343.1R_12.pdf

ACI 343.1R-12

Guide for the Analysis and Design of Reinforced and Prestressed Concrete Guideway Structures

Reported by Joint ACI-ASCE Committee 343

First Printing November 2012

Guide for the Analysis and Design of Reinforced and Prestressed Concrete Guideway Structures Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ACI. The technical committees responsible responsibl e for ACI committee reports and standards strive to avoid ambiguities, omissions, and errors in these documents. In spite of these efforts, the users of ACI documents occasionally find information or requirements that may be subject to more than one interpretation or may be incomplete or incorrect. Users who have suggestions for the improvement of ACI documents are requested to contact ACI via the errata website at www.concrete.org/committees/errata.asp. www.concrete.org/committees/ errata.asp. Proper use of this document includes periodically checking for errata for the most up-to-date revisions. ACI committee documents are intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. Individuals who use this publication in any way assume all risk and accept total responsibility for the application and use of this information. All information in this publication is provided “as is” without warranty of any kind, either express or implied, including but not limited to, the implied warranties of merchantability, fitness for a particular purpose or non-infringement. ACI and its members disclaim liability for damages of any kind, including any special, indirect, incidental, or consequential damages, including without limitation, l ost revenues or lost profits, which may result from the use of this publication. It is the responsibility of the user of this document to establish health and safety practices appropriate to the specific circumstances involved with its use. ACI does not make any representations with regard to health and safety issues and the use of this document. The user must determine the applicability of all regulatory limitations before applying the document and must comply with all applicable laws and regulations, including but not limited to, United States Occupational Safety and Health Administration (OSHA ) health and safety standards. Participation by governmental representatives in the work of the American Concrete Institute and in the development of Institute standards does not constitute governmental endorsement of ACI or the standards that it develops. Order information: ACI documents are available in print, by download, on CD-ROM, through electronic subscription, or reprint and may be obtained by contacting ACI. Most ACI standards and committee reports are gathered together in the annually revised ACI Manual of Concrete Practice (MCP). American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 U.S.A.

Phone: 248-848-3700 Fax: 248-848-3701 www.concrete.org

First Printing November 2012

Guide for the Analysis and Design of Reinforced and Prestressed Concrete Guideway Structures Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ACI. The technical committees responsible responsibl e for ACI committee reports and standards strive to avoid ambiguities, omissions, and errors in these documents. In spite of these efforts, the users of ACI documents occasionally find information or requirements that may be subject to more than one interpretation or may be incomplete or incorrect. Users who have suggestions for the improvement of ACI documents are requested to contact ACI via the errata website at www.concrete.org/committees/errata.asp. www.concrete.org/committees/ errata.asp. Proper use of this document includes periodically checking for errata for the most up-to-date revisions. ACI committee documents are intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. Individuals who use this publication in any way assume all risk and accept total responsibility for the application and use of this information. All information in this publication is provided “as is” without warranty of any kind, either express or implied, including but not limited to, the implied warranties of merchantability, fitness for a particular purpose or non-infringement. ACI and its members disclaim liability for damages of any kind, including any special, indirect, incidental, or consequential damages, including without limitation, l ost revenues or lost profits, which may result from the use of this publication. It is the responsibility of the user of this document to establish health and safety practices appropriate to the specific circumstances involved with its use. ACI does not make any representations with regard to health and safety issues and the use of this document. The user must determine the applicability of all regulatory limitations before applying the document and must comply with all applicable laws and regulations, including but not limited to, United States Occupational Safety and Health Administration (OSHA ) health and safety standards. Participation by governmental representatives in the work of the American Concrete Institute and in the development of Institute standards does not constitute governmental endorsement of ACI or the standards that it develops. Order information: ACI documents are available in print, by download, on CD-ROM, through electronic subscription, or reprint and may be obtained by contacting ACI. Most ACI standards and committee reports are gathered together in the annually revised ACI Manual of Concrete Practice (MCP). American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 U.S.A.

Phone: 248-848-3700 Fax: 248-848-3701 www.concrete.org

ACI 343.1R-12 Guide for the Analysis and Design of Reinforced and Prestressed Concrete Guideway Structures Reported by Joint ACI-ASCE Committee 343 Nur Yazdani Chair Hossam M. Abdou Hamid Ahmady Sameh S. Badie Shrinivas B. Bhide Selvakumar Buvanendaran W. Gene Corley Om P. Dixit Mamdouh M. El-Badry Noel J. Everard Apostolos Fafitis Andrew J. Foden Amin Ghali Angel E. Herrera

Danielle D. Kleinhans Secretary David Hieber Thomas T. C. Hsu Mohsen A. Issa Richard G. Janecek Bruce C. Kates*† Zhongguo John Ma Barney T. Martin Jr. * Alan B. Matejowsky Amir Mirmiran Aftab A. Mufti Hani H. A. Nassif John P. Newhook Andrzej S. Nowak

Consulting members F. Arbabi John L. Carrato V. M. Davidge Tim Delis Mingzhu Duan Allan C. Harwood Jenn-Shin Hwang Clellon L. Loveall

Claudia P. Pulido Ayman E. Salama Harold R. Sandberg Johan C. F. Schor Jeffrey L. Smith Khaled S. Soubra Steven L. Stroh Maria M. Szerszen Gamil S. Tadros Raj Valluvan* Jim J. Zhao Qun Zhong-Brisboi Zhong-Brisboiss *

*

Indicates members of the subcommittee that prepared this guide. Subcommittee Chair. The committee acknowledges C. A. Banchik, D. Bilow, K. Hjorteset, T. T. T. C. Hsu, A. S. Nowak, A. M. Okeil, G. S. Tadros, and K. Wongkaew for their contributions to this guide. A special acknowledgment is due to M. Y. Riad* for his significant contributions to this guide. †

This guide presents a procedure for the design and analysis of reinforced and prestressed concrete guideway structures for public transit, and design guidance for elevated transit guideways. The engineer is referred to the appropriate highway and railway bridge design codes for items not covered in this document. Limit state philosophy is applied to develop design criteria. A reliability approach is used in defining load combinations and deriving load and resistance factors. Different target reliability indexes (4.0 for design strength, strength, 2.5 for serviceability serviceability design for cracking, cracking, and 2.0 for serviceability design for fatigue) and a service life of 75 years were were used as the basis for safety analysis. analysis. A 75-year 75-year service life is consistent with the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design Specifications. Keywords: cracking; deformation; fatigue; guideway structures; precast Keywords: concrete; prestressed concrete; prestressing loads; reinforced concrete; vibration.

ACI Committee Reports, Guides, and Commentaries are intended for guidance in planning, designing, executing, and inspecting construction. This document is intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. The American Concrete Institute disclaims any and all responsibility for the stated principles. The Institute shall not be liable for any loss or damage arising therefrom. Reference to this document shall not be made in contract documents. If items found in this document are desired by the Architect/Engineer to be a part of the contract documents, they shall be restated in mandatory language for incorporation by the Architect/Engineer.

CONTENTS Chapter 1—Introduction and scope, p. 2 1.1—Introduction 1.2––Scope

Chapter 2––Notation and definitions, p. 2 2.1—Notation 2.2—Definitions

Chapter 3—General design considerations, p. 4 3.1—Scope 3.2—Structural considerations 3.3—Functional considerations 3.4—Economic considerations 3.5—Urban impact 3.6—Transit operations 3.7—Structure/vehicle 3.7—Structure/veh icle interaction 3.8—Geometries 3.9—Construction considerations 3.10—Rails and trackwork

ACI 343.1R-12 was adopted and published November 2012.. Copyright © 2012 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 photo process, or by electronic or mechanical device, printed, written, or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.

2

ANALYSIS AND DESIGN OF REINFORCED AND PRESTRESSED CONCRETE GUIDEWAY STRUCTURES (ACI 343.1R-12)

Chapter 4—Loads, p. 17 4.1—General 4.2—Sustained loads 4.3—Transient loads 4.4—Loads due to volumetric changes 4.5—Exceptional loads 4.6—Construction loads

these criteria for advanced technologies other than those discussed in this guide requires an independent assessment. AASHTO LRFD Bridge Design Specifications (AASHTO 2012) and ACI 343R are referenced for specific items not covered in these recommendations, including materials, construction considerations, and segmental construction.

CHAPTER 2––NOTATION AND DEFINITIONS Chapter 5—Load combinations, load factors, and strength reduction factors, p. 23 5.1—Scope 5.2—Basic assumptions 5.3—Service load combinations 5.4—Strength load combinations

Chapter 6—Serviceability design, p. 24 6.1—General 6.2—Basic assumptions 6.3—Permissible stresses 6.4—Loss of prestress 6.5—Fatigue 6.6—Vibration and dynamic response 6.7—Deformations and rotations 6.8—Crack control

Chapter 7—Strength design, p. 29 7.1—General design and analysis considerations 7.2—Design for flexure and axial loads 7.3—Shear and torsion

Chapter 8—References, p. 31 CHAPTER 1—INTRODUCTION AND SCOPE 1.1—Introduction The recommendations in this guide provide public agencies, consultants, and other interested personnel with comprehensive criteria for the design and analysis of concrete guideways for public transit systems. They differ from those given for bridge design and analysis in ACI 343R, American Association of State Highway and Transportation Officials (AASHTO) bridge specifications (AASHTO 2002, 2009, 2011, 2012), and the American Railway Engineering and Maintenance-of-Way Association (AREMA) Manual of Railway Engineering (AREMA 2012). This document provides guidance related chiefly to the design of guideway superstructures. For the design of substructure units, the reader is referred to other references such as AASHTO LRFD Bridge Design Specifications (AASHTO 2012).

1.2––Scope Design criteria specifically recognize the unique features of concrete transit guideways—namely, guideway/vehicle interaction, rail/structure interaction, special fatigue requirements, and aesthetic requirements in urban areas. Criteria are based on current state-of-the-art practice for moderatespeed (up to 100 mph [160 km/h]) vehicles. Application of

2.1—Notation A

=

exposed area of pier perpendicular to the direction of stream flow, ft 2 (m2) Acp = area enclosed by the outer boundary of cross section, in.2 (mm2) Al = area of longitudinal reinforcement in a member, in.2 (mm2) Ao = lever arm area enclosed by the centerline of the shear flow, in.2 (mm2) Aoh = area enclosed by the centerline of the outermost closed transverse torsion reinforcement, in. 2 (mm2) Ar = cross-sectional area of a rail, in. 2 (mm2) As′ = area of compression reinforcement, in. 2 (mm2) At = area of one leg of a closed stirrup resisting torsion, in.2 (mm2) Av = area of shear reinforcement, or area of shear reinforcement perpendicular to main reinforcement for deep beams, in.2 (mm2) a = center-to-center distance of shorter dimension of closed rectangular stirrup, in. (mm) B = buoyancy BR = broken rail forces b = center-to-center distance of longer dimension of closed rectangular stirrup, in. (mm) C D = flowing water drag coefficient C d = horizontal wind drag coefficient CE = centrifugal force, lb (N) C e = wind exposure coefficient C g = wind gust effect coefficient COLFH = horizontal collision load, lb (N) COLFV = vertical collision load, lb (N) CR = forces due to creep in concrete, lb (N) CT = collision load, lb (N) c = clear concrete cover, in. (mm) DC = dead load, lb (N) DR = transit vehicle mishap load, due to vehicle derailment, lb (N) DW = dead load of wearing surfaces and utilities, lb (N) d = distance from extreme compressive fiber to centroid of longitudinal tension reinforcement, in. (mm) d v = distance from centroid of tensile steel to centroid of concrete struts, in. (mm) E c = modulus of elasticity of concrete, psi (MPa) E ci = modulus of elasticity of concrete at transfer of prestress, psi (MPa) E r = modulus of elasticity of rail steel, psi (MPa) E s = modulus of elasticity of reinforcement, psi (MPa) EH = loads due to weight and pressure of soil, water in


EI = EL =

EQ = ER = F h = F R = F r F sj F v f 1 f c

= = = = =

f c′ = f ci′ = f r = f cri = f f

=

f min = f pbt = f pe

=

f pu

=

f py

=

f rr f s

= =

f sr

=

f st

=

f sv

=

f y = g = H = HF = h = I cr = I e

=

I g

=

IC = IM =

flexural stiffness of compression members, lb-in. 2 (kN-mm2) accumulated locked-in force effects resulting from construction process, including secondary forces from post-tension earthquake force, lb (N) external restrained force, lb (N) horizontal design drag load due to wind, psi (Pa) radial force per unit length due to curvature of continuously welded rail, k/in. (Pa/mm) axial force in the continuously welded rail, kip (kN) jacking force in a post-tensioning tendon, kip (kN) vertical design drag load due to wind, psi (Pa) first mode flexural (natural) frequency, Hz extreme fiber compressive stress in concrete at service loads, psi (MPa) specified compressive strength of concrete, psi (MPa) specified compressive strength of concrete at time of initial prestress, psi (MPa) cracking strength of concrete, psi (MPa) cracking stress of concrete at time of initial prestress, psi (MPa) stress range in straight flexural reinforcing steel, ksi (MPa) algebraic minimum stress, tension positive, compression negative, ksi (MPa) stress in prestressing steel immediately prior to transfer, psi (MPa) effective stress in prestressing steel after losses, psi (MPa) specified tensile strength of prestressing steel, psi (MPa) specified yield strength of prestressing steel, psi (MPa) axial stress in the continuously welded rail, ksi (MPa) calculated tensile stress in reinforcement at service loads, psi (MPa) stress range in shear reinforcement or in welded reinforcing bars, ksi (MPa) change in stress in torsion reinforcement due to fatigue loadings, ksi (MPa) change in stress in shear reinforcement due to fatigue loadings, ksi (MPa) specified yield strength of reinforcement, psi (MPa) acceleration due to gravity = 32.2 ft/s2 (9.81 m/s2) height from ground level to the top of the superstructure hunting force, lb (N) overall thickness or height of member, in. (mm) moment of inertia of cracked section transformed to concrete, in.4 (m4) effective moment of inertia for computation of deflections, neglecting the reinforcement, in. 4 (m4) moment of inertia of gross concrete section about the centroidal axis neglecting reinforcement, in. 4 (m4) ice pressure, lb (N) impact factor

jd =

l L

= =

LF e = LF n = LF = LL = LR = LS = M = M a =

M cr = P = P D = PL = PS = pcp = q y = r / h =

R RS S SE SH s

= = = = = =

sl st T 0

= = =

T 1

=

T u = TG = TU = t t d

= =

U V V cr V u v

= = = = =

WA =

3

distance between tensile and compression forces at a section based on an elastic analysis, in. (mm) span length, ft (m) live load during construction, lb (N); wave length, ft (m) emergency longitudinal braking force, lb (N) normal longitudinal braking force, lb (N) longitudinal force, lb (N) vertical standard vehicle load, lb (N) load on safety railing, lb (N) live load surcharge, lb (N) mass per unit length of guideway, lb/in.-s 2 /in. (kg/m) maximum moment in member due to service loads at stage for which deflection is being computed, in.-lb (N-mm) cracking moment, in.-lb. (N-mm) live load on service walkway, lb (N) dynamic wind pressure, lb/ft2 (MPa) pedestrian live load, lb (N) secondary force effects due to prestressing periphery of outer boundary of the member, in. (mm) shear flow at yield, lb/in. (N/mm) ratio of base radius to height of transverse deformations of reinforcing bars; when actual value is unknown, use 0.3 radius of curvature, ft (m) rail-structure interaction, lb (N) service load combinations differential settlement effects forces due to shrinkage in concrete, lb (N) spacing of reinforcement to resist bursting, shear, or pitch of spiral reinforcement, center- to-center spacing of longitudinal shear, or torsion reinforcement, in. (mm) spacing for longitudinal reinforcement, in. (mm) spacing of hoop reinforcement, in. (mm) stress-free temperature of the continuously welded rail, °F (°C) final temperature in the continuously welded rail, °F (°C) torsional moment, in.-lb (N-mm) loads due to temperature gradient in the structure exclusive of rail forces, lb (N) loads due to uniform temperature in the structure exclusive of rail forces, lb (N) time, days shear flow zone thickness of a member subjected to torsional forces, in. (mm) ultimate load combinations speed, ft/s (m/s) critical speed, ft/s (m/s) ultimate shear force, lb (N) velocity of stream flow, mean hourly velocity of wind, or maximum operating speed of the vehicle, ft/s (m/s) stream flow load, lb (N)

4


WS = wc = wn = yt =

a = DT = DV = f g l

= = =

q

=

r

=

x

=

wind load on structure, lb (N) unit weight of concrete, lb/ft3 (kg/m3) natural frequency of the structure (rad/s) distance from the centroidal axis of cross section, neglecting the reinforcement, to the extreme fiber in tension, in. (mm) coefficient of thermal expansion change in torsion at section due to fatigue loadings, in.-kip (N-mm) change in shear at section due to fatigue loading, kip (kN) strength reduction factor mass density of water = 62.4 lb/ft3 (1000 kg/m3) multiplier for additional deflection due to longterm effects angle in degrees between the wind force and a line normal to the guideway centerline density of air at sea level at 32°F (0°C) = 0.0765 lb/ ft3 (1.226 kg/m3) time-dependent factor for sustained load

environment (Fig. 3.1.1b), the operation of the transit system, the system suppliers, and the structural options available. A guideway becomes a permanent feature of the urban scene. Materials and features, therefore, should be efficiently used and built into the guideway to produce a structure that will support an operating transit system and fit the environment. This guide provides an overview of key issues to be considered in guideway design. It is intended to suggest minimum materials, workmanship, technical features, design, and construction for producing a guideway that performs satisfactorily. Serviceability and strength considerations are also given. It includes analysis and design guidelines to meet serviceability and strength limit states. Sound engineering judgment should be used in implementing these recommendations. 3.1.2 Guideway structures—A guideway structure should support a transit vehicle, guide it through the alignment, and restrain stray vehicles. Guidance of transit vehicles includes the ability to switch vehicles between guideways. A guideway should also generally provide emergency evacua-

2.2—Definitions ACI provides a comprehensive list of definitions through an online resource, “ACI Concrete Terminology,” http:// terminology.concrete.org. Definitions provided herein complement that resource. bogie—wheeled frame connected via a suspension system to a railway vehicle body or underframe. broken rail—fracture of a continuously welded rail. continuously welded rail (CWR)—running rails that act as a continuous structural element as a result of full penetration welding of individual lengths of rail; continuously welded rails may be directly fastened to the guideway, in which case their combined load effects should be included in the design. flexural natural frequency—first vertical frequency of vibration of a guideway, including all the sustained load, based on the flexural stiffness and mass distribution of the superstructure. linear induction motor (LIM)—AC linear motor that works by the same general principles as other induction motors but which has been designed to directly produce motion in a straight line. standard vehicle—loading, design vehicle-forces representing the wheel pattern and total weight including carriage, bogie, and passenger loads, of a railway vehicle.

