Derivation of Development length in Pretensioned Prestressed [PDF]

code provision on development length of prestressing strands and investigate the bond characteristics, a comprehensive t

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Derivation of Development length in Pretensioned Prestressed Concrete Members Young-Cheol Choi1, a, Ki-Jun Kwon2,b and Sung-Tae Chae1,c 1

Construction Material Research Center, Korea Institute of Construction Materials, 1465-4, Seochodong, Seocho-gu, Seoul, Korea, 137-707 2 Hankyong National University, 267 Seokchen-dong, Ansung-si, Gyeonggi-do, Korea, 456-749 a [email protected], [email protected], [email protected]

ABSTRACT

In pretensioned concrete structure, bond between prestressing steel and concrete is an essential component to ensure the integrity of a pretensioned member. The anchorage and development of the prestressing force are dependent exclusively on bond. For cases such as short pretensioned cantilevers, railroad ties, truss members and similar components with high bending moments near their ends, improved bond conditions are desirable. The purpose of this study is to investigate the characteristics of bond and development length between pretensioned steel and concrete. To resolve the controversy over the adequacy of the current code provision on development length of prestressing strands and investigate the bond characteristics, a comprehensive test program has been scheduled and twenty-four rectangular prestressed concrete beams were tested to determine development length. Major Test variables included diameter of strands (12.7mm, 15.2mm) and concrete covers (3cm, 4cm, 5cm). The test results indicated that the development length increases with strand diameter and decrease with an increase of concrete cover. From the experimental data, the current code provision has tendency to overestimate the bond characteristics of prestressing strand. A theoretical model has been derived to calculate the development length based on the bond stress-slip relation. The proposed model can evaluate realistically the development length of pretensioned prestressed concrete members and can be the good basis for the future basis of code equations on development length of PSC members. KEYWORDS: Development length, Pretension, Flexural bond length, bond-slip relationship

1. INTRODUCTION 1.1 Flexural Bond Mechanics When a pretensioned beam is loaded, tension in the strand must increase to resist the applied moments. As loads increase and concrete cracks, strands are required to carry greater tension. Additional strand tension is resisted by bond stresses. Bond stresses that resist external loads have been called flexural bond stresses. Fig. 1 illustrates bond stress changes along the length of a cracked beam. The illustration shows large increases in steel stress at the crack locations. High increases in steel stress are generated by bond stresses. If a crack occurs in the concrete, the strands must slip for some finite distance on either side of the crack. Slip is dependent on the value of the bond stresses adjacent to the crack. Mechanical interlocking is developed upon cracking: the opening of the crack attempts to pull

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the strand through the concrete. The interlocking of the individual wires with the ridges in the concrete resists strand tension. Figure 1 shows an assumed distribution of bond stresses are highest immediately adjacent to the cracks and decrease with distance away from the cracks. Equilibrium between bond stress and concrete tension must be satisfied. secondary crack M

M

Lt′

Concrete Stress

NPps ∫ f b ( x)dx = f r Act f r: modulus of rupture

0 Umax : max bond stress

Bond Stress

(1)

0

0

Where, N = number of strands Pps = strand perimeter,

f r = modulus of rupture f b ( x ) = bond stress distribution Lt′ = length required resist to addition tension, Act = Tension area of concrete

: Stresses before secondary crack : Stresses after secondary crack

Figure 1. Bond stress adjacent to crack 1.2 Bond Failure Bond failure will occur when external loads require strand tension to increase within the transfer zone. Increase in strand tension cause the strand diameter to reduce slightly resulting in a loss of bond from Hoyer’s effect. When bond from Hoyer’s effect is destroyed, the strands also lose its twist restraint. As the strands are allowed twist, bond stresses from mechanical interlocking begin to lose their effectiveness. The end result is complete bond failure and collapse of the pretensioned member.

2. EXPERIMENTAL PROGRAMS AND RESULTS 2.1 Test variables Twenty-four tests were performed on beams that were rectangular sections. Twelve tests were performed on specimens with 12.7mm strands and twelve tests were performed on specimens with 15.2mm strands. Main variables are nominal diameters (12.7mm, 15.2mm) and concrete bottom covers (30mm, 40mm, 50mm) as shown in Figure 2(a). For each variable, four specimens were fabricated in same condition. The specimen numbering system is given in Figure 2(b).

