fig. 5.8.2(a) Symmetrical Prism Concept

The stress in the reinforcement should notexceed 30 ksi (200 MPa) nor 0.854.

Reinforcement to control spalling cracks inboth the horizontal and vertical planes at theanchorage zones should be provided within 0.2h ofthe end of the member. The spalling force may bedetermined by the method described in Reference5.11. The end stirrup should be placed as closelyto the end of the member as practicable withadequate cover. The reinforcement should extendover the full depth and width of the member. Thestress in the reinforcement should not exceed 20ksi (140 MPa).

5.8.2.2 - Pretensioned MembersEnd blocks are not required where all tendons

are pretensioned strand.Vertical stirrups to resist a tension equal to at

least four percent of the prestressing force attransfer should be distributed uniformly over alength equal to 0.2h from the end of the girder.The end stirrup should be placed as closely to theend of the member as practicable. The stress inthe reinforcement should not exceed 20 ksi (140MPa).

The ends of members with flanges should bereinforced to enclose the prestressing steel in theflanges.

Transverse reinforcement should be providedin the flanges of box girders and should beanchored into the webs of the girder.

Xm= 0.54 (I - I#)u2 (5-13)


loaded force

0.52% >c, a2

DISTANCEFig. 5.8.2(b) Distribution of Stress Causing Bursting

REFERENCES*

5.1. PC1 Committee on Prestress Losses,“Recommendations for Estimating Prestress Losses,” Journal,Prestressed Concrete Institute, V. 20, No. 4, July-Aug. 1975,pp. 43-75. Also, Discussion, V. 21, No. 2. Mar.-Apr. 1976, pp.108-126.

5.2. Zia, Paul, Kent, Preston H., Scott, Norman L, andWorkman, Edwin B., “Estimating Prestress Losses,” ConcreteInternationaI: Design and Construction, V. 1, No. 6, June 1979,pp. 32-38.

5.3. Huang, Ti., “A New Procedure for Estimation OfPrestress Losses,” Report No. 470.1, Research Project No.80-23, Pennsylvania Department of Transportation/FritzEngineering Laboratory. Lehigh University, Bethlehem, May1982.

5.4. Rigon, C., and Thurlimann, B., “Fatigue Tests onPost-Tensioned Concrete Beams,” BERICHT No. 8101-1,Institut fur Baustatik und Konstruktion. ETH, Zurich, Aug.1984, 74 pp.

5.5. Billing, J.R., “Estimation of Natural Frequencies ofContinuous Multi-Span Bridges,” Report. No. RR219, Ministryof Transportation and Communications, Downsview, 1979.

5.6. Csagoly, P.F., Campbell, T.I., and Agarwal, A.C.,“Bridge Vibration Study,” Report No. RR 181, Ministry ofTransportation and Communications, Downsview, 1972.

5.7. Campbell, T.I., “Natural Frequencies of CurvedBeams and Skew Slabs,” Report, OJT & CRP Project 8303,Queen’s University, Kingston, Mar. 1978.

5.8. Thompson, W.T., Theory of Vibration WithApplications, Prentice-Hall, Inc., Englewood Cliffs, 1972.

5.9. PC1 Design Handbook, 2nd Edition, PrestressedConcrete Institute, Chicago, 1978, 384 pp.

5.10. Iyengar, Kashi T.S.R., and Mandanapalle, K.Prabhakara, “Anchor Zone Stresses in Prestressed Concrete

Beams: Proceedings, ASCE, V. 97, ST3, Mar. 1971, pp.807-824.

5.11. Gergely, Peter, and Sozen, Mete A., “Design ofAnchorage-Zone Reinforcement in Prestressed ConcreteBeams,” Journal, Prestressed Concrete Institute, V. 12, No. 2,Apr. 1967, pp. 63-75.

5.12 “OHBD (Ontario Highway Bridge Design) Code,”3rd Edition, 1991, Ministry of Transportation, Downsview,Ontario, 1991, V. 1 and V. 2.

* For recommended references, see Chapter 8.

CHAPTER 6 -STRENGTH DESIGN

6.1 -General Design and Analysis Con-siderations

The recommendations in this chapter are in-tended for reinforced concrete guideways pro-portioned for adequate strength using load com-binations, load factors, and strength reductionfactors as specified in Chapter 4. The recom-mendations are based principally on ACI 318,“Building Code Requirements for ReinforcedConcrete,” hence, may also be applied to non-prestressed components of a guideway structure,where applicable.

All members of statically indeterminatestructures should be designed for the maximumeffects of the specified loads as determined by 1)elastic analysis, or 2) any acceptable method thattakes into account the nonlinear behavior of re-inforced concrete members when subjected tobending moments approaching the strength ofthe member. Analysis should satisfy the condi-tions of equilibrium, compatibility and stabilityat all points in the structure and at all magni-


tudes of loading up to ultimate.Negative moments calculated by elastic ana-

lysis at the supports of continuous pre-stressed andnon-prestressed flexural members, for anyassumed loading arrangement, may be increasedor decreased in accordance with the provisions ofACI 318.