Fig. 3.1.1a—Example of a transit structure that blends with the environment (courtesy of MGM Mirage, Inc.).

CHAPTER 3—GENERAL DESIGN CONSIDERATIONS 3.1—Scope 3.1.1 General—Transit structures frequently carry loads through urban areas. Demands for aesthetics (Fig. 3.1.1a), performance, cost, efficiency, and minimum urban disruption during construction and operation are greater than for most bridge structures. The design of transit structures requires an understanding

Fig. 3.1.1b—Example of a transit structure in an urban


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Fig. 3.1.3b––Vehicle style (courtesy of Clarian Health). Fig. 3.1.2—Repetition of span lengths and column details (courtesy of PCA).

Fig. 3.1.3c––Vehicle style (courtesy of Hitachi Corporation).

Fig. 3.1.3a––Vehicle style (courtesy of Jacksonville Trans portation Authority).

tion, support wayside power distribution services, and house automatic train controls. Within a modern transit guideway, there is a high degree of repeatability (Fig. 3.1.2) and nearly an equal mixture of tangent and curved alignments. Guideways often consist of post-tensioned concrete members. Post-tensioning may provide principal reinforcement for simple-span structures and continuity reinforcement for continuous structures. Bonded post-tensioned tendons are recommended for all primary load-carrying guideway applications, and their use is assumed in this guide. Unbonded tendons, however, may be used where approved, especially for strengthening or expanding existing structures. 3.1.3 Vehicles—Transit vehicles have a wide variety of physical configurations, propulsion, and suspension systems. The most common transit vehicles are steel-wheeled vehicles running on steel rails, powered by conventional guidance systems. Transit vehicles also include rubber-tired vehicles and vehicles with more advanced suspension or guidance systems, such as air-cushioned or magnetically levitated

vehicles. Transit vehicles may be configured as individual units or combined into trains. Their styles vary as shown in Fig. 3.1.3a through 3.1.3d.

3.2—Structural considerations 3.2.1 General—Transit systems are constructed in four types of right-of-way (ROW): exclusive; shared-use rail corridor; shared-use highway corridor; and urban arterial. Constraints of ROW affect the type of structural system that can be employed for an individual transit operation. Constraints resulting from a particular ROW might include limited construction access; restricted working hours; limits on environmental factors such as noise, dust, foundation, and structure placement; and availability of skilled labor and equipment. Various guideway locations within the ROW are shown in Fig. 3.2.1a through 3.2.1c. 3.2.2 Concrete girder types —Categorized by construction methods, three types of concrete girders are used for transit superstructures: precast, cast-in-place, and composite. 3.2.2.1 Precast girder construction —When site conditions are suitable, entire beam elements can be prefabricated and transported to the site. Box girder sections are frequently used for their torsional stiffness, especially for short-radius

6


Fig. 3.2.1c––ROW at median location (courtesy of PCA). Fig. 3.1.3d––Vehicle style (courtesy of PCA).

Fig. 3.2.1a––Shared ROW (courtesy of PCA).

Fig. 3.2.1b––Side of ROW (courtesy of Las Vegas Monorail Company).

curves. Some transit systems with long-radius horizontal curves have used double-T beams for the structure. Continuous structures are frequently used. Precast beams are made continuous by developing continuity at the supports. A continuous structure has less depth and increased structural redundancy than a simple-span structure. Rail systems using continuously welded rail are typically limited

Fig. 3.2.2.1a—Precast box girders for sharp curvature (courtesy of PCA). Continuity has been provided through curved alignment.

to simple-span or two-span continuous structures to accommodate thermal movements between the rails and structure. Longer lengths of continuous construction are used more readily in systems with rubber-tired vehicles. Examples of girder types and continuity may be seen in Fig. 3.2.2.1a through 3.2.2.1d. Segmental construction techniques may be used for major structures, such as river crossings or where schedules or access to the site favors delivery of segmental units. The use of segmental construction is discussed in ACI 343R. 3.2.2.2 Cast-in-place structures—Cast-in-place construction is used when site limitations preclude delivery of large precast elements or the guideway structure has a complex geometry, like being located on sharp curves. Cast-in-place construction has not been used extensively in modern transit structures unless warranted by the specific project situation. 3.2.2.3 Composite structures—Transit structures can be constructed in a similar manner to highway bridges, using precast concrete or steel girders with a cast-in-place composite concrete deck. Composite construction is especially common for special structures such as switches, turnouts, and long spans where the weight of an individual precast element limits its shipping to the site. The girder


7

Fig. 3.2.2.1b––Precast concrete girders (courtesy of MGM Mirage, Inc.). Example of simple span construction.

Fig. 3.2.2.1d––Precast box girder on tangent (courtesy of PCA). May be simple span or continuous over multiple spans. May be span-by-span or balanced cantilever construction.

Fig. 3.2.2.1c––Precast box girder on curve (courtesy of PCA). Balanced cantilever construction provides continuity over the pier.

Fig. 3.3.2a––Walkway between rails (courtesy of Jacksonville Transportation Authority).

provides a working surface that allows accurate placement of transit hardware on the cast-in-place deck.

3.3—Functional considerations 3.3.1 General—The structural functions are to support present and future transit applications, satisfy serviceability requirements, and provide for passenger safety. The transit structure may also be designed to support other loads such as automotive or pedestrian traffic. However, mixed-use applications are not included in the loading requirements of Chapters 4 and 5. 3.3.2 Safety considerations—Considerations for a transit structure should include transit technology, human safety, and external safety in accordance with the requirements of the National Fire Protection Association document NFPA 130 (NFPA 2003). Transit technology considerations include both normal and extreme longitudinal, lateral, and vertical vehicle loads.

speeds, environmental factors, transit operations, collision conditions, and vehicle retention should also be considered. The geometric envelope of a disabled vehicle is a function for the suspension system, support system, and vehicle design. This information must be provided by the system supplier. Human safety addresses emergency evacuation and access, structural maintenance, and fire control. Transit operations require facilities for evacuating passengers from stalled or disabled vehicles and access for emergency personnel. In most cases, emergency evacuation is accomplished by a walkway that may be adjacent to the guideway or incorporated into its structure. Figure 3.3.2a and 3.3.2b show walkways provided between the guideway rails. The exact details of the emergency access and evacuation methods on the guideway should be resolved among the transit operator, transit vehicle supplier, and engineer. NFPA 130 (NFPA 2003) gives detailed requirements for safety provisions on fixed guideway transit systems. External safety considerations include safety precautions during construction, prevention of local street traffic colli-

8


Fig. 3.3.2b––Walkways between rails (courtesy of Las Vegas Monorail Co.).

Fig. 3.3.5––Bearings should be designed for easy replacement (courtesy of PCA).

tional hazards when transit structures pass over navigable waterways. 3.3.3 Lighting—The requirements for transit structure lighting should be followed in accordance with provisions of the authority having jurisdiction. Provisions may require lighting for emergency use only, for properties adjacent to the guideway structure, or that lighting be eliminated altogether. 3.3.4 Drainage—To prevent accumulation of water within the track area, transit structures should be designed so that surface runoff is drained to the edge or center of the superstructure, where the water can be carried longitudinally.

Longitudinal drainage of transit structures is usually accomplished by providing a longitudinal slope to the structure; with a minimum slope of 0.5 percent preferred. Scuppers or inlets of a size and number that are designed and detailed to drain the structure should be provided. Downspouts, where required, should be of a rigid, corrosionresistant material preferable a minimum of 6 in. (150 mm) but not less than 4 in. (100 mm) in diameter. Downspouts should be provided with cleanouts. Details of the downspout and its deck inlet and outlet should prevent water discharge against any portion of the structure and erosion at ground level. Slopes should be arranged so that runoff drains away from stations. Longitudinal grades to ensure drainage should be planned with the natural topography of the site to avoid an unusual structural appearance. Architectural treatment of exposed downspouts is important to the aesthetic appearance of the facility. When treatment becomes complicated, the use of internal or embedded downspouts is preferred. For internal or external downspouts, prevention of ice accumulation in cold-weather climates should be considered. This may require localized heating of the drain area and downspout. All overhanging portions of the concrete deck should have a drip bead or notch. 3.3.5 Expansion joints and bearings—Expansion joints should be provided at span ends, allowing beam ends to accommodate movements from volumetric changes within the structure. These movements come from several primary sources: temperature change, concrete shrinkage, creep effects from prestressing, and post-tensioning shortening. Joints should be designed to reduce noise transmission and prevent moisture from seeping to the bearings. Adequate detailing should be provided to facilitate maintenance of bearings and their replacement if or when needed during the life of the structure. Figure 3.3.5 shows bearings between the box girder and the bent cap that are clearly visible. Access for jacking the structure for bearing replacement is enhanced. When using aprons or finger plates, they should be designed to span the joint and prevent debris accumulation on the bearing seats. 3.3.6 Durability—To satisfy a design life of 75 years or more, details affecting durability of the structure—materials selection, structural detailing, and construction quality control—should be given adequate consideration. Materials selection includes concrete and its mixture proportion, allowing for a low water-cementitious material ratio ( w / cm) and air entrainment in areas subject to freezing-and-thawing action. Epoxy-coated reinforcement and concrete sealers may be beneficial if: a) Chloride use is anticipated as part of the winter snowclearing operations b) The guideway may be exposed to salt spray from a coastal environment c) Adjacent highways are treated with deicing chemicals In structural detailing, reinforcement or noncorrosive reinforcement placement and methods to prevent deleterious conditions from occurring should be considered. Reinforce-


distribution and size (ACI SP-66 [ACI Committee 315 2004]). The cover should provide adequate protection to the reinforcement and follow a nationally recognized code (ACI 318 or AASHTO LRFD Bridge Design Specifications [AASHTO 2012]) or specific project requirements. Incidental and accidental loadings should be accounted for and adequate reinforcement provided to intersect potential cracks. Stray electrical currents, which could precipitate galvanic corrosion, should be accounted for in electrical hardware and equipment design and their grounding. Construction quality control is essential to ensure that design intent and durability considerations are properly implemented. Construction inspectors should be qualified, experienced, and certified as ACI Concrete Special Inspectors. Quality control should follow a pre-established formal plan with inspections performed as specified in the contract documents. ACI 311.4R provides guidance for establishing formal plans. To satisfy a 75-year service life, regular inspection and maintenance programs should be instituted to ensure the integrity of structural components. Programs may include periodic placement of coatings, sealers, or chemical neutralizers. Adequate lighting may be necessary where natural light may be insufficient, such as inside box girder structures.

3.4—Economic considerations The economy of a concrete guideway is measured by the annual maintenance cost and capitalized cost for its service life. The design process should include provisions to minimizing operations and maintenance cost. Consideration, therefore, should be given to the service life cost of the guideway structure. The owners should establish guidelines for a cost analysis. Economy is considered by comparative studies of reinforced, prestressed, and partially prestressed concrete construction. Trade-offs should be considered for using higher-grade materials in sensitive areas during the initial construction, against the impact of system disruption at a later date if the transit system must be upgraded. For example, higher-quality aggregates may be selected for the traction surface where local aggregates have a tendency to polish with continuous wear. The argument in support for higher-grade materials is especially important because guideway traffic cannot be rerouted during service disruptions.

3.5—Urban impact 3.5.1 General—The guideway affects an urban environment in three general areas: visually, physically, and through access of public safety equipment. Figure 3.5.1 shows the integration of the guideway within the other transportation corridors in the vicinity. Visual impact includes guideway appearance from the surrounding area and the appearance of the surrounding area from the guideway. Physical impact includes placement of columns and beams and the dissipation of noise, vibration, and electromagnetic radiation. Electromagnetic radiation is usually a specific design consideration of the vehicle

9

Fig. 3.5.1––Urban impact (courtesy of PCA).

emergency service access, and the emergency evacuation of passengers. Access to the guideway requires stairs, walkways, and platforms. How they are configured, attached, and where they are located will affect the visual reception by the public. 3.5.2 Physical appearance —A guideway constructed in any built-up environment should meet high standards of aesthetics for physical appearance. The size and configuration of guideway elements should ensure compatibility with its surroundings. Whereas the range of sizes and shapes is unlimited in the selection of guideway components, the following should be considered: a) View disruption b) Shade and shelter created by the guideway c) Blockage of pedestrian walkways d) Blockage of streets and the effect on traffic and parking e) Impairment of sight distances for traffic f) Guideway size as it relates to adjacent structures g) Construction in an urban environment h) Methods of delivery for prefabricated components and cast-in-place construction i) Interaction with roadway and transit vehicles j) Visual continuity Figure 3.5.2a shows the location of guideway columns to avoid disruption of pedestrian traffic, vehicular traffic on local streets, and traffic sight distances. Figure 3.5.2b demonstrates how smooth curves for both structure and vehicle allow the system to blend into its suburban surroundings. Detailing considerations should include: a) Surface finish b) Color c) Joint detailing d) Provision to alleviate damage from water dripping from the structure e) Control and dissipation of surface water runoff f) Differences in texture and color between cast-in-place and precast elements 3.5.3 Sightlines—In guideway design, the view of the

10


Fig. 3.5.2a––Design decisions to fit guideway around existing features (courtesy of Las Vegas Monorail Co.).

Fig. 3.5.2b––Clean lines and smooth finishes (courtesy of Clarian Health).

ered. The engineer should recognize that patrons riding on the transit system will have a different view than pedestrians at street level; the guideway placement and sightlines should reflect sensitivity to intrusion on private properties and adjacent buildings. In some cases, the use of noise barriers and dust screens should be considered. Figure 3.5.3 provides an example of clean sightlines as the guideway span straddles the projected lines of the water channel beyond. Views of the guideway from a higher vantage point are important for a positive impression of the transit system on potential patrons. The interior should present a clean, orderly appearance to transit patrons and adjacent observers. 3.5.4 Noise suppression—A transit system will add to the ambient background noise. Specifications for new construction generally require that the wayside noise 50 ft (15 m) from the guideway not exceed a range of 65 to 76 dBA. This noise is generated from on-board vehicle equipment, such as propulsion and air-conditioning units, and from vehicle/ track interaction, especially when jointed rail is used. Normally, it is the vehicle engineer’s responsibility to control noise emanating from the vehicle. Parapets and other

Fig. 3.5.3––Example of the importance of sightlines (courtesy of Clarian Health).

hardware on the guideway structure should be designed to meet general or specific noise-suppression criteria. Determination of these criteria is made on a case-by-case basis, frequently in conjunction with the vehicle supplier. ASCE 21 provides additional information regarding acceptable exterior noise levels emanating from the system. 3.5.5 Vibration–– Transit vehicles on a guideway generate vibrations that may be transmitted to adjacent structures. For most rubber-tired transit systems, this ground-borne vibration is negligible. In many rail transit systems, especially those systems with jointed rails, the noise and vibration can be highly perceptible. In these situations, vibration isolation of the structure is necessary. ASCE 21 contains additional information regarding system-induced vibrations. 3.5.6 Emergency services access–– A key concern in an urban area is the accessibility by fire or other emergency equipment to buildings adjacent to a guideway. Within the confined right-of-way (ROW) of an urban street, space limitations make this a particularly sensitive concern. In most cases, a clearance of approximately 15 ft (5 m) between the face of a structure and a guideway provides adequate access. Access over the top of a guideway may not represent a safe option.

