Unbonded Tendon Stress Increases in Multi-Span Convention...  Unbonded Tendon Stress Increases in

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  • Unbonded Tendon Stress Increases in Multi-Span

    Members

    Presenter: Marc Maguire William Collins, Kedar Halbe and

    Carin Roberts-Wollmann

  • Unbonded Tendons

    Strain compatibility cannot predict fps

    Many research programs and design codes have empirical or semi-empirical design predictions

  • fps Calibration/Validation

    All design equation predictions were calibrated or validated using mostly simple span test results and very limited multi-span tests

    The largest known database of multi-span tests (Harajili 2006) contains 15 individual tests from only three research programs.

  • fps Calibration/Validation

    Literature suggests the multi-span tests used for design code calibration may not be ideal candidates: Burns, Charney, and Vines (1978)

    6 Tests Brittle Bond Failure Scordelis et al. (1959), Brotchie and Beresford (1967),

    Burns and Hemakon (1977), and more Punching Shear Failure

    Many programs performed collapse load tests on the same specimen multiple times

    Odd test setups

  • Prediction Equations

    Three prediction equations were selected for comparison ACI 318 08 100% Empirical AASHTO LRFD Not Empirical (Mechanical Model) Naaman and Alkhairi (1991) Partially Empirical

  • Current ACI 318 Equation

    '10,000 cps sep

    ff f

    = + +

    Span-to-depth ratio 35: Span-to-depth ratio 35:

    100300

    ==

    psp

    ps

    Ab d

    =

    not greater than lesser of fpy or (fse + 60,000)

  • Current ACI 318 Equation

    '10,000 cps sep

    ff f

    = + +

    Entirely Empirical (Mojtahedti and Gamble 1978)

  • Current AASHTO Equation

    ( )2

    2eLN

    =+

    900 psps pee

    d cf f

    = +

    where N equals number of support hinges crossed by tendon

    zp

    Lp

    L/2L/2

    cdps N=0

  • /2

    /2 /2

    N=1

    N=2

    Current AASHTO Equation

    N=1

    N=2

    ( )2

    2eLN

    =+

    900 psps pee

    d cf f

    = +

  • Naaman and Alkahairi Equation

    Bonded Stress Reduced to Unbonded Stress u = Bond Reduction Coefficient Simple Span Converted to Continuous L1 = Length of Loaded Span L2 = Total Tendon Length

    1

    2

    1psps pe u ps cud Lf f Ec L

    = +

  • Database

    Previous equation calibration combined simple and multi-span data points (Naaman, Mojtahedi, Mattock, Harajili etc.) Note that AASHTO equation IS NOT CALIBRATED

    Should we mix simple and multi-span beams? Mechanisms are similar, but there are significant

    differences in behavior at ultimate Pattern loadings Moment redistribution Strand elongation is over longer distance

    Database was created using same criteria as other test programs

  • Simple Span Database

    Du and Tao (1985) Cooke, Park and Yong (1981) Mattock, Yamazaki and Kattula (1971) Tam and Pannell (1969) Pannell Harajli and Kanj (1991) Campbell and Chouinard (1991) Chakrabarti et al. (1994)

    Total 146

  • Multi - Span Database

    Burns et al. (1978) Mattock et al. (1971) Scordelies et al. (1959) Burns and Hemakom (1977) Lim et al. (2003) Hemakom (1970) Chen (1971) Kosut et al. (1985) Burns et al. (1991) Macgregor (1989) Brotchie and Beresford (1967) Halbe (2007)

    Total 58

  • ACI 318-08 Comparison

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    delta

    fps,

    ksi

    Measured delta fps, ksi

    ACI 318-08 Single Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100C

    alcu

    late

    d de

    lta fp

    s, k

    si

    Measured delta fps, ksi

    ACI 318-08 - Multi-Span

  • AASHTO LRFD Comparison

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta fp

    s, k

    si

    Measured Delta fps, ksi

    AASHTO LRFD Simple Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100C

    alcu

    late

    d D

    elta

    fps,

    ksi

    Measured Delta fps, ksi

    AASHTO LRFD Multi-Span

  • Naaman and Alkhairi Comparison

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta fp

    s, k

    si

    Measured Delta fps, ksi

    Naaman Single Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100C

    alcu

    late

    d D

    elta

    , fps

    , ksi

    Measured Delta fps, ksi

    Naaman Multi-Span

  • Multi-Span Database Shortcomings

    Many of these tests have been used for equation calibration by various researchers! 3 tests ended in shear failure (more were borderline) 15 tests ended in bond failure 8 test used improper test setups The majority of tests did not indicate how fps was

