Structural Design Guidelines RC PC Bridges

Department: ED11 K&A–CEC Company Confidential Rev. Date: Aug 2007

Structural Design Guidelines for Reinforced Concrete and Prestressed Concrete Bridges

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Table of Contents Introduction Design Codes Design Loads (general) Design Loads (moving load) Design Loads (environmental loads) Load Combinations Components of bridge structural system Selection of deck type Selection of bearings type Selection of piers/pier head types Selection of abutment types Selection of foundation types Selection of analysis model Design of parapets Analysis of deck transverse direction Analysis of deck longitudinal direction Analysis of diaphragms Analysis for environmental loads Design of prestress Selection of tendons Determining tendon profile Calculation of immediate losses (friction, draw-in, elastic shortening) Calculation of long term losses (creep, shrinkage, relaxation) Anchor zone reinforcement (surface, bursting, diffusion) Special reinforcement for curved tendon regions (in web, deviators) Continuity slab Expansion joint support Ultimate strength design shear Ultimate strength design strut and tie Ultimate strength design shear-friction Ultimate strength design flexure Design of bearing supports Design of pier heads Design of piers Design of pier foundations Design of abutments


1.0 Introduction: This document describes the procedure to be used in the design of the structural elements of reinforced concrete or prestressed concrete bridges. The purpose of the guidelines presented in this document is to speed up the design process, make it more uniform across different engineers and less prone to mistakes and omissions. It is not the purpose of this document to replace design codes, design courses or engineering judgement. The document briefly reviews the components of the structural system that have to be designed, the possible alternatives for each component, and then describes the design procedure for each component. For each component, the design guideline lists the elements to be designed, the checks to be performed, the typical extreme values of the design variables, detailing hints, the relevant code sections and the relevant references for more detailed information. 2.0 Design Codes: The design code used in this document is the AASHTO-LRFD 2007. Other design codes used in the office for bridge design are the AASHTO-LFD and the Eurocode. 2.1 Design Loads (general): The code specified design loads and design load factors are deemed to provide a minimum design service life of 75 years. The ultimate design load combinations are further multiplied by modification factors: For ductility

1.05 for non-ductile components and connections, 1.00 for conventional design and details, 0.95 for components and connections with special ductility enhancing measures

For redundancy

1.05 for non-redundant elements, 1.00 for conventional levels of redundancy, 0.95 for exceptional levels of redundancy

For operational importance 1.05 for important bridges (critical),

1.00 for typical bridges (essential), 0.95 for secondary bridges

Typically, the combined modification factor (product of the above three factors) for ultimate loads is 1.00x1.05x1.05=1.10. The combined modification factor may be increased for longer design life, or decreased for temporary structures. Although AASHTO-LRFD does not indicate how the modification factor may be changed for design periods other than 75 years, taking guidance from BS6399:2-1997 Appendix D one can derive the following correction factors for different design lives:

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Design life (years) Scale factor 1 0.73 5 0.83 10 0.88 75 1.00 120 1.03 200 1.06 2.2 Design Loads (moving load): 2.2.1 Live Load LL+IM (AASHTO-LRFD 3.6.2) The design normal moving live load will be AASHTO LRFD HL-93 loading multiplied by a factor of 1.5. Dynamic allowance = 1.33 will be applied in accordance with AASHTO LRFD Article 3.6.2 leading to the following axle loads (impact included): -Truck load: 3 axles of 70KN, 290KN and 290KN, separated by 4.3m and 4.3m to 9m

-Tandem load: 2 axles of 220KN each, separated by 1.2m.

-Lane load: 14KN/m uniformly distributed in longitudinal direction and uniformly distributed over 3m width, without impact is applied in addition to the truck or tandem axle load.

Multiple presence factors shall be applied by considering each possible combination of number of loaded lanes to account for the probability of simultaneous lane occupation by full HL-93 design live load:

for 1 lane loaded 1.20 for 2 lanes loaded 1.00 for 3 lanes loaded 0.85 for 4 lanes loaded or more 0.65.

For box girder decks, the multiple presence factor is not less than 1. In addition, for negative moment calculations in decks continuous over supports, two trucks are considered with minimum axle spacing in each truck, but with a variable spacing between trucks (from x to 15m). Similarly, for negative moment calculations two tandem axle loads are considered, with a variable spacing between tandem axles (from 8m to 12m). Moving loads for negative moment calculations are multiplied by a factor of 0.9. An exceptional moving load may be specified, according to client requirement, consisting for example of either:

The French code Mc110 tank (1200KN applied as two uniformly distributed load patches of 1m width by 6.1m length each, separated transversely by 2.3m. The CALTRANS P13 of 1400KN total weight shall be applied without dynamic allowance for the strength II limit state.

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Wheel contact area is a rectangle 0.5m wide by 0.25m long. For load distribution through fill thicker than 0.6m, each dimension of the wheel contact area is increased by an amount equal to the depth of fill. Where patches overlap, the sum of patch loads is divided over the combined patch area (AASHTO-LRFD 3.6.1.2.6). Impact factor decreases linearly to 1 at a depth of 2.44m (AASHTO-LRFD 3.6.2.2). 2.2.2 Centrifugal force CE (AASHTO-LRFD 3.6.3): For curved decks, a transverse load equal to C times the truck load or tandem axle load in each lane, is applied in the outward direction at 1.8m above the deck surface, where:

C = fV2/(G.R) F =4/3, 1 for fatigue load combination. V =design speed in m/s. R =radius of curvature of deck in the horizontal plane G = gravitational constant (9.81m/s2)

Lane multiple presence factors apply. 2.2.3 Braking/accelerating load BR (AASHTO-LRFD 3.6.4): A horizontal equal to the largest of the 25% of the axle load of a truck or tandem, or 5% of the lane load and truck or tandem is applied as a distributed load in each lane at 1.8m above the deck surface. All lanes are assumed loaded in the same direction. Lane multiple presence factors apply. 2.2.4 Vehicle collision load with piers/abutments CT (AASHTO-LRFD 3.6.5): Unless protected by a suitable barrier, all pier and abutment columns or walls within 9m from the edge of the roadway or within 15m from the centreline of the track, shall be subjected to a horizontal 1800KN load at 1.2m above ground surface in any direction in the horizontal plane. Suitable barriers consist of either:

an embankment a barrier higher than 1.37m at a distance less than 3m from the element a barrier higher than 1.07m at a distance more than 3m from the element. 2.2.5 Vehicle collision load with parapets CT (AASHTO-LRFD 13): Parapets and the supporting structure shall be designed for the following loads, according to the approved protection level (from AASHTO-LRFD Table A 13.2.1): Force\Designation Units TL4 TL5 TL6 Transverse force Ft (KN) KN 240 550 780 Longitudinal force Fl (KN) KN 80 183 260 Vertical force Fv (KN) KN 80 355 355 Distribution length for Ft and Fl m 1.07 2.44 2.44 Distribution length for Fv m 5.50 12.20 12.20 Min height of barrier and level for Ft and Fl m 0.81 1.07 2.29 The concrete barrier shall be designed using the yield line method of AASHTO-LRFD Article A13.3.1. The deck overhang supporting the concrete barrier shall be checked for each of the following design cases considered separately:

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Design case 1: Ft and Fl together in Extreme Event Load Combination II Design case 2: Fv only in Extreme Event Load Combination II Design case 3: The normal traffic loads on the overhang in Strength I limit state. The deck overhang shall have to resist a tension force T per unit length, concomitant with the moment applied through the parapet. T = Ft/(Lc+2H), where Lc = Critical length of yield line failure pattern H = Height of barrier. The effective overhang width resisting the wheel load moment is W=1.14+0.833X (AASHTO-LRFD 4.6.2.1.3), where: X = Distance from wheel load to point of support. Alternatively, for overhangs shorter than 1.8m, the overhang can be designed for uniformly distributed load of Fx14.6KN/m, where F is the scaling factor for the HL93 loading (in the above F=1.5). The live load is placed at 0.3m from the inside face of the edge barrier (AASHTO-LRFD 3.6.1.3.4). 2.2.6 Pedestrian live load PL (AASHTO-LRFD 3.6.1.6): A uniformly distributed load of 3.6 kN/m2 will be considered on the footway. In addition, the footway cantilever will be designed for vehicles accidentally mounting the footway. 2.2.7 Live load surcharge LS (AASHTO-LRFD 3.11.6.4): A live load surcharge of12 kN/m2 will be used to calculate horizontal soil pressure due to live load surcharge on buried structures. 2.2.8 Fatigue load (AASHTO-LRFD 3.6.1.4): For fatigue calculations, the stress cycle magnitude due to the specified fatigue load must be computed, along with an estimate of the number of cycles, to be compared with the allowable stress range for that number of cycles (or to compare with the allowable number of stress cycles for the calculated stress range). For fatigue load calculations, the moving load consists of a single truck, with the variable axle spacing set at 9m, and an impact factor of 1.15 instead of 1.33. A single lane is loaded at a time. According to AASHTO-LRFD Article 5.5.3.1 fatigue loading need not be considered for concrete decks in multigirder applications, nor for fully prestressed concrete sections, nor if the minimum compression stress is larger than twice the maximum tensile stress in absolute value, for the fatigue load combinations. The last condition for reinforced concrete sections where the fatigue load moment is less than the permanent moment, is equivalent to having the distance yc from the neutral axis to the extreme compression fiber larger than 2/3 the section depth (yc > 2/3H). The last condition for prestressed concrete sections where the fatigue load moment Mf is less than the permanent load moment Mp, and where the distance yc is

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approximately 1/2 H, is equivalent to having the average compression prestress satisfying the following: H/I (3Mp+Mf)/4 > sav >H/I (Mp-Mf)/6 Where I is the section moment of inertia. When fatigue loading needs to be considered, the maximum stress range has to satisfy the following limits (AASHTO-LRFD 5.5.3.2, 5.5.3.3): For reinforcing steel: fs <166Mpa-1/3fmin For prestressing steel: fs<125Mpa for R>9m, 70Mpa for R>3.6m 2.3 Design Loads (Permanent and environmental) 2.3.1 Self-weight dead load DC (self-weight) (AASHTO-LRFD 3.5.1): The dead load DC is calculated based on the volume of the structural components times the unit weight of the material of the structural components, as shown in the following table: Material Unit weight (KN/m3) Concrete 25 Steel 78.5 Bituminous wearing surface 22 Soil 20 2.3.2 Wearing surfaces and utilities dead load DW (AASHTO-LRFD 3.5.2): Unless otherwise noted, the total thickness of the deck surfacing is considered to be 120mm having 50mm asphalt and 20mm sand/cement screed for protection of waterproofing membrane and 50mm future wearing surfacing overlay for a total, wearing surface load of 2.66KN/m2. Utilities actual weight to be considered 2.3.3 Differential settlement load SE (AASHTO-LRFD 3.12.4): Unless the final geotechnical report requires larger values, a minimum differential settlement allowance of 20mm between successive supports along the span shall be considered for shallow foundations (with a reduced modulus of elasticity of ½Ec). 2.3.4 Temperature loads TU and TG (AASHTO-LRFD 3.12.2 and 3.12.3): A concrete coefficient of thermal expansion is taken as 1 x 10-5 / °C. A uniform temperature change of +/-25C will be considered in the design, starting from a service temperature of 30C. A temperature gradient to temperature Zone 1 will be applied in accordance with AASHTO LRFD Table 3.12.3-1 2.3.5 Shrinkage and creep loads SH and CR (AASHTO-LRFD 3.12.4 and 3.12.5): Shrinkage and creep coefficient shall be calculated according to AASHTO LRFD article 5.4.2.3. An ambient humidity of 40% shall be used for calculation of creep and shrinkage losses, unless otherwise specified. 2.3.6 Wind loads on live load WL and on structure WS (AASHTO-LRFD 3.8):

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3s gust wind velocity shall be taken as 160km/hr in accordance with AASHTO LRFD Bridge Design Specifications and as generally used for highway structures in the region, and 90km/hr in presence of live load or during construction. Transverse wind loading on the structure: Essentially a transverse horizontal pressure of 2.4Kpa is applied on the transverse wind section of the superstructure and of 1.9Kpa on the transverse wind section of the substructure. Concomitantly, an upward vertical pressure of 1Kpa is applied on the deck, with the resultant at ¼ the deck width from the windward side. This vertical force is considered only for the Service IV and Strength III load combinations (AASHTO-LRFD 3.8.2). Transverse wind loading on live load: A transverse linearly distributed load of 1.46KN/m is applied at 1.8m above deck surface (AASHTO-LRFD 3.8.1.3). Longitudinal wind loading on the structure: Essentially a longitudinal horizontal pressure of 0.9Kpa is applied on the transverse wind section of the superstructure and of 1.9Kpa on the transverse wind section of the substructure. Longitudinal wind loading on live load: A transverse linearly distributed load of 0.55KN/m is applied at 1.8m above deck surface (AASHTO-LRFD 3.8.1.3). 2.3.7 Earthquake load EQ (AASHTO-LRFD 3.10): One needs to obtain the site design ground acceleration A (determined from a seismic risk study or from applicable local regulations), the importance classification of the bridge (critical, essential or other as per AASHTO-LRFD article 3.10.3),and the site amplification factor S corresponding to the soil profile type (AASHTO-LRFD 3.10.5). Next, the applicable response spectrum is prepared (AASHTO-LRFD 3.10.6), and the allowable response modification factors R selected (AASHTO-LRFD 3.10.7). Seismic loads directions are combined in absolute value as 100% from one direction with 30% from the perpendicular direction, unless inelastic analysis is being performed (AASHTO-LRFD 3.10.8). Based on the seismic zone, the importance classification and the geometric configuration of the structure, the required type of analysis is determined (AASHTO-LRFD 4.7.4). For seismic zone I a static analysis is sufficient with the lateral seismic force equal to 20% of the permanent vertical force (AASHTO-LRFD 3.10.9.2). For seismic zone 2, a modal analysis is required. The seismic load applied to the foundations is based on the use of ½.R for the substructure (when R>2 has been used) or on capacity considerations (plastic hinging). For seismic zones 3 and 4, the seismic loads applied to the foundations shall be based on capacity considerations.

