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Design Guide for Bridges for Service Life (2013)

Chapter: A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System

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Page 545
Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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Suggested Citation:"A--Design Provisions for Self-Stressing System for Bridge Application with Emphasis on Precast Panel Deck System." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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543 Steel girder bridges often use continuity over the interior supports to reduce interior forces on the spans. In continuous structures with composite concrete decks, the loca- tion of maximum negative bending moment is over the interior supports. This moment produces tensile stresses in the concrete deck and compressive stress in the bottom flanges of the girders. The tensile stress in the deck leads to cracking, which allows in- trusion of moisture and road salt, causing corrosion of the reinforcement and support- ing girders. Continued maintenance is required to forestall the deterioration; however, replacement of the deck is eventually required. To help alleviate this problem, a self-stressing system was developed as part of SHRP 2 Project R19A. Additional details of the development can be found in the forthcoming final report. The method induces a compressive force in the deck that is accomplished by raising the interior supports above their final elevation while the deck is cast (cast-in-place construction) or placed (precast construction). Once the concrete has cured, the supports are lowered to their final elevation. Continuity of the steel member and the composite action with the deck produce a compressive stress in the concrete slab, which is balanced by tensile stresses in the bottom of the steel member. As a result, the cracking over the interior support is reduced, increasing durability. In addition, the need for girder splices may be eliminated, making the overall bridge design more efficient and less expensive than a conventional design. This appendix describes the construction procedure, design considerations, and implementation details for using the self-stressing method. A flowchart is provided to aid in implementation. Simplified formulas applicable to two-span bridges, which represent the most likely use of the method, are also included. A DESiGN pROviSiONS FOR SELF- STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM

544 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE A.1. conStruction Procedure overview This section briefly describes the major steps in the construction procedure in order to establish a frame of reference and to introduce vocabulary used throughout the appen- dix. Table A.1 illustrates the major steps required for constructing a bridge using the self-stressing method. These steps will be used as points of reference in the remaining discussion. The first stage consists of simply placing the girder on the level supports. The resulting moments and deflections are those obtained from a continuous beam analysis. During the second stage, the interior support is raised. The bare steel girder responds as a simply supported beam subjected to an upward directed point load at the location of the interior support. Note that the supports could be in the raised posi- tion before placing the girder. However, due to superposition, the analysis would be the same as described. Next, the concrete deck is cast, or precast panels are placed and grouted. The structure responds like a continuous bare steel beam, just as it would be for conven- tional construction. During the fourth stage, the interior support is lowered to its final position. Just as in Stage 2, the response is that of a beam supported at the exterior supports only and subjected to a point load. However, the structure is now composite and the point tABLE A.1. SeLF-StreSSing method mAjor StePS Step Stage Structure Loading Moment Deflection 1 Place girder on level supports St e p Stage Structure Loading Moment Deflection 1 Place girder on level supports 2 2 Raise interior support 3 Cast concrete 4 Lower interior support 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place girder on level supports 2 2 Raise interior support 3 Cast concrete 4 Lower interior support 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place girder on level su ports 2 2 Raise interior su port 3 Cast concrete 4 Lower interior su port 5 a Relaxatio n 5 b Restoring force St e p Stage Str cture Loading Moment D flection 1 Place gi der on level supports 2 2 Raise inte ior support 3 Cast concr te 4 Lower inte ior support 5 a Relaxatio n 5 b Restoring force 2 Raise int rior support St e p Stage Structure L ading Moment D fl ction 1 Place girder on level supports 2 2 Rais interior support 3 Cast concrete 4 Lower interior support 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place girder on leve su ports 2 2 Rais interior su port 3 Cast concrete 4 Lower interior su p t 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place girder on l v l su ports 2 2 Rais interior su port 3 Cast concrete 4 Lower interior su port 5 a Rel xatio n 5 b Restoring force St e p Stage Str cture Loading Moment Deflection 1 Place girder on level supports 2 2 Raise interior support 3 Cast concr te 4 Lower i terior support 5 a Relaxatio n 5 b Restoring force 3 Cast concrete St e p Stage Structure Loading Moment Deflection 1 Place girder on level supports 2 2 Raise interior support 3 Cast concrete 4 Lower interior support 5 a Relaxatio n b storing force St e p Stage Structure Loading Moment Deflection 1 Place girder on lev l supports 2 Raise interi r support 3 Cast co crete 4 Lower interior support 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place gird r on level supports 2 Raise nt rior s t 3 Cast concr te 4 Lower interior supp t 5 a Relaxatio n 5 b Restoring force St e p Stage Str cture Loading Moment Deflection 1 Place gi d r on level su ports 2 Rai e nterior 3 Cast concr te 4 Lower int ior su port 5 a Relaxatio n 5 b Restoring force 4 Lower i te ior support St e p Stage Structure Loading Moment Defl ction 1 Place gird r on lev suppo ts 2 Raise interio supp t 3 Cast concrete 4 Lower interi supp t 5 a Relax tio n 5 b Restoring forc t t t t i t fl ti l ir r l l rt i t t n r t r i t ri r rt l ti t ri f r t t t t i t fl ti l ir r l l rt i i teri r u p rt t r t r i t ri r rt l ti t ri f r t e t t t i t fl ti l i r l l s rts is i t ri r su port st et r i t i r s rt l ti st ri f r 5a Relaxation St e p Stage Structure Loading Moment Deflection 1 Place gird r on level support 2 Raise interior suppo t 3 Cast concrete 4 Low r interi suppo t 5 a Relaxatio n 5 b Rest ring forc St e p Stage Str cture Loading Mom nt Deflection 1 Place gird r on lev supports 2 Rais interior su p rt 3 Cast re e 4 Lower interior supp rt 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loadi g Moment Deflection 1 Place girder on lev l su ports 2 Rais int r su port 3 Cast concrete 4 Lower int rior su port 5 a Relaxatio n 5 b Restoring force St e p Stage St cture Loading Moment D flecti n 1 Place gi d r on l vel su p rts 2 Rai int i r su port 3 Cast oncr te 4 Lower inte ior su po t 5 a Relaxatio n 5 b Restoring f rce 5b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place gird r on level 2 2 Raise interi r support 3 Cast c ncrete 4 Lower interior supp r 5 a Relaxatio n 5 b Rest ring force St e p Stage Structure Loading Moment Deflection 1 Place girder n level s 2 2 Ra se interior su port 3 Cast concrete 4 Lower interior support 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place girder on level supports 2 2 Raise interior support 3 Cast concrete 4 Lower interior support 5 a Relaxatio n 5 b Restoring force St e p Stage Structure Loading Moment Deflection 1 Place girder on level su ports 2 2 Raise interior su port 3 Cast concr te 4 Lower interior su port 5 a Relaxatio n 5 b Rest ring force

545 Appendix A. DESiGN pROviSiONS FOR SELF-STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM load is directed downward. This action places the concrete deck over the supports into compression. Over time, creep and shrinkage occur in the concrete deck. This may be accounted for in two stages. First, the creep and shrinkage are seen as an applied curvature on the structure. If the beam were simply supported by the exterior supports, this applied curvature would result in additional deflection without inducing additional load. However, because of the continuity, a restoring force is generated that prevents the displacement and results in additional stresses. A.2 deSign conSiderAtionS This section discusses the design issues specific to the use of the self-stressing method. Design of bridges using the self-stressing method should follow the provisions for I-section and box-section flexural members contained in Sections 6.10 and 6.11, respec- tively, of the LRFD Bridge Design Specifications (LRFD specifications) ( AASHTO 2012), except as modified here. A.2.1 general The use of the self-stressing method is limited to straight I- and box-section steel girders and is applicable only to continuous multispan structures with a composite deck. Prac- tical limitations dictate that the method is most likely to be used in two-span struc- tures. Simplified design aids are provided in Section A.5 for structures with two spans. A.2.2 Analysis Two options provided for the analysis of the structure are described in the following section. Note that the analysis methods should only be used when analyzing the con- struction steps associated with the self-stressing method and not the overall analysis procedures covered in Chapter 4 of the LRFD specifications. A.2.2.1 Simplified Analysis The simplified analysis method relies on first-order techniques that disregard time effects in the concrete. These effects are accounted for using conservative correction factors presented in the implementation details portion of the provisions (Section A.3). The correction factors account for the effects of creep and shrinkage in the evaluation of stresses and deflections. As an alternative, advanced methods of analysis may be used that directly evaluate these effects. A.2.2.2 Advanced Analysis Advanced methods of analysis explicitly consider the effects of creep and shrinkage to evaluate stresses and deflections. Several examples of advanced methods are the effec- tive modulus method, adjusted effective modulus method, step-by-step method, and the rate of creep method.