3.6—Transit operations 3.6.1 General—Once a transit system is opened for service, the public depends on its availability and reliability. Shutdowns to permit maintenance, operation, or expansion of the system can affect the availability and reliability. These concerns often lead to long-term economic, operational, and planning analyses of the transit system design and construction. In most transit operations, a shutdown period between 1:00 and 5:00 a.m. can be tolerated; slightly longer shutdowns may be possible in certain locations and on holidays. It is during shutdown that routine maintenance work is performed. Many transit systems also perform maintenance during normal operating hours. This practice tends to compromise work productivity, guideway access rules, and a safe working space. Transit operators should provide the engi-


neer with guidelines regarding capital cost objectives and their operation and maintenance plans. 3.6.2 Special vehicles—Transit systems frequently use special vehicles for special tasks such as retrieving disabled vehicles and repairing support or steering surfaces. While the design may not be predicated on the use of special vehicles, their frequency of use and their weights and sizes should be considered in the design of the structure. 3.6.3 System expansion—Expansion of a transit system can result in substantial disruption and delay to transit operation while equipment, such as switches, is being installed. In the initial design and layout of a transit system, consideration should be given to future expansion possibilities. Provisions should be incorporated in the initial design and construction phases if expansion after construction is contemplated within the foreseeable future and the probable expansion points are known.

3.7—Structure/vehicle interaction 3.7.1 General—Vehicle interaction with the guideway can affect its performance on support, steering, power distribution, and traction components of the system. It is usually considered in design through the specification of serviceability requirements for the structure. In the final design stage, close coordination with the vehicle supplier is imperative. 3.7.2 Ride quality 3.7.2.1 General—Ride quality is influenced to a great degree by the quality of the guideway surface. System specifications usually present ride quality criteria as lateral, vertical, and longitudinal accelerations and jerk (change in rate of acceleration), as measured inside the vehicle. These specifications should be translated into physical dimensions and surface qualities on the guideway and in the vehicle suspension. Two elements that most immediately affect transit vehicle performance are the support and steering surfaces. Figure 3.7.2.1 shows guideway surfaces discussed in the following sections. 3.7.2.2 Support surface—The support surface is the horizontal surface of the guideway that supports the transit vehicle against the forces of gravity. It influences the vehicle performance by the introduction of random deviations from a theoretically perfect alignment. These deviations are input to the vehicle suspension system. Influence of the support surface on the vehicle is a function of the suspension system type, the support medium (such as steel wheels or rubber tires), and vehicle speed. There are three general components of support surfaces to consider: local roughness, misalignment, and camber. 3.7.2.2.1 Local roughness—Local roughness is the amount of distortion on the surface from a theoretically true surface. In most transit applications, the criterion of a 1/8 in. (3 mm) maximum deviation from a 10 ft (3 m) straightedge is used (ACI 117). With steel rails, a Federal Railway Administration (FRA) Class 6 (FRA 2004) tolerance is acceptable. FRA provisions include requirements for longitudinal and transverse (roll) tolerances. These tolerances are consistent with operating

11

Fig. 3.7.2.1––Guideway surfaces (courtesy of Clarian Health).

stricter tolerance requirements should be applied, as determined by the owner/engineer, with reference to the FRA, which provides track tolerances based on track classifications that are related to permissible speed. 3.7.2.2.2 Vertical misalignment —Vertical misalignment most often occurs when adjacent beam ends meet at a column or other connection. There are two types of vertical misalignment. The first is physical displacement of adjacent surfaces, which occurs when one beam is installed slightly lower or higher than the adjacent beam. This type of misalignment should be limited to l/16 in. (1.5 mm) (ACI 117). The second type of vertical misalignment occurs when there is angular displacement between beams, which may result from excessive deflection, sag, or camber. Excessive camber or sag creates a discontinuity that imparts a noticeable input to the vehicle suspension system. It is desirable to have the girder camber close to zero at the time that the guideway structure is made continuous. The engineer must also consider the smooth crossing of expansion joints, and detail accordingly. In the design and construction of beams, the effects of service load deflection, initial camber, and long-time deflections should be considered. There is no clear definition on the amount of angular discontinuity that can be tolerated at a beam joint. Designs that tend to minimize angular discontinuity, however, generally provide a superior ride. Continuous guideways are particularly beneficial in controlling such misalignment. 3.7.2.2.3 Camber —Camber or sag in the beam can also affect ride quality. Consistent upward camber in structures with similar span lengths can create a harmonic vibration in the vehicle, resulting in dynamic amplification, especially in continuous structures. When there is no specific deflection or camber criteria cited for a project, the engineer should account for these dynamic effects by analytical or simulation techniques. The deflection compatibility requirements between structural elements and station platform edges should be checked. 3.7.2.3 Steering surface—The steering surface provides horizontal input to the vehicle. Steering surfaces may be running rails for a flanged steel-wheel-rail system on concrete

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Table 3.7.2.3––Track construction tolerances* Variations†

Type and class of track Direct fixation and ballasted main line Ballasted yard and secondary lines

Track alignment deviation Middle ordinate 62 ft (19 m) cord, in. (mm)

Gauge, in. (mm)

Cross level and superelevation, in. (mm)

Horizontal

Vertical

Horizontal

Vertical

1/8 (3)

1/8 (3)

1/4 (6)

1/4 (6)

1/8 (3)

1/8 (3)

+1/4, –1/8 (+6, –3)

1/4 (6)

1/2 (12)

1 (24)

1/8 (3)

1/4 (6)

Total, in. (mm)

*

Tolerances are all positive, unless otherwise indicated.

†

Variations from theoretical gauge, cross level, and superelevation are not to exceed 1/8 in. (3 mm) per 15 ft 6 in. (4.7 m) of track.

Note: The total deviation in distance from the platform should be 0 in. toward the platform and 1/4 in. (6 mm) away from the platform. Total deviation is measured between the theoretical and the actual alignments at any point along the track.

Fig. 3.7.2.3—Interaction between support and steering.

ture for a rubber-tired system. The steering surface condition is particularly important because few vehicles have sophisticated lateral suspension systems. In most existing guideways, the tolerance of 1/8 in. (3 mm) deviation from a 10 ft (3 m) straightedge (ACI 117), corrected for horizontal curvature, has proven to be adequate for rubber-tired vehicles operating at 35 mph (56 km/h) or less. In steel-rail systems, an FRA Class 6 (FRA 2004) rail tolerance has proven to be satisfactory for speeds up to 70 mph (112 km/h). Additional tolerance limits are provided in Table 3.7.2.3. There is an interaction between the steering surface and support surface, which is technology-dependent and requires specific consideration by the engineer. This interaction results from a coupling effect that occurs when a vehicle rolls on the primary suspension system, causing the steering mechanism to move up and down (Fig. 3.7.2.3). The degree of this up-and-down movement is dependent on the steering mechanism, which is typically an integral part of the vehicle truck (bogie) system, and the stiffness of the primary suspension, which is also within the truck assembly. Depending on the relationship between support and steering surfaces, and the vehicle’s support and guidance

mechanisms, a couple can be created between the two that causes a spurious steering input to the vehicle. While there are no general specifications for this condition, the engineer should be aware of this condition. If there is a significant distance between the horizontal and two vertical contact surfaces, additional tolerance requirements for the finished surfaces should be imposed. This should reduce the considerable steering input, which can cause oversteering or understeering, leading to an accelerated wear of components and degraded ride comfort. 3.7.3 Traction surfaces—Transit vehicles derive their traction from the physical contact of the wheels with the concrete or running rail or through an electromagnetic force. In systems where traction occurs through physical contact with the guideway, specific attention should be given to the traction surface. In automated transit, the traction between the wheel and the reaction surface is essential to ensure a consistent acceleration, a safe stopping distance between vehicles, and for automatic control functions. The engineer should determine minimum traction required for specific technology employed. If the traction surface is concrete, appropriate aggregates should be provided in the mixture proportion to maintain minimum traction for the structure’s working life. Operation in freezing rain or snow may also affect guideway traction. The engineer should determine the degree of traction maintenance required under all operating conditions. If full maintenance is required, the engineer should examine methods to mitigate effects of snow or freezing rain. Mitigating effects may include heating or enclosing the guideway, or both. If deicing chemicals are contemplated, proper material selection and protection should be considered. Corrosion protection may require consideration of additional concrete cover, sealants, epoxy-coated reinforcing steel or other noncorrosive reinforcement alternatives, and special concrete mixtures. 3.7.4 Electrical power distribution ––There are two components to electrical power distribution: the wayside transmission of power to the vehicle and the primary power distribution to the guideway. Wayside power distribution to the vehicle is normally achieved through power rails or an overhead catenary. Provisions should be made on the guideway for mounting support equipment for this type of installation.


For systems using steel running rails where the running rail is used for return current, provisions should also be made to control any stray electrical currents that may cause corrosion in the guideway reinforcement or generate other stray currents in adjacent structures or utilities. The primary power distribution network associated with a guideway may require several substations along the transit route. Power should be transmitted to the power rails on the guideway structure at various intervals. This is usually done through conduits mounted on or embedded in the guideway structure. Internal conduits are an acceptable means of transmitting power; they may be used to route power from the substation to the guideway. Access to internal conduits, however, is difficult to detail and construct. Sufficient space should be provided within the column-beam connection and within the beam section for the conduit turns. Space should also be provided for safe electrical connections. Exterior conduits can detract from the guideway appearance and require increased maintenance requirements. 3.7.5 Special equipment —A guideway normally carries several pieces of special transit equipment, which may consist of switches, signaling, command and control wiring, or supplemental traction and power devices. The specialized transit supplier should provide the engineer with explicit specifications of special equipment and their spatial restrictions. For example, the placement of signaling cables may be restricted within a certain distance of the wayside power rails or reinforcing steel. The transit supplier should also provide the engineer with details and performance requirements of special equipment satisfying forces and fatigue requirements so that proper connections to the structure can be designed and installed. An example of connection requirements would be linear induction motor (LIM) reaction rail attachments. When no system supplier has been selected, the engineer should design for anticipated services and equipment. A survey of potential supplier needs for the specific application may be required before design.

3.8—Geometries 3.8.1 General—Geometric alignment of the transit line can have a substantial impact on the system cost. Standardization of guideway components can lead to cost savings. During the planning and design stages of the transit system, the benefits of standardizing the structural elements, in terms of ease and time of construction and maintenance, sh ould be examined with effective options being implemented . Figure 3.8.1 illustrates example sections of bridges carrying transit line tracks. 3.8.2 Standardization—Straight guideways can be produced at a lower cost than curved ones. Geometric alignments and column locations that yield a large number of straight beams tend to be cost effective. Note that physical constraints at the ground can influence column locations. Figure 3.8.2 shows a straight alignment with repetitive substructure units and span lengths that result in cost reductions. Note also the limitations on column locations.

13

When choices are available, however, the placement of columns to generate straight beams, as opposed to those with a slight horizontal or vertical curvature, will usually prove to be more cost effective. Standardization and coordination of internal components and fixtures of the guideway also tend to reduce overall cost. These include inserts for power equipment, switches, or other support elements. Methods to achieve this are discussed in 3.9.3. 3.8.3 Horizontal geometry—The horizontal geometry of a guideway alignment consists of circular curves connected to tangent elements with spiral transitions. Most types of cubic spirals are satisfactory for the transition spiral. The vehicle manufacturer may provide additional constraints on the spiral geometry selection to match the dynamic characteristics of the vehicle. The horizontal geometry is often developed by the engineer in conjunction with constraints provided by the vehicle manufacturers. 3.8.4 Vertical geometry—Vertical geometry consists of tangent sections connected by parabolic curves. In most cases, the radius of curvature of the parabolic curves is sufficiently long so that a transition between th e tangent section and the parabolic section is not required. Figure 3.8.4 is an example of a guideway as well as box girder geometry providing gentle, appealing lines. The engineer should verify the radius of curvature for the parabolic curves providing a vertical acceleration that should be less than the maximum specified by the design criteria for the given project. 3.8.5 Superelevation—Superelevation is applied to horizontal curves to partially offset the effect of lateral acceleration on passengers. To achieve the required superelevation, the running surface away from the curve center is raised increasingly relative to the running surface closer to the curve center. This results in the outer rail or wheel track being raised while the inner rail or wheel track is kept at the profile elevation. The amount of superelevation is a function of the vehicle speed and the degree of curvature. It is usually limited to a maximum value of 10 percent. Further information on superelevations can be found at the Transportation Research Board’s TCRP Report 57 (Transportation Research Board 2000).

3.9—Construction considerations 3.9.1 General ––Guideway construction in an urban environment has an impact on residents, pedestrians, road traffic, and merchants along the route. Consideration should be given to the cost and length of disruption in terms of street closures, traffic detours, and construction details. 3.9.2 Street closures and disruptions—The amount of time streets are closed and neighborhoods are disrupted should be kept to a minimum. A traffic detour or alternate route should be provided for public and private use during street closures. Coordination with the public should begin at the planning stage. Figure 3.9.2 illustrates an example of staged construction. The selection of precast or cast-in-place concrete compo-

14


Fig 3.8.1—Example sections of bridges carrying transit line tracks.

of construction time and ease of stockpiling equipment and finished products at the site proximity. Construction systems that allow for rapid placement of footings and columns and for reopening of the street before the installation of beams may have an advantage in the maintenance of local traffic. 3.9.3 Guideway beam construction—Guideway beams may be cast-in-place or precast. To determine the preferred construction technique, the following items should be considered early in the design process: typical section and alignment; span composition (uniform or variable); structure types (simple span or continuous, I-girder, box girder or spliced girder, constant or variable depth); span-depth ratios;

Although cast-in-place construction offers considerable design and construction flexibility, it also requires a greater amount of support equipment on the site. This equipment, especially shoring and falsework, has to remain in place while the concrete cures. Precast concrete beam construction offers the potential for reduced construction time on site and allows better quality control and assurance. Advantages of precast concrete are best realized when the geometry and the production methods are standardized if precast concrete segmental equipment may be needed to transport and lift the segments into place.


15

Fig. 3.8.4––Horizontal and vertical geometry (courtesy of PCA). Fig. 3.8.2––Straight, repetitive geometry (courtesy of PCA).

Two types of guideway beam standardization appear to offer substantial cost benefits: modular construction and adjustable form construction. Modular construction uses a limited number of beam and column types to make up guideways. Thus, like a model train set, these beams are interwoven to provide a complete transit guideway. Final placement of steering surfaces and other system hardware on the modular elements provides the precise geometry necessary for transit operation. Modules may be complete beams; segmental construction also typifies this construction technique. Adjustable form construction allows the fabrication of curved beams to precisely match geometric requirements at the site. For alignments where a substantial amount of variation in geometry is dictated by the site, this solution provides a high degree of productivity at a reasonable cost. 3.9.4 Shipping and delivery—Before completing the final design, the engineer should be aware of limitations that may be placed on the delivery of large precast elements. Weight limitations imposed by local departments of transportation, as well as dimensional limitations on turnoff radii, width, and length of beam elements, may play an important role in final guideway design. The deployment of large cranes and other construction equipment along the site is also a consideration. 3.9.5 Approval considerations—These recommendations for transit guideways are intended to provide procedures based on the latest developments in serviceability and strength design. Other pertinent regulations issued by state, federal, and local agencies should be followed. Specific consideration should be given to the following: a) Alternative designs b) Environmental impact statements c) Air, noise, and water pollution statutes d) Historic and park preservation requirements e) Permits f) Life-safety requirements g) Construction safety requirements 3.9.6 Engineering documents—The engineering docu-

Fig. 3.9.2––Staged construction along busy thoroughfare (courtesy of PCA).

should show all dimensions of the finished structure in sufficient detail to facilitate the preparation of an accurate estimate of the quantities of materials and costs and permit the full realization of design. Contract documents should define test methods, inspection methods, and the allowable procedures and tolerances to ensure good workmanship, quality control, and application of unit costs when required. The contractor’s responsibilities should be clearly defined. Where new or innovative structures are employed, suggested construction procedures to clarify the engineer’s intent should also be provided. Computer graphics or integrated databases can assist in this definition. Where the concrete finish is critical to acceptance, the contract documents (or special provisions) should call for demonstration panels to be prepared for review and approval to establish the acceptable finish for the production members.