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2.4 Design load combinations (AASHTO-LRFD 3.4): The design load combinations are divided into 4 broad categories: service, strength, extreme and fatigue. In each category there are several groups of combinations that may be used depending on the type and configuration of the structure: 2.4.1 Service load combinations (AASHTO-LRFD 3.4.1): Service I: applicable to all types of structures. Service II: applicable to steel structures only. Service III: applicable to prestressed concrete structures, may conservatively be replaced by Service I. Service IV: applicable to tension in prestressed concrete columns For reinforced concrete and prestressed concrete structures, only Service I and Service III need to be considered, or even only Service I. 2.4.2 Strength load combinations (AASHTO-LRFD 3.4.1): Strength I: applicable to all types of structures. Strength II: applicable to exceptional/permit type moving load vehicles. Strength III: applicable to above ground structures (not buried). Strength IV: applicable to all types of structures (particularly with large permanent loads). Strength V: applicable to above ground structures (not buried). For reinforced concrete and prestressed concrete structures, all five groups need to be considered. For buried structures, only Strength I,II and IV groups need to be considered. 2.4.3 Extreme event load combinations (AASHTO-LRFD 3.4.1): Extreme event I: consists of seismic loads to be applied with concomitant permanent loads. Extreme event II: consists of vehicle impact loads on parapets or substructure, applied with concomitant permanent loads. For reinforced concrete and prestressed concrete structures, both groups need to be considered. 2.4.2 Fatigue load combinations (AASHTO-LRFD 3.4.1): This category consists of a single load combination of 0.75x(LL+IM+CE). Normally, this case does not need to be considered for reinforced concrete structures (see 2.2.8 above). For convenience, the applicable combinations for reinforced concrete and prestressed concrete structures are reproduced herein: Table 1 for reinforced or prestressed concrete structures above ground Load\Cat Srv

I Srv III

Str I

Str II

Str III

Str IV

Str V

Ext I

Ext II

Fat

DC 1.00 1.00 0.9 /1.25

0.9 /1.25

0.9 /1.25

0.9 /1.50

0.9 /1.25

0.9 /1.25

0.9 /1.25

_

DW 1.00 1.00 0.65 0.65 0.65 0.65 0.65 0.65 0.65 _

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/1.50 /1.50 /1.50 /1.50 /1.50 /1.50 /1.50 LL+IM 1.00 0.80 1.75 1.35 _ _ 1.35 0.50 0.50 0.75 CE 1.00 0.80 1.75 1.35 _ _ 1.35 0.50 0.50 0.75 BR 1.00 0.80 1.75 1.35 _ _ 1.35 0.50 0.50 _ PL 1.00 0.80 1.75 1.35 _ _ 1.35 0.50 0.50 _ WA+FR 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 _ WS 0.30 _ _ _ 1.40 _ 0.40 _ _ _ WL 1.0 _ _ _ _ _ 1.00 _ _ _ TU 1.00 1.00 0.50 0.50 0.50 0.50 0.50 _ _ _ CR+SH 1.00 1.00 0.50 0.50 0.50 0.50 0.50 _ _ _ TG 0.50/

1.00 0.50/ 1.00

_ _ _ _ _ _ _ _

SE 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 _ EQ _ _ _ _ _ _ _ 1.00 _ _ CT _ _ _ _ _ _ _ _ 1.00 _ CV _ _ _ _ _ _ _ _ 1.00 _ TG factor is 0.50 in presence of LL, 1.00 in absence of LL. CT and CV are not applied simultaneously. Table 2 for reinforced or prestressed concrete structures below ground Load\Cat Srv I Srv III Str I Str II Str IV Ext I Ext II Fat DC 1.00 1.00 0.90

/1.25 0.90 /1.25

0.90 /1.25

0.90 /1.25

0.90 /1.25

_

DW 1.00 1.00 0.65 /1.50

0.65 /1.50

0.65 /1.50

0.65 /1.50

0.65 /1.50

_

EH 1.00 1.00 0.90 /1.50

0.90 /1.50

0.90 /1.50

0.90 /1.50

0.90 /1.50

_

EV 1.00 1.00 0.90 /1.35

0.90 /1.35

0.90 /1.35

0.90 /1.35

0.90 /1.35

_

ES 1.00 1.00 0.75 /1.50

0.75 /1.50

0.75 /1.50

0.75 /1.50

0.75 /1.50

_

LL+IM 1.00 0.80 1.75 1.35 _ 0.50 0.50 0.75 BR 1.00 0.80 1.75 1.35 _ 0.50 0.50 _ PL 1.00 0.80 1.75 1.35 _ 0.50 0.50 _ LS 1.00 0.80 1.75 1.35 _ 0.50 0.50 _ TU 1.00 1.00 0.50 0.50 0.50 _ _ _ TG 0.50

/1.00 0.50 /1.00

_ _ _ _ _ _

EQ _ _ _ _ _ 1.00 _ _ CT _ _ _ _ _ _ 1.00 _ EH assumes active pressure, for at-rest replace 1.50 by 1.35. TG factor is 0.50 in presence of LL, 1.00 in absence of LL. 3.0 Components of bridge structural system The major components of the structural system of a bridge structure are three:

-The superstructure (deck system). -The substructure system -The foundations system

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For each of these components several alternatives are available; the selection of the most appropriate choice is done based on several parameters listed below, with the ultimate goal of achieving maximum economy over the useful life of the bridge while meeting safety and serviceability requirements. The selection of the structural system is done during the conceptual phase of the project by a senior engineer, in coordination with the other disciplines senior engineers (Geometric Alignment, Traffic, Drainage and Hydrology). 3.1 Selection of superstructure system: In selecting a superstructure system, the following parameters are used in order of decreasing importance:

Cost: Since the superstructure system in a bridge constitutes approximately half of the total cost of the structure, then the unit cost per unit area of the floor system is a major comparison parameter. Depth: In many cases where the allowable depth a bridge deck is limited, or where the length of the bridge embankments must be minimized, limiting the depth of the deck is a desirable objective. Therefore, the deck depth is a significant comparison parameter. Weight: Since the superstructure system in a bridge constitutes the major part of the bridge structure, its weight contributes the most to the weight of the structure. Increased weight leads to more seismic loads, larger column sizes and larger foundations. Therefore the weight per unit area of the floor system is a major comparison parameter. Local availability of materials and skilled labor: The local availability of materials (special forms) and skilled labor experienced in the construction of the system is major factor in obtaining a construction of good quality within a reasonable time and cost. Therefore, local availability of materials and skilled labor is a major comparison parameter. Speed of construction: The speed of construction is an important parameter that ultimately affects the cost of the bridge, particularly where the bridge is built over an existing road or transportation link. Therefore speed of construction is a significant comparison parameter. Shape of soffit: Some deck systems provide a flat soffit that can be exposed as is or with minor plastering, others present a soffit that has cavities or other irregularities that may be objectionable. If a flat soffit is desired, then the systems with irregular soffit have to be ruled out. Therefore, the shape of soffit is a significant comparison parameter.

3.1.1 Bridge deck systems: The commonly available bridge deck systems in reinforced or prestressed concrete are: Portal frame

Description: is a reinforced concrete frame monolithically cast-in-situ consisting of a top slab supported on concrete walls on shallow or pile foundations.

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Typical range of spans: 4-16m Limitations: skew less than 30 Advantages: simple construction, low deck height, suitable for wide decks. Disadvantages: limited span length

R/C solid slab

Description: is a reinforced concrete solid slab, connected to its substructure by means of bearings. The substructure may consist of walls, columns or frames. Typical range of spans: 15-25m. Limitations: skew less than 30. Advantages: simple construction, low deck height, suitable for sharp radii of curvature. Disadvantages: limited span length

P/C solid slab

Description: is a prestressed concrete solid slab, connected to its substructure by means of bearings. The substructure may consist of walls, columns or frames. Typical range of spans:20-25m Limitations: skew < 30 Advantages: simple construction, very low deck height Disadvantages: limited span length, not suitable for sharp radii of curvature.

P/C voided slab:

Description: is a prestressed concrete slab with stay-in-place low weight void formers (expanded polystyrene foam) or removable inflatable/deflatable bladders. Bearings connect the superstructure and substructure. The substructure may consist of walls, columns or frames. Typical range of spans: 25m-40m. Limitations: skew < 30, constant width deck, no sharp radii of curvature. Advantages: relative low deck height and low deck weight. Disadvantages: not suitable for sharp radii of curvature or variable width decks.

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R/C girder and deck Description: consists of precast reinforced concrete T section girders with a cast-in-situ top slab and end diaphragms. The girders may be contiguous or separated (in which case precast slab elements may be used as stay-in-place forms). Bearings connect the superstructure and substructure. The substructure may consist of walls, columns or frames. Typical range of spans: 10-20m Limitations: skew < 30, no sharp radii of curvature or variable width deck, design as simply supported span only (continuity for live load often not practical). Deck depth is significant. Advantages: fast construction, no need for shuttering, suitable for use over existing traffic. Disadvantages: limited span length, no sharp radii of curvature or variable deck width, two rows of bearings over each intermediate support. Deck depth is significant.

P/C girder and deck

Description: consists of precast prestressed concrete I/T section girders with a cast-in-situ top slab and end diaphragms. The girders may be contiguous or separated (in which case precast slab elements may be used as stay-in-place forms). Bearings connect the superstructure and substructure. The substructure may consist of walls, columns or frames. Typical range of spans: 25-42m Limitations: skew < 30, no sharp radii of curvature or variable width deck, design as simply supported span only (continuity for live load often not practical). Deck depth is significant. Advantages: fast construction, no need for shuttering, suitable for use over existing traffic. Disadvantages: no sharp radii of curvature or variable deck width, two rows of bearings over each intermediate support. Deck depth is significant.

R/C multicell box girder

Description: consists of a reinforced concrete box section with thin top and bottom flanges and webs, with transverse interior diaphragms over supports. Bearings connect the superstructure and substructure. The substructure may consist of walls, columns or frames. Typical range of spans:20-30m Limitations: Deck depth is significant Advantages: most suitable for sharp radii of curvature. Relatively light deck. Disadvantages: complicated construction, requires shuttering.

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P/C single cell or multicell box girder

Description: consists of a prestressed concrete box section with thin top and bottom flanges and webs, with transverse interior diaphragms over supports. Bearings connect the superstructure and substructure. The substructure may consist of walls, columns or frames. Typical range of spans:30-80+m. Limitations: Deck depth is significant. Advantages: most suitable for long spans or limited radii of curvature. Disadvantages: complicated construction, requires shuttering.

3.2 Selection of bearing type: Bearings are provided between the superstructure (deck) and the underlying substructure (abutment, pier). The commonly available bearing types are the following: 3.2.1 Laminated elastomeric bearing: Description: consists of an alternation of layers of virgin rubber or neoprene with plates of steel, vulcanised together in a single unit. Limitations: axial load capacity limited to about 5000KN. Limited rotation capacity. Advantages: Cost effective, rugged, provides some base isolation to reduce seismic forces. Disadvantages: See limitations. 3.2.2 Pot bearing: Description: consists of a virgin rubber or neoprene disk confined between a steel piston and a steel cylinder. Normal condition is that of pinned support. A top sliding or guided plate may be provided to obtain roller or guided bearing function. Limitations: In the pinned or guided condition, the lateral load capacity is limited. Advantages: Most cost effective alternative to laminated elastomeric bearing when higher axial load capacity is needed. Disadvantages: A combination of pinned, guided and free bearings is needed for deck support. Concrete stops may be needed when large lateral forces need to be transmitted. 3.2.3 Spherical bearing: Description: consists of two machined spherical surfaces (male and female) with a Teflon coating in-between. Normal condition is that of pinned support. A top sliding or guided plate may be provided to obtain roller or guided bearing function. Limitations: In the pinned or guided condition, the lateral load capacity is limited.

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Advantages: More compact than pot bearing of equivalent axial load capacity. Disadvantages: Most expensive type of bearing for a given axial load capacity. Required when large axial loads need to be transmitted in a limited area. A combination of pinned, guided and free bearings is needed for deck support. Concrete stops may be needed when large lateral forces need to be transmitted. 3.3 Selection of expansion joint type: Expansion joints are provided between successive decks or between deck and abutments. Their function is to allow traffic over the gap necessary to accommodate the unrestricted longitudinal movements of the deck. The following are the most common expansion joint types for bridges: 3.3.1 Precompressed closed cell expansion joint: Description: consists of a natural rubber or neoprene strip with closed interior voids. The strip is squeezed and inserted in the expansion joint space. Typical total movement range: 25-50mm Limitations: Limited movement range Advantages: cost effective and simple to install and replace. Disadvantages: see limitations. 3.3.2 Toothed expansion joint: Description: consists of two opposing steel strips with the teeth on one side moving in the space between the teeth of the opposite side. The teeth may be like those of a comb or like those of a saw. A flexible gutter is often provided underneath. Typical total movement range: 50-200mm Limitations: Cannot be used for skew expansion joints. Advantages: cost effective in its movement range. Disadvantages: in addition to limitations above, may be a traffic hazard in case of broken or twisted teeth. Requires careful installation and regular maintenance. 3.3.3 Laminated neoprene expansion joint: Description: consists of overlapping metal plates connected by natural rubber or neoprene bands. Typical total movement range: 50-300mm Limitations: easily damaged by snow plows or street cleaning machines. Advantages: smooth ride Disadvantages: in addition to limitations above, requires careful installation and regular maintenance.