For guideways made continuous by post-tensioning over two or more spans, the effects ofsecondary moments due to the reactions inducedby prestressing should be included.

Any reasonable assumption may be adoptedfor computing the relative flexural and torsionalstiffness of members in a statically indeterminatesystem. The moments of inertia used to obtain therelative stiffnesses of the various members may bedetermined from either the uncracked concretecross section, neglecting the reinforcement, orfrom the transformed cracked section, providedthe same method is used throughout the analysis.The effect of variable cross sections should beconsidered in analysis and design.

The span length of members that are not builtintegrally with their supports should be the clearspan plus the depth of the member. It need notexceed the distance between centers of supports.In analysis of statically indeterminate members,center-to-center distances should be used todetermine moments. Moments at faces of supportsmay be used for design of members.

The possible buckling of a slender member orflange subject to compressive loading should beconsidered.

6.2 -Design for Flexure and Axial LoadsGuideways should be designed to have design

strengths at all sections at least equal to therequired strengths calculated for the factoredloads and forces in such combination as stipu-lated in Chapter 4. Design strength of a memberor cross section should be taken as the nominalstrength calculated in accordance with re-quirements and assumptions of this chapter,multiplied by a strength reduction factor, 4, asdefined in Chapter 4. The strength design ofmembers for flexure and axial loads should bebased on the provisions of ACI 318.

6.3 -Shear and Torsion6.3.1 -Introduction

In transit guideways, torsional moments areproduced by wind load on the vehicles and on thestructures, by the horizontal hunting action of thevehicles, by the centrifugal forces of the vehicleson curved tracks, and by vertical loads on curvedmembers. These torsional effects must becombined with the shear effects in the design of

reinforcement. Large shear and torsion effectsmay also be caused by derailment of vehicles.

Guideway structures are often made continu-ous to better resist the torsional effects as well asto allow more slender structures. The use ofcontinuity, particularly with horizontal curvature,can create a shear and torsion condition that isquite complex.

6.3.2 -Conventional Design MethodsThe conventional design method for shear and

torsion in the United States is covered in Chapter11 of ACI 318. This method was later adopted inthe AASHTO bridge specification except that thecriteria are augmented by requirements for fatiguedesign.

Chapter 11 of ACI 318 includes shear pro-visions for prestressed concrete as well as non-prestressed concrete. However, the torsion designprovisions in this code are applicable only to non-prestressed concrete and not to prestressedconcrete. This represents a severe limitation,because transit girders are normally prestressed.Generalized design methods, based on ACIcriteria, have been proposed for prestressedconcrete.6.1,6.7,6.7,6.8

The conventional ACI method was originallyformulated for building structures, in which theelements are relatively small and the cross sec-tions are made up of rectangular components.Careful consideration must be given when thismethod is applied to transit guideways which arerelatively large and frequently consist of thin-wallbox sections or double-tee sections.

When applied to transit guideways, the con-ventional ACI method has the following limita-tion. First, this method is applicable to beams thatare made up of rectangular components. It mustbe generalized when applied to arbitrary crosssections, such as a box girder with a trapezoidalsection.

Second, in this method, the shear web rein-forcement and torsion web reinforcement aresimply added, resulting in a conservative design.In a large box girder, it should be possible todesign for less web reinforcement for the wallwhere shear and torsion are additive.

Third, in the ACI method, the flexural steeland the torsional longitudinal steel are added.This simple addition of the flexural compressionsteel to the torsional longitudinal steel in theflexural compression zone is quite conservative. Ina large transit guideway, considerable economycan be obtained when a more rigorous treatmentis made.

Fourth, although the generalized ACI meth-od is able to unify the design of prestressed and


non-prestressed concrete, the method becomesvery tedious because of its empirical nature.

6.3.3 -Truss Model ApproachDesign methods based on the truss model or

the Compression Field Theory, provide a clearconcept of how reinforced concrete elements resistshear and torsion after cracking. 6.7,6.8 It allows alogical unification of shear and torsion, and isapplicable to prestressed and non-prestressedconcrete. The interaction of shear and torsion withbending and axial load also becomes consistentand comprehensible.

The truss model approach was first adoptedby the CEB - FIB Model Code.6.5 This code hasbeen successfully used for the design of curved boxgirders. It has recently gained acceptance in NorthAmerican Codes.6.6

First, the arbitrary definitions of the centerline of shear flow and the wall thickness in tor-sion may be unconservative for relatively smallelements. Second, the provisions to prevent thecompression failure of the concrete diagonal strutsmay become unreasonable in some cases. Third,omission of torsional moment in the so-calledcompatibility torsion condition could causeexcessive cracking.

