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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