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3.3.4 Modular expansion joint: Description: consists of a series of plates moving a linkage system and with guide plates. Typical total movement range: 300-1000+mm. Limitations: Cannot be used for skew expansion joints. Advantages: Large movement range. Disadvantages: Very expensive and bulky. 3.4 Selection of pier/pier head type: Piers are provided under the deck, either directly (in case of monolithic connection), or under the bearings. The following are the most common types of bearings: 3.4.1 Single column with hammer head: Description: Consists of a single column, which expands at the top to form a hammer head (with cantilever sections on either side of the column). The hammer head receives the bearings connecting the deck to the pier. Limitations the cantilever section of the hammer heads needs to be limited or its root depth needs to be significant. Advantages: frees up horizontal clearance under the bridge and provides attractive shape. Necessary for tall piers, when framing monolithically with deck. Disadvantages: may consume vertical clearance under the bridge, and lead to unfavourable seismic behaviour (e.g. Kobe). 3.4.2 Multiple columns: Description: Consists of multiple columns framing into the deck at the support diaphragm. Limitations: Requires a monolithic connection between deck and pier. Advantages: No bearings or other structures between deck and pier. Disadvantages: See limitations. 3.4.3 Multiple columns with cap beam (or frame): Description: Consists of two or more columns supporting a capping beam, which receives the bearings supporting the deck. Limitations: None. Advantages: Very flexible, can accommodate wide decks and skew arrangements. Disadvantages: May be bulky. 3.4.4 Wall:

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Description: Consists of a single wall either framing monolithically with the deck or enlarged at the top to receive bearings supporting the deck. Limitations: Height limited by slenderness considerations. Advantages: Very low horizontal footprint. Disadvantages: See limitations in addition to visual obstruction. 3.4.5 Twin wall: Description: Consists of two successive walls in the longitudinal direction of deck, oriented perpendicular to the axis of the deck and either framing monolithically with the deck or connected to a horizontal platform supporting the deck bearings. Limitations: Height limited by slenderness considerations. Advantages: This arrangement is used when more than one pier is rigidly connected to the deck in the longitudinal direction, to minimize longitudinal restraint on the deck, particularly for short piers. Disadvantages: See limitations. 3.5 Selection of abutment type: Abutments are provided at each end of the deck, either directly (in case of integral abutments), or under the bearings. The following are the most common types of bearings: 3.5.1 Bank seat abutment: Description: Consists of a back wall retaining the backfill and supporting the approach slab, a seat supporting the bearings and a footing supporting the back wall and seat, with wing walls at each side of the deck (left and right) to retain the fill. This type of abutment is used either in cut situations, or on top of reinforced earth walls. Limitations: Requires good bearing capacity and stable support condition immediately under the bearings level. Advantages: Compact and low cost. Disadvantages: See limitations. 3.5.2 Open abutment: Description: Consists of a back wall retaining the backfill and supporting the approach slab and connected to a transverse beam supporting the bearings. This beam in turn, is supported by columns on a common footing. The footing may be supported directly on soil, or connected to piles. Wing walls extend from the back wall at each side of the deck (left and right) to retain the fill. This type of abutment is used whenever possible and particularly in cases of high fill. Limitations: Not usable where traffic lanes or drainage ditches need to be close to the limit of the bridge.

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Advantages: Light and economical, particularly for high fills. Disadvantages: See limitations. 3.5.3 Closed (or wall) abutment: Description: Consists of a main wall extending from the footing level to the deck bearings level, where a thickening of the wall supports the bearings and the back wall. Wing walls extend from the main wall on each side of the deck (left and right) to retain the fill. The footing may be supported directly on soil, or connected to piles. Limitations: Not economical for high fill situations. Advantages: Required when traffic lanes or drainage ditches need to be close to the limit of the bridge. Disadvantages: See limitations. 3.5.4 Integral abutment: Description: Consists of a wall supported on a shallow foundations or on a single row of piles, monolithically connected to the deck. At one extreme, the wall may be inexistent, and the shallow foundation or piles are connected directly to the end diaphragm of the deck. Limitations: Not usable in skew conditions (> 10 deg), on curved alignments or where the total length of deck exceeds about 100m. Advantages: No expansion joints are needed. Disadvantages: See limitations. 3.6 Selection of foundations type: The selection of a foundation system depends mainly on the nature of the soil under the structure, and secondly on the type of structure, its height and its width. There are four main types of foundations: Shallow isolated footings: Each pier or abutment is supported by a shallow isolated footing. This system is used when the loads applied to the foundation are light or the soil resistance at a shallow depth is high. Pile foundation: Piles consist mainly of vertical concrete elements cast in holes drilled in the ground or of precast concrete elements driven into the soil, and connected to the vertical load carrying elements of the structure by means of pile caps. Piles are used when the soil resistance at a shallow depth is not sufficient to permit the use shallow isolated footings or rafts (either because the resistance to failure is low, or the expected settlements are high). Drilled pier foundation: As the name implies, the drilled piles extend above ground to connect directly to the deck as in integral abutments or to a cap beam supporting the bearings of the deck. This type of foundation is used mainly in crossings over water to simplify construction.

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Caisson foundation: As the name implies, this consists of a hollow concrete box of circular or elliptical or rounded rectangle section, that is prefabricated and sunk in place, or that is built in place inside temporary sheet piles. It may rest directly on the soil or it may be supported on piles. This type of foundation is used mainly in crossings over water or in very poor soil subject to liquefaction under seismic load. 4.0 Selection of analysis model: In order to determine the design forces in the components of a bridge structure, detailed structural analyses are required. For a few elements, simple hand calculations models can be used (e.g. parapets, cantilever slabs, back walls, wing walls, approach slabs). However, for the majority of the elements, a finite element FEM structural analysis model or models need to be used. It is recommended to use the simplest models that achieve the required accuracy. The following types of FEM models can be used: 4.1 Spine model: Description: The deck is modelled by a single line element whose mechanical properties represent those of the complete deck. The substructure elements may be represented by a single line element, or each column of the substructure may be represented by a line element. Tall piers may be discretized into a series of elements of approximately 4m length each. Bearings are represented by individual line elements or by link elements representing a group of bearings. Eccentricity of connections between the various line elements is modelled by means of rigid ends or links or by degree of freedom constraints. Skew supports are handled by rotating the local axes of the equivalent link element. Foundations are represented by support fixities or by elastic springs. Loads are applied as distributed loads along line elements or as nodal loads. A span may be discretized into several consecutive line elements. Each span should have at least three intermediate nodes (quarter points and midspan) along the deck centerline at the centroid level. More nodes may be required if the deck section properties change significantly along the span, or the span is curved. Limitations: This type of model is suitable to represent the effect of load variation in one dimension only (e.g. longitudinal direction for bridge spine models, transverse direction for slice model of box decks, or line model of diaphragms). It has to be supplemented by other models to capture the effect of load variation in other directions. In the longitudinal direction, each span needs to be discretized into at least 4 segments in case of straight alignments, or to subtend an arc of less than 10 degrees in case of curved alignments. The span/radius ratio should be less than 0.8 (NCHRP Report 620) or the subtended angle per span should be less than 34 deg for multicell box girders (AASHTO-LRFD 4.6.1.2.3) to 46 deg for single cell box girders (NCHRP Report 620), and the span/width ratio should be larger than 2.5 (AASHTO-LRFD 4.6.1.1). Advantages: This technique is simple and fast, and may be used for preliminary design at least, where it is not applicable by code. Disadvantages: See limitations.

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4.2 Grillage model: Description: As the name implies, the deck is modelled by a grid of longitudinal and transverse beams. For decks on beams, each longitudinal beam is modelled by a set of line elements in series. For box girders or voided slabs, each web is modelled by a set of line elements in series. Rules are available to calculate the effective section properties for the longitudinal and transverse beam elements for each type of deck (NCHRP Report 620). The remainder of the structure is modelled as in spine models. Limitations: There are many rules and recommendations for mesh discretization, for calculating the equivalent member properties, and for interpreting the results obtained. Preparing a grillage model and interpreting the results requires experience and is not straight forward. Advantages: Allows the use of beam element based models where spine models are not applicable. The output in terms of section forces is supposed to be directly usable in structural design. Disadvantages: Since there are many rules and recommendations for preparing a grillage model, such model may be difficult to have approved and to use. 3D shell or solid element models with section cut capability are now preferable to grillage models. 4.3 3D shell model: Description: The structure is discretized into an assembly of shell elements; planar triangles or quadrangles, in a 3D arrangement. Limitations: Regions with sudden variation in thickness cannot be modelled properly. Mesh must be sufficiently fine to provide good results. Advantages: Relatively simple and fast with modern software. Disadvantages: Relatively expensive in computer time. Direct results consist of stresses unless the software has section cut reporting capability. Should be reserved for final runs for documenting design. 4.4 3D solid model: Description: The structure is discretized into an assembly of 3D solids; cubes or pyramids in a 3D arrangement. Limitations: Requires a specialized graphical modelling software. Very expensive to run. Mesh must be sufficiently fine to provide good results. Advantages: Relatively simple to prepare with modern software. Disadvantages: Very expensive in computer time. Direct results consist of stresses unless the software has section cut reporting capability. Should be reserved for final runs for documenting design. 4.5 Analysis of deck in transverse direction: Although the available software allows analysis of the bridge in one go as a 3D structure, for design purposes, it is necessary to proceed in stages as follows:

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-Transverse analysis of deck. -Longitudinal analysis of deck. -Overall 3D analysis of bridge structure. -Analysis of specific elements (parapets, diaphragms, consoles, etc…).

The purpose of transverse analysis of the deck is to determine the following:

-Moments and shear in the transverse direction in the top slab of the deck on which moving loads are applied. -Moments and shear due to section distortion in the webs and bottom flange of box girders, due to moving load (in case no 3D analysis is performed). -Determining the moving loads applied to longitudinal elements of the deck (girders in girder and slab decks, or webs in box girder decks), if no grillage or 3D analysis is performed.

The following methods are available for transverse analysis of the deck: 4.5.1 Approximate moment formulae: The live load moment for main reinforcement perpendicular to traffic may be approximated by the following formulae adapted from AASHTO-LRFD 4.6.2.1.8:

M=0.159.L0.459.C.Paxle for 0<L<3. M=0.307.L0.350.C.Paxle for 3<=L.

Where: M = design live load moment (KNm/m). L = span length between supports (m). Paxle = design axle load including impact (KN). C = continuity factor: 1.0 for simply supported, 0.8 for continuous. This meets the first objective of transverse deck analysis defined above and is applicable to box girder deck sections (single cell or multicell) and beam-slab decks. 4.5.2 Finite strip method: A slice of the deck of constant width (normally unit width) is modelled as a 2D frame. The elements of the frame are of rectangular section, of constant width, and of thickness according to the thickness of the deck section being represented. The frame is supported under all webs by roller supports and one pin support. Pavement and sidewalk loads are represented by uniformly distributed loads. Edge barriers may be represented by a point load or a uniformly distributed load. Temperature gradients may be applied to the top flange of the deck. Axle loads are represented by concentrated loads or patches of uniformly distributed load (AASHTO-LRFD 3.6.1.2.5) moving along the top members of the frame, over the width of the deck. The axle loads are scaled up for impact and down by the ratio of effective strip width to the actual beam width in the model. The effective strip width is obtained conservatively from the minimum applicable value according to AASHTO-LRFD 4.6.2.1.3 as follows: Cantilever section: E=1.14+0.833X Interior positive moment: E=0.66+0.55S Interior negative moment: E=1.22+0.25S Where:

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X= distance from wheel load to support of cantilever. The wheel load is taken at 0.3m from the interior face of the edge barrier. S= distance between supports of interior strip. This method meets the first two objectives of transverse deck analysis defined above and is applicable to box girder deck sections (single cell or multicell). 4.5.3 Transverse load distribution factor: For beam and slab deck structures, the transverse load distribution factors for shear and moment define the fraction of lane load applicable to a single beam unit (with its tributary slab section). It is then possible to design the interior and exterior beams of a beam and deck structure independently (no grillage or 3D analysis are needed). This method is applicable within a given range of values for span length, beam spacing, skew and other parameters. For each type of deck, a distribution factor is calculated for moment in the interior girder (AASHTO-LRFD 4.6.2.2.2b). A correction factor is calculated for the exterior girder moment (AASHTO-LRFD 4.6.2.2.2.d). A correction factor is calculated for skew (AASHTO-LRFD 4.6.2.2.2.e). For each type of deck, a distribution factor is calculated for shear in the interior girder (AASHTO-LRFD 4.6.2.2.3a). A correction factor is calculated for the exterior girder shear (AASHTO-LRFD 4.6.2.2.3b). A correction factor is calculated for skew (AASHTO-LRFD 4.6.2.2.3c). This method meets the third objective of transverse deck analysis define above and applies to beam and slab deck structures. 4.6 Analysis of deck in the longitudinal direction: Except for simply supported girders, where the design forces may be established by simple statics along with the transverse load distribution factors discussed above, the design forces must be obtained by means of a comprehensive 3D structural analysis model (spine, grillage, shell or solid) as discussed above. 4.6.1 Modelling of beam-slab deck section: In beam-slab decks, the deck is often of a lower grade of concrete strength than the reinforced or prestressed concrete girders supporting it. The deck width used in the calculation of the equivalent composite section properties should be equal to the real width scaled by the factor fcdeck/fcgirder (<1). However, the full deck width should be used in the calculating dead weight of deck. Where precast reinforced concrete panels are used as stay-in-place formwork between the horizontal precast girder flanges that are set on a transverse slope, this will lead to a variable deck thickness. The average thickness of such decks is larger than the nominal thickness; and this has to be taken into account when calculating the dead weight of the deck. The effective flange width in calculating the composite section properties should not exceed the following (AASHTO-LRFD 4.6.2.6.1): For interior girders:

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-The spacing between girders. -1/4 of the span length. -12 times the slab thickness + the web width. For exterior girders one half of the effective width for interior girder plus: -The overhang width. -1/8 of the span length. -6 times the slab thickness as overhang. For calculation of shear-lag stresses due to prestressing force anchorages, the effective flange width may be assumed to grow from zero to its full value at a rate of 1:2 with respect to the distance from the edge of the girder (AASHTO-LRFD 4.6.2.6.2). 4.6.2 Modelling of box girder section: For cast-in-place multicell box girders analysed as a single unit, the effective flange width may be considered equal to the full flange width (AASHTO-LRFD 4.6.2.6.3). For cast-in-place single cell box girders and for segmental box girders, the effective flange width may be considered equal to the full flange width (AASHTO-LRFD 4.6.2.6.3) if the following conditions are satisfied: B<0.1L B<0.3D Where: B = Flange overhang from web. L = Span length between inflection points. D = Section depth. Otherwise, charts are available to compute the effective flange width. For calculation of shear-lag stresses due to prestressing force anchorages, the effective flange width may be assumed to grow from zero to its full value at a rate of 1:2 with respect to the distance from the edge of the girder (AASHTO-LRFD 4.6.2.6.2). 4.7 Analysis of diaphragms: The deck diaphragms at the ends of each span may be modelled as:

-Beam elements spanning from girder to girder in case of beam-slab decks. -Continuous beam with supports at bearing locations and concentrated loads at web location, or with linearly varying distributed load representing the deck load, in case of multicell box girders, voided slab and solid slab decks. -Strut and tie truss spanning between webs and bearings, in case of single cell or twin-cell box girders.