    measured

  • Multi-Span Database Shortcomings

    Remove non-flexural failures: 41 tests remain Remove improper test setups only 33 remain Of the remainder, alternate span loading is

    not very well represented Adjacent Span Loading 22

    Primary hinge forms at negative moment Alternate Span Loading 11

    Primary hinge forms in positive moment

  • 0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    ACI P

    redi

    cted

    fp

    s, k

    si

    Measured delta fps, ksi

    ACI 318-08 - Multi-Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta fp

    s, k

    si

    Measured Delta fps, ksi

    AASHTO LRFD Multi-Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta, f

    ps, k

    si

    Measured Delta fps, ksi

    Naaman Multi-Span

    Trimmed Database

  • 0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    ACI P

    redi

    cted

    fp

    s, k

    si

    Measured delta fps, ksi

    ACI 318-08 - Multi-Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta fp

    s, k

    si

    Measured Delta fps, ksi

    AASHTO LRFD Multi-Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta, f

    ps, k

    si

    Measured Delta fps, ksi

    Naaman Multi-Span

    Adjacent Span

    Loading

  • 0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    ACI P

    redi

    cted

    fp

    s, k

    si

    Measured delta fps, ksi

    ACI 318-08 - Multi-Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta fp

    s, k

    si

    Measured Delta fps, ksi

    AASHTO LRFD Multi-Span

    0

    20

    40

    60

    80

    100

    0 20 40 60 80 100

    Cal

    cula

    ted

    Del

    ta, f

    ps, k

    si

    Measured Delta fps, ksi

    Naaman Multi-Span

    Alternate Span

    Loading

  • Multi-Span Beams Simple Statistics

    R2 values are too low to be of statistical significance! (< 0.1!!!)

    Bias (Calculated)-(Measured) A measure similar to accuracy of prediction Negative Value indicates conservative

    Mean Square Error Bias2 A measure similar to precision of prediction Similar to R2 value Smaller value indicates better fit

    Percent Error 100*|Bias|/(Measured)

  • Multi-Span Beams Simple Statistics

    Whole Multi-span Database Trimmed Database

    Average Bias MSE Average % Error AASHTO -18.01 1164 85%

    ACI -9.75 869 134% Naaman -5.13 1661 224%

    Average Bias MSE Average % Error

    AASHTO -27.40 1801 54%

    ACI -18.68 1406 68%

    Naaman -9.78 2734 208%

  • Multi-Span Beams Simple Statistics

    Whole Multi-span Database Trimmed Database

    Average Bias MSE Average % Error AASHTO -18.01 1164 85%

    ACI -9.75 869 134% Naaman -5.13 1661 224%

    Average Bias MSE Average % Error

    AASHTO -27.40 1801 54%

    ACI -18.68 1406 68%

    Naaman -9.78 2734 208%

  • Multi-Span Beams Simple Statistics

    Whole Multi-span Database Trimmed Database

    Average Bias MSE Average % Error AASHTO -18.01 1164 85%

    ACI -9.75 869 134% Naaman -5.13 1661 224%

    Average Bias MSE Average % Error

    AASHTO -27.40 1801 54%

    ACI -18.68 1406 68%

    Naaman -9.78 2734 208%

  • Statistical Analysis What does this mean?

    There are huge amounts of scatter in the available data from many factors

    It is evident that the current equations do not adequately reflect the behavior of the data set

    All methods are conservative, but the AASHTO and ACI methods seem to be the most conservative

  • Addition to the Database

    Four representative slabs were fabricated at the Thomas M. Murray Structural Engineering Laboratory at Virginia Tech.

    Goal was to add high quality ductile and design relevant, failures to the database.

  • Specimen Design

    Four Representative Slabs Two Continuous 20 ft spans Parabolic 0.5 unbonded tendon Minimum mild reinforcement

  • Testing Scheme

    Moment Redistribution and Pattern Loading Single Span Loading Maximum

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