12.3 Flexure

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  • 112.3.1

    FLEXURAL DESIGN

    z Service Limit State Transformed Section Compute Stresses Compare with Stress Limits

    z Strength Limit Statez Moment - Curvature

    12.3.2General Assumptions for Flexural Design

    z Plane sections before bending remain plane after bending

    z Equilibrium of external forces and internal stresses

    z Compatibility of strains

    12.3.3General Assumptions for Flexural Design of Prestressed Concrete Members

    Service Load Design: Concrete is uncracked Stress in prestressing steel is linearly proportional to strain Iterate to determine strand pattern

    - satisfy stress limits for concrete and prestressing steel

    Check Strength at Critical Sections: Concrete

    - inelastic in compressive regions- tensile strength neglected

    Prestressing steel- inelastic

  • 212.3.4Determine Strand Pattern

    Add strands until stress limits at midspan are satisfied

    Fill rows from bottom Minimum strand spacing

    - LRFD Article 5.10.3.3.1 Minimum Cover Minimum Cover

    - LRFD Article 5.12.3

    Then check stresses at ends

    12.3.5Typical Strand Pattern

    12.3.65.10.3.3.1 Minimum Strand Spacing

    Strand Size (in.) Spacing (in.)0 6000

    Minimum clear distance between starnds at ends of pretensioned girders:

    1.33 x maximum aggregate size 3db

    0.60000.5625 Special

    0.56252.00

    0.50000.4375

    0.50 Special1.75

    0.3750 1.50

  • 312.3.7Minimum Concrete CoverLRFD 5.12.3

    12.3.8Minimum Concrete Cover

    LRFD 5.12.3

    Modification factors for W/C ratio

    z For W/C 0.40 . . . . . . . . . . . 0.8

    z For W/C 0.50 . . . . . . . . . . . 1.2

    Minimum cover to main bars, including epoxy-coated bars = 1.0 IN.

    Minimum cover to ties and stirrups may be 0.5 IN. less than the values specified in Table for main bars, but shall not be less than 1.0 IN.

    12.3.9Design for Flexure at Service Limit State

    Compute Section Properties Determine effective width of deck Transform deck to girder concrete Transform strand (optional)

    Compute Stresses At release At Service Limit State

    - Permanent loads only- Permanent and transient loads

    Compare Stresses to Stress Limits Concrete Prestressing Steel

  • 412.3.10Transform Composite Deck Concrete to Girder Concrete

    Effective deck width - (LRFD 4.6.2.6.1)

    Transformed effective deck width

    Use same modular ratio for short- and long-term effects

    12.3.11Transform Prestressing Steel to Girder Concrete

    LRFD 5.9.1.4

    Section properties may be based on either the gross or transformed section

    Prestressing steel may be transformed using the same procedure used for mild reinforcement

    12.3.12Assumptions for Service and Fatigue Limit States

    LRFD 5.7.1

    The following should apply to modular ratios between steel and concrete:

    the modular ratio, n, is rounded to the nearest integer number,

    the modular ratio is not less than 6.0, and

    an effective modular ratio of 2n is applicable to permanent loads and prestress.- intended to apply to compression

    reinforcement - see Std Specs Article 8.15.3.5

  • 512.3.13Compute Stresses at Release

    Non-Composite Section (Bare Girder)

    Loads Girder dead load Initial prestress

    Top of girder

    Bottom of girder

    b

    gdl

    b

    iiRb

    t

    gdl

    t

    iiRt

    SM

    SeP

    APf

    SM

    SeP

    APf

    +=

    +=

    12.3.14Compute Stresses at Release

    12.3.15Compute Stresses at Service Limit State After Losses with Permanent Loads Only

    Composite Section (Girder + Deck)

    Loads on Non-Composite Section Girder, deck dead loads Other dead loads applied before placing deck

    ( di h )(e.g., diaphragms) Final prestress (after losses)

    Loads on Composite Section Barrier and future wearing surface Other dead loads (utilities, etc.) Vehicular live load

  • 612.3.16Compute Stresses at Service Limit State After Losses with Permanent Loads Only

    Top of deck

    tcd

    cdlPtd S

    Mf =

    Top of girder

    Bottom of girder

    bcg

    cdl

    b

    ncdlgdl

    b

    eePbg

    tcg

    cdl

    t

    ncdlgdl

    t

    eePtg

    SM

    SMM

    SeP

    APf

    SM

    SMM

    SeP

    APf

    ++=

    +++=

    12.3.17

    Compute Stresses at Service Limit State After Losses with Permanent and Transient Loads

    Top of deck

    tcd

    ILLcdlLPtd S

    M Mf +++=

    Top of girder

    Bottom of girder

    bcg

    ILLcdl

    b

    ncdlgdl

    b

    eeLPbg

    tcg

    ILLcdl

    t

    ncdlgdl

    t

    eeLPtg

    SM M

    SM M

    S

    eP APf

    SM M

    SM M

    S

    eP APf

    ++

    ++

    +++=

    ++++=

    12.3.18

    Compute Stresses at Service Limit State After Losses with Permanent and Transient Loads