In all cases, diaphragms are subjected to the following loads: 4.7.1 Vertical forces due to the deck weight and live loads on it: These forces may be applied as concentrated loads where girders (or box webs) frame into the diaphragm, or they may be represented as a distributed load (uniform or trapezoidal). The maximum live load force may be obtained by summing the

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maximum live load shears from the spans connected at the diaphragm (corrected for impact and multilane reduction). 4.7.2 Horizontal forces due to transverse loads on the deck: These loads (due to centrifugal force, transverse wind, transverse earthquake) are applied at the level of the centroid of the girder-deck slab system. This level is in general different from the level of the diaphragm supports. Therefore, these loads induce moments and shears in the diaphragm in addition to axial forces. 4.7.3 Torsion forces due to imposed twisting: This torsion may occur whenever the deck consists of several girders (I, T, or box), or when the diaphragm is not normal to the axis of the deck (skew support). This torsion is a “compatibility torsion” i.e. it may be disregarded without compromising the stability of the structure, but doing so may lead to cracks that affect the durability of the structure. Exact evaluation of the imposed twisting requires a detailed 3D model. An upper bound for the amount of twist may be obtained by taking the end rotation of a typical girder under live load and assumed as simply supported, multiplied by two if girders are actually continuous over the diaphragm. 4.7.4 Vertical loads due to jacking forces near bearings: In order to replace bearings, temporary jacks must be placed near the bearings to lift off the deck. The diaphragm is then analysed for permanent loads but with different support locations. Differential support movements may be included to account for the unequal movement of the jacks (precision in controlling jack movements, say +/-5mm). 4.8 Strength reduction factors: The nominal ultimate strength capacity of a section is reduced by an amount φ (strength reduction factor). The strength reduction factors φ to be used are (AASHTO-LRFD 5.5.4.2.1):

• φ = 1.00 for tension steel in anchorage zones • φ = 1.00 for tension controlled flexure in post tensioned concrete • φ = 0.90 for tension controlled flexure in reinforced concrete • φ = 0.90 for shear (normal weight concrete) • φ = 0.80 for compression in anchorage zones • φ = 0.75 for compression controlled flexure • φ = 0.70 for bearing on concrete • φ = 0.70 for compression in strut-and-tie models

For segmental construction, the following strength reduction factors are applicable (AASHTO-LRFD 5.5.4.2.2):

• φ = 0.95 for tension controlled flexure and fully bonded tendons • φ = 0.90 for shear and fully bonded tendons • φ = 0.90 for tension controlled flexure and unbonded tendons • φ = 0.85 for shear and unbonded tendons

4.9 Ultimate strength strut and tie design (AASHTO-LRFD 5.6.3): Strut and tie design is used in regions of concentrated load application, such as anchorage, bearing, sudden change in section and pile caps (L/d<2). A truss system is assumed between the applied loads and the supporting points. The ultimate

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compression force in compression members of the truss (struts) must be less than the compression strength of the strut times a reduction factor (f=0.7 for compression). The ultimate tension force in tension members of the truss (ties) must be less than the tensile strength of the strut times a reduction factor (f=0.9 for tension). The tension reinforcement of a strut must be properly developed within the nodal region, otherwise a reduced tension stress must be used. The compression stress within a nodal region must satisfy some requirements. The dimensions of the struts and ties are determined from geometric constraints (size of bearing area and of load application areas). In general, several truss systems are possible in any situation, the most appropriate is the most direct, and the one where the minimum angle between a strut and a tie is larger than 25deg. 4.9.1 Unreinforced compression strut strength (AASHTO-LRFD 5.6.3.3.3): The compression strength of an unreinforced strut is given by the following formula: Pn = fcu.Acs Where:

Acs = effective area of strut, may exceed geometric dimension by 6db where db is the diameter of the anchoring bars.

fcu = f’c/(0.8+170el) < 0.85f’c f’c = 28 days compressive strength of concrete. el = es+(es+0.002)/tan2as es = tensile strain in tie (=ey for ties with passive reinforcement, =0 for

ties with prestressed reinforcement not yielded). ey = yield strain of passive reinforcement as = angle between tension tie and compression strut

4.9.2 Reinforced compression strut strength (AASHTO-LRFD 5.6.3.3.4): If the compression force in the strut is large, additional compression reinforcement may be provided as follows: Pn = fcu.Acs+fy.Ass Where: Ass = strut longitudinal reinforcement. In case of inclined struts where it is not practical to provide reinforcement parallel to the axis of the strut, an equivalent grid of reinforcement may be provided such that: Ass = Abv/sv.B/sin.a.sin2.a+Abh/sh.b.sin.a.cos2.a Where: Abv = Area of vertical bar sv = spacing of vertical bars Abh = Area of horizontal bar sh = spacing of horizontal bars b = depth of strut

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a = angle of strut with horizontal axis 5.6.3 Tension tie strength (AASHTO-LRFD 5.6.3.4): The tension tie strength is given by the following formula (slightly modified from that of AASHTO): Pn = fy.Ast+fpy.Aps Where: fy = yield strength of passive reinforcement Ast = area of passive reinforcement fpy = yield strength of prestressed reinforcement Aps = area of prestressed reinforcement The tension reinforcement must be properly developed in the nodal zone, otherwise the yield strength is scaled down by the ratio of available to required development length. 4.9.4 Nodal regions strength (AASHTO-LRFD 5.6.3.5): The nodal region nominal compression strength (before applying strength reduction factor) depends on the configuration of the nodal region: fcn = 0.85f’c when bounded by struts and bearing areas = 0.75f’c when anchoring one tie direction = 0.65f’c when anchoring more than one tie direction 4.10 Ultimate shear strength design AASHTO-LRFD introduces a new design procedure for shear design based on what is called Modified Compression Field Theory (MCFT), that allows for higher design shear stress, and that requires increasing the horizontal steel reinforcement to achieve the equilibrium of the strut-and-tie mechanisms at the heart of this method. The earlier conventional shear design method is still allowed within certain conditions, and for a lower maximum design shear stress. Only the strut-and-tie method is applicable near regions of discontinuities. In the following, we use:

vc =1/6fc0.5 as the nominal concrete shear strength (Mpa). fr =0.5fc0.5 as the nominal concrete tensile modulus (Mpa).

4.10.1 Minimum shear reinforcement (AASHTO-LRFD 5.8.2.4): Except for slabs, footings and culverts, transverse reinforcement shall be provided where: Vu>0.5.f.(Vc+Vp). Where: Vu = Ultimate design shear Vc = Concrete shear strength Vp = Shear resisting component of prestress force F = shear strength reduction factor (see 4.8 above)

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Where shear reinforcement is required, the minimum amount provided Av_min shall not be less than (AASHTO-LRFD 5.8.2.5): Av_min > 0.5.vc.bv.s/fy Where: s = spacing of transverse shear reinforcement. fy = yield strength of transverse shear reinforcement (<=420Mpa).

bv = width of web adjusted for presence of ducts= b-0.25Dduct for grouted tendons or =b-0.5Dduct for ungrouted tendons (AASHTO-LRFD 5.8.2.9).

b = web width Dduct = sum of prestressing duct diameters in web at the same level.

4.10.2 Maximum shear transverse reinforcement spacing (AASHTO-LRFD 5.8.2.7): The maximum shear transverse reinforcement spacing s shall not exceed the following limits: s<min(0.8dv, 0.6m) for vu<0.125f’c s<min(0.4dv,0.3m) for vu>=0.125f’c Where: f’c = concrete compressive strength. vu = ultimate shear stress

dv = effective shear depth or moment arm of flexural resisting forces in the section Mn/(As.fy+Aps.fps)>=max(0.9dc, 0.72h) (AASHTO-LRFD 5.8.2.9).

dc = effective flexural depth h = depth of section

4.10.3 MCFT shear design (AASHTO-LRFD 5.8.3.3): The nominal shear resistance shall be determined from: Vn = min(Vc+Vs+Vp,0.25f’c.bv.dv+Vp) Where: Vc = 0.5.b.bv.dv concrete shear strength Vp = shear resisting component of prestress force b = 4.8/(1+750.es) shear strength enhancement factor q = 29+3500.es shear crack inclination angle (deg).

es =(|Mu|/dv+|Vu-Vp|+0.5.Nu-Aps.fpo)/(Es.As+Ep.Aps+Ec.Ac.ff), -0.4e-3<es<6e-3.

ff = 0 if numerator is positive, 1 if numerator is negative. Vu = ultimate design shear Nu = ultimate axial force concomitant with Vu, tension positive Mu = ultimate design moment concomitant with Vu, > |Vu-Vp|.dv Aps = prestressing steel area fpo = prestressing steel stress = 0.7fpu. As = tensile passive flexural reinforcement area Ac = concrete cross-section area

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Es = modulus of elasticity of passive reinforcement Ep = modulus of elasticity of prestressed reinforcement Ec = modulus of elasticity of concrete

Vs = shear strength provided by transverse shear reinforcement The required transverse shear reinforcement is obtained from: Vs = (Vu/f-Vc) Av= Vs.s/(fy.dv.cot(q)) Where:

Vu = ultimate design shear, at critical section at dv from support (or section) if support reaction induces compression in section or at section otherwise (AASHTO-LRFD 5.8.3.2)

s = transverse shear reinforcement spacing dv = effective shear depth cot(q) = cotangent of shear crack angle

In addition, the longitudinal flexural reinforcement of the section must satisfy the following inequality (AASHTO-LRFD 5.8.3.5): As.fy+Aps.fps>|Mu|/(ff.dv)+0.5Nu/f+cot(q).(|Vu/fv-Vp|-0.5.Vs) Where: Vu = ultimate design shear Mu = ultimate design moment concomitant with Vu Nu = ultimate axial force concomitant with Vu (tension positive) Vp = shear resisting component of prestress force Vs = shear resistance of transverse shear reinforcement < Vu/ fv dv = effective shear depth ff = strength reduction factor for flexure fv = strength reduction factor for shear f = strength reduction factor for axial force (tension or compression) 4.10.4 Alternative conventional shear design (AASHTO-LRFD 5.8.3.4.3): For concrete sections not subjected to significant tension, the concrete shear strength may be determined as:

Vc=min(Vci, Vcw)

Where:

Vci =0.3vc.bv.dv+Vd+Vi.Mcr/Mmax>vc.bv.dv Vcw =(vc+0.3*fpc).bv.dv+Vp

bv = width of web adjusted for presence of ducts= b-0.25Dduct for grouted tendons or =b-0.5Dduct for ungrouted tendons (AASHTO-LRFD 5.8.2.9).

b = web width Dduct = sum of prestressing duct diameters in web at the same level.