Cs

15.2mm

13C3-1 Strand Diameter (13=12.7mm,15=15.2mm)

200.0mm

200.0mm

12.7mm

Cs

Cb

Cb

112.7mm

115.2mm

Concrete Cover (C3=30 mm, C4=40 mm,C5=50 mm) The number of the specimen in a particular series

(a) details of cross section Figure 2. Test variables

(b) key to specimen numbering system

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2.2 Transfer length In pretensioned beams, transfer length is the distance required to transfer the fully effective prestressing force from the strand to the concrete. Measured transfer lengths are reported in table 1. All reported measured transfer lengths were obtained with 95% Average Maximum strain Method. Table 1. Measured Transfer lengths Specimen

f ci′ (MPa)

13C3-1 13C3-2 13C3-3 13C3-4

34.88 32.71 34.12 35.41

13C3-1 13C3-2 13C3-3 13C3-4 13C5-1 13C5-2 13C5-3 13C5-4

35.20 35.23 33.37 34.01 34.88 32.71 34.12 35.41

Transfer length (mm)

Specimen

f ci′ (MPa)

Transfer length (mm)

737.5

15C3-1 15C3-2 15C3-3 15C3-4

35.20 35.23 33.37 34.01

874.8

15C4-1 15C4-2 15C4-3 15C4-4 15C5-1 15C5-2 15C5-3 15C5-4

34.88 32.71 34.12 35.41 35.20 35.23 33.37 34.50

668.5

623.5

730.0

674.8

2.3 Development length The instruments included a loading frame, a hydraulic actuator, a spreader beam to create a constant moment region, and support beams that allowed the support locations to be varied from test to test. Development length testing requires that embedment length be varied from test to test. Results from previous tests are used to determine the embedment length for future tests. By varying the support locations, embedment lengths could also be varied accordingly. Figure 3 illustrates a typical loading condition. Embedment length and span were varied from test to test. Actuator Load Cell LVDT

ERSG

Clamp

Displacement Transducer

Test Specimen

LVDT for Deflections measurement Demec Point Clamp

Slip Measuring Device

Figure 3. Instruments of development length test Two types of failures were observed in this test series, flexural failure and bond failure. Flexural failure is evidence by crushing of the concrete after yielding of the strand. The ultimate flexural capacity of the section must be developed. Flexural failures are desirable because they achieve an easily predicted limit state while providing warning before collapse. Results from the beam tests are presented in Table 3. Concrete strain is a good indicator of the failure mode. Generally, if the concrete strain reached or exceeded 0.003 mm/mm, then the failure was probably flexural. Conversely, beams that failed in bond generally did not develop ultimate concrete strain because the strand anchorage failed before large deformations could occur. A flexural failure is demonstrated by Specimen 13C5-3. The calculated

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ultimate flexural capacity of 21.60kN-m was exceeded by the ultimate moment define the test by 21%. Flexural failure occurred at a load of 37.30kN. Concrete strain at the top 0.003194 mm/mm. The slip between concrete and strand does not occur, and there is no abrupt increase of strand strain within transfer zone. This means crack near transfer zone no not occur. Load versus deflection is plotted in Figure 4(a) along with end slips. And Steel strain versus steel gauge location for loading level is plotted in Figure 4(b). 50

16000

3 140.0cm

13C5-3

P

13C5-3

12000

30 Flexural Failure 20

Load

Steel strain

2

Slip (mm)

Load (k N)

40

End slip

Flexural Failure

8000

1 At transfer 1531kg 2147kg 2682kg

4000 10

0 0

15

0

0 45

30 Deflection (mm)

3407kg 3655kg 3701kg 3730kg

0

(a) Load vs. deflection with end slips Figure 4. Flexural failure

400 800 1,200 Distance from the end of beam (mm)

1,600

(b) Steel strain vs. loading level

3

50

127.5cm

13C4-3

P

15000 13C4-3

12000

2 30 Bond Failure Load

20

End slip

Steel strain

Slip (mm)

Load ( kN)

40

1 10

0

9000

Bond Failure

6000 At transfer 1433kg 2366kg 2861kg

3000

0

10

20 Deflection (mm)

30

0 40

3402kg 3833kg 3879kg 3971kg

0 0

(a) Load vs. deflection with end slips Figure 5. Bond failure

400 800 1,200 Distance from the end of beam (mm)