  • 712.3.19Stress Limits for Prestressing Tendons

    LRFD 5.9.3

    For Pretensioned Construction:

    Low relaxation strand ( fpy = 0.90 fpu ):0 75f Immediately prior to transfer0.75fpu Immediately prior to transfer 0.80fpy At Service Limit State, after

    losses

    Stress Relieved strand ( fpy = 0.85 fpu ):0.70fpu Immediately prior to transfer 0.80fpy At Service Limit State, after

    losses

    12.3.20Stress Limits for Concrete

    LRFD 5.9.4.1.1 and 5.9.4.1.2

    For Temporary Stresses Before Losses (Fully Prestressed Components):

    Compression: Pretensioned components

    Tension (non-segmental bridges):Precompressed tensile zone without bonded

    reinforcement 0.200 KSI Other than precompressed tensile

    zone, and without bonded reinforcementIn areas with bonded reinforcement sufficient to

    resist concrete tensile force (fs = 0.50fy)

    cif0948.0 A/N

    cif 60.0

    cif24.0

    12.3.21

    LRFD 5.9.4.2.1

    For Stresses At Service Limit State After Losses (Fully Prestressed Components):

    Compression (non-segmental bridges):

    Stress Limits for Concrete

    Compression (non-segmental bridges):

    c

    c

    c

    f 40.0

    f 60.0f 45.0

    Permanent loads

    Permanent and transient loads, and during shipping and handlingLive load and 0.5 the sum of effective prestress and permanent loads

  • 812.3.22Stress Limits for Concrete

    LRFD 5.9.4.2.2

    For Stresses At Service Limit State After Losses (Fully Prestressed Components):

    Tension in precompressed tensile zone (other th t l b id )than segmental bridges):

    Components with bonded prestressing tendons other than piles

    Components subjected to severe corrosive conditions

    Components with unbonded prestressing tendons

    tension no

    f0948.0

    f190.0

    c

    c

    12.3.23

    LRFD 5.9.4.2.2

    For Stresses At Service Limit State After Losses (Fully Prestressed Components):

    Tension in other areas (segmental only):

    Stress Limits for Concrete

    Note other tensile stress limits for segmentally constructed bridges.

    cf190.0 If bonded reinforcement is provided which is sufficient to carry the tensile force in the concrete at a stress of 0.5fsy

    12.3.24Control of Stresses at Ends of Pretensioned Members

    The following methods can be used individually or in combination with other methods

    1. Draping, Harping or Deflecting Reduce eccentricity at ends Raise center group of strands until stressRaise center group of strands until stress

    limits are satisfied

  • 912.3.25Control of Stresses at Ends of Pretensioned Members

    2. Debonding, Blanketing or Shielding Reduce prestress force at ends by preventing

    bond of selected strands with concrete Increase number of debonded strands until

    stress limits are satisfied

    12.3.26Special Provisions for Debonded Strands

    Std Specs 9.27.3 requires: Development length for debonded strands is

    doubled

    LRFD 5.11.4.3 further requires: Number of strands debonded 25% of totalNumber of strands debonded 25% of total

    strands Number of strands debonded in any row 40%

    of total strands in that row Exterior strands in each row must be fully

    bonded All limit states must be satisfied

    12.3.27Control of Stresses at Ends of Pretensioned Members

    3. Adding Mild Reinforcement If tensile stress > , but not more

    than , add mild reinforcement to resist 120% of the tensile force

    cif0948.0 cif22.0

    ( )( )s

    toptopcis f

    bx2f2.1A =

    where fs = 0.5 fsy = 30 KSI

  • 10

    12.3.28Control of Stresses at Ends of Pretensioned Members

    4. Adding Top Strands Reduce moment at ends by adding

    strands at the top of the girder Can debond top strands in center

    portion of the girderportion of the girder- Must provide access hole for cutting

    strand

    12.3.29

    5. Increasing Compressive Strength of Concrete at Release,

    Increase until stress limits are satisfied

    Control of Stresses at Ends of Pretensioned Members

    cif

    cif

    Use reasonable value for that can be achieved economically by local producers

    Maintain reasonable balance between cci fand f

    cif

    12.3.30Fatigue Limit State Stress Range Requirements

    LRFD 5.5.3.3

    Prestressing Tendons

    18.0 KSI for radii of curvature in excess of 30.0 FT 10 0 KSI for radii of curvature not exceeding 12 0 FT 10.0 KSI for radii of curvature not exceeding 12.0 FT Linear interpolation may be used between the limits

    Fatigue loading is a design truck (no lane load) with constant axle spacing of 30.0 FT.

  • 11

    12.3.31Basic Assumptions for Design at Streng