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

39
Unbonded Tendon Stress Increases in Multi-Span Members Presenter: Marc Maguire William Collins, Kedar Halbe and Carin Roberts-Wollmann

Transcript of Unbonded Tendon Stress Increases in Multi-Span … Convention... · Unbonded Tendon Stress...

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Unbonded Tendon Stress Increases in Multi-Span

Members

Presenter: Marc Maguire William Collins, Kedar Halbe and

Carin Roberts-Wollmann

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Unbonded Tendons

• Strain compatibility cannot predict Δfps

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

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Δfps 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.

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Δfps 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

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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

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Current ACI 318 Equation

'10,000 cps se

p

ff fψρ

= + +

Span-to-depth ratio ≤ 35: Span-to-depth ratio ≥ 35:

100300

ψψ

==

psp

ps

Ab d

ρ =×

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

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Current ACI 318 Equation

'10,000 cps se

p

ff fψρ

= + +

Entirely Empirical (Mojtahedti and Gamble 1978)

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Current AASHTO Equation

( )2

2eLN

=+

900 psps pe

e

d cf f

− = +

where N equals number of support hinges crossed by tendon

zp

δθ

Lp

L/2L/2

cdps N=0

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θ/2

θ

θ

θ/2 θ/2

N=1

N=2

Current AASHTO Equation

N=1

N=2

( )2

2eLN

=+

900 psps pe

e

d cf f

− = +

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Naaman and Alkahairi Equation

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

1

2

1psps pe u ps cu

d Lf f Ec L

ε

= + Ω −

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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

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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

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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

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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

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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

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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

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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 Δfps was

measured

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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

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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

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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

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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

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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)

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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%

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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%

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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%

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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

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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.

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Specimen Design

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

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Testing Scheme

• Moment Redistribution and Pattern Loading • Single Span Loading – Maximum Positive Moment

• Two Span Loading – Maximum Negative Moment

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Instrumentation

• Tendon Force at Anchorages • Deflection at Expected Hinge Locations

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Test Setup

• Four point loading on loaded spans to simulate distributed load

• Concrete blocks for dead load on unloaded span

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Test Results – Load vs. Deflection

• Four

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Test Results – Unloaded Span Failure

• Failure on unloaded span

• Over-strength at second hinge

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Test Results – Unloaded Span Failure

• Recommend minimum mild steel throughout member to prevent brittle failure

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Test Results

• Ultimate Load Comparison:

• All methods result in very conservative ultimate strength

Load Case Max Distributed Load

(lb/ft) (Measured)/(Predicted) Ratio

AASHTO ACI Naaman Specimen 1* South Span 467 1.03* 1.00* 0.99* Specimen 2 North Span 582 1.29 1.24 1.23 Specimen 3 Both Spans 607 1.34 1.28 1.16 Specimen 4 Both Spans 698 1.54 1.47 1.34

Average 1.39 1.33 1.25

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Test Results

• Δfps Comparison:

• Very conservative estimation, even for the premature failure

Load Case Tendon Force Increase

(lb) Estimated

Δfps (psi)

Δfps (Measured)/(Predicted) Ratio

Live End Dead End AASHTO ACI Naaman

Specimen 1 South Span 5,373 2,647 26,209* 1.74 1.17 1.10

Specimen 2 North Span 6,087 6,852 42,284 2.81 1.89 1.77

Specimen 3 Both Spans 8,578 7,419 52,278 3.48 2.34 1.18

Specimen 4 Both Spans 9,110 9,270 60,065 3.99 2.68 1.36

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Summary

• Issues can be identified with many multi-span beam testing programs (including this one) • Failure Modes • Test Setups

• Issues have been identified with the current pool of data, resulting in only 33 tests considered “acceptable”

• This testing program added three data points to the pool

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Recommendations and Conclusions

• Section over-strength should be considered when specifying reinforcement cut-off lengths • OR specify minimum reinforcement as continuous

throughout beam

• AASHTO, ACI and Naaman prediction equations resulted in conservative Δfps predictions for the specimens tested and for the database.

• We need more tests

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References

Brotchie, J. F., and Beresford, F. D., “Experimental Study of a Prestressed Concrete Flat Plate Structure,” Civil Engineering Transactions, V. 9, No. 2, 1967, pp. 276-282.

Burns, N. H.; Charney, F. A.; and Vines, W. R., “Tests of One-Way Post-Tensioned Slabs With Unbonded Tendons,” PCI Journal, V. 33, No. 5, Sep.-Oct. 1978, pp. 52-80.

Burns, N. H., and Hemakom, R. "Test of Scale Model Post Tension Flat Plate," Journal of the Structural Division, ASCE, V. 103, No. 6, Jun. 1977, pp. 1237-1255.

AASHTO, “LRFD Bridge Design Specifications,” American Association of State Highway and Transportation Officials, Washington, DC, 2010, 1632 pp.

ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2008, 473 pp.

Naaman, A. E., and Alkhairi, F. M., “Stress at Ultimate in Unbonded Post-Tensioning Tendons: Part 2- Proposed Methodology,” ACI Structural Journal, V. 88, No. 6, Nov.-Dec. 1991, pp. 683-692.

Scordelis, A. C.; Lin, T. Y.; and Itaya, R., “Behavior of a Continuous Slab Prestressed in Two Directions,” ACI Journal, V.

31, No. 6, 1959, pp. 441-459. Harajili, M., H.; “On the stress in Unbonded Tendons at Ultimate: Critical Assessment and Proposed Chagnes” ACI

Structural Journal, V. 103, No. 6, 2006, pp. 803-812