3.10—Rails and trackwork 3.10.1 General—Guideways for transit systems that use vehicles with steel wheels operating on steel rails require particular design and construction considerations, including

16


rail string assembly, use of continuous structures, and attachment of the rails to the structure. There are two options for assembling rails: they may be jointed with bolted connections in standard 39 ft (11.9 m) lengths, or welded into continuous strings. Rails may be fastened directly to the structure or installed on tie-and-ballast. 3.10.2 Jointed rail— The traditional method of joining rail is by bolted connections. Longitudinal rail movement can develop in these connections, preventing the accumulation of thermal stresses along the rail length. Space between the rail ends presents a discontinuity to the vehicle support and steering systems. Vehicle wheels hitting this discontinuity causes progressive deterioration of the joints, generates loud noise, reduces ride comfort, and increases dynamic forces on the structure. Because of these disadvantages, most modern transit systems use continuously welded rail. Jointed rail conditions will exist in switch areas, maintenance yards, and other locations where physical discontinuities are required. Even in these areas, however, discontinuities can be reduced greatly by the use of bonded rail joints. 3.10.3 Continuously welded rail 3.10.3.1 General—To improve ride quality and decrease track maintenance, individual rails are welded into continuous strings. There is no theoretical limit to the length of continuously welded rail if minimum restraint is provided. Minimum rail restraint consists of preventing horizontal or vertical buckling of rails and anchorage at the end of a continuous rail. This prevents excessive rail gaps from forming at low temperatures if accidental breaks in the rail should occur. Continuously welded rail (CWR) has become the transit industry standard over the past several decades. CWR requires particular attention to several design details, which include thermal forces in the rails, rail break gap and forces, welding of CWR, and fastening of CWR to the structure (AWS D15.2). The principal variables used in the evaluation of rail forces are rail size in terms of its cross-sectional area, the characteristics of the rail fastener, the stiffness of the structural elements, rail geometry, and operational environment in terms of temperature range. In cases where accumulation of thermal effects would produce conditions too severe for the structure, slip joints can be used. Slip joints allow limited movement between rail strings. They generally cause additional noise and require increased maintenance. Their use, therefore, is not desirable. Location of rail anchors and rail expansion joints will affect the design of the structure. 3.10.3.2 Thermal forces—Changes in the temperature of CWR will cause stresses in the rail and structure. Rails are typically installed at a design, stress-free, ambient temperature to reduce the risk of rail buckling at high temperatures and rail breaks at low temperatures. Depending on the method of rail attachment to the structure, the structure should be designed for: a) Horizontal forces resulting from a rail break

b) Radial forces resulting from thermal changes in the rails on horizontal or vertical curves c) End anchorage forces 3.10.3.3 Rail breaks—CWR will occasionally fail in tension because of rail wear, low temperature, defects in the rail, defects in a welded joint, fatigue, or some combination of these effects. The structure should be designed to accommodate horizontal thrust associated with the break. 3.10.3.4 Rail welding—CWR is accomplished by thermite welding process or electric flash butt-welding process (AWS D15.2). Proper written weld procedures should ensure that: a) Adjacent rail heads are accurately aligned b) Rail joint is clean of debris c) The finished weld is free of intrusions d) The weld is allowed to cool before tightening the fasteners Ultrasonic or X-ray inspection at random locations chosen by the engineer is highly recommended. The agency performing these inspections should be qualified to ASTM E543. 3.10.4 Rail installation 3.10.4.1 General—Rails are attached to either crossties on ballast or directly to the guideway structure. Preference in recent years has become direct rail fixation as a means of improving ride quality, maintaining rail tolerances, reducing maintenance costs, and reducing structure size. 3.10.4.2 Tie and ballast —Tie and ballast construction is the conventional method of installing rails at grade and occasionally on elevated structures. Ties are used to align and anchor the rails. Ballast provides an intermediate cushion between the rails and structure, stabilizes the tracks, and prevents transmission of thermal forces from rails to structure. Ballast substantially increases the structure dead load. Tie-and-ballast installations make control of rail break gaps difficult because ties are not directly fastened to the primary structure. Rail breaks can develop horizontal, vertical, and angular displacements of the rail relative to the structure. 3.10.4.3 Direct fixation—Direct fixation of the rail to the structure is accomplished by a mechanical rail fastener. Elastomeric pads are incorporated in the fastener to provide the required vertical and horizontal flexibilities and provisions for adjustment between adjacent fasteners and the structure. The elastomeric pads also assist in the reduction of noise, vibration, and impact. Important design and construction considerations for the direct fixation fasteners include: a) Method of attachment to the structure b) Vertical stiffness c) Allowance for horizontal and vertical adjustment d) Ability to restrain the rail against rollover e) Longitudinal restraint Direct fixation fasteners are one of the most important elements in trackwork design. They are subjected to a high number of cyclic loads, and thousands of them are in place. Progressive failure does not generally create catastrophic results, but it leads to a substantial maintenance effort and possible operational disruptions.


No industry-wide specifications exist for the definition or procurement of direct fixation fasteners. A thorough examination of the characteristics and past performance of available fasteners, and the characteristics of the proposed transit vehicle, should be done before fastener selection for any specific installation (Transportation Research Board 2000) 3.10.4.4 Continuous structure—Direct fixation of continuous rail to a continuous structure creates a strain discontinuity at each structural expansion joint. Fasteners should be designed to provide adequate slip at these joints while limiting the rail-gap size in the event of a break. In climates with extreme ranges in temperature (–40 to +90°F [–40 to +30°C]), structural continuity is generally limited to 200 to 300 ft (60 to 90 m) lengths. In more moderate climates, longer runs of continuous structure may be possible. For more information on rail installation and site-specific neutral rail temperature, refer to AREMA (2012).

CHAPTER 4—LOADS 4.1—General The engineer should investigate all special, unusual, and standard loadings that may occur in the guideway construction and operation. Special or unusual loads may include emergency, maintenance, or evacuation equipment or conditions. The following loads commonly occur and should be considered when assessing load effects on elevated guideway structures (Calgary Transit 2001), with notation following AASHTO LRFD abbreviations wherever applicable: 4.1.1 Sustained loads a) Dead load ( DC , DW ) b) Earth pressure ( EH ) c) External restraint forces ( ER) d) Differential settlement effects ( SE ) e) Prestress forces ( PS ) f) Buoyancy ( B) 4.1.2 Transient loads a) Live load and its derivatives ( LL, LS , PL) b) Impact factor ( IM ) c) Wind load and its derivatives ( WS , WL) d) Loads due to ice ( IC ) e) Loads due to stream current ( WA) 4.1.3 Loads due to volumetric changes a) Temperature ( TU , TG) b) Rail-structure interaction ( RS ) c) Shrinkage (SH ) d) Creep (CR) 4.1.4 Exceptional loads a) Earthquake ( EQ) b) Derailment/crash ( DR) c) Broken rail ( BR) d) Impact loads at street level ( ILST ) 4.1.5 Construction loads a) Dead loads ( DC , DW , EL) b) Live loads ( LL, LS , PL)

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Table 4.3.1.2—Minimum dynamic load (impact)

Structure types

Rubber-tired and continuously welded rail

Jointed rail

IM ≥ 0.10

IM ≥ 0.30

IM ≥ 0.10

IM ≥ 0.30

Simple-span structures, VCF

IM

=

−

0.1

f

1

Continuous-span structures, VCF

IM

=

−

0.1

2 f 1

4.2—Sustained loads 4.2.1 Dead loads (DC + DW)—The following components of dead load should be considered a) Weight of factory-manufactured elements b) Weight of cast-in-place elements c) Weight of trackwork and appurtenances including running and power rails, second-pour plinths and fasteners, barrier walls, and noise-suppression panels d) Weight of other ancillary components such as walk decks, stairways, light standards, and signage 4.2.2 Other sustained loads—Loads from differential settlement ( SE ), earth pressure ( EH ), effects of prestress forces (PS ), or external structural restraints ( ER) should be included in the design as they occur. The beneficial effects of buoyancy ( B) may only be included when its existence is ensured. AASHTO LRFD Bridge Design Specifications (AASHTO 2012) may be used as a guide to evaluate the effects of these sustained loads.

4.3—Transient loads 4.3.1 Live load and its derivatives 4.3.1.1 Vertical standard vehicle loads ( LL)—The vertical live load should consist of the weight of one or more standard vehicles positioned to produce a maximum load effect in the element under consideration. The weight and configuration of the maintenance vehicle should be considered in the design. The weight of passengers should be computed on the basis of 175 lb (780 N) each and should comprise those occupying all seats (seated) and those who are standing (standees) in the remaining space (no seats). The number of standees shou ld be based on one passenger per 1.5 ft 2 (0.14 m2). For torsion-sensitive structures, such as monorails, the possibility of passengers being crowded on one side of the vehicle should be considered in the design. 4.3.1.2 Impact factor (IM)—The minimum dynamic load (Government of Ontario 1983) shown in Table 4.3.1.2 should be applied to the vertical vehicle loads unless alternative values based on tests or dynamic analysis are approved. The vehicle crossing frequency (VCF) is defined as VCF =

vehicle speed, ft/s (m/s) span length, ft (m)

(4.3.1.2a)

18


Table 4.3.1.4—Minimum hunting force on guideway as fraction of standard vehicle load Bogie type

Hunting force

Nonsteerable

0.08 LL

Steerable

0.06 LL

Note: Vehicle supplier may have more severe requirements.

The first mode flexural (natural) frequency, f 1, (Billing 1979) is expressed as

f 1 =

π

Ec I g

2l 2

M

, Hz

(4.3.1.2b)

The dynamic load component should not be applied to footings and piles. 4.3.1.3 Centrifugal force (CE)—The CE , acting radially through the vehicle’s center of gravity at a curved track, may be computed from CE =

V 2

LL , lb (N) R × g

(4.3.1.3)

The centrifugal force CE should be applied simultaneously with other load combinations (refer to Chapter 5) to produce the maximum force effect on the structure. 4.3.1.4 Hunting force (HF)—The HF is caused by the lateral interaction of the vehicle and the guideway. It should be applied laterally on the guideway at the point of wheelrail contact, as a fraction of the standard vehicle load LL (Table 4.3.1.4). When centrifugal and hunting forces act simultaneously, only the larger force needs be considered. For rail and structure design, the hunting force will be applied laterally by a steel wheel to the top of the rail at the lead axle of a transit train. It does not need to be applied for rubber-tired systems. Typically, linear induction motor (LIM)-propelled vehicles run on steel wheel and rail and require consideration of hunting effects. 4.3.1.5 Longitudinal force (LF)—The LF acts simultaneously with the vertical standard vehicle live load on all wheels. It may be applied in either direction: forward in braking or deceleration or reverse in acceleration. The LF should be applied as indicted in Table 4.3.1.5. Continuously welded rail trackwork can distribute longitudinal forces to adjacent components of guideway structures. This distribution may be considered in design. The use of slip joints may prevent transfer and distribution of longitudinal forces. The specified emergency braking force of LF e = 0.30 LL should be reviewed on a project-specific basis derived from the type of braking system that will be deployed during emergency braking. Other factors in the assessment of the magnitude of LF e include rail fastener stiffness, column stiffness, and structure articulation.

Table 4.3.1.5—Longitudinal force applied Emergency braking

LF e = 0.30 LL

Normal braking

LF n = 0.15 LL

4.3.1.6 Service walkway load (P) — Live load on service or emergency walkways should be based on a minimum of 60 lb/ft2 (2.82 kPa) of area. This load should be used together with empty vehicles on the guideway because the walkway load is the result of vehicles being evacuated. 4.3.1.7 Loads on safety railing (LR) — The lateral load from pedestrian traffic on railings should be a minimum of 500 lb/ft (0.73 kN/m) distributed load, or 200 lb (0.89 kN) concentrated load, which ever produces the greatest effect, applied at the top rail, at a height between 34 and 38 in. (0.864 and 0.965 m). 4.3.2 Wind load (WL) 4.3.2.1 General—Design wind loads for elevated guideways and special structures are provided in 4.3.2.2. Wind loads based on the reference wind pressure should be treated as equivalent static loads as defined in 4.3.2.3. Wind forces are applied to the structure and to vehicles in accordance with load combinations i n Chapter 5. The WL abbreviation is used to designate wind loads applied to a vehicle, while WS indicates wind loads applied to the structure only. The net exposed area is defined as the net area of a body, member, or combination of members as seen in elevation. For a straight superstructure, the exposed frontal area is the sum of the areas of all members, including railings and deck systems, as seen in elevation perpendicular to the assumed wind direction. For a structure curved in plan, the exposed frontal area is taken normal to the beam centerline and computed in a similar manner to straight structures. The exposed plan area is defined as the net area of an element as seen in plan from above or below. In the case of a superstructure, the exposed plan area is the plan area of the deck and that of any laterally protruding railings, members, or attachments. The gust effect coefficient is defined as the ratio of the peak wind-induced response of a structure, including both static and dynamic actions, to the static wind-induced response. Buildings and other adjacent structures can affect the wind forces. Wind tunnel tests may be considered as a method to improve wind force predictions or to validate design coefficients in the alternative design approach provided in 4.3.2.3. Wind tunnel testing is well beyond the scope of this document, though the reader may be referred to “AASHTO LRFD Bridge Design Specifications” (AASHTO 2012), Section 3.8.3.1. 4.3.2.2 Design for wind —The guideway superstructure must be designed for wind-induced horizontal F h and vertical F v drag loads acting simultaneously. For a structure that is curved in plan, the wind should be considered to act in a direction such that the resulting force effects are maximized. For a structure that is straight in plan, the wind direction should be taken perpendicular to the longitudinal axis of the structure.


Table 4.3.2.2—Uniformly distributed load intensities Wind-induced horizontal drag load F h Superstructure components

Windward load, lb/ft2 (kPa)

Leeward load, lb/ft2 (kPa)

Trusses, columns, and arches

50 (2.4)

25 (1.2)

Beams

50 (2.4)

NA

Large flat surfaces

40 (1.9)

NA

In the absence of more stringent specifications, the uniformly distributed load intensities shown in Table 4.3.2.2 may be used for design. The total wind loading should not be less than 300 and 150 lb/ft (4.4 and 2.2 kN/m) in the planes of windward and leeward chords, respectively, on truss and arch components and not less than 300 lb/ft (4.4 kN/m) on beam or girder spans. The vertical drag load F v should be taken equal to 20 lb/ft 2 (0.95 kPa) times the width of the deck, including parapets and sidewalks. This force may be applied only for limit states that do not involve wind on live load. The wind loads F h and F v should be applied to the exposed areas of the structure and vehicle (refer to 5.3 and 5.4). These loads and provisions are consistent with recommendations of the latest edition of “AASHTO LRFD Bridge Design Specifications” (AASHTO 2012) that are derived from base wind velocities of 100 mph (160 km/h). Wind loads may be reduced or increased by the ratio of the square of the design wind velocity to the square of the base wind velocity, provided the maximum probable wind velocity can be ascertained with reasonable accuracy or there are permanent features of the terrain that make such changes safe and viable. The substructure should be designed for wind-induced loads transmitted from the superstructure and wind loads acting directly on the substructure. Loads for wind directions both normal to and skewed to the longitudinal centerline of the superstructure should be included. 4.3.2.3 Alternative wind load —The alternative wind load method may be used in place of 4.3.2.1. Alternative wind loads are suggested for projects involving unusual height guideways and gust conditions, or guideway structures that are judged by the engineer as more streamlined than highway structures (CSA 2008). The wind load per unit exposed frontal area of the superstructure, WS , and of the vehicle, WL, applied horizontally, may be taken as F h = P DC eC gC d

(4.3.2.3a)

Similarly, the wind load per unit exposed plan deck or soffit area applied vertically, upward, or downward, should be taken as F v = P DC eC gC d

(4.3.2.3b)

where C d = 1.0 for the wind load applied vertically. The maximum vertical wind velocity may be limited to 30 mph (50 km/h).