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dv = effective shear depth or moment arm of flexural resisting forces in the section Mn/(As.fy+Aps.fps)>=max(0.9dc, 0.72h) (AASHTO-LRFD 5.8.2.9).

dc = effective flexural depth h = depth of section Vd = unfactored shear due to self-weight and superimposed dead load. Vi = Vu-Vd Mmax = maximum factored ultimate load concomitant with Vu. Mcrk = Sc.(fr+fcpe-Mdnc/Snc) external load moment increment to cracking Sc = (composite) section modulus for fiber tensioned by external loads Snc = noncomposite section modulus for fiber tensioned by external loads Mdnc = unfactored permanent load moment on section fcpe = compression prestress stress after all losses on fiber tensioned by

external load fr = concrete tensile modulus. The required transverse shear reinforcement is obtained from: Vs = (Vu/f-Vc) Av= Vs.s/(fy.dv.cot(q)) Where:

Vs = transverse shear reinforcement strength Vu = ultimate design shear, at critical section at dv from support (or

section) if support reaction induces compression in section or at section otherwise (AASHTO-LRFD 5.8.3.2)

Vc = concrete shear strength s = transverse shear reinforcement spacing dv = effective shear depth cot(q) = cotangent of shear crack angle = 1 if Vc=Vci or 1+fpc/(5.vc)<1.8 if

Vc=Vcw. In addition, the longitudinal flexural reinforcement of the section must satisfy the following inequality (AASHTO-LRFD 5.8.3.5): As.fy+Aps.fps>|Mu|/(ff.dv)+0.5Nu/f+cot(q).(|Vu/fv-Vp|-0.5.Vs) Where: Vu = ultimate design shear Mu = ultimate design moment concomitant with Vu Nu = ultimate axial force concomitant with Vu (tension positive) Vp = shear resisting component of prestress force Vs = shear resistance of transverse shear reinforcement < Vu/ fv dv = effective shear depth ff = strength reduction factor for flexure fv = strength reduction factor for shear f = strength reduction factor for axial force (tension or compression)

DRAFT 29 / 29


4.10.5 Alternative shear design for segmental post-tensioned box girders (AASHTO-LRFD 5.8.6): For segmental box girders, transverse shear reinforcement needs to be provided where: Vu>0.5.f.Vc The nominal shear strength of the section shall be the smaller value of: Vn=min(Vc+Vs,6.vc.bv.dv) And: Vu/(bv.dv)+Tu/(2.Ao.be)< 7.5.vc Where: vc = 1/6.f’c0.5 < 1.38Mpa

Vc =vc.K.bv.dv concrete shear strength Vs = Av.fy.dv/s Vu = ultimate shear, at critical section at h/2 from support (or section) if

support reaction induces compression in section or at section otherwise (AASHTO-LRFD 5.8.6.5)

bv = width of web adjusted for presence of ducts= b-0.5Dduct for grouted tendons or =b-Dduct for ungrouted tendons (AASHTO-LRFD 5.8.6.1).

dv = effective shear depth or distance from compression fiber to centroid of prestressing force>=0.8.h (AASHTO-LRFD 5.8.6.5).

Dduct = sum of prestressing duct diameters in web at the same level. h = depth of section K =(1+fpc/vc)0.5 < 2.0 (AASHTO-LRFD 5.8.6.3) fpc = average compression stress in concrete after all prestress losses. Ao = area enclosed by shear flow path around box. be = effective width of shear flow path (min(bv, tf_top, tf_bot) tf_top = top flange thickness tf_bot = bottom flange thickness

Where transverse shear reinforcement is required, the minimum transverse shear reinforcement Av_min to be provided in the section is (AASHTO-LRFD 5.8.2.5): Av_min > 0.35(Mpa).bv.s/fy And the maximum transverse shear reinforcement spacing s is: s < min(0.5h,0.3m) (AASHTO-LRFD 5.8.2.7) The principal tensile stress in the web calculated using Mohr circle, for service III load combinations and prestress after all losses or for construction stage load combinations and prestress after immediate losses, shall not exceed the following value (AASHTO-LRFD 5.8.5): s_max < 0.578.fr (AASHTO-LRFD 5.9.4.2.2)

DRAFT 30 / 30


Where: s_max = maximum tensile stress from Mohr circle at section centroid. For sections subjected to combined shear and torsion, torsion reinforcement needs to be provided if Tu>1/3.fvTcr: Where: Tcr = vc.K.2.Ao.be

Ao = area enclosed by shear flow path in box sections K =(1+fpc/vc)0.5 < 2.0 (AASHTO-LRFD 5.8.6.3) be = effective width of shear flow path (min(bv, tf_top, tf_bot) s = longitudinal spacing of transverse reinforcement

Where torsional reinforcement is required, the transverse torsional reinforcement is: At = Tu/fv.s/(2.Ao.fy) And the longitudinal torsional reinforcement is: Al = At.ph/s 4.11 Ultimate torsion strength design (AASHTO-LRFD 5.8.3.6): For sections subjected to combined shear and torsion, torsion reinforcement needs to be provided if Tu>0.25.fvTcr: Where:

Tcr = 2.vc.Acp2/pc.(1+fpc/(2.vc))0.5 torsional cracking moment Acp = area enclosed by outside perimeter of concrete section pcp = outside perimeter of concrete section fpc = average concrete prestress stress after all losses. Ao = area enclosed by shear flow path in box sections

And: Acp2/pcp<2.Ao.bv for single cell or muticell box sections. For the purpose of calculating the transverse shear crack inclination q, the equivalent ultimate shear force is (AASHTO-LRFD 5.8.2.1): Vu_eq = Vu+Tu.ds/(2.Ao) for box sections = (Vu2+(0.9.ph.Tu/(2.Ao))2)0.5 for solid sections Where: Vu = ultimate design shear Tu = ultimate design torsion concomitant with Vu ds = flexural depth ph = perimeter of closed torsion reinforcement

DRAFT 31 / 31


The transverse torsional reinforcement is calculated from the following formula: At = Tu/fv.s/(2.Ao.fy.cot(q)) The corresponding longitudinal torsion reinforcement is calculated from the following formula (AASHTO-LRFD 5.8.3.6.3): Al = Tu/fv.ph/(2.Ao.fy) And the longitudinal reinforcement should satisfy the following inequality (AASHTO-LRFD 5.8.3.6.3): Aps.fps+As.fy>|Mu|/(ff.dv)+0.5.Nu/f+ cot(q).((|Vu/fv-Vp|-0.5.Vs)2+(0.45.ph.Tu/(2.Ao.fv))2)0.5 4.12 Ultimate shear-friction design (AASHTO-LRFD 5.8.4): Interface shear friction shall be considered at the following locations: -Existing or potential crack. -Interface between dissimilar materials. -Interface between concrete cast at different times -Interface between different elements of a monolithic section (e.g. web and flange) The nominal shear-friction strength is given by the following formula: Vn = c.Acv+m.Av.fy < min(K1.f’c.Acv, K2.Acv) Where: Vn = nominal shear-friction strength Acv = shear-friction contact area Av = shear-friction reinforcement area fy = reinforcement yield strength c = cohesion stress see table below m = friction factor see table below K1 = factor see table below Case c

(MPa) m K1

Monolithic concrete 2.80 1.4 0.25 Cast-in-place concrete slab on clean concrete girder surface with surface roughened to an amplitude 6mm

1.90 1.0 0.30

Concrete cast against clean surface roughened to an amplitude of 6mm

1.70 1.0 0.25

Concrete cast against clean surface not intentionally roughened

0.52 0.6 0.20

Cast-in-place concrete slab on clean steel girder free of paint, with studs or welded rebars

0.17 0.7 0.20

Monolithic concrete bracket, corbel and ledge 0.00 1.4 0.25 Note that the above assumes the following: -Normal weight concrete

DRAFT 32 / 32


-Clean surface free of laitance or other contaminants -Compression force normal to surface conservatively neglected -Tension force normal to surface will require additional reinforcement -K2.Acv>K1.f’c.Acv 4.12.1 Minimum shear friction reinforcement (AASHTO-LRFD 5.8.4.4): The minimum shear friction reinforcement shall be 0.35Acv/fy. For cast-in-place concrete slab, the minimum shear-friction reinforcement shall be the minimum required for 1.33Vu (instead of Vu) and 0.35Acv/fy. If the surface between girder and slab is roughened to an amplitude of 6mm, the interface shear stress is less than 1.4MPa and the girder shear reinforcement extends into the slab, then no shear-friction reinforcement is required between girder and slab. 4.13 Ultimate flexural strength design (AASHTO-LRFD 5.7): 4.13.1 Minimum design ultimate moment (AASHTO-LRFD 5.7.3.3.2): For ultimate strength flexural design the minimum design moment shall be: Mu=max(Mu,min(1.2Mcrk,1.33Mu)) Where: Mcrk = Sc.(1.94.fr+fcpe)-Mdnc(Sc/Snc-1)>1.94.fr.Sc

Sc = (composite) section modulus for fiber tensioned by external loads Snc = noncomposite section modulus for fiber tensioned by external loads Mdnc = unfactored permanent load moment on section fcpe = compression prestress stress after all losses on fiber tensioned by

external load fr = concrete tensile modulus as defined above. 4.13.2 Ultimate flexural strength using code equations (AASHTO-LRFD 5.7.3.2): In calculating the ultimate flexural strength of the section, the compression strain of concrete shall not exceed 0.003. If the passive reinforcement strain exceeds 0.005 when the concrete has reached its ultimate strain, the section is said to be tension controlled, otherwise it is compression controlled. The ultimate flexural strength of the section is calculated from first principles by strain compatibility, or using the approximate equations below. For compression flanges of width to thickness ratio wtr > 15, the effective concrete strength is multiplied by a reduction factor fw as follows (AASHTO-LRFD 5.7.4.7.2): Fw = 1.00 for wtr < 15 = 1.00-0.025.(wtr-15) for 15 < wtr < 25 = 0.75 for 25 < wtr < 35 For rectangular sections: a = (Aps.fps+As.fy-A’s.f’s)/(0.85.fc.b) Mn = Aps.fps.(dp-a/2)+As.fy.(ds-a/2)-A’s.f’s.(d’s-a/2) Where:

DRAFT 33 / 33


a = compression block depth b = section width Aps = prestressing steel area fps = prestressing steel stress at ultimate

dp = distance from extreme compression fiber to centroid of prestressing steel

As = tension side passive flexural reinforcement area ds = distance from extreme compression fiber to centroid of tensile

passive reinforcement A’s = compression side passive flexural reinforcement area

d’s = distance from extreme compression fiber to centroid of compression passive reinforcement

fy = yield strength of passive reinforcement f’s = compression stress of compression reinforcement (by strain

compatibility) For T sections: a = (Aps.fps+As.fy-A’s.f’s-0.85.fç.(b-bw).tf)/(0.85.fc.bw)

Mn = Aps.fps.(dp-a/2) + As.fy.(ds-a/2)+ 0.85/2.fc.(b-bw).tf.(a-tf) -A’s.f’s.(d’s-a/2)

Where: b = compression flange width bw = webs total width tf = compression flange thickness The tensile stress of the prestressing steel fps, depends on the type of prestressing steel and whether it is bonded or not, or whether there is a mix of bonded and unbonded prestressing steel (AASHTO-LRFD 5.7.3.1): fps = fpu.(1-k/b.a/dp) for bonded prestressing reinforcement

fps = fpe+6300.(dp-a/b)/le < fpy for unbonded prestressing reinforcement

fps = fpe for unbonded prestressing in a mix of bonded and unbonded prestressing

Where: fpu = ultimate tensile stress of prestressing steel fpy = yield stress of prestressing steel (~0.9.fpu) a = compression block depth

dp = distance from extreme compression fiber to centroid of prestressing steel

b = ratio of compression block depth to neutral axis depth (0.85>0.85-0.07.(fc-28)/7>0.65).

k = 0.28 for low relaxation strands. = 0.38 for stress relieved strands and type I high strength bars = 0.48 for type II high strength bars

le = li/(1+Ns/2) effective unbonded tendon length li = tendon length between anchorages

DRAFT 34 / 34


Ns = number of support hinges crossed by unbonded tendon between anchorages.

4.13.3 Control of cracking by distribution of reinforcement (AASHTO-LRFD 5.7.3.4): Although research shows that there is no correlation between crack width and reinforcement corrosion (which is more correlated with concrete cover), it is often required to limit crack width at service, by limiting the tensile service stress fs in the reinforcement and the reinforcement spacing s. These parameters are tied together by the following relations: ge = 0.50+0.50.(w-0.2)/0.2 exposure factor fs = 861000.ge.(h-c)/(s-2c)/(7h+3c) (Mpa) < 0.66fy service steel stress Where: w = allowable service crack width 0.2mm to 0.3mm h = section depth s = rebar spacing (>2c) c = concrete cover to centroid of reinforcing steel A crack width of 0.3mm may be acceptable for structures exposed to non-corrosive atmosphere. A crack width of 0.25mm may be acceptable for structures in contact with non-corrosive soil. A crack width of 0.20mm may be acceptable for structures exposed to corrosive atmosphere or soil. 4.14 Prestress design: Designing the prestressing system for a bridge involves the following tasks:

-Selecting the prestressing system characteristics: pretensioned or post-tensioned, bonded or unbonded, internal or external or a combination of some or all those. -Selecting the amount of prestressing steel required and its articulation into tendons. -Selecting the tensioning mode; from one end only or from both ends. -Selecting the stressing stages; one stage or multiple stages. -Defining the prestressing tendons path to minimize the amount of prestressing steel, the friction losses and secondary moments while meeting service stress limits and ultimate strength requirements. -Providing the passive reinforcement at and around the prestressing anchor zones.