546 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE When the creep and shrinkage strains are known, or otherwise assumed, then LRFD specifications Section C4.6.6 can be used for calculating the resulting stresses and deformations. A.2.3 forces The forces and stresses in all components that arise as a result of the self-stressing con- struction procedure should be considered in evaluating the load effects during design. For the purpose of design, the locked-in prestressing force shall be considered a dead load force applied to the composite long-term section (DC2). LRFD specifications Section 3.4.1 states that when prestressed components are used in conjunction with steel girders, the force effect should be considered as locked- in construction loads. However, in this situation the prestressing forces are being developed by gravity effects rather than applied by prestressing devices. As such, the variability in the resulting stresses will be of the same magnitude as the variability of the dead load effects, which leads to the decision of considering the prestress stress as DC2 loading. Note that the self-stressing procedure will generate tensile stresses in the bottom of the steel girders that will serve to offset some of the compressive dead and live load stresses. The stresses resulting from the self-stressing procedure should be kept sepa- rate from other dead load stress sources, and the minimum load factor for dead load (0.9) should be used. A.2.4 Deflections The final deflected shape is necessary for determining the camber requirements of the girders and can be obtained by summing the deflections from the various construction stages. A.3 deSign Procedure And imPLementAtion detAiLS This section provides a step-by-step procedure for designing a bridge incorporating the self-stressing method. All grout and/or adhesives must be adequately cured before low- ering the interior support. The creep and shrinkage properties of the materials must be compatible with the intended use and properties assumed during analysis. Step 1. Determine Required Amount of Prestress The self-stressing method is a way to introduce compressive stresses in the concrete deck of a multispan continuous beam. The compressive stresses are generally located near the interior supports and therefore work to counter the tensile stresses that arise in this vicinity due to gravity and live loading. The result is a reduction in cracking and an accompanying increase in service life. The magnitude of the prestress that must be applied to achieve the desired effects has been determined based on past experience with decks that have been prestressed using traditional mechanical methods.

547 Appendix A. DESiGN pROviSiONS FOR SELF-STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM Minimum Final Prestress The recommended minimum level of prestress at the top fiber of the concrete deck over an interior support, after all losses, is 750 psi. The simplified (Bernoulli assumption) analysis methods predict a linear variation of stresses through the thickness of the deck, which produces a maximum stress value at the face of the concrete. In practice, creep effects quickly blunt this maximum stress value, resulting in a more uniform stress profile through the depth of the concrete. The prescribed minimum prestress value at the face of the slab is intended to provide a final uniform value over the top half of the slab of 250 psi, which is the value recommended in LRFD specifications Section 9.7.5.3 for longitudinal prestressing of concrete slabs. Figure A.1 shows the initial stress distribution in the concrete deck and the distri- bution that develops after some period of time has elapsed. Initial Final Top of Slab Bottom of Slab 250 σ Figure A.1. Stress distribution in concrete deck. Maximum Initial Prestress The maximum initial prestress to be applied shall be no greater than 60% of the con- crete compressive strength. There is no upper limit recommendation in the literature because the material maximum strength is a natural upper bound. However, to maintain a safe margin, the upper limit shall not be greater than 60% of the concrete compressive strength (0.6 fc′ ), which is the compressive stress limit recommended in LRFD specifications Section 5.9.4.1.1 for pretensioned and posttensioned concrete components, including segmentally constructed bridges. Prestress Adjusted for Losses In lieu of an exact analysis, the prestress loss may be conservatively estimated as 20% when the initial prestress value is less than 40% of the concrete compressive strength, and 30% when the initial prestress value is greater than 40% of the concrete compres- sive strength.