19

In the application of F v, as a uniformly distributed load over the plan area of the structure, the effects of a possible eccentricity should be considered. For this purpose, the same total load should be applied as an equivalent vertical line load at the windward quarter point of the superstructure width in conjunction with the horizontal wind loads. 4.3.2.4 Reference wind pressure—The reference wind pressures at a specific site should be based on the hourly mean wind velocity of a 75-year return period. A 10-year return period may be used for structures under construction. The reference wind pressure P D may be derived from the following expression

P D = r

V 2

2g

, lb/ft2 (MPa)

(4.3.2.4a)

For structures not sensitive to wind-induced dynamics, which include elevated guideways and special structures up to a span length of 400 ft (122 m), the gust effect coefficient C g may vary between 1.25 and 1.50. For design purposes, a factor of 1.33 may be used for C g. For structures that are sensitive to wind action, C g should be determined by an approved method of dynamic analysis or by model testing in a wind tunnel. For guideway appurtenances, such as signposts, lighting poles, and flexible noise barriers, C g may be taken as 1.75. The exposure coefficient or height factor C e may be computed from Ce

=

0.5 5 H

≥ 1.0,

for H , in ft

=

(4.3.2.4b)

0.625 5 H ≥ 1.0, for H , in m

where H should be measured from the foot of cliffs, hills, or escarpments when the structure is located on uneven terrain or from the low water level when the structure is located over bodies of water. Where funneling may be caused by the topography at the site, C e should be increased by 20 percent. The drag coefficient or shape factor C d is a function of many variables, the most important of which are the skew angle (horizontal angle of wind) and aspect ratio (ratio of length to width of structure). For box girder or I-girder superstructures and solid-shaft piers with wind acting at zero skew, C d may vary between 1.2 and 2.0. A factor of 1.5 for C d may be used for design purposes. For unusual exposure shapes, the drag coefficient C d should be determined from wind-tunnel tests. Where wind effects are considered at a skew angle q in degrees measured from a line perpendicular to the longitudinal axis of a structure, C d should be multiplied by 0.007q for the longitudinal wind load component and by (1 – 0.00018q2) for the transverse or perpendicular wind load component. 4.3.2.5 Wind load on slender elements and appurtenances—Slender elements, such as light and sign supports

20


loads provided for in 4.3.2.3 and 4.3.2.4, as well as lateral and crosswind load effects caused by vortex shedding. Both serviceability and strength considerations should be investigated. Details that may cause stress concentrations due to fatigue or resonance should be avoided. The wind drag coefficient C d for sign and barrier panels with aspect ratios of up to 1.0, between 1.0 to 10.0, and more than 10.0, should be 1.1, 1.2, and 1.3, respectively. For light fixtures and sign supports with rounded surfaces, octagonal sections with sharp corners, or rectangular flat surfaces, the values of C d should be 0.5, 1.2, or 1.4, respec tively. A value of 1.2 for C d should be used for suspended signal units. When ice accumulation is expected on the surface of slender components, the total frontal area should include the thickness of ice. The dynamic effects of vortex shedding should be analyzed and the stress limits for a minimum of 2 × 10 6 cycles of loading may be applied. 4.3.3 Loads due to ice pressure (IC)—Floating ice forces on piers and exposed pier caps should be evaluated according to the local conditions at the site. Consideration should be given to the following types of ice action on piers erected in bodies of water: a) Dynamic ice pressure due to ice sheets and ice floes in motion caused by stream or current flow and enhanced by wind action b) Static ice pressure caused by thermal action on continuous stationary ice sheets over large bodies of water c) Static pressure resulting from ice jams at a guideway site d) Static uplift or vertical loads due to ice sheets in water bodies of fluctuating level Ice loads resulting from freezing rain or consolidation of compact snow on the guideway superstructure and vehicle should be included, as appropriate. 4.3.4 Loads due to stream current (WA) 4.3.4.1 Longitudinal loads—The load acting on the longitudinal axis of a pier due to flowing water may be computed by the following expression (Buckle and Priestley 1978) WA = 0.5C D AV 2 g

(4.3.4.1)

4.3.4.2 Transverse loads— The lateral load on a pier shaft due to stream flow and drift should be resolved from the main direction of flow. The appropriate component should be applied as a uniformly distributed load on the exposed area of the pier below the high water level in the direction under consideration.

an ongoing basis. Effects due to thermal gradients within the section should also be considered (Priestley 1978). 4.4.2 Loads due to temperature (TU, TG) 4.4.2.1 Temperature range—The minimum and maximum mean daily temperatures should be based on local meteorological data for a 75-year return period. The range of effective temperature for computing thermal movements of the concrete structure should be the difference between the warmest maximum and the coldest minimum effective temperatures, which may be considered to be 5°F (2.5°C) above the mean daily maximum temperature and below the mean daily minimum temperatures, respectively. If local temperature data are not available, the structure may be designed for a minimum temperature rise of 30°F (17°C) and a minimum temperature drop of 40°F (23°C) from the installation temperature. 4.4.2.2 Effective construction temperature—If the guideway needs to accommodate continuously welded rails, an effective construction temperature should be selected. This temperature, which should be based on the mean daily temperature prevalent for the site under consideration and time of year, is used to establish the baseline for rail force. 4.4.2.3 Thermal gradient effects—Curvature caused by a temperature gradient should be considered in the design of the structure. The temperature differential between the top and bottom surfaces varies nonlinearly according to the depth and exposure of the structural elements and their locality. “AASHTO-LFRD Bridge Design Specifications” (AASHTO 2012) may be used as a guide in this regard. 4.4.2.4 Coefficient of thermal expansion—In place of a more precise value, the coefficient of linear thermal expansion for normalweight concrete may be taken as 6.5 × 10 –6 /°F (12 × 10–6 /°C). 4.4.3 Rail-structure interaction (FR, Fr)—Continuously welded rail (CWR) directly fastened to the guideway induces an axial force in the structure through the fastener restraint when the structure expands or contracts due to variations in temperature. CWR should be installed in a zero stress condition at an effective installation temperature T 0. If the CWR is installed at a temperature that is different from the effective installation temperature, then the rail should be physically stressed to be compatible with the zero stress condition for which it is designed at the installation temperature (Grouni and Sadler 1986). 4.4.3.1 Thermal rail forces—Axial rail stress f rr in CWR due to a change in the temperature after installation is expressed by f rr = E ra (T 1 – T 0)

(4.4.3.1a)

4.4—Loads due to volumetric changes 4.4.1 General—Provisions should be made for all movements and forces that can occur in the structure as a result of shrinkage, creep, and variations in temperature. Load effects that may be induced by a restraint to these movements should be included in the analysis. These restraints include those imposed during construction on a temporary basis and those imposed by the rail-fastener interaction on

If the bridge and the rail increase or decrease in temperature by the same amount, then they will both expand or contract together in a relatively stress-free state because the coefficient of expansion is almost identical between concrete and steel. For a temperature decrease, T 1 may be taken as the minimum effective temperature described in 4.4.2.1. For a temperature rise, T 1 may be taken as the maximum effective


temperature plus 20°F (12°C). The corresponding rail force F r is expressed by F r = S Ar f r = S Ar E ra (T 1 – T 0)

(4.4.3.1b)

where S implies that the forces in all rails must be summed. The movement of the structure through the fasteners induces either a tensile or compressive axial force on the rail, depending on whether the temperature rises or drops, respectively, from installation. A vertically- or horizontally-curved structure experiences a radial force resulting from the thermal rail forces. This radial force per unit length of rail is expressed as F R

=

F r R

(4.4.3.1c)

Note that F R always occurs in combination with F r . The preceding expressions apply where there is no motion of the rail relative to the structure. Where rail motion may occur, the relaxation of the rail should be analyzed to determine its effect on the structure. Rail motion may occur when a) Rail expansion joints are present b) Radial or tangential movements of rail and guideway structure at curves occur c) A rail break takes place d) Continuous rails cross structural joints e) Creep and shrinkage strains in prestressed concrete elements continue to take place 4.4.3.2 Broken rail forces—At very low temperatures, the probability of a rail break increases. The most likely place for a rail break to take place is at an expansion joint in the structure. A rail break at this location generally creates the largest forces in the structure. When the rail breaks, it slips through the fasteners on both sides of the break until the tensile force in the rail (before the break) is counteracted by the reversed fastener restraint forces. The unbalanced force from the broken rail is resisted by both the unbroken rails and the guideway support system in proportion to their relative stiffnesses. The probability that more than one rail will break at the same time is small and is generally not considered in the design. Allowances for eccentric loading can be found in the Transportation Research Board TCRP Report 57 (Transportation Research Board 2000). 4.4.3.3 Rail gap—The relative system stiffness should be proportioned so that the magnitude of the gap between broken rail ends is equal to the maximum allowable to prevent vehicle derailment. Typically acceptable rail gaps are in the range of 2 in. (50 mm) for a 16 in. (400 mm) diameter wheel and up to 4 in. (100 mm) for larger wheels. Rail gap is controlled by the spacing and stiffness of the fasteners. 4.4.4 Shrinkage in concrete (SH)—Shrinkage is a function of a number of variables, the most significant of which are: a) Characteristics of the aggregates b) Water-cementitious material ratio ( w / cm) of the mixture c) Type and the duration of curing d) Volume-to-surface ratio of the member

21

e) Ambient temperature f) Relative humidity at the time of placing the concrete For a major transit project, shrinkage and creep behavior of the concrete mixture should be tested and validated as part of the design process. ASTM test procedures exist to test for shrinkage in various aggregate, cement, and admixture combinations. For precast members, only the portion of shrinkage or creep remaining after the element is integrated into the structure needs to be considered. In the absence of more accurate data or method of analysis, shrinkage strain t days after casting of normalweight concrete may be computed by following the methods described in ACI 209R. 4.4.5 Creep in concrete (CR)—Creep is a function of relative humidity, volume-to-surface ratio, and time t after application of load. Creep is also affected by the amount of reinforcement in the section, the magnitude of sustained prestress load ( PS ), the age of the concrete when the force is applied, and the properties of the concrete mixture. If the design is sensitive to volumetric change, then an experimental validation of creep behavior, based on the ingredients to be used, may be necessary. In the absence of more accurate data and procedure, creep at t days after application of load may be found, by following the methods described in ACI 209R.

4.5—Exceptional loads 4.5.1 Earthquake effects (EQ)—Structures should be designed to resist seismic motions by considering the relationship of the site to active fault locations, the seismic response of the soils at the site, and the dynamic response characteristics of the total structure in accordance with the latest edition of “AASHTO LRFD Bridge Design Specifications” (AASHTO 2012). Certain local jurisdictions may have higher seismic zone/risk requirements for analysis and design. 4.5.2 Derailment load (DR)—Derailment may occur when the vehicle steering mechanism fails to respond on curves or when the wheels jump the rails at too large a pullapart gap, which may be the result of a break in a continuous welded rail (CWR) (Calgary Transit 2001). Derailment may also be caused by inter-vehicle collision. For the design of the top slab and the barrier wall of the guideway, both the vertical and horizontal derailment loads need to be considered simultaneously. The force effects caused by a single derailed standard vehicle should be considered in the design of the guideway structure components. These effects, whether local or global, should include flexure, shear, torsion, axial tension or compression, and punching shear through the deck. The derailed vehicle should be assumed to come to rest as close to the barrier wall as physically possible to produce the largest force effect. In the design of the deck slab, a dynamic load effect (1.0 × wheel load) should be added to the wheel loads. This results in a load of: wheel load + dynamic load = 2(wheel load), or dynamic load = 100 percent (wheel load). The magnitude and line of action of a horizontal derailment load on a barrier wall is a function of a number of

22


barrier wall, the vehicle weight and speed at derailment, the flexibility of the wall, and the frictional resistance between the vehicle and the wall. In place of a detailed analysis, the barrier wall should be designed to resist a lateral force equivalent to 50 percent of a standard vehicle weight distributed over a length of 15 ft (5 m) along the wall and acting at the axle height. Collision forces between vehicles result from the derailment of a vehicle and its subsequent resting position against the guideway sidewall. This eccentric load on the guideway causes torsional effects that should be accounted for in the design. The magnitude and eccentricity of this vertical collision load are functions of the distance of the guideway centerline from the side wall, the axle width, and the relative position of the centerlines of the vehicle body and the truck after the collision. Due to collision of a moving train with a stationary train on a guideway, one or both trains may be toppled and collide with the barrier wall. The minimum height of the barrier should be 28 in. (710 mm) above the top of the rail. The collision loads have a horizontal component (COLFH) and vertical component (COLFV). Both loads are applied simultaneously to the guideway structure at the top of the barrier wall. The major assumptions used in calculating the aforementioned forces (defined in the following) are: a) The moving train is travelling at 11.2 mph (20 km/h) when it strikes the stationary train. This velocity is known to be consistent with the two-red system of LRT traffic control used in major cities in N orth America b) Two-thirds of the kinetic energy is converted into potential energy of upward tilt The most severe effect of any of the following three cases may be considered (Calgary Transit 2001).

Case 1 Case 1 applies to a barrier height of 36 in. (910 mm) or more above the top of the rail. Horizontal collision load (COLFH) is 20 percent of the standard vehicle weight distributed over a length of 18 ft (6 m). Vertical collision load (COLFV) is 8 percent of the standard vehicle weight distributed over a length of 18 ft (6 m).

Case 2 Case 2 applies to a barrier height of 32 in. (810 mm) or less above the top of the rail. COLFH is 25 percent of the standard vehicle weight distributed over a length of 18 ft (6 m). COLFV is 20 percent of the standard vehicle weight distributed over a length of 18 ft (6 m).

Case 3 Case 3 applies to a vehicle resting on the barrier after a collision. COLFH is 0. COLFV is the weight of one vehicle distributed over the length of the vehicle. A linear interpolation for the loads can be used for a barrier height above the top of the rail between 36 in. (910

Either the derailment load or the collision load should be considered. 4.5.3 Broken rail forces (BR)—Forces on the guideway support elements due to a broken rail are discussed in 4.4.3. 4.5.4 Collision load (CT)—Based on AASHTO LRFD (AASHTO 2012) recommendations, piers or other guideway support elements that are located less than 30 ft (10 m) to the edge of an adjacent street or highway, or less than 50 ft (16 m) to the centerline of a railway track, should be designed to withstand a minimum horizontal static force of 400 kips (1800 kN) unless protected by a suitable barrier. The force is to be applied on the support element, or the protection barrier, at an angle of 10 degrees from the direction of the road traffic and at a height of 4 ft (1.20 m) above ground level. Suitable protection to piers and other support elements are as follows: (a) An embankment (b) Structurally independent, crashworthy, groundmounted, 54 in. (1.3 m) high barrier located within 10 ft (3 m) of the component being protected (c) A 42 in. (1.1 m) high barrier located more than 10 ft (3 m) from the component being protected To qualify for these exceptions, such barriers should be structurally and geometrically capable of surviving the crash test for Performance Level 5, as specified in AASHTO LRFD (AASHTO 2012) Section 13. The possibility of overheight vehicles colliding with the guideway beam should be considered for guideways with less than 16.5 ft (5.0 m) clearance over existing roadways.

4.6—Construction loads Construction loads should be considered in accordance with SEI/ASCE 37. 4.6.1 General—Loads due to construction equipment and materials that may be imposed on the guideway structure should be accounted f or during construction. Refer to Figures 4.6.1a and 4.6.1b for examples of different construction loading conditions to be accommodated in design. Additionally, transient load effects during construction due to wind, ice, stream flow, and earthquakes should be considered with return periods and probabilities of single or multiple occurrences commensurate with the expected life of the temporary structure or the duration of a particular construction stage. 4.6.2 Dead loads (DC + DW)— Dead loads on the structure during construction should include the weight of formwork, falsework, fixed appendages, and stored materials. The dead weight of mobile equipment that may be fixed at a stationary location on the guideway for long durations should also be considered. Such equipment includes lifting and launching devices. 4.6.3 Live loads (L)—Live loads on the structure during construction should include the weight of workers and all mobile equipment, such as vehicles, hoists, cranes, and structural components used during the process of erection. Construction live load limits should be identified on the contract documents.


Fig. 4.6.1a––Cantilever construction (courtesy of PCA).

Fig. 4.6.1b––Span-by-span construction (courtesy of PCA).

CHAPTER 5—LOAD COMBINATIONS, LOAD FACTORS, AND STRENGTH REDUCTION FACTORS 5.1—Scope This chapter specifies load factors, strength reduction factors, and load combinations to be used in serviceability and strength designs. Structural safety is used as the acceptance criterion. The derivation of load and strength reduction factors is based on probabilistic methods using available statistical data and making certain basic assumptions. Specific projects may use a load modifier for operational importance as specified in the “AASHTO LRFD Bridge Design Specifications” (AASHTO 2012). Such a load modifier, however, may only be applied to the strength load combinations presented in 5.4. The owner may declare/classify the guideway structure or any similar structural component and connection to be of operational importance. Such declaration/classification should be based on social/survival, security/defense requirements, or both.

5.2—Basic assumptions The design economic life of a transit guideway is 75 years. Load and resistance models should be developed accordingly. Guideway structures should meet the require-

23

ments for both serviceability and strength design. Serviceability design criteria are derived by elastic analysis, and stresses and section resistance are derived from that analysis. Strength design criteria are also determined by elastic analysis. Whereas stresses are developed from elastic analysis, section resistance is determined based on inelastic behavior. The load and resistance models used in this study were based on available test data, analytical results, and engineering judgment (Nowak and Grouni 1988; Nowak and Lind 1979). Live load is defined by a fully loaded standard vehicle. The weight of vehicles should include an allowance for potential weight growth. Resistance models take into account the degree of quality control during casting. The properties of factory-produced members are therefore considered more reliable than those of cast-in-place members. ACI 318 specifications are assumed in this document for requirements of concrete strength control. Safety is measured in terms of the target reliability index. A higher target reliability index reflects a lower probability of failure. A target reliability index of 4.0 is adopted for strength design. The target reliability index adopted for serviceability design is 2.5 for cracking and 2.0 for fatigue. The objective in deriving reliability-based load factors is to provide a uniform safety level to load-carrying components. The uncertainties in methods of analysis, material properties, and dimensional accuracies are taken into account in the derivation of strength reduction factors. Uncertainties regarding the magnitude of imposed loads and their meanto-nominal ratios are accounted for in the derivation of load factors. Because of the high number and frequency of train loads passing or traveling on a guideway structure, environmental and emergency loads are combined with maximum live load. The derivation of load and strength reduction factors is based on this reliability approach.

5.3—Service load combinations Four service load combinations—S1, S2, S3, and S4—are listed in Table 5.3. When warranted, more load combinations may be used on specific projects. Load and strength reduction factors are not used for serviceability design.