The following verifications must be made: -Check that anchorage stresses are within allowable limits and that required anchorage reinforcement is provided. -For each stressing stage, calculate applicable losses, flexural stresses and check that flexural stresses are within limits. -Calculate deflections for each stage and necessary initial camber. -Calculate passive reinforcement necessary to cater for tensile forces, and for ultimate strength state. In performing the above tasks, the following requirements must be met:

DRAFT 35 / 35


4.14.1 Stress limits: The following stress limits apply to prestressing steel (AASHTO-LRFD 5.9.3): For postensioned tendons and bars, assuming fpy=0.9fpu Condition Low relaxation strands Plain and deformed high

strength bars Prior to seating <0.80fpu <0.80fpu At anchorages/couplers after seating

<0.70fpu <0.70fpu

Elsewhere immediately after seating

<0.74fpu <0.70fpu

After all losses >0.50fpu >0.50fpu The following stress limits apply to the compressive flexural stress in concrete: Condition Allowable compression

stress AASHTO-LRFD article

Initial, during construction 0.60.f’ci 5.9.4.1.1 Service, permanent 0.45.f’c 5.9.4.2.1 Service, comb. I 0.60.fw.fc > 0.45.f’c 5.9.4.2.1 Where fw is a slenderness correction factor as per AASHTO-LRFD 5.7.4.7.2 The following stress limits apply to the tensile flexural stress in concrete of non-segmentally constructed bridges: Condition Allowable tension stress AASHTO-LRFD article Initial, during construction 1.26.fri * 5.9.4.1.2 Service, comb. III moderate corrosion conditions

fr 5.9.4.2.2

Service, comb. III severe corrosion conditions

0.50.fr 5.9.4.2.2

* provided passive reinforcement is provided to take total tensile force at 0.5fy. The following stress limits apply to the tensile flexural stress in concrete of segmentally constructed bridges with bonded reinforcement across joints. Condition Allowable tension stress AASHTO-LRFD article Initial 1.26.fri * 5.9.4.1.2 Initial, principal tensile stress at n.a in web

0.58.fri 5.9.4.1.2

Service, comb. III 0.50.fr* 5.9.4.2.2 Service comb. III, principal tensile stress at n.a in web

0.58.fr 5.9.4.2.2

* provided passive reinforcement is provided to take total tensile force at 0.5fy. The following stress limits apply to the tensile flexural stress in concrete of segmentally constructed bridges without bonded reinforcement across joints. Condition Allowable tension stress AASHTO-LRFD article Initial 0 5.9.4.1.2 Initial, principal tensile stress at n.a in web

0.58.fri 5.9.4.1.2

Service, comb. III 0 5.9.4.2.2

DRAFT 36 / 36


Service comb. III, principal tensile stress at n.a in web

0.58.fr 5.9.4.2.2

4.14.2 Calculation of immediate losses (AASHTO-LRFD 5.9.2.2): The immediate prestress losses consist of friction losses and of anchorage draw-in (in case of post-tensioned construction) and of elastic shortening (for both post-tensioned construction and pre-tensioned construction). Friction loss is expressed by the following relation P(x)=P0.exp(-(K.x+m.q) ), where: X = distance from anchorage

q = cumulative absolute value change of angle from anchorage to point x.

P0 = initial force at anchorage, before anchorage draw-in. P(x) = force at distance x from anchorage after friction losses K = wobble coefficient = 0.00066/m m = friction coefficient The friction coefficient may be taken from the following table: Case Friction coefficient Strand in galvanized metal sheathing 0.15-0.25 Strand in polyethylene duct 0.23 Strand in rigid steel pipe deviator 0.25 High strength bar in galvanized metal sheathing 0.30 The anchorage draw-in loss with power seating of the anchorage wedges may range from 3mm to 10mm. A typical value of 6mm is assumed. A more conservative value would be 8mm. The elastic shortening loss at every section depends on the type of construction; pre-tensioned construction or post-tensioned construction. For pretensioned construction, the elastic shortening loss is estimated by the following formula:

Dfps = Eps/Eci.fpcgp Where: Eps = modulus of elasticity of prestressing steel Eci = modulus of elasticity of concrete at time of stressing

fpcgp = concrete stress at centroid of prestressing steel after occurrence of friction loss and in presence of self-weight moment.

The elastic shortening loss for post-tensioned construction is estimated by the following formula:

Dfps =1/2.(N-1)/N.Eps/Eci.fpcgp or as an upper bound 1/2.Eps/Eci.fpcgp Where: N = Number of identical tendons.

DRAFT 37 / 37


4.14.3 Calculation of long-term losses (AASHTO-LRFD 5.9.5.3): The long-term losses consist of creep, shrinkage and relaxation losses and are applicable to all types of construction (pre-tensioned and post-tensioned). Long-term losses may be calculated either by lump-sum or by approximate formulae or by detailed step-by-step time integration. The first method is usually reserved for preliminary design, and the last method is usually reserved for segmental construction and multistage construction. The second method (approximate formulae) is sufficient for the most common cases. The lump-sum long-term losses (Mpa) for fully prestressed sections may be taken as: Type of beam section

Level Low relaxation Wires and strands 1620 <

fpu < 1860 Mpa

Bars 1000 < fpu < 1100

Mpa Rectangular beams and solid slabs

Upper bound Average

187 167

171

Box girders Upper bound Average

145 130

100

Single T, Double T, Hollow core and voided slabs

Upper bound Average

256-(f’c-41)* 216-0.85(f’c-41)*

251-0.76(f’c-41)

* f’c is concrete compressive strength in Mpa The long-term losses (Mpa) for pre-tensioned girders with low-relaxation strands may be estimated by the following formula: Dfplt = gh.gst.(10.fpi.Aps/Ag+83)+17 Where: gh = 1.7-0.01.H humidity correction factor gst = 35/(f’ci+7) strength at stressing correction factor Aps = area of prestressing steel Ag = cross-section area H = average ambient humidity (%) f’ci = concrete strength at stressing time (Mpa) fpi = prestressing steel stress at transfer The long-term losses for post-tensioned girders may be estimated according to the provisions of AASHTO-LRFD 5.9.5.4. 4.14.4 Anchor zone reinforcement (AASHTO-LRFD 5.10.9): Anchor zones are designed for a factored load Pu=1.2.P, where P is the maximum prestress load before anchorage draw-in. The strength reduction factor for reinforcing steel f=1.0. In designing the anchor zone, two distinct regions are considered: the local zone (concerned with compressive stresses) and the general zone (concerned with tensile stresses). In detailing anchor zone reinforcement, the smallest bar size possible, at

DRAFT 38 / 38


the smallest spacing compatible with good concrete placement and avoidance of congestion should be selected. 4.14.4.1 Local zone around each anchor plate: The local zone starts at the location of the anchor and extents sideways and in the direction of the prestressing force a certain distance determined as follows:

Transverse extent, in case no reliable manufacturer data exists, c=a+2cover. Transverse extent, with reliable manufacturer data, c=min(2d_edge, s_bearing) Longitudinal extent d=min(c,d_burst)

The compression bearing stress under anchorage plate must satisfy the following equation: Pu<f.fn.Ab Where: f = 0.7 strength reduction factor for concrete fn = min(2.25.f’ci,0.7.f’ci.(A/Ag)0.5) f’ci = concrete strength at time of stressing fpu = ultimate tensile strength of prestressing strand/bar. Aps = area of prestressing steel at anchor Ag = gross area of bearing plate Ab = Effective bearing area (Ag-Aduct) Aduct = cross-section area of duct

A = maximum area similar to Ag not overlapping with another anchor similar area, and not extending outside concrete section.

Note: In case no reliable manufacturer information, the square base plate dimension can be estimated as a = 0.8.(Aps.fpu/f’ci)0.5. 4.14.4.2 General zone of anchorage zone: The general zone starts where the local zone ends, and extents away from the anchorage a certain distance determined as follows:

Transverse extent: min(transverse dimension, longitudinal dimension) Longitudinal extent in direction of prestress: min(1.5 max. transverse dimension, longitudinal dimension) Longitudinal extent in direction opposite to prestress (in case of intermediate section): min. transverse dimension

The general zone may be analysed by one of three methods: strut-and-tie, elastic analysis or approximate method. In all cases, three types of reinforcement must be provided: surface (spalling), bursting and diffusion. Spalling reinforcement shall be provided immediately under the anchor in the plane perpendicular to the prestress force:

Asp = 0.02.Pu/fy

DRAFT 39 / 39


Bursting reinforcement shall be provided in both directions perpendicular to the prestress force after the spalling reinforcement over a distance d=min(2.5d_burst, 1.5 min transverse dimension): Tu = 0.25.Pu.(1-a/h)+0.5.Pu.sin(a) Abst = Tu/fy d_burst= 0.5.(h-2|e|)+5.|e|.sin(a) a = anchor plate dimension in plane considered h = section dimension in plane considered e = eccentricity of prestress force in plane considered a = angle of prestress force with member axis in plane considered Diffusion reinforcement shall be provided based on flexural principles or shear friction over the distance from the anchorage plane to where the prestress forces have diffused uniformly over the section, assuming a diffusion angle of 30 deg from each edge of the anchor plate. 4.14.4.3 Intermediate anchorages and blisters: Where anchorages are not located at the end of the section, such as couplers at construction joints or at blisters, additional longitudinal reinforcement must be provided behind the anchorage: As = 0.42.Pu/fy In addition, blisters must be provided with additional reinforcement (shear-friction and flexural) to anchor the blister into the face of web or flange, and take care of the eccentricity of the applied anchor force. 4.14.5 Special reinforcement for curved tendon regions (AASHTO-LRFD 5.10.4.3): Tendons in curved webs are subjected to an out-of-plane force T=P/R, which may require special reinforcement. It can be shown that as long as the out-of-plane radius R>320.Dduct, no special reinforcement is required, otherwise, the reinforcement required is: As = 1.40.Pu/(R.fy) Where: Pu = factored tendon ultimate force R = out-of-plane radius of curvature of tendon fy = yield strength of reinforcing steel It can be shown that as long as the clear cover to tendon is larger than the tendon diameter (or 50mm), no special side-bursting reinforcement is required. 4.15 Special requirements for segmental construction bridges (AASHTO-LRFD 5.14.2): For segmentally constructed prestressed concrete bridges, there are additional requirements in terms of construction load cases to consider, transverse analysis of deck section, estimation of long-term prestress losses, detailing and proportioning. 4.15.1 Construction load cases and combinations:

DRAFT 40 / 40


The following are the load cases that may have to be considered for segmental construction, in addition to those previously defined for normal service: A = static weight of precast segment AI = dynamic load increment due to sudden release of segment (100% of segment weight). CE = specialized construction equipment (e.g. typical values for form travellers

are 710-800KN for 2 lane deck and 1250KN for 3 lane deck) CLE = longitudinal force due to construction equipment (e.g. 10% of CE) CLL = 0.48Kpa distributed construction live load, not applicable to incremental launching, for balanced cantilever construction apply full value on one cantilever and half on the opposite cantilever CR = creep effects DC = self-weight of the structure DIFF = differential load, applicable only to balanced cantilever construction, equal

2% of the cantilever dead load IE = dynamic load from equipment (e.g. 10% of segment weight) SH = shrinkage effects T = thermal; the sum of uniform temperature change TU and temperature

gradient change TG U = segment unbalance, for balanced cantilever construction WE = 4.8Kpa horizontal wind pressure on exposed deck surface (for wind on

equipment) WS = horizontal wind on structure WUP = 0.24Kpa upward uplift wind pressure, for balanced cantilever construction

only, applicable to one cantilever at a time The cases that have to be actually considered depend on the type of construction; whether it is balanced cantilever, or incremental launching or span-by-span assembly, as shown in the following table: Item\Construction method

Balanced cantilever Incremental launching

Span by span

DC V V V DIFF V U V CLL V V CE V V V IE V V CLE V V V WS V V V WUP V WE V V V CR V V V SH V V V TU V V V TG V V V WA V V V EH,EV,ES V V V

DRAFT 41 / 41


The following service load combinations have to be considered during construction: Item\Case 1 2 3 4 5 6 DC 1 1 1 1 1 1 DIFF 1 1 1 U 1 1 CLL 1 1 1 1 1 IE 1 1 1 1 CLE 1 WS 0.7 0.7 0.3 0.3 WUP 0.7 1 WE 0.7 0.3 0.3 CR SH TU TG WA EH,EV,ES 1 1 1 1 1 1 fta fr fr fr fr fr fr smax_a 0.58.fr 0.58.fr 0.58.fr 0.58.fr 0.58.fr 0.58.fr and Item\Case 7 8 9 10 11 12 DC 1 1 1 1 1 1 DIFF 1 1 1 U 1 1 CLL 1 1 1 1 1 IE 1 1 1 1 CLE 1 WS 0.7 0.7 0.3 0.3 WUP 0.7 1 WE 0.7 0.3 0.3 CR 1 1 1 1 1 1 SH 1 1 1 1 1 1 TU 1 1 1 1 1 1 TG 1 1 1 1 1 1 WA 1 1 1 1 1 1 EH,EV,ES 1 1 1 1 1 1 fta 1.16.fr 1.16.fr 1.16.fr 1.16.fr 1.16.fr 1.16.fr smax_a 0.66.fr 0.66.fr 0.66.fr 0.66.fr 0.66.fr 0.66.fr Where: fca = 0.5f’c maximum allowable flexural stress compression fta = maximum allowable flexural stress tension for type A joints smax_a = maximum allowable principal stress tension for type A joints fr = modulus of rupture of concrete Type A joints are those where passive reinforcement crosses the joint between segments (as in cast-in-situ segments). Type B joints are those where no passive

DRAFT 42 / 42


reinforcement crosses the joint (as in precast segments). No tension is allowed in type B joints. The following ultimate strength construction stage combinations need to be considered:

1.1(DL+DIFF)+1.3CE+A+AI DC+CE+A+AI

4.15.2 Detailing and proportioning (AASHTO-LRFD 5.14.2.3.10): The following are minimum dimensions and proportions for segmental construction box girders: Overall depth d for constant depth decks:

1/5 < d/L< 1/30, opt 1/18 to 1/20 (L = span length between supports) For incrementally launched decks: For L < 30m 1/15 < d/L < 1/12 For 30 < L < 60m 1/13.5 < d/L < 1/11.5 For 60 < L < 90m 1/12 < d/L < 1/11 Overall depth for variable depth decks with straight haunches: 1/16 < d/L < 1/20, opt 1/18 at haunches 1/22 < d/L < 1/28, opt 1/24 in center section Number of cells: 1 preferably if d/b >= 1/6 (b = top flange width) 2 preferably if d/b < 1/6 Length of top flange cantilever: <= 0.45 interior cell span Cantilever thickness at edge: > 250mm or depth necessary for barrier reinforcement development. Cantilever thickness at root: > Lc/8 (Lc = length of cantilever) Top flange thickness: > S/30, 250mm (S=clear span between webs or haunches). If S>4.5m transverse post-tensioning shall be used with strands <= 12.7mm. Web thickness: 200mm > d/15 without any internal post-tensioning 300mm with either longitudinal or vertical prestressing 375mm with both longitudinal and vertical prestressing Bottom flange thickness: > bf_bot/30, 200mm (bf_bot = clear span at bottom of cell) 5.0 Design of specific elements of the structure:

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In the following, we list for each element of the structure the verifications to be made, and the points to watch for. We follow the load path from the barrier and deck, all the way down to the foundations. 5.1 Barrier design: The barrier is designed for the loads and load cases defined in section 2.2.5 above. The barrier reinforcement is designed according to the yield line method defined in Appendix A13 of AASHTO-LRFD. The critical case is that near an expansion joint, where the yield line length is reduced. The vertical reinforcement of the barrier must be detailed such that its hook development length fits within the thickness of the top flange of the deck (db< (t_deck-c)/14). The deck edge section (thinner than the barrier) must be able to resist the moment applied to it from the barrier. The available flexural reinforcement, reduced by the ratio of barrier width to development length of deck reinforcement must be sufficient for both flexure and direct tension. 5.2 Deck transverse design: The deck transverse design is conducted either using the approximate formulae for moving load moments of 4.5.1 above, or using the finite strip method of 4.5.2, or as a 3D analysis. For the cantilever section, the transverse reinforcement must account for the transverse tension concomitant with impact on the barrier. For box girders, the transverse reinforcement directly calculated for flanges and webs must be cumulated with the torsion transverse reinforcement, as well as with the section distortion reinforcement (except when 3D analysis has been used, where the combination of these effects is automatically accounted for). For box girders, the bottom flange transverse reinforcement must be at least equal to 0.5% of the flange section. The longitudinal reinforcement in the bottom flange of box girders must be at least equal to 0.4% of the flange section (AASHTO-LRFD XXX). The longitudinal bottom reinforcement in the top flange must be equal to at least 2/3 the transverse bottom flexural reinforcement. Near expansion joints, the effective transverse strip width is reduced by half, and the transverse reinforcement must be increased, or the top flange thickness must be increased (particularly the cantilevers). The increase in flange thickness near expansion joints must allow for proper installation of expansion joints. The end diaphragms width may be increased to offset the reduction in effective strip width (set the diaphragm width to at least half the effective transverse strip width). Transverse reinforcement must be located outside the longitudinal reinforcement. 5.3 Continuity slab design: The continuity slab is essentially designed to accommodate the rotation imposed on it from the deflection of the connected spans (due to live loads, thermal gradient,

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support settlement, deck jacking) and to transmit axial forces between spans as well as resist wheel loads on top of it. The slab thickness must be as small as possible to minimize the imposed deformation moments. The longitudinal reinforcement will tend to be heavy and closely spaced to minimize crack width. 5.4 Expansion joint support design: The slab cantilevering from the end diaphragm to support the expansion joint and to protect the prestressing anchors from direct drip is designed as a corbel. The load applied to it is the wheel load, with an impact factor of 1.75 instead of 1.33 (i.e the wheel load already multiplied by 1.33 must be further multiplied by 1.30). The concomitant horizontal tension load is equal to 25% of the vertical load. The effective width of the resisting section is equal to the wheel width (0.51m) plus twice the length of the cantilever section (1:1 distribution of load). The depth of the cantilever section must allow for the recess of the expansion joint, and be sufficient to transmit the shear load without shear reinforcement or to require one layer of reinforcement that can developed within the cantilever length. 5.5 Bearing support design: In designing the geometry of the bearing support, sufficient vertical and horizontal clearance around the bearing must be provided to allow for the possibility of jacking and replacement of the bearing in the future, when necessary. For bearings supporting precast elements, provision must be made for: -The type of connection between the bearing and the element (simple bearing contact, contact with adhesive, bolted connection). -The need for sliding restraint or not. -The need to accommodate longitudinal or transverse slope of the precast element (e.g. precast concrete wedge). The bearing support pedestal is reinforced for spalling and bursting as for the prestress anchorage (4.12.4 above). The bearing support is further checked for shear and bending due to the moment arm of the horizontal forces on the bearing, and for edge wedge equilibrium, when located near a free edge. 5.6 Pier head design: Depending on the type of pier head, the pier head may be designed as a continuous beam, or as a corbel. The following sets of load cases must be considered: -The normal exploitation load cases (with the bearings at their design locations). -The bearing jacking condition, where 1.3 times the permanent load is applied at the jack locations. -The construction load cases, if required by the construction method (especially for segmental construction). In addition, the longitudinal reaction from bearings applied at the top of the pier head will induce a torsional moment in the pier head section and a moment about a vertical axis in the cantilever part of the pier head. Reinforcement should be provided for these forces.

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5.7 Pier design: The pier shaft is designed as a column for the loads it receives from the pier head, as well as for an accidental vehicle impact load (2.2.4 above). The flexural stiffness of the pier shafts must be reduced if the design moments are larger than the cracking moment. For tall piers (K.L/d>15) , P-Delta effects must be considered and safety against buckling must be checked, where:

K = restraint factor; 2 for flexurally unrestrained at top, 1 for flexurally restrained at top L = pier height from top of foundation d = transverse pier section dimension in the direction of considered

To minimize reinforcement wastage in tall piers (> 10m) , longitudinal reinforcement bars are detailed as 6m long bars, with 2m bar overlap, leading to 4m high concrete pour lifts. The first lift is only 2m high (to account for 2m embedment in the foundation). Even if bar couplers are used, the couplers need to be staggered and the 4m concrete lifts are maintained. 5.8 Pier foundation design: The pier foundations as any other foundations are designed for two sets of criteria; geotechnical criteria and structural criteria. The geotechnical criteria are as follows: -Net bearing stress less than allowable value for all service load combinations. -Factor of safety against overturning larger than minimum value of 2 (or alternatively contact ratio larger than a certain value XXX, or vertical load eccentricity smaller than a certain value XXX). -Factor of safety against sliding larger than minimum value of 1.5. -Long term settlement under permanent load less than a limiting value (e.g. 25mm). -Settlement under live load less than a limiting value XXX. -Minimum soil cover over footing of 0.6m. Where foundations on piles are used, the geotechnical criteria are replaced by the following: -Maximum service compression or tension on a pile less than the corresponding allowable service load. -Long term settlement under permanent load less than a limiting value (e.g. 25mm). -Settlement under live load less than a limiting value XXX . The structural criteria are as follows: -Flexural service stress under a limiting value corresponding to allowable crack width. -Ultimate flexural strength greater than applied ultimate moment at critical sections. -Ultimate shear strength greater than applied ultimate shear at critical sections. -Ultimate punching shear strength greater than applied punching shear at pier-foundation interface and at corner piles. Where foundations on piles are used, the structural criteria are supplemented by the following: -Maximum ultimate shear and moment per pile less than the corresponding available strength at the concomitant axial load.

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-Base shear is not equally distributed to all piles; “front” piles receive more shear than piles behind, “in their shadow”. The distribution factor depends on the pile spacing as specified in AASHTO-LRFD 10.7.2.4. Conservatively, the piles in the shadow of the front row may be considered to receive 40% of the load received by the front piles. -A choice has to be made to design the piles as fixed at the foundation level or as pinned. In the former case, the pile maximum moment is larger but decreases faster than in the latter case. -Refer to section 6.0 for more details about piles. 5.9 Abutment design: The abutment consists of several components: 5.9.1 Backwall design: The backwall supports the expansion joint, the approach slab and retains the fill behind the abutment. The backwall is designed for the soil pressure of the retained soil, and for the horizontal breaking/accelerating wheel load on top of the wall (25% of the wheel load with 1.75 impact factor). The thickness of the wall at its intersection with the wingwall should be sufficient to develop the horizontal reinforcement of the wingwall. 5.9.2 Approach slab design: The approach slab can be designed either as a simply supported beam, or as a beam on elastic foundations. It is safer to design the approach slab as a simply supported beam to account for possible settlement of the fill under the slab. A strip of width equal to one lane width is subjected to the axle or tandem axle load, with an impact factor of 1.75 (instead of 1.33), in addition to the weight of fill and pavement on top of it. The length of the approach slab should be about half the abutment height from top of footing. The thickness of the slab should be sufficient to resist beam shear without transverse reinforcement, and to require only one layer of flexural reinforcement. The fill thickness on top of the approach slab depends on the design of the pavement but should not be less than 0.5m. 5.9.3 Wingwall design: There are two types of wingwalls, those in open abutments, connected to the abutment along one vertical edge, and those in closed (or wall) abutments, connected to the abutment along two consecutive edges, one vertical and one horizontal. The wingwall in open abutments has to be designed for the following loads: -Horizontal soil pressure perpendicular to the wall face. -Horizontal surcharge pressure perpendicular to the wall face. -Vertical weight of wingwall and traffic barrier on top. -Horizontal accidental impact load perpendicular to wall surface at edge of wingwall and concomitant vertical load (as per barrier protection level). The wingwall in closed abutments has to be designed for the following loads: -Horizontal soil pressure perpendicular to the wall face.

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-Horizontal surcharge pressure perpendicular to the wall face. -Horizontal accidental impact load perpendicular to wall surface at edge of wingwall and concomitant vertical load (as per barrier protection level). The wall thickness should be sufficient to support the barrier on top of it. 5.9.4 Abutment seat design: The abutment seat as a beam exists only in open abutments. The beam is designed as a continuous beam supported by the abutment columns, and subjected to concentrated loads at the bearing locations and at the temporary jacking locations. It is also subjected to uniformly distributed vertical load and uniformly distributed torsion moment from the backwall. The abutment seat in a closed abutment is simply a thickened section joining the back wall to the main wall and transmitting the back wall base forces to the top of the main wall. 5.9.5 Main wall design: The main wall in closed abutment is mainly subjected to horizontal soil pressure, horizontal surcharge load and horizontal seismic surcharge load. It is designed essentially as a cantilever wall, although for narrow abutments, it could be designed as a two way slab (restrained at the base by the foundation slab and at each vertical edge by the wingwalls). The wall thickness at any section should be sufficient to provide the required shear resistance without need of transverse shear reinforcement. 5.9.6 Columns design: The columns in an open abutment resist the vertical and horizontal loads applied from the abutment seat in addition to horizontal soil pressure in the longitudinal direction. The effective width for calculating the longitudinal soil pressure on a column is equal to two to three times the actual width of the column. The columns may be considered as a cantilever for bending about the axis parallel to the long direction of the abutment, and as fixed at both ends for bending about the axis perpendicular to the long direction of the abutment. 5.9.7 Abutment footing design: The abutment footing is designed in the same manner as the pier footing above (5.8). 6.0 Foundation piles design: Foundation piles are designed for two sets of criteria: geotechnical and structural. The geotechnical criteria for piles are the achievement of the required bearing and uplift resistance within the constraints of the available soil properties, and the limit allowable displacements. Downdrag, and soil liquefaction are additional issues to be considered by the geotechnical specialist. The structural criteria are the provision of sufficient shear and moment strength for the shear and moments developed in the pile due to lateral loading. In addition, the axial tension service stress in the reinforcement should be within the allowable limits corresponding to the allowable crack width (0.25mm for non aggressive environment and 0.20mm for aggressive environment). The pile axial compression stress at the

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allowable pile service load should not exceed 0.25f’c, where f’c is the 28 day compressive strength of the pile concrete. When subjected to lateral loads, the piles in the “front” row receive more load than the piles “behind, in their shadow”. The fraction of loads received by the front piles is obtained from the AASHTO-LRFD 10.7.2.4 formula: Where foundations on piles are used, the following detailing issues must be considered:

-When pile spacing is less than 6 pile diameters, the drilling sequence should be indicated (AASHTO-LRFD 10.8.1.2). -When pile spacing is less than 4 pile diameters, a pile efficiency reduction factor shall be applied (AASHTO-LRFD 10.8.1.2), varying linearly for cohesionless soil from 0.65 to 1 as the pile spacing varies from 2.5 to 4.0 (AASHTO-LRFD 10.8.3.6.3). -Pile spacing should not be less than 2.5 to 3 pile diameters center to center. -The edge distance from a pile to the edge of footing should not be less than 0.3m (AASHTO-LRFD 10.8.1.2). -The pile shall penetrate into the footing a distance of 0.10m to 0.15m; this distance should be added to the calculated footing structural depth.

For preliminary estimation purposes, given the required equivalent allowable bearing stress q_eq, the minimum pile dimensions may be estimated as follows: Dmin = q_eq/400 > 0.80m Lmin = q_eq/14 Where: q_eq = equivalent allowable bearing capacity desired (KPa) Dmin = minimum pile diameter (m) Lmin = minimum pile length (m) (preferably <30.Dpile) The longitudinal reinforcement ratio shall not be less than 0.8% (AASHTO-LRFD 5.13.4.6). It shall extend over the full length of the pile. The longitudinal reinforcement clear spacing shall not be less than 5xmax aggregate size or 125mm (AASHTO-LRFD 5.13.4.6.XXX). The transverse reinforcement diameter shall not be less than 10mm (AASHTO-LRFD 5.10.6). The transverse reinforcement spacing shall not exceed Dpile or 300mm (AASHTO-LRFD 5.10.6). For seismic zones 2, 3 and 4 the following shall apply: Vcs = Vcxmin(1,Pu/(0.1.f’c.Ag)>0) (AASHTO-LRFD 5.10.11.4.1.c) Ash > max(0.3s.h.f’c/fy.(Ag/Ac-1),0.12.s.h.f’c/fy) (AASHTO-LRFD 5.10.11.4.1.d) Lph > 2Dpile (AASHTO-LRFD 5.13.4.6.XXX) Where:

Vcs = concrete shear strength used for seismic design

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Vc = concrete shear strength as of (AASHTO-LRFD 5.8) Pu = ultimate axial force (compression positive) f’c = concrete 28 day compressive strength fy = yield strength of transverse reinforcement Ag = section gross area Ac = confined section area (inside transverse reinforcement) Ash = transverse reinforcement parallel to section dimension h s = transverse reinforcement longitudinal spacing h = section dimension parallel to transverse reinforcement legs Lph = length of plastic hinge where tranverse reinforcement spacing is

reduced by half Dpile = pile diameter

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Material Characteristics Concrete Concrete shall be made using low alkali Portland cement (with less than 0.6% sodium equivalent). Compressive strength Several concrete can be used. The minimum strength requirements shall be as follows:

• For Pre-stressed Concrete Deck f’c = 42MPa • For Reinforced Concrete Deck f’c = 35MPa • For pier and pier cap f’c = 35MPa • For foundations f’c = 30MPa.