548 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE Equation A.1 gives the initial prestress at the top fiber that is to be applied: r1pi pf s σ σ ( )= − (A.1) where spf = final prestress stress, spi = initial prestress stress, and rs = loss due to creep and shrinkage. Step 2. Calculate Amount of Deflection to obtain Desired Prestress Determine the height to which the interior support must be raised so that on release it will provide the desired amount of prestress. The problem at hand is essentially that of support settlement. How far must the interior support settle so that the stress in the top of the deck is the value chosen in the previous design step? For the following steps (a to d), the structure to be considered is a composite struc- ture being supported at the exterior supports only, as shown in Figure A.2. a. Determine the stress at the top fiber of the deck due to point loading applied at the interior support location. b. Use the result from (a) to solve for the magnitude of the forces required to produce the desired prestress determined in Step 1. c. Calculate the stiffness with respect to point load applied at the interior sup- port location. d. Use the stiffness from (c) to solve for the displacement required to produce the necessary force. L1 L2 P Composite Figure A.2. Equivalent structure used for calculating stresses during lowering of support.

549 Appendix A. DESiGN pROviSiONS FOR SELF-STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM For the structure shown in Figure A.2, this displacement (δ) is given by Equation A.2: δ σ = L L E c3 ts ts 1 2 conc (A.2) where sts = initial prestress stress, L1 = length of Span 1, L2 = length of Span 2, Econc = modulus of elasticity of concrete, and cts = distance from neutral axis to top fiber of slab. Step 3. Determine forces Due to Lifting Bare Steel Beam The results obtained from this step are used to complete the constructability check of the structure. For the following steps, the structure to be considered is the bare steel beam being supported at the exterior supports only, as shown in Figure A.3. Figure A.3. Equivalent structure used for calculating stresses during the raising of support. L1 L2 P Bare Steel a. Calculate the stiffness with respect to point loads applied at the interior sup- port locations. b. Use the stiffness from (a) to calculate the force required to lift the interior sup- ports to the height determined in the previous design step. For the structure shown in Figure A.3, this force is given by Equation A.3: δ ( ) = + P E I L L L L 3 steel steel 1 2 1 2 2 2 (A.3) where P = reaction at support due to deflection of support, d = deflection of support, L1 = length of Span 1, L2 = length of Span 2, Esteel = modulus of elasticity of steel, and Isteel = moment of inertia of bare steel girder.

550 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE c. Using the force given by (b), the reactions, moments, and stresses can be calculated as needed for design. The steel girders and any temporary or permanent support structures must be designed for the concentrated forces that are developed as a result of lifting the girders. End Anchorages The calculated vertical displacement may require a lifting force that is greater than the self-weight of the steel girder, such that the girder would lift off the end supports. In this situation, the exterior ends of the girder may be anchored to prevent uplift. Once the concrete deck is in place, the weight of the deck will replace this anchorage force. Note that loading within the spans can affect uplift at the end supports. Consider the structure shown in Figure A.4. Loading in the first span will create uplift at the end support of the opposite span. Therefore, the progression of deck casting or pre- cast panel placement may affect the need for end anchorages. This possibility must be properly accounted for through either design or the specification of explicit procedures to avoid the condition described. L1 L2 Bare Steel R1 R2 R3 Figure A.4. Loading in Span 1 producing uplift at Support R3. Equation A.4 gives the reaction at the end of Span 2 (unloaded span) caused by the following combination of loading: • Self-weight of the steel girder (wsteel), • An upward displacement of the interior support (δ), and • Uniform load within Span 1 due to deck placement (wdeck). Equation A.4 will aid in evaluating the need and magnitude of end anchorages. The critical condition occurs when Span 1, the loaded span, is longer than Span 2. When the spans are different lengths, the deck within the shorter span should be cast first. δ ( ) ( ) + − − − + w L L L L L E I L L w L L L L 3 8 3 8 steel 2 2 1 2 1 2 2 steel steel 1 2 2 deck 1 3 2 1 2 (A.4)