5.4—Strength load combinations 5.4.1 General requirements—For strength design, the factored strength of a member should exceed the total factored load effect. The factored strength of a member or cross section is obtained by taking the nominal member strength, calculated in accordance wit h Chapter 7, and multiplying it by the appropriate strength reduction factor f given in 5.4.3. The total factored load effect should be obtained from relevant strength combination U incorporating the appropriate load factors given in Table 5.4.1. Simultaneous occurrence of loads is modeled by using available data. For the purposes of reliability analysis, loads are divided into categories according to their duration and the probability of their joint occurrence as follows: a) Permanent loads: dead load, earth pressure, and struc-

24


Table 5.3—Service load combinations S1 = DC + DW + LL + IM + PS + LF n + (CE or HF )

Table 5.4.1—Design load combinations and load factors Load component

S2 = S1 + [0.3( WL + WS ) or IC or WA] S3 = S2 + TU + TG + SH + CR S4 = PS + DC + DW + WS + TU + TG + SH + CR

b) Gradually varying loads: prestressing effects, creep and shrinkage, differential foundation settlement, and temperature effects c) Transitory loads: live load (static and dynamic) and wind d) Exceptional loads: ice flow, flood, foundation load associated with flood, vessel collision, earthquake, emergency braking, broken rail, derailment, and vehicle collision Gradually varying loads act simultaneously with permanent loads. The former are taken at their maximum or minimum level—whichever yield the worst-case scenario for structural performance—for the duration considered. Transitory and exceptional loads are combined according to Turkstra’s rule (Turkstra 1970), which stipulates that the maximum total load occurs when one load component is at its maximum value simultaneously with the others, taken at their average values. All possible combinations are considered to determine the combination that maximizes total load effect. Load factors corresponding to time-varying load combinations reflect the reduced likelihood of simultaneous occurrence of these loads. 5.4.2 Load combinations and load factors— Load combinations, together with the corresponding factors for strength design, are listed in Table 5.4.1. Values of load components are specified in Chapter 4. 5.4.3 Strength reduction factors (Nowak and Grouni 1983)— The theoretical capacity of a section should be reduced by a strength reduction factor f, as follows for: a) Flexure only, or flexure with axial load in prestressed concrete: f = 0.95 b) Flexure only, or flexure with axial load in reinforced concrete: f = 0.90 c) Shear and torsion: f = 0.75 d) Axial tension: f = 0.85 e) Compression in members with spiral confinement reinforcement for the main longitudinal reinforcement: f= 0.75 f) Compression in other members: f = 0.70 For low values of axial compression, f may be increased linearly to 0.90 or 0.95 for reinforced or prestressed concrete, respectively, as the axial load decreases from 0.l0 f c′ Ag to zero. (Refer to ACI 318-11, 9.3.2.2, for additional information). The f factors were computed with the assumption that precast concrete guideway components with bonded posttensioning tendons are used. Nonbonded tendons are less reliable because of the higher probability of corrosion and other forms of deterioration, which would result in a larger coefficient of variation. For this reason, it is suggested to reduce the f value by 0.1 for the case of elements with nonbonded post-tensioning tendons.

U0

U1

*

1.3

*

1.3

1.0

1.3

1.7

1.4

1.0

1.4†

—

SH and CR

1.0

1.0

1.0

1.0

—

PS

1.0

1.0

1.0

1.0

1.0

DC + DW LL, IM , and either or HF

CE

U3

U5 *

U6 1.3*

WL + WS

1.0

1.5

1.0

1.5

—

IC , TU + TG, WA, or EQ

—

—

1.0

—

—

LF e

—

—

1.0

—

—

BR (F R, F r)

—

—

—

—

1.2

CT

—

—

—

—

1.3

DR or CT

—

—

—

1.4

—

*

Use 0.9 when effect is more conservative.

†

Use the weight of an empty train only.

CHAPTER 6—SERVICEABILITY DESIGN 6.1—General Chapter 6 covers the performance of reinforced concrete guideways (both prestressed and nonprestressed) under service loadings. Serviceability requirements to be investigated include stresses, fatigue, vibration, deformation, and cracking. Fatigue is included in serviceability design because high cyclic loading influences the permissible design str esses. Load combinations for serviceability design are given i n 5.3. Durability considerations are given i n 3.3.6.

6.2—Basic assumptions Force effects under service loads should be determined by a linear elastic analysis. For investigation of stresses at service conditions, the following assumptions are made: a) Strains are directly proportional to distance from the neutral axis b) At cracked sections, concrete does not resist tension c) Stress is directly proportional to strain

6.3—Permissible stresses 6.3.1 Nonprestressed members—Fatigue and cracking are controlled by limiting the stress levels in the concrete and the nonprestressed reinforcement. The stress limitations are discussed in 6.5 and 6.8. 6.3.2 Prestressed members 6.3.2.1 Concrete—Flexural stresses in prestressed concrete members should not exceed the following. 6.3.2.1.1 At transfer —Stresses before losses due to creep, shrinkage, and relaxation, and before redistribution of force effect take place, should not exceed: 1. Compression a) Pretensioned members: 0.60 f ci′ b) Post-tensioned members: 0.55 f ci′ 2. Tension a) Tension in members without bonded nonprestressed reinforcement in the tension zone: 0.40 f cri. Tension in


members with bonded nonprestressed reinforcement in the tension zone: 1.0 f cri b) Where the calculated tensile stress is between 0.40 f cri and 1.0 f cri, reinforcement should be provided to resist the total tensile force in the concrete computed on the basis of an uncracked section. The stress in the reinforcement should not exceed 0.60 f y, or 30 ksi (200 MPa), whichever is smaller c) Tension at joints in segmental members: i. Without bonded nonprestressed reinforcement passing through the joint in the tension zone: 0.0 ii. With bonded nonprestressed reinforcement passing through the joint in the tension zone: 0.40 f cri In the absence of more precise data, f cri may be taken as 7.5 f ci′ (psi) (0.62 f ci′ [MPa]). Where the calculated tensile stress is between zero and 0.40 f cri, reinforcement should be provided to resist the total tensile force in the concrete computed based on uncracked section. The stress in the reinforcement should not exceed 0.60 f y or 30 ksi (200 MPa), whichever is smaller. 6.3.2.1.2 Service loads—Concrete stresses, after allowance for all losses due to creep, shrinkage and relaxation, and redistribution of force effects, should not exceed: a) Compression i. Load combination S1 or S2 Precast members: 0.45 f c′ Cast-in-place members: 0.40 f c′ ii. Load combination S3 or S4 Precast members: 0.60 f c′ Cast-in-place members: 0.55 f c′ b) Tension i. Tension in precompressed tensile zones For severe exposure conditions, such as coastal areas, members in axial tension, and load combination S1: 0.0 For moderate exposure conditions or for load combination S2, S3, or S4: 0.40 f r Other cases and extreme operating conditions under load combinations S3 and S4: 0.80 f r For segmental members without bonded prestressed reinforcement passing through the joints: 0.0 For design against fatigue: 0.0 Tension in other areas should be limited by allowable stresses at transfer. In the absence of more precise data, the cracking stress of • •

• •

•

•

•

•

• •

concrete, f r, may be taken as 7.5 f c′ psi (0.62 f c′ MPa). 6.3.2.1.3 Additional considerations—It is recommended that the principal tensile stress in webs of post-tensioned concrete girders be checked against allowable tensile stress limits that consider the complex state of stress caused by shear, flexure, torsional straining actions, or combinations of these. The check is intended to ensure the adequacy of webs for longitudinal shear under service conditions. Whereas several sections should be checked across the height of the cross section, a single check at the neutral axis is recommended as a minimum procedure. The principal stress check should only be carried out at sections away from any discontinuities caused by bearings, diaphragms, saddles, and blisters

25

using classical beam theory and Mohr’s circle. The allowable tensile stress limit can be taken as 3.0 f c′ psi ( 0.25 f c′ MPa) (Florida DOT 2003; Okeil 2006). 6.3.2.2 Prestressing steel—The stress in prestressing steel should not exceed the values given in Table 6.3.2.2. Curved structures are common in guideway structures. Local stresses in the web induced by post-tensioning due to the horizontal curvature need to be considered. These stresses need to be combined with the stresses induced by global shear, flexure, or torsion. In the curved structures with post-tensioning, it is not unusual that the combined stresses in the web can exceed the 3.0 f c′ psi ( 0.25 f c′ MPa). 6.3.3 Partial prestressing—The preceding tensile strength limitations for concrete may be waived if calculations, based on approved or experimentally verified rational procedures, demonstrate adequate deflection, cracking, and fatigue control under specified loading combinations.

6.4—Loss of prestress In determining the effective prestress, allowance should be made for of the following prestress loss: a) Slip at the anchorage b) Friction losses due to intended and unintended (wobble) curvature in the tendons c) Elastic shortening of concrete d) Creep of concrete e) Shrinkage of concrete f) Relaxation of steel The amount of prestress loss due to the aforementioned depends on a number of factors that include properties of the materials used in the structure, the environment, and the stress levels at various loading stages. The prestress loss due to creep depends on the magnitude of stress on the concrete. Due to shrinkage and tendons’ relaxation, the magnitude of stress on the concrete varies with time; thus, creep is dependent on shrinkage and relaxation. The relaxation of a tendon is measured by a test on the tendon stretched between two fixed points and the relaxation is dependent on the magnitude of the initially applied tension. Therefore, the higher the initial tension, the higher the relaxation. The relaxation test gives the intrinsic relaxation. In a prestressed member, the tendon is stretched between the end anchors and these points move toward each other due to the creep and the shrinkage of concrete. Thus, the relaxation of the tendon in a prestressed member is smaller than the intrinsic relaxation—the difference is dependent on creep and shrinkage. The interdependence of the different sources should be taken into account when the deflection is critical (Ghali et al. 2012). When the deflection is not critical, the prestress losses may be estimated using the methods outlined by ACI 343R, ACI 209R, AASHTO (2012), PCI Committee on Prestress Losses (1975), NCHRP Report 496 (NCHRP 2003); Zia et al. (1979); and Huang (1982). For preliminary design of structures using normal-density concrete, the lump sum losses shown in Table 6.4 may be used. Lump sum losses do not include anchorage and friction losses in post-tensioned tendons. The losses due to the higher

26


jacking stresses are higher than those in the “AASHTO LRFD Bridge Design Specifications” (AASHTO 2012). For members constructed and prestressed in multiple stages, or for segmental construction, the stress level at the commencement and termination of each stage should be considered.

6.5—Fatigue 6.5.1 General—A transit guideway may undergo 6 million or more vehicle passes at various load levels during its lifetime (NCHRP 267 [NCHRP 1982]). This may be equivalent to 3 to 4 million cycles at maximum live load level. Such high levels of cyclic loading render guideways prone to fatigue failure. Areas of concern are the prestressing steel and the reinforcing bars located at cracked sections where a large number of stress cycles may occur.

Tendon type

Condition

Low-relaxation strand

f f

At service limit state after all losses ( f pe)

0.70 f pu

0.80 f py

0.75 f pu

0.80 f py

24 − 0. 33 f min ksi

f f

≤ 166 − 0.33 f min

Deformed highstrength bars

(6.5.3a)

MPa

For bent flexural bars, stirrups and bars containing welds conforming to requirements of AWS D1.4 (6.5.3b)

Bends and welds in principal reinforcement should not be used in regions of high stress variation. For shear reinforcement, the change in stress, f sv, may be computed as follows f sv

Pretensioning Immediate prior to transfer ( f pbt )

≤

f sr = 0.5 f f ksi (MPa)

Table 6.3.2.2—Maximum stress in prestressing steel Stress-relieved strand and plain high-strength bars

6.5.2 Concrete —Under service load combination, the flexural compressive stress in concrete should not exceed 0.45 f c′ at sections subject to cyclic loading and no tensile stresses are allowed. 6.5.3 Nonprestressed reinforcement —Under service load condition, the stress range in straight and bent flexural reinforcing bars— f f and f sr , respectively—in accordance with AASHTO LRFD (AASHTO 2012), should not exceed For straight bars:

=

∆Vs

Av jd

ksi (MPa)

(6.5.3c)

—

For torsion reinforcement, the change in stress, f st , may be computed for box sections or sections where a / b < 0.6, as follows

0.80 f py

Post-tensioning Prior to seating—shortterm f pbt may be allowed At anchorages and couplers immediately after anchor set

0.90 f py

0.90 f py

f st =

0.90 f py

∆Ts

(1.7 Aoh At )

(6.5.3d)

For combined effects of shear and torsion 0.70 f pu

0.70 f pu

0.70 f pu

f sv + f st < f f

Elsewhere along length of member away from anchorages and couplers immediately after anchor set

0.70 f pu

0.74 f pu

0.70 f pu

At service limit state after losses ( f pe)

0.80 f py

0.80 f py

0.80 f py

(6.5.3e)

6.5.4 Prestressed reinforcement —The stress range in prestressing tendons should not exceed a) 18.0 ksi (124.11 MPa) for radii of curvature in excess of 30.0 ft (9.14 m) b) 10.0 ksi (68.95 MPa) for radii of curvature not exceeding 12.0 ft (3.66 m) A linear interpolation may be used for radii between 12.0 and 30.0 ft (3.66 and 9.14 m).

Table 6.4—Lump sum losses for preliminary design (CAN/CSA-S6-00) Pretensioned, psi (MPa)

Post-tensioned, psi (MPa)

Stress relieved

Low relaxation

Stress relieved

Low relaxation

At transfer

29,000 (200)

19,000 (130)

4000 (30)

4000 (30)

After transfer

37,000 (255)

22,000 (150)

37,000 (255)

20,000 (135)


6.6—Vibration and dynamic response

Table 6.6.2a—Unacceptable deflections

6.6.1 General—Guideway vibration during passage of a transit vehicle induces a motion that results in poor ride quality. Guideways should therefore be designed to provide an acceptable level of passenger comfort. This entails consideration of the vehicle-guideway interaction. The most significant factor affecting ride quality is the acceleration level experienced by the passenger. As a result, comfort criteria are usually expressed in terms of acceleration limits. In the design of guideway structures, appropriate measures should be taken to prevent resonant-type buildup of structural vibrations caused by the moving train wheel loads. If not handled by proper design, vibrations can endanger safety, reduce the structure’s service life, impose unnecessary constraints on train operations, and cause discomfort to passengers. Discomfort caused by vertical vibrations is a function of the vibration frequency, amplitude, and duration. For a conventional line with slower-moving trains, a proper design can be attained by stiffening the guideway structural system sufficiently enough to raise the critical vehicle speeds at which a quasi-resonant-type structural vibration occurs above the maximum operating speed. A moving vehicle reaches the critical speed when vibrations induced by a rough track profile are produced with a frequency that matches one of the natural frequencies of the structure. If a rough track profile can be approximated with a sine wave with a wavelength L, the corresponding critical speed V cr is V cr =

wn

2π

× L

27

(6.6.1)

Span/deflection One or two adjacent spans*

Three to five adjacent spans*

Spans up to 82 ft (25 m)†

Spans above 98 ft (30 m)†



<75 mph (<120.7 km/hr)

<350

<350

400

400

75 to 125 mph (120.7 to 201.2 km/hr)

<350

<350

500

600

>125 mph (>201.2 km/hr)

<350

<350

500

700

Speed range

*

Simply supported or continuous decks.

†

Use linear interpolation for spans between 82 and 98 ft (25 and 30 m).

Note: More stringent ratios may be required at the owner’s discretion.

Table 6.6.2b—Reasonable deflections Span/deflection One or two adjacent spans*






<75 mph (120.7 km/h)

350

350

450

800

75 to 125 mph (120.7 to 201.2 km/h)

450

600

700

2000

>125 mph (>201.2 km/h)

550

700

700

2000

Speed range

*


†


For lines with vehicles operating at high speed, this is not easily accomplished because it is economically unacceptable to have too many critical speeds existing below the maximum operating speed. So when a quasi-resonance condition cannot be avoided, dynamic analysis should be conducted to predict the vibration amplitudes of the guideway structure and the vehicle. The results should be compared with prescribed levels of performance. Requirements on acceptable levels of performance for structural safety are based on structural strength requirements. The maximum dynamic stresses induced in the structures may be limited to the values specified in 6.5.3 and 6.5.4, or applicable codes such as “AASHTO LRFD Bridge Design Specifications” (AASHTO 2012). 6.6.2 Deflections—Excessive structural deflections can endanger traffic by causing unacceptable changes in track geometry. Excessive vibrations in guideway structures and in vehicles passing over the guideway structure may lead to passenger discomfort. The International Union of Railways UIC Code 776-3 recommends limitations on bridge deflection to avoid traffic risk and reduce passenger discomfort. Several span/deflection ratios have been tabulated to identify degree of passenger comfort (UIC 776-3) (refer to Tables 6.6.2a through 6.6.2c).