A truss model approach was developed byCollins and Mitchell for shear and torsiondesign.6.7,6.8 The method uses a compression fieldtheory and allows for the introduction of prestressforces. With some modifications, it was incor-porated into CAN3-A23-3, and the method hasbeen used in the United States and Canada.6.6

The method contains several features. First,the omission of concrete cover is a departure fromthe American design practice. Second, theequation for calculating the wall thickness intorsion when relatively large percentages of webreinforcement are present may result in conser-vative wall thicknesses.

6.3.4 -Warping TorsionAll the torsion design provisions currently

available deal with members of bulky cross sec-tions. For such members, St. Venant torsionpredominates and the warping torsional resistancecan be ignored without appreciable error.However, thin-wall open sections, such as double-tees, are used in transit systems. For suchstructures, the working torsional resistance shouldbe considered. The CEB Code6.5 allows for thedesign of warping effects to be accomplished byassuring that equilibrium exists between eachthin-wall element of the open section.Alternatively, a conservative design can beobtained by conducting an elastic analysis of thewarping torsion and adding the warping stresses to

the other shear and longitudinal stresses in thesection.

REFERENCES*

6.1. Hsu, T.T.C., Torsion of Reinforced Concrete, VanNostrand Reinhold Co., New York, 1984, Chapter 5:Prestressed Concrete, pp. 171-203.

6.2. Zia, P., and Hsu, T.T.C., “Design for Torsion andShear in Prestressed Concrete,” Proceedings, Symposium onShear and Torsion (ASCE Fail Convention, Oct. 1978),American Society of Civil Engineers, New York, 1978.

6.3. Zia, P., and McGee, W.D., “Torsion Design ofPrestressed Concrete,” Journal, Prestressed Concrete Institute,V. 19, No. 2, Mar.-Apr. 1974. pp. 46-65.

6.4. Hsu, T.T.C., and Hwang, C.S., “Shear and TorsionDesign of Dade County Rapid Transit Aerial Guideways."Concrete in Transportation, SP-93, American Concrete Institute,Detroit, 1986, pp. 433-466.

6.5. CEB-FIP Model Code for Concrete Structures, 3rdEdition, Comite Euro-International du Beton/FederationInternational de la Precontrainte, Paris, 1978, 348 pp.

6.6 “OHBD (Ontario Highway Bridge Design) Code,” 3rdEdition, Ministry of Transportation, Downsview. Ontario 1991,V. 1 and V. 2.

6.7 Collins, M.P., and Mitchell, D., “Shear and TorsionDesign of Prestressed and Non-prestressed Beams,” Journal,Prestressed Concrete Institute, V. 25, No. 5. Sept.-Oct. 1980,pp. 32-100.

6.8 Collins, M.P. and Mitchell, D. Prestressed ConcreteStructures, Prentice Hall, 1991 (pp. 766). Ch. 7-9, (pp. 309-478).


CHAPTER 7 -REINFORCEMENT DETAILS

For nonseismic and nonfatigue design the re-inforcement details should be in accordance withACI 315 and ACI 318. For seismic design or whenfatigue conditions exist, the reinforcement detailsgiven in the AASHTO bridge specifications shouldbe used.

CHAPTER 8 -REFERENCES

8.1 -Recommended ReferencesThe documents of the various standards-

producing organizations referred to in this docu-ment are listed below with their serial designation.

American Association of State Highwav andTransportation Officials (AASHTO), Standard


Specifications for Highway Bridges.

American Concrete Institute

116R Cement and Concrete Terminology

117 Standard Specifications for Tolerances forConcrete Construction and Materials

215R Considerations for Design of ConcreteStructures Subjected to Fatigue Loading

315 Details and Detailing of ConcreteReinforcement

318 Bui ld ing Code Requirements forReinforced Concrete

318R Commentary on Bui lding CodeRequirements for Reinforced Concrete

318M Building Code Requirements forReinforced Concrete

343R Analysis and Design of ReinforcedConcrete Bridge Structures

358R State-of-the-Art Report on ConcreteGuideways

American Railway Engineering AssociationManual of Standard Practice (AREA)

American Welding Society

D1.4 Structural Welding Code-ReinforcingSteel

Canadian Standards Association

CAN3-A23.3 Design of Concrete Structures forBuildings

CAN3-S6-M88 Design of Highway Bridges

These publications may be obtained from thefollowing organizations:

American Association of State Highway andTransportation Officials444 N. Capitol St., N.W., Suite 225Washington, D.C. 20001

American Concrete InstituteP.O. Box 9094Farmington Hills, MI 48333-9094

American Railway Engineering Association50 F Street, N.W., Suite 7702Washington, D.C. 20001-2183

American Welding Society550 N.W. 42nd AvenueMiami, FL 33126

Canadian Standards Association178 Rexdale Blvd.Rexdale (Toronto), OntarioCanada M9W lR3

This report was submitted to letter ballot of thecommittee and was approved in accordance with ACI ballotingprocedures.