551 Appendix A. DESiGN pROviSiONS FOR SELF-STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM where wsteel = uniform load due to self-weight of steel, wdeck = uniform load due to deck placement, d = deflection of support (positive upward) L1 = length of Span 1, L2 = length of Span 2, Esteel = modulus of elasticity of steel, and Isteel = moment of inertia of bare steel girder. For the case of two equal spans (L1 = L2 = L), Equation A.4 can be simplified to Equation A.5: δ− − Lw E I L Lw3 8 3 16 steel steel steel 3 deck (A.5) where L is the length of Spans 1 and 2 (equal). End anchorages, when necessary, must be designed to withstand the concentrated force that is to be applied. Step 4. Determine forces and Stresses Caused by Lowering Composite Bridge The forces and stresses imparted on the structure caused by lowering the composite bridge are obtained from a similar analysis to that performed when the amount of deflection was originally calculated in Step 3. For the following steps, the structure to be considered is the composite structure being supported at the exterior supports only, as shown in Figure A.5. Figure A.5. Equivalent structure used for calculating stresses during lowering of support. L1 L2 PReduced Composite a. Calculate the stiffness with respect to a point load applied at the interior sup- port location. b. Use the stiffness from (a) to calculate the equivalent point force caused by the lowering of the support. c. Reduce the force calculated in (b) to account for the prestress loss due to creep and shrinkage, as determined in Step 2.

552 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE d. Using the reduced force applied to the composite structure supported at the ex- terior supports, calculate the internal forces and stresses necessary for design. The resulting forces and stresses from this step should be considered dead load forces applied to the composite structure for the purpose of design. Step 5. Determine Deflected Shape The final deflected shape is necessary for determining the camber requirements of the girders. The final deflection is the summation of deflections from the various construc- tion stages. Bare Steel Deflection Sources of deflection of the bare steel girder are • Self-weight of steel; • Initial lift of interior supports; and • Casting of wet concrete. The deflection due to the self-weight of the steel and casting of the wet concrete is calculated in a conventional manner by using the continuous bare steel structure, as shown in Figure A.6. Equations for calculating the deformation along the length of the beam can be found in Section A.5. L1 L2 Bare Steel R1 R2 R3 w Figure A.6. Structure for calculating bare steel deflections. Calculation of the deflection caused by the initial lift of the interior support is determined considering the bare steel girder supported at the exterior supports only, as shown in Figure A.7. The structure is subjected to point forces applied at the interior supports as determined in Step 3. Equations for calculating the deformation along the length of the beam can be found in Section A.5.

553 Appendix A. DESiGN pROviSiONS FOR SELF-STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM Composite Deflection Calculation of the deflection caused by the lowering of the interior support is deter- mined by considering the composite bridge girder supported at the exterior supports only, as shown in Figure A.8. The structure is subjected to point forces applied at the interior supports as determined in Step 3 without the reduction in load meant to ac- count for creep and shrinkage. Creep and shrinkage have the opposite effect, resulting in an increase of the total deflection. This effect is discussed in the following section. Equations for calculating the deformation along the length of the beam can be found in Step 2. L1 L2 P Bare Steel Figure A.7. Structure for calculating composite deflections caused by lowering the support. L1 L2 P Composite Relaxation Deflection Additional deflections arise due to curvature induced along the beam due to the effects of creep and shrinkage. The resulting loading can be seen in Figure A.9. Figure A.8. Structure for calculating bare steel deflections caused by initial lifting of support.

554 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE The steps for calculating the deflected shape can be performed using the following steps, considering the structure supported at the exterior supports only, as shown in Figure A.10. L1 L2 Composite sh cr Figure A.9. Curvature applied to continuous structure due to creep and shrinkage. L1 L2 Composite sh cr Figure A.10. Structure for determining restoring force. a. Calculate the stiffness with respect to a point load applied at the interior sup- port location. b. Determine the curvature along the length of the beam. The curvature at a section can be obtained from Equation A.6. LRFD specifications Section 5.4.2.3.1 provides methods for determining the values of esh and ecr.