Table 6.6.2c—Acceptable deflections Span/deflection One or two adjacent spans*




<75 mph (120.7 km/h)

400

400

500

900

75 to 125 mph (120.7 to 201.2 km/h)

500

800

1000

2200

>125 mph (201.2 km/h)

800

1000

1200

2200

Speed range

Spans up to Spans 82 ft above 98 ft (25 m)† (30 m)†

*


†



6.6.3 Natural frequency—The expression for the fundamental flexural frequency of a simply supported beam is given in 4.3.1.2. The fundamental frequency of a continuous beam, having a series of equal spans, is the same as that of a simply supported beam of the same span length. For a continuous beam where the spans are unequal, a reasonable estimate of the fundamental frequency may be obtained by assuming the

28


Table 6.7.3.2—Suggested multipliers used as guide in estimating long-term cambers and deflections for typical members (PCI 2004) Without composite topping

With composite topping

Deflection (downward) component—apply to the elastic deflection due to the member weight a t release of prestress

1.85

1.85

Camber (upward) component—apply to the elastic camber due to prestress at the time of release of prestress

1.80

1.80

Deflection (downward) component—Apply to the elastic deflection due to the member weight at release of prestress

2.70

2.40

Camber (upward) component—Apply to the elastic camber due to prestress at the time of release of prestress

2.45

2.20

Deflection (downward) component—Apply to elastic deflection due to superimposed dead load only

3.00

3.00

—

2.30

At erection

Final

Deflection (downward) component—Apply to elastic deflection caused by the composite topping

of the fundamental frequency may be obtained using various approaches (Billing 1979; Csagoly et al. 1972). Effects of the horizontal curvature can be accounted for as shown in Campbell (1978). Frequencies of higher flexural modes for continuous beams are closer to the fundamental frequency than those for simply supported beams. Therefore, care should be taken to ensure that one of these higher frequencies for a continuous beam does not coincide with vehicle frequency. Attention should be given to torsional frequencies of the guideway and the vehicle in the guideway where not all supports can resist torsional effects. Methods for computing torsional frequencies can be found in standard textbooks on vibrations of structures (Thompson 1972). 6.6.4 Modulus of elasticity—The modulus of elas1.5 ticity E c for concrete may be taken as wc 33 f c′ psi

( wc1.5 0.043 f c′ MPa ) for values of wc between 90 and 160 lb/ft3 (1500 and 2500 kg/m 3). For normalweight concrete, E c may be taken as 57,000 f c′ psi (4730 f c′ MPa). The modulus of elasticity E s for nonprestressed reinforcement may be taken as 29,000,000 psi (200,000 MPa). The modulus of elasticity E s for prestressing tendons may be taken as 28,500,000 psi (196,550 MPa) unless determined by tests or supplied by the manufacturer.

6.7—Deformations and rotations 6.7.1 General—Deformations and rotations due to external loading, prestress, and volume changes due to temperature, creep, and shrinkage should be considered in the design; excessive deformations can affect the structure and the ride quality. Therefore, the deformation at the angular discontinuity on guideway surfaces (for example, expansion joints at beam ends) is of particular importance. Deformation in members under sustained loading should be calculated as the sum of both the immediate and longterm deformations. Deflections that occur immediately upon application of load should be computed as elastic deflections by the usual methods.

6.7.2 Nonprestressed members 6.7.2.1 Immediate deflection—For simple spans, the effective moment of inertia, I e, should be taken as 3

I e

 M   M  =  cr  I g + 1 − ( cr )3  I cr ≤ I g  M a   M a 

(6.7.2.1)

For continuous spans, the effective moment of inertia may be taken as the average of the values obtained using the preceding equation for the critical positive and negative moment sections. 6.7.2.2 Long-term deflection—In place of a detailed analysis, the additional long-term deflection resulting from creep and shrinkage for both normalweight and lightweight concrete flexural members may be estimated by multiplying the immediate deflection, caused by the sustained load being considered, by the factor

λ =

ξ 1 + 50ρ′

(6.7.2.2)

6.7.3 Prestressed members—The effects induced by prestress should be included in the computation of deformation. 6.7.3.1 Immediate camber/deflection—The moment of inertia should be taken as that of the gross concrete section. 6.7.3. 2 Long-term camber/deflection—In place of a detailed analysis, long-term camber and deflection, as a function of instantaneous camber and deflection for members constructed and prestressed in a single stage, may be estimated by multiplying the initial camber or deflection by the factors shown in Table 4.8.4.1 of the PCI Design Handbook (PCI 2004). These factors apply to simple spans. For continuous spans, in the absence of a detailed analysis, long-term deflections may be estimated by applying two-thirds of the factors given in Table 6.7.3.2.


6.8—Crack control Cracking should be controlled in nonprestressed reinforced members by suitable detailing and sizing of the reinforcement (ACI SP-66 [ACI Committee 315 2004]). Prestressed concrete members should contain nonprestressed reinforcement in the precompressed tensile zone. Provisions should be made in the design for moment reversals (due to a variety of factors that may include creep, shrinkage, and temperature gradient) that may develop in precast, prestressed units erected as simple span and made continuous for live loads. The effects of loading in remote spans, as well as shrinkage, creep, and elastic shortening of the piers, should also be considered in the design. 6.8.1 Nonprestressed members—To control cracking by distribution of reinforcement, the spacing of reinforcement closest to a surface in tension should not exceed that given by

 40, 000   40, 000  − 2.5c ≤ 12     f s   f s 

s = 15 

in. (6.8.1)

 280   280  − 2.5c ≤ 300     f s   f s 

s = 380 

mm

6.8.2 Prestressed members —The anchorage zone in posttensioned members is typically divided into two zones: 1) the local zone immediately surrounding the anchorage device; 2) and the general zone, which includes the local zone. ACI 318-11, Chapter 18, and AASHTO (2012), Section 5, contain recommendations for the design of reinforcement to control cracking in these areas. The post-tensioning supplier should specify proper anchorage requirements for local zones.

CHAPTER 7—STRENGTH DESIGN

29

of ACI 318 and “AASHTO LRFD Bridge Design Specifications” (AASHTO 2012). For guideways made continuous by post-tensioning over two or more spans, the effects of secondary moments due to the reactions induced by prestressing should be included. Any reasonable assumption may be adopted for computing the relative flexural and torsional stiffness of members in a statically indeterminate system. The moments of inertia used to obtain the relative stiffness of the various members may be determined from either the uncracked concrete cross section, neglecting the reinforcement, or from the transformed cracked section, provided the same method is used throughout the analysis. The effect of variable cross sections should be considered in analysis and design. The span length of members that are not built integrally with their supports should be the clear span plus the depth of the member. It need not exceed the distance between centers of supports. In analysis of statically indeterminate members, center-to-center distances should be used to determine moments. Moments at faces of supports may be used for design of members. The possible instability or overstressing of a slender member during transportation, construction, and in-service conditions should be considered (Mast 1989, 1993).

7.2—Design for flexure and axial loads Guideways should be designed to have the required strengths at all sections by the factored loads and forces in such combinations as stipulated in Chapter 5. Design strength of a member or cross section should be taken as the nominal strength calculated in accordance with requirements and assumptions of Chapter 7 multiplied by a strength reduction factor f as defined in Chapter 5. The strength design procedures for members subjected to flexure and axial loads should be based on the provisions of AASHTO LRFD (AASHTO 2012).

7.1—General design and analysis considerations Recommendations in this chapter are intended for reinforced concrete guideways, including nonprestressed and prestressed structures proportioned for adequate strength using load combinations, load factors, and strength reduction factors as specified in Chapter 5. The recommendations are principally based on ACI 318 and may also be applied to nonprestressed components of a guideway structure where applicable. All members of statically indeterminate structures should be designed for the maximum effects of the specified loads as determined by elastic analysis or any acceptable method that considers the nonlinear behavior of reinforced concrete members, nonprestressed or prestressed, when subjected to bending moments, approaching the strength of the member. Analysis should satisfy the conditions of equilibrium, compatibility, and stability at all points in the structure and all magnitudes of loading up to ultimate condition. Negative moments calculated by elastic analysis at the supports of continuous prestressed and nonprestressed flexural members, for any assumed loading arrangement, may be increased or decreased in accordance with the provisions

7.3—Shear and torsion 7.3.1 Introduction—In transit guideways, shear forces are induced by the vertical loads of vehicles and structures. Torsional moments are imposed by wind load on the vehicles and on the structures, horizontal nosing action of the vehicles, vertical loads of vehicles when derailed, curved alignment, and substructure geometry. These shear forces and torsional moments should be considered in combination with the bending moments in the reinforcement design. Guideway structures are often built in a continuous fashion to better resist torsional effects and allow for more slender structures. Continuity in structures, particularly those with horizontal curvature, can create a shear and torsion condition that is complex (Laskar et al. 2010; Hsu et al. 2010). A comprehensive treatment of shear and torsion in reinforced concrete structures is provided in ACI 445R and Hsu and Mo (2010). Sections 7.3.2 through 7.3.5 summarize the basic concepts of shear and torsion that are relevant to the design of guideways. 7.3.2 Shear strength of reinforced concrete beams —The

30


(1902) was a truss model. These investigators treated a reinforced concrete beam as a plane truss where bending was resisted by the top and bottom chords and shear was resisted by the inclined concrete struts and vertical steel ties in the web. These struts and ties were idealized as lines without cross-sectional dimensions. In the 1960s, the reinforced concrete members with dimensionless linear elements to resist shear were replaced by members made up of more realistic two-dimensional membrane elements. By treating a membrane element after cracking as a truss made up of compression concrete struts and tensile steel ties, Nielsen (1967) and Lampert and Thurlimann (1968) derived three equilibrium equations for a membrane element that satisfied Mohr’s stress circle. This advance was followed by the derivation of three strain compatibility equations by Baumann (1972) and Collins (1973) that satisfied Mohr’s strain circle. When an reinforced concrete membrane element is subjected to shear, it creates a two-dimensional problem; shear stress can be resolved into a principal tensile stress and a principal compressive stress in the 45-degree direction. Robinson and Demorieux (1968, 1972) found the principal compressive stress was reduced or softened by the principal tensile stress in the perpendicular direction, resulting in a softened stress-strain curve in concrete compression struts. This observation explained why all shear theories to this point had over-estimated the experimental results because a nonsoftened stress-strain curve of concrete was used in the analysis. Using a biaxial test facility called a shear rig, Vecchio and Collins (1981) showed that the softening coefficient in the stress-strain curve of concrete was a function of the principal tensile strain rather than the principal tensile stress. Incorporating equilibrium equations, the compatibility equations, and using the softened stress-strain curve of concrete, Collins and Mitchell (1980) developed a compression field theory (CFT) that could predict the nonlinear shear behavior of an element in the post-cracking region up to the peak response. Later, Vecchio and Collins (1986) proposed the modified compression field theory (MCFT) that included a constitutive relationship for concrete in tension to better model the post-cracking shear stiffness. In 1995, a rotating-angle softened truss model (RA-STM) was developed at the University of Houston (UH) (Pang and Hsu 1995; Belarbi and Hsu 1994, 1995). The RA-STM made two improvements over the CFT: 1. The tensile stress of concrete was taken into account so that the deformations could be correctly predicted 2. The smeared (or average) stress-strain curve of steel bars embedded in concrete was derived on the smeared crack level so that it could be correctly used in the equilibrium and compatibility equations that are based on continuous materials. In 1996, the UH group reported that the fixed-angle softened truss model (FA-STM) (Pang and Hsu 1996; Hsu and Zhang 1997) is capable of predicting the concrete contribution (V c) by assuming the cracks to be oriented at the fixed angle, rather than the rotating angle. Zhu et al. (2001) derived

sive and tensile stress-strain curves of concrete. Using this simple shear modulus, the solution algorithm of FA-STM became greatly simplified. Using a universal panel tester with a servo-control system (Hsu et al. 1995a,b) to perform strain-controlled tests, Zhu et al. (2001) and Zhu and Hsu (2002) quantified the Poisson effect and characterized this property by two Hsu/Zhu ratios. Considering the Poisson effect, Hsu and Zhu (2002) developed the softened membrane model (SMM) that can satisfactorily predict the entire monotonic response of the reinforced concrete membrane elements, including both the ascending and the descending branches, as well as both the precracking and post-cracking responses. To design the steel reinforcement in a shear element, however, it is possible to use only the three equilibrium equations if both the transverse steel and the longitudinal steel are assumed to reach yielding before concrete crushing. The three equations, consequently, can be combined to give the equation V u d v

=

q y

=

At f y A f y l

st

s

(7.3.2)

l

7.3.3 Torsional strength of reinforced concrete beams — According to St. Venant’s circulatory shear flow pattern, the largest shear stresses occur at the outer periphery of a cross section, and the most efficient cross section to resist torsion is tube-shaped. In reinforced concrete beams, the best way to resist torsion is to provide hoop steel along the outer periphery, in addition to longitudinal steel. The amount of hoop steel required in the tube depends on the shear flow q, which can be determined from Bredt’s (1896) equilibrium equation of a cross section ( q y = T u /2 A0)). Substituting Bredt’s equation into Eq. (7.3.2) results in

Tu

=

2 A0

At f y A f y l

st

s

(7.3.3a)

l

Equation (7.3.3a) represents the basis of torsion provisions since the 1995 ACI Code. The lever arm area A0 in Eq. (7.3.3a) is formed by sweeping the lever arm of the centerline of shear flow one full circle around the axis of twist. Prior to 1995, the centerline of shear flow was taken by Rausch (1929) to be the centerline of the hoop steel bar, and the corresponding lever arm area is denoted as A0h. This definition of area A0h, however, was found to overestimate the torsional strength by up to 30 percent. As a result, empirical equations were derived based on the experimental results of Hsu (1968), and used in the ACI Code from 1971 to 1995. Equation (7.3.3a) shows two basic characteristics of torsion. First, both the hoop steel and the longitudinal steel are required to resist torsion. This is illustrated by Rausch’s (1929) space truss model, which is made up of both types of steel bars. Second, Eq. (7.3.3a) is applicable to hollow sections and beams with solid sections. Tests (Hsu 1968)


have shown that the concrete core inside a tube does not contribute to the ultimate torsional strength of a solid beam. When a reinforced concrete tube is under torsion, elements isolated from its walls are shown to be subjected to pure shear. Under such a biaxial stress condition, the compressive stress-strain curve used in the principal compressive direction should be multiplied by a softening coefficient. This softening coefficient is a function of the principal tensile strain and the compressive strength of concrete (Zhang and Hsu 1998) and varies from approximately 0.25 to 0.50. Applying this softened stress-strain curve of concrete to the study of a reinforced concrete tube under torsion (Hsu and Mo 1985), the thickness t d of the shear flow zone can be determined, and the lever arm area A0 can be calculated from the centerline of the shear flow zone. The thickness t d increases as the ultimate torque T u increases, and the rela Acp f c′. tionship was derived (Hsu 1990, 1993) to be t d = 4T u / The corresponding A0 becomes Ao

=

Acp

−

t d pcp

2

= Acp −

2Tu pcp Acp f c′

(7.3.3b)

When the lever arm area A0 in Eq. (7.3.3b) is used in conjunction with Eq. (7.3.3a), the amount of the hoop steel, A / t st , can be accurately determined to resist the ultimate torque T u. Prior to the use of the softened stress-strain curve in torsion, the determination of the thickness t d was based on the nonsoftened stress-strain curve of a standard cylinder—for example, taking the softening coefficient as unity. Because the softened coefficient varies from approximately 0.25 to 0.5, the thickness t d obtained from the nonsoftened stress strain curve is expected to be reduced in the same proportion based on the softened stress-strain curve. The corresponding A0 will become much too large, and Eq. (7.3.3a) will seriously overestimate the experi mental torsional strength. Equations (7.3.2), (7.3.3a), and (7.3.3b) were incorporated into the 1995 ACI Code for a more rational design of reinforcement to resist torsion. This version of the Code also provides a simpler, but less accurate, formula for calculating the lever arm area A0 as follows A0 = 0.85 A0h

(7.3.3c)

Whereas Eq. (7.3.3c) is intended for the torsion design of small beams encountered in buildings, the implicit understanding is that Eq. (7.3.3b) is more suitable for large beams, especially box beams, as in the case of guideways. The background of the 1995 ACI Code was given by Hsu and Zhang (1997). 7.3.4 Design for shear and torsion—Hsu and Zhang (1997) describe a detailed design of a hollow box girder to resist shear and torsion according to the 1995 ACI Code and using the accurate Eq. (7.3.3b) for A0. This prestressed box girder design was included in the construction bid for building the aerial guideways of the Dade County Rapid Transit System in Florida, where the box girder was 80 ft (24 m) long and

31

simply supported. Its cross section was 4 ft 2 in. (1.28 m) deep and 12 ft (3.6 m) wide with overhanging flanges. In addition to ACI 318, design provisions for combined shear and torsion are available in other design codes, such as CAN/CSA-S6-00 and Eurocode 2 (CEN 2006). Although these codes have not been applied to guideways, they could provide additional guidance. A box section subjected to shear and torsion was designed by a method in Collins and Mitchell (1991) that was later modified and adopted for use in AASHTO (2012). 7.3.5 Warping torsion––In the design of beams with closed sections, it is safe to neglect warping torsional resistance. This is because St. Venant torsional resistances of closed sections are large, whereas the warping torsional resistance is small in comparison. In the design of beams with open sections, however, warping torsion resistance needs to be considered because it could have a magnitude comparable to that of St. Venant torsion resistance. The following example illustrates a design for warping torsion. The 22 mi (35 km) aerial guideways of the Dade County Rapid Transit System were designed using a standard 80 ft (24.4 m) long, prestressed double-T girder with an open cross section of 5 ft (1.5 m) deep and 12 ft (3.6 m) wide. The shear and torsion design of this double-T girder was reported by Hsu and Hwang (1986). When such an open cross section was subjected to torsion, it was resisted by both the St. Venant torsion and the warping torsion. A mixed torsion analysis according to Hwang and Hsu (1983) showed that warping torsion resisted approximately half of the applied torsional moment. The total torsional strength of the double-T girder was sufficient to resist the most severe case of derailment, and the maximum torsional rotation was well within the desirable limit to ensure rider comfort. The mixed torsion theory was validated by the test results of two 3/5-scale models (Russell et al 1986).