Where: f’c is the specified compressive strength of concrete at 28 days (based on tests of cylinders made and tested in accordance with AASHTO Division II, Section 8, “Concrete Structures”). Concrete density Mass density of the reinforced concrete shall be taken is 2.45 t/m3 (AASHTO Division I, § 3.3.6). Young modulus Instantaneous Young modulus for normal weight concrete in MPa shall be calculated using the following equation (AASHTO Division I, § 8.7.1):

cc fE '4730= Long time (differed) modulus shall be taken as the third of instantaneous modulus. Shear modulus Shear modulus of concrete, G, is calculated using the following equation:

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( )υ+=

12cE

G

Poisson’s ratio may be assumed as υ = 0.2

Thermal expansion coefficient According to AASHTO Division I, § 8.5.3, thermal expansion coefficient for normal weight concrete shall be taken as α = 1.08x10-5 per °C. Reinforcement Rebar Only thermo-mechanically treated reinforcement bars of grade 60 conform to ASTM A615 or to AASHTO Division I, § 8.3.3 will be used. Yield strength Minimum specified yield strength fy = 400MPa Young Modulus Modulus of elasticity Es = 200 000MPa (AASHTO Division I, § 8.7.2). Nominal diameter Diameters of rebar can be used are: 10,12, 16, 20, 22, 25, 28, 32, and 40 Maximum length of bars can be used is 12m. Nominal cover The nominal concrete clear cover to be provided for steel reinforcement is:

• 40mm for viaduct superstructures • 50mm for pier shafts and pier caps • 100mm for foundations with concrete in direct contact with the soil.

This cover could be reduced when protective coating (such as bituminous coating, waterproofing membranes…) is provided (depending on Manufacturer’s specifications).

Pre-stressing Steel Pre-stressing steel shall conform to ASTM A416-96a - Uncoated Seven Wire Strands T15 Class 1860MPa Pre-stressing characteristic For strand T15 with corrugated steel ducts, the following characteristics can be adopted:

• Nominal diameter 15.2 mm • Nominal area 140 mm² • Nominal mass 1.102 kg/m • Angular friction coefficient µ = 0.25 rd-1 • Wobble coefficient k = 0.003 m-1 • Low relaxation strand ρ1000 = 2.5%

Tensile stress For low-relaxation strands T15, the tensile stress shall be as follows:

• Ultimate tensile stress f’S = 1860MPa • Yield stress f*y = 1670MPa • Jacking stress 1395MPa (0.75 f’s)

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Young modulus As per ASTM A 416-96a, elasticity modulus shall be taken as: ES = 200 000MPa Pre-stressing units Pre-stressing units are governed by the pre-stressing system. However, the following units are frequently used:

7T15, 12 or 13T15, 19T15, 22T15, 25 or 27T15, 31T15 and 37T15

Anchorage slip shall conform to the pre-stressing system and to the unit used. Average value of 7mm can be considered. Maintenance of bridges For maintenance operation the following requirement shall be considered:

• All bearings shall be accessible for inspection. They shall be replaceable. Train operation will be disrupted when replacing the bearing.

• For box girder bridges, access openings with steel gratings for inspection and maintenance shall be provided in the bottom slab close to the expansion joint piers. In case of isolated bridges this access shall be provided at one location; in case of adjacent bridges, this access shall be provided at intervals not greater than 100m.

• A 3 ton capacity lifting hook shall be embedded in the underside of the superstructure top slab above each access opening.

• A clear space of at least 1.6m high and 1.5m wide shall be provided all along the box girder.

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Design of prestressing cables profile and spacing: The minimum concrete cover is set based on ACI318-7.7.2 and UBC97-1907.7.3 for the required fire resistance (usually 2hr). Then, the tendon profile and spacing are calculated to achieve the required load balancing ratio and average prestress force.

The specific verifications to be performed are:

Checking of stresses during the various phases: The main phases for which the top and bottom slab flexural stresses must be checked are: initial prestressing under self-weight only (may be partial prestress), final prestressing under self-weight and some or all superimposed dead load, prestress after occurrence of all time-dependant losses and in presence of all permanent loads (self weight and superimposed dead loads), and finally prestress after occurrence of all time-dependant losses and in presence of all loads (permanent and live). The flexural stresses must be within the allowable limits for tension and compression stress (ACI318-18.3.3 and 18.4.1 to 18.4.4).

Calculation of passive reinforcement: passive reinforcement is calculated based on two criteria; ultimate flexural strength (ACI318-18.8.2) and total tensile service force (ACI318-18.9.3.2). Moreover, in the case of unbonded tendons, there is a minimum amount of passive reinforcement to be provided (ACI318-18.9).

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Calculation of punching shear reinforcement: prestressed concrete slabs are often quite thin and punching shear becomes a critical item. At least two tendons need to cross over each column in each direction, to prevent catastrophic failure (ACI318-21.11xxx). Punching shear check and punching shear reinforcement are calculated as per ACI318-11.12.2.2.

Calculation of anchor zone reinforcement: the reinforcement of the anchor zone consists of surface reinforcement, bursting reinforcement and diffusion reinforcement (ACI318-18.13, UBC97-1918.13, AASHTO-LRFD-xxx).

Design of columns: The design elements of a cast-in-situ reinforced concrete column include the following items:

Section shape: The column section shape is generally rectangular or circular (but other shapes may occur) and is generally agreed upon with the architect. No drainage pipes should be allowed inside columns. Section dimensions: are determined based on the column length, required fire resistance and column design loads. The transition in dimensions from one floor to the next should be such that the maximum deviation in longitudinal bars does not exeed 1/6 (this is equivalent to 1/3 of the floor thickness as maximum dimension change). Longitudinal reinforcement: is determined based on the column design loads. The reinforcement ratio should range between 0.8% and 4%. Moreover, the minimum bar size should be 12mm. The center-to-center bar spacing should range between 120mm and 150mm. Transverse reinforcement: is determined based on the column design loads. The minimum tie diameter is 10mm. The maximum spacing of ties is the minimum of half the column dimension (for shear resistance), eight times the smallest longitudinal bar diameter (to avoid longitudinal bar buckling), or 200mm (ACI318-xxx). The tie spacing is reduced in the potential plastic hinge region, which extends at least one sixth the column height, largest column dimension, or 450mm (ACI318-21.12.5.2). Outside the plastic hinge region, spacing of transverse reinforcement should conform to ACI318-7.10 and 11.5.4.1. The spacing of tie legs should not exceed 300mm (ACI318-xxx), and should not be much smaller than this value to allow easy access for the concreting tremie. The transverse ties should be continued through the beam-column joint (ACI318-21.12.5.5 and 11.11.2).

The specific verifications to perform are:

Minimum dimensions: to satisfy fire resistance (UBC-xxx) and seismic resistance (UBC-xxx). Column slenderness: and the attendant moment magnification. Flexural strength: is calculated using PCACOL or similar programs.

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Shear strength: is calculated for the applied loads and may take advantage of the shear strength enhancement due to compression caused by axial loads (gravity load cases). Alternatively, a capacity approach may be taken such that the shear strength is larger than the maximum shear that can be caused by the flexural moment strength (fVn > (Mntop+Mnbot)/H, ACI318-xxx). Curvature ductility: In ductile moment resisting frames, the strength reduction factor R implies a displacement ductility factor md = R or (R-1)^2/(2R). A curvature ductility mm = xxx is necessary to achieve the displacement ductility md.

Design of isolated centered footings: The design elements of an isolated centered footing include the following items:

Plan dimensions: The plan dimensions of a footing are determined from bearing stress considerations. For footings with mainly vertical loads (low eccentricity), the plan dimensions are selected such that a constant width overhang is provided outside the column limit. For footings with relatively large moments (high eccentricity) the plan dimensions are determined from bearing stress considerations, using Meyerhoff’s approach (for a reduced uniformly loaded bearing area). Thickness: The thickness of the footing is determined from four considerations: punching shear strength, beam shear strength, flexural reinforcement economy and development length for the column’s longitudinal bars. A minimum thickness of 35cm is recommended. Reinforcement: The footing main reinforcement is flexural reinforcement at the bottom face of the footing. The minimum reinforcement ratio (after applying the 4/3r provision of ACI318-xxx) should be rmin > 0.25ft/fy, where:

-ft = tensile strength of concrete. -fy = yield strength of reinforcement.

The reinforcement on the top face of the footing is calculated for the moment caused by the weight of the overburden soil, but not less than temperature and shrinkage requirements (r > 0.0009). For footing thickness greater than 60cm a side reinforcement of 5cm2/m should be provided along the edges of the footing.

The specific verifications to perform are:

Bearing stress: The net bearing stress due to vertical loads and moments may be checked using Meyeroff’s approach where:

s = Pnet/(Lx’.Ly’) Bearing stress Lx’=Lx-2*ex Effective uniform contact area x length Ly’=Ly-2*ey Effective uniform contact area y length ex = |My|/Pnet Load eccentricity in x direction ey=|Mx|/Pnet Load eccentricity in y direction Pnet Net vertical load (external load + footing weight - overburden weight) Mx Moment about x axis on footing centroid My Moment about y axis on footing centroid

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This verification is done using service load combinations. Stability against overturning: The ratio of overturning moment to restoring moment for x and y directions should be larger than 2. The overturning moment consists of the applied external moment. The restoring moment is the total vertical load (external load+footing weight+overburden weight) multiplied by half the footing length in the concerned direction. This verification is done using service load combinations. Stability against sliding: The ratio of resisting force to sliding force for x and y directions should be larger than 2. The sliding force is the external horizontal force. The resisting force is Fres = m.Ptot+c.Afoot where:

m = coefficient of friction between footing and soil tan(2/3f) Ptot = total vertical force (external load+footing weight+overburden weight) f = internal angle of friction of foundation soil c = foundation soil cohesion

Afoot = footing area This verification is done using service load combinations. Punching shear: The punching shear in the footing due to externally applied ultimate vertical load and moments is calculated at a perimeter at d/2 away from the column limit as per ACI318-xxx. The thickness of the footing should be such that punching shear check is satisfied without having to use punching shear reinforcement. Beam shear: Beam shear in the footing due to externally applied ultimate vertical load and moments is calculated at two orthogonal sections d away from the column limit as per ACI318-xxx. The thickness of the footing should be such that punching shear check is satisfied without having to use punching shear reinforcement. Flexural strength: Flexural strength in the footing due to externally applied ultimate vertical load and moments is calculated at two orthogonal sections at the face of the column limits as per ACI318-xxx. The thickness of the footing should be such that the reinforcement ratio is within allowable limits, the number and spacing of reinforcement bars within acceptable limits, and the overall design is optimized costwise. Calculation of equivalent spring stiffness: In some cases where the distribution of the loads to the foundations is affected by the relative stiffness of the foundations, the stiffness of the foundations in the vertical direction and in rotation about the principal axes needs to be accounted for in the analytical model (instead of the usual fixed base assumption). In those cases, the design shall proceed by iteration, starting with a fixed base calculation, estimating the required footing dimensions, calculating and inserting the corresponding foundation stiffness in the model and redesigning the footings for the new force distribution. The process is repeated until the assumed and the required footing dimensions are within an allowable tolerance (5% or 10cm). The foundation spring stiffness is calculated as follows:

Kz = Af.Ks Kxx = Lx/12.Ly3.Ks

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Kyy = Lx3.Ly/12.Ks Ks = Modulus of subgrade reaction (~120qa) qa = Allowable net bearing capacity.

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX References: 1-AASHTO-LRFD Bridge Design Specifications SI 2007. 2-NCHRP Report 432 High Load Multirotational Bearings. 3-NCHRP Report 449 Bridge Elastomeric Bearings. 4-NCHRP Report 596 Rotation Limits Elastomeric Bearings. 5-NCHRP Report 620 Development of Design Specifications and Commentary for Horizontally Curved Concrete Box-Girder Bridges.

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Terminology: V design speed (m/s) R horizontal radius of curvature (m) g Gravitational acceleration (9.81 m/s2) L Span length (m) S Girder spacing o.c. (m) Dduct Diameter of post-tensioning duct Dps Diameter of prestressing reinforcement f’s Guaranteed ultimate tensile strength f*y Effective yield strength (0.02% offset) fci Concrete strength at day i. < 28 vci Concrete shear strength at day i. < 28 f’c Concrete compressive strength at 28 day vc Concrete shear strength at 28 day Eps Prestressing steel modulus of elasticity Δfs Time dependent prestress loss Eci Concrete modulus of elasticity at day i ES Elastic shortening loss SH Shrinkage loss RH Ambient humidity (%) CRc Creep loss CRs Stress relaxation loss fcir Concrete stress increment at level of prestressing steel centroid at transfer fcds Concrete stress increment at level of prestressing steel centroid due to

superimposed dead load FR Stress fraction below 0.70 f’s due to immediate friction losses P Axial force V Shear M Moment DL Dead load case L+I Live load + impact case RST Imposed deformations case (support settlement, shrinkage, temperature) W Wind load case WL Wind on live load case EQ Earthquake load case lon Longitudinal direction trn Transverse direction

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