555 Appendix A. DESiGN pROviSiONS FOR SELF-STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM ∫ ε ε( )ϕ = +I z dz 1 c sh cr (A.6) where j = curvature of section, Ic = composite moment of inertia, esh = strain due to shrinkage, ecr = strain due to creep, and z = distance from neutral axis. c. Calculate the displaced shape of the structure due to the applied curvature, as shown in Figure A.11. The displacement can be calculated using the integra- tion given in Equation A.7. ∫∫δ ( ) ( )= ϕx x dx dx xx 00 (A.7) where j(x) is the curvature along the length of the beam. d. Using the stiffness from (a), determine the force required to offset the displace- ment at the support location calculated in (c). e. The resulting deflection due to the relaxation is the sum of the deflections ob- tained from the applied curvature (Equation A.6) and the application of the point load determined in (d) on the structure shown in Figure A.10. Step 6. Carry out Remainder of Design The remainder of the design proceeds as it would for a conventional steel girder bridge with concrete deck. L1 L2 Composite sh cr Figure A.11. Structure for determination of deflection due to curvature.

556 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE A.4 deSign FLowchArt Figure A.12 provides a design criteria flowchart for the conventional design method and the self-stressing design method. Figure A.12. Design criteria flowchart. Design Criteria Conventional design method Calculate loads/stress due to girder weight. Calculate load/stress due to deck weight. Check constructability. (LRFD specifications) Calculate load/stress due to live load. Service limit state (LRFD specifications) Strength limit state (LRFD specifications) Calculate load/stress due to time- dependent effect. Self-stressing design method Choose level of compressive stress. Determine amount of displacement. Calculate load/stress due to lifting. Calculate load/stress due to lowering. Determine force to anchor girder ends. Determine force needed to raise bridge. Determine bridge geometry and dimensions. Figure A.12. Design flowchart.

557 Appendix A. DESiGN pROviSiONS FOR SELF-STRESSiNG SySTEM FOR BRiDGE AppLiCATiON WiTh EMphASiS ON pRECAST pANEL DECK SySTEM A.5 deSign AidS For two-SPAn bridgeS The following figures offer design aids for continuous beam two-span bridges. Figures A.13 and A.14 are for bridges with equal spans, and Figures A.15 and A.16 are for bridges with unequal spans. 1 1 2 2 3 3 3 2 7............................................. 16 5...................................... 8 1............................................. 16 .................................. lwVR lwVVR lwVR V == =+= == 2 max 2 1 2 2 9................... 16 7 49at ............................ 16 512 1(at support ) ............................ 16 (when ) ............................... (7 8 ) 16x wl lwlxM lwRM wl xllxM = = = = < = Figure A.13. Continuous beam—two equal spans—uniform load on one span. 1 1 3 3 2 2 max 1 3....................................... 8 10............................................................. 8 5.................................................... 8 .......... wlR V R V wlR wlV V M ==== = == 2 2 2 4 31xam .................................................. 8 93at ................................................ 8218 (at 0.4215 ,approx.from and ).. 185 wl lwlM wll R R EI = = = Figure A.14. Continuous beam—two equal spans—uniformly distributed load.

558 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE Figure A.16. Continuous beam—two unequal spans—uniformly distributed load. 1 1 1 1 1 3112 1 3 2 112 3 ................................. 2 ........................................ ........................................ ......................................... wl MR V l RRlwR MR l RlwV V = = = = = 3 3 2 1 1 2 2 1 1 ......................................... ....................................... 8( ) when ........... 2max R wlM l l R w xM x R x w = = + = = 1 1 1 1 1 31212 1 2 3 4 2 12 ................................. 2 ........................................ ................................. 2 ......................................... M wlR V l RRlwlwR M wlR V l lwV = = + = + = = + = 1 2 1 323 3 3 2 1 1 1 2 2 11 111 2 3 2 232 ......................................... ....................................... 8( ) when ............ 2 when ............ 2 x x R RlwV wl wlM l l R w xM x R x w R w xM x R x w = + = + = = = = Figure A.15. Continuous beam—two unequal spans—uniformly distributed load on one span.

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TRB’s second Strategic Highway Research Program (SHRP 2) Report S2-R19A-RW-2: Design Guide for Bridges for Service Life provides information and defines procedures to systematically design new and existing bridges for service life and durability.

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