CHAPTER 8—REFERENCES Committee documents are listed first by document number and year of publication followed by authored documents listed alphabetically. American Concrete Institute ACI 117-10—Specifications for Tolerances for Concrete Construction and Materials and Commentary ACI 209R-92—Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures (Reapproved 2008) ACI 311.4R-05—Guide for Concrete Inspection ACI 318-11—Building Code Requirements for Structural Concrete and Commentary ACI 343R-95—Analysis and Design of Reinforced Concrete Bridge Structures (Reapproved 2004) ACI 445R-99—Recent Approaches to Shear Design of Structural Concrete (Reapproved 2009) ACI 445.1R-12—Report on Torsion in Structural Concrete American Society of Civil Engineers ASCE 21-05—Automated People Mover Standards

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SEI/ASCE 37-02—Design Loads on Structures During Construction American Welding Society AWS D1.4:2005—Structural Welding Code—Reinforcing Steel AWS D15.2:2003—Recommended Practice for Welding ASTM International ASTM E543-09—Standard Specification for Agencies Performing Nondestructive Testing Canadian Standards Association CAN/CSA-S6-06(R2012)—Canadian Highway Bridge Design Code (CHBDC) Union Internatinale des Chemins de Fer (International Union of Railways) UIC Code 776-3—Deformation of Bridges (First edition of 1.1.89)

AASHTO, 2002, “Standard Specifications for Highway Bridges,” Association of State Highway and Transportation Officials, Washington, DC, 1028 pp. AASHTO, 2009, “LRFD Guide Specifications for Design of Pedestrian Bridges,” second edition, Association of State Highway and Transportation Officials, Washington, DC, 36 pp. AASHTO, 2011, “AASHTO Guide Specifications for LRFD Seismic Bridge Design,” second edition, Association of State Highway and Transportation Officials, Washington, DC, 286 pp. AASHTO, 2012, “AASHTO LRFD Bridge Design Specifications,” sixth edition, American Association of State Highway and Transportation Officials, Washington, DC, 1672 pp. ACI Committee 315, 2004, ACI Detailing Manual, SP-66, American Concrete Institute, Farmington Hills, MI, 219 pp. AREMA, 2012, Manual for Railway Engineering, American Railway Engineering and Maintenance-of-Way Association, Lanham, MD. Baumann, T., 1972, “Zur Frage der Netzbewehrung von Flachentragwerken,” Der Bauingenieur , V. 47, No. 6, pp. 367-377. Belarbi, A., and Hsu, T. T. C., 1994, “Constitutive Laws of Concrete in Tension and Reinforcing Bars Stiffened by Concrete,” ACI Structural Journal, V. 91, No. 4, July-Aug., pp. 465-474. Belarbi, A., and Hsu, T. T. C., 1995, “Constitutive Laws of Softened Concrete in Biaxial Tension-Compression,” ACI Structural Journal, V. 92, No. 5, Sept.-Oct., pp. 562-573. Billing, J. R., 1979, “Estimation of the Natural Frequencies of Continuous Multi-Span Bridges,” Report No. RR.219, Ministry of Transportation, Downsview, ON, Canada, Jan., 20 pp. Bredt, R., 1896, “Kritische Bemerkungen zur Drehungselastizitat,” Zeitschrift des Vereines Deutsher Ingenieure, Band 40, No. 28, July 11, pp. 785-790; July 18, pp. 813-817.

Buckle, I. G., and Priestley, M. J. N., 1978, “Methods of Analysis for Highway Bridges,” Structures Committee, Road Research Unit, National Roads Board, 89 pp. Calgary Transit, 2001, “Calgary Light Rail Transit Design Guidelines,” Calgary Transit Division Transportation Department, Jan. Campbell, T. I., 1978, “Natural Frequencies of Curved Beams and Skew Slabs,” Report, OJT & CRP Project 8303, Queen’s University, Kingston, ON, Canada, Mar. Canadian Standards Association, 2008, “Guide to Canadian Wind Turbine Codes and Standards,” CSA, Toronto, ON, Canada, 28 pp. Collins, M. P., 1973, “Torque-Twist Characteristics of Reinforced Concrete Beams,” Inelasticity and Non-Linearity in Structural Concrete, Study No. 8, University of Waterloo Press, Waterloo, ON, Canada, pp. 211-232. Collins, M. P., and Mitchell, D., 1980, “Shear and Torsion Design of Prestressed and Non-Prestressed Concrete Beams,” PCI Journal, V. 25, No. 5, pp. 32-100. Collins, M. P., and Mitchell, D., 1991, Prestressed Concrete Structures, Prentice Hall, Englewood Cliffs, NJ, pp. 405-409. Csagoly, P. F.; Campbell, T. I.; and Agarwal, A. C., 1972, “Bridge Vibration Study,” Report No. RR 181, Ministry of Transportation and Communications, Downsview, ON, Canada. European Committee for Standardization (CEN), 2006, “Eurocode 2 – Design of Concrete Structures,” BSI British Standard, London, UK. Federal Railroad Administration, 2004, “Code of Federal Regulations 49—Transportation,” Federal Railroad Administration, Washington, DC. Florida DOT, 2003, “New Directions for Florida Posttensioned Bridges,” Florida Department of Transportation, Tallahassee, FL, V. 10. Ghali, A.; Favre, R.; and Elbadry, M., 2012, Concrete Structures, Stresses and Deformations: Analysis and Design for Serviceability, fourth edition, Spon Press, 637 pp. Government of Ontario, 1983, “Design Criteria for Go ALRT Elevated Guideway and Special Structures,” Government of Ontario Advanced Light Rail Transit, Sept. Grouni, H., and Sadler, C., 1986, “Thermal Interaction between Continuously Welded Rail and Elevated Transit Guideway,” Proceedings of the International Conference on Short and Medium Span Bridges , Ottawa, ON, Canada. Hsu, T. T. C., 1968, “Ultimate Torque of Reinforced Rectangular Beams,” Journal of the Structural Division, ASCE, V. 94, No. ST2, Feb., pp. 485-510. Hsu, T. T. C., 1990, “Shear Flow Zone in Torsion of Reinforced Concrete,” Journal of Structural Engineering, V. 116, No. 11, pp. 3205-3225. Hsu, T. T. C., 1993, Unified Theory of Reinforced Concrete, CRC Press Inc., Boca Raton, FL, 329 pp. Hsu, T. T. C.; Belarbi, A.; and Pang, X. B., 1995a, “A Universal Panel Tester,” Journal of Testing and Evaluation, V. 23, No. 1, pp. 41-49. Hsu, T. T. C., and Hwang, C. S., 1986, “Shear and Torsion


Concrete in Transportation, SP-93, American Concrete Institute, Farmington Hills, MI, pp. 433-466. Hsu, T. T. C.; Laskar, A.; and Mo, Y. L., 2010, “Shear Strengths of Prestressed Concrete Beams—Part 2: Comparisons with ACI and AASHTO Provisions,” ACI Structural Journal, V. 107, No. 3, May-June, pp. 340-345. Hsu, T. T. C., and Mo, Y. L., 1985, “Softening of Concrete in Torsional Members—Theory and Tests,” ACI J OURNAL, Proceedings V. 82, No. 3, May-June, pp. 290-303. Hsu, T. T. C., and Mo, Y. L., 2010, Unified Theory of Concrete Structures, John Wiley and Sons, Ltd., London, 516 pp. Hsu, T. T. C., and Zhang, L. X., 1997, “Nonlinear Analysis of Membrane Elements by Fixed-Angle Softened-Truss Model,” ACI Structural Journal, V. 94, No. 5, Sept.-Oct., pp. 483-492. Hsu, T. T. C.; Zhang, L. X.; and Gomez, T., 1995b, “A Servo-Control System for Universal Panel Tester,” Journal of Testing and Evaluation, V. 23, No. 6, pp. 424-430. Hsu, T. T. C., and Zhu, R. R. H., 2002, “Softened Membrane Model for Reinforced Concrete Elements in Shear,” ACI Structural Journal, V. 99, No. 4, July-Aug., pp. 460-469. Huang, T. L., 1982, “A New Procedure for Estimation of Prestress Losses,” Report No. 470.1, Research Project No. 80-23, Pennsylvania Department of Transportation/Fritz Engineering Laboratory, Lehigh University, Bethlehem, PA, May. Hwang, C. S., and Hsu, T. T. C., 1983, “Mixed Torsion Analysis of Reinforced Concrete Channel Beams—A Fourier Series Approach,” ACI JOURNAL, Proceedings V. 80, No. 5, Sept.-Oct., pp. 377-386. Lampert, P., and Thurlimann, B., 1968, “Torsionsversuche an Stahlbetonbalken (Torsion Tests of Reinforced Concrete Beams),” Bericht Nr. 6506-2, Institut für Baustatik, ETH, Zürich, June. Laskar, A.; Hsu, T. T. C.; and Mo, Y. L., 2010, “Shear Strengths of Prestressed Concrete Beams. Part 1: Experiments and Shear Design Equations,” ACI Structural Journal, V. 107, No. 3, May-June, pp. 330-339. Mast, R. F., 1989, “Lateral Stability of Long Prestressed Concrete Beams – Part 1,” PCI Journal, Jan.-Feb., pp. 34-53. Mast, R. F., 1993, “Lateral Stability of Long Prestressed Concrete Beams – Part 2,” PCI Journal, Jan.-Feb., pp. 70-78. Mörsch, E., 1902, Der Eisenbetonbau, seine Anwendung und Theorie, first edition, Wayss and fretag, A. G., Im Selbstverlag der Firma, Neustadt a d. Haardt, 118 pp. NCHRP (National Cooperative Highway Research Program), 1982, “Fatigue Behavior of Variable Loaded Bridge Details Near the Fatigue Limit,” NCHRP Report 267 , Transportation Research Board, Washington, DC. NCHRP (National Cooperative Highway Research Program), 2003, “Prestress Losses in Pretentioned HighStrength Concrete Bridge Girders,” NCHRP Report 496 , Transportation Research Board, Washington, DC. NFPA, 2003, “Standard for Fixed Guideway Transit and Passenger Rail Systems (NFPA 130),” National Fire Protec-

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Nielsen, M. P., 1967, “Om forskydningsarmering i jernbetonbjaelker (On Shear Reinforcement in Reinforced Concrete Beams),” Bygningsstatiske Meddelelser , V. 38, No. 2, pp. 33-58. Nowak, A. S., and Grouni, H. N., 1983, ““Development of Design Criteria for Transit Guideways,” ACI J OURNAL, Proceedings V. 80, No. 5, Sept.-Oct., pp. 387-395. Nowak, A. S., and Grouni, H. N., 1988, “Serviceability Consideration for Guideways and Bridges,” Canadian Journal of Civil Engineering, V. 15, No. 4, Aug., pp. 534-538. Nowak, A. S., and Lind, N. C., 1979, “Practical Bridge Code Calibration,” Proceedings, ASCE, V. 105, No. ST12, Dec., pp. 2497-2510. Okeil, A. M., 2006, “Allowable Tensile Stress for Webs of PT Segmental Concrete Bridges,” ACI Structural Journal, V. 103, No. 4, July-Aug., pp. 488-495. Pang, X. B., and Hsu, T. T. C., 1995, “Behavior of Reinforced Concrete Membrane Elements in Shear,” ACI Structural Journal, V. 92, No. 6, Nov.-Dec., pp. 665-679. Pang, X. B., and Hsu, T. T. C., 1996, “Fixed-Angle Softened-Truss Model for Reinforced Concrete,” ACI Structural Journal, V. 93, No. 2, Mar.-Apr., pp. 197-207. PCI, 2004, PCI Design Handbook , sixth edition, Precast/ Prestressed Concrete Institute, Chicago, IL. PCI Committee on Prestress Losses, 1975, “Recommendations for Estimating Prestress Losses,” PCI Journal, V. 20, No. 4, July-Aug., pp. 43-75, and Discussion, V. 21, No. 2, Mar.-Apr. pp. 108-126. Priestley, M. J. N., 1978, “Design of Concrete Bridges for Thermal Gradients,” ACI J OURNAL, Proceedings V. 75, No. 5, May, pp. 209-217. Rausch, E., 1929, “Design of Reinforced Concrete in Torsion (Berachnung des Eisanbetons gegen verdrehung),” Technische Hochschule , Berlin, Germany, 53 pp. Ritter, W., 1899, “Die Bauweise Hennebique,” Schweizerishe Bauzeitung, V. 33, No. 7, pp. 59-61. Robinson, J. R., and Demorieux, J. M., 1968, “Essais de Traction-Compression sur Modeles d’ame de Poutre en Béton Armé,” Part 1, Institut de Recherches Appliquees du Béton Armé (IRABA), June. Robinson, J. R., and Demorieux, J. M., 1972, “Essais de Traction-Compression sur Modeles d’ame de Poutre en Béton Armé,” Part 2, Institut de Recherches Appliquees du Béton Armé (IRABA), May. Russell, H. G.; Rabbat, B. G.; and Hsu, T. T. C., 1986, “Testing of Double-Tee Concrete Girders for Dade County Rapid Transit System,” Concrete in Transportation, SP-93, American Concrete Institute, Farmington Hills, MI, pp. 467-490. Thompson, W. T., 1972, Theory of Vibration with Applications, Prentice-Hall, Inc., Englewood Cliffs, NJ. Transportation Research Board, 2000, TCRP Report 57— Track Design Handbook for Light Rail Transit (Part D) , National Academy Press, Washington DC. Turkstra, C. J., 1970, “Theory of Structural Design Decisions,” Study No. 2, Solid Mechanics Division, University of Waterloo, ON, Canada, 124 pp.

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Vecchio, F., and Collins, M. P., 1981, “Stress-Strain Characteristic of Reinforced Concrete in Pure Shear,” IABSE Colloquium, Advanced Mechanics of Reinforced Concrete, Final Report, International Association of Bridge and Structural Engineering, Zurich, Switzerland, pp. 221-225. Vecchio, F. J., and Collins, M. P., 1986, “Modified Compression-Field Theory for Reinforced Concrete Element Subjected to Shear,” ACI Structural Journal, V. 83, No. 2, Mar.-Apr., pp. 219-231. Zhang, L. X., and Hsu, T. T. C., 1998, “Behavior and Analysis of 100 MPa Concrete Membrane Elements,” Journal of Structural Engineering, V. 124, No. 1, Jan., pp. 24-34.

Zhu, R. H.; Hsu, T. T. C.; and Lee, J. Y., 2001, “Rational Shear Modulus for Smeared Crack Analysis of Reinforced Concrete,” ACI Structural Journal, V. 98, No. 4, July-Aug., pp. 443-450. Zhu, R. R. H., and Hsu, T. T. C., 2002, “Poisson Effect in Reinforced Concrete Membrane Elements,” ACI Structural Journal, V. 99, No. 5, Sept.-Oct. pp. 631-640. Zia, P.; Kent, P. H.; Scott, N. L.; and Workman, E. B., 1979, “Estimating Prestress Losses,” Concrete International, V. 1, No. 6, June, pp. 32-38.

As ACI begins its second century of advancing concrete knowledge, its original chartered purpose remains “to provide a comradeship in finding the best ways to do concrete work of all kinds and in spreading knowledge.” In keeping with this purpose, ACI supports the following activities: · Technical committees that produce consensus reports, guides, specifications, and codes. · Spring and fall conventions to facilitate the work of its committees. · Educational seminars that disseminate reliable information on concrete. · Certification programs for personnel employed within the concrete industry. · Student programs such as scholarships, internships, and competitions. · Sponsoring and co-sponsoring international conferences and symposia. · Formal coordination with several international concrete related societies. · Periodicals: the ACI Structural Journal and the ACI Materials Journal, and Concrete International. Benefits of membership include a subscription to Concrete International and to an ACI Journal. ACI members receive discounts of up to 40% on all ACI products and services, including documents, seminars and convention registration fees. As a member of ACI, you join thousands of practitioners and professionals worldwide who share a commitment to maintain the highest industry standards for concrete technology, construction, and practices. In addition, ACI chapters provide opportunities for interaction of professionals and practitioners at a local level.

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