1,600

(b) Steel strain vs. loading level

Table 2. Failure modes and Development length Specimen Number

Failure Mode

13C3-1 13C3-2 13C3-3 13C3-4

F B F B

13C4-1 13C4-2 13C4-3 13C4-4

F B B F

13C5-1 13C5-2 13C5-3 13C5-4

B F F B

Ld

Ld

Specimen Number

Failure Mode

135.0

15C3-1 15C3-2 15C3-3 15C3-4

B F B B

150.0

131.2

15C4-1 15C4-2 15C4-3 15C4-4

S/B F B F

132.0

127.5

15C5-1 15C5-2 15C5-3 15C5-4

B F F B

128.0

(cm)

F: Flexural failure, B: Bond failure, S: Shear failure

1200

(cm)

Bond failure denotes the complete or nearly complete loss of bond strength. Bond failures are characterized by gross displacements of the strands relative to the concrete, and strand end slips into the concrete are noted. Almost beams failing in bond do not develop the full flexural capacity of the section, or if they do, they cannot sustain load capacity through large deformations. Bond failures were typically more sudden and explosive than flexural failures. Bond failure is demonstrated by Specimen 13C4-3. Slip between concrete and strand occurs as shown Figure 5(a), and there is abrupt increase of strand strain within transfer zone because of cracking near transfer zone, Figure 5(b).

3. THEORETICAL DEVELOPMENT OF PRETENSIONED STRAND 3.1 Bond-slip relationships between concrete and strand For the bond-slip relationship of multi-wire strands, the power function is proposed:

 s( x )   f b ( x ) = C   db 

b

(2) Where, C (with dimension of stress) and b are experimental constants. A bond-slip relationship of seven-wire strand was evaluated from test results. The tests carried out for two type of strand (12.7mm strand, 15.2mm strand). The tendon stresses and slips were evaluated from the concrete surface strains and bond stresses were obtained from the change of prestressing force between the points of measurement. A curves in the form of equation (3) were fit by the least squares method providing in Figure 6.

f b, 12.7

 s(x)   = 13.787 d  b 

0.3301

, f b, 15.2

10

0.2688

(3)

8 12.7mm Diameter Strand

15.2mm Diameter Strand

f b = 13.787 (s/ db ) 0.3301 r = 0.91

f b = 9.331 (s/ db ) 0.2688 r = 0.90

Bond stress (MPa)

8

Bond stress (MPa)

 s(x)   = 9.331 d  b 

6

4

6

4

2

2 0

0 0

0.3

0.6 0.9 Slip (mm)

1.2

0

1.5

(a) 12.7mm diameter Figure 5. Bond slip relationship of prestressing strand

0.4

0.8 1.2 Slip (mm)

1.6

2

(b) 15.2mm diameter

3.2 Local flexural length by using bond-slip relationship & design model Considering equilibrium, compatibility, elastic behavior of steel and concrete, governing equation of the phenomenon is given by s( x )′′ − Kf b ( x ) = 0 (4) Where, K =

Pps ( 1 + nρ ) As Es

The governing equation is obtained:

d 2 s(x) Pps (1 + nρ ) = fb ( x ) dx 2 As E s

1201

(5)

Substituting equation (2) into equation (5):

s( x )′′ − KC(

s( x ) 2 ) =0 db

(6)

Assume s( x ) = αx β and substituting it into equation (18): b

1   2 ( 1−b )  ′  K ( 1 − b ) 1  f r Act 1 + b   Lt′ =   , K ′′ = NC  2( 1 + b )  db    Pps K ′′ 1 − b    Where, Act = concrete area in tension, f r = Modulus of rupture, Lt′ = Local flexural length

1−b 1+b

(7)

To prevent bond failure the cracking moment must exceed the applied moment throughout he sum of transfer length and local flexural length. The result of this condition is that the development length becomes a function of the transfer length and local flexural length.

M Ld M = u , Ld = ( Lt + Lt′ ) u Lt + Lt′ M cr M cr

(8)

Development lengths by equation (8) are 4% higher than test results in 12.7mm strand, 9% higher than test results in 15.2mm strand. And Development lengths by equation (8) and test results do not increase linearly as like current provisions. Current provisions have no effect of concrete cover, but equation (8) and test results decrease as concrete cover size. 4. CONCLUSIONS These tests have demonstrated that bond failure of pretensioned strands is prevented if cracking does not occur in the transfer zone of pretensioned strands. Therefore, to prevent anchorage failure, beams should be designed so that no concrete crack will propagate through the transfer zone of a pretensioned strand. Through these tests, following conclusions were obtained: 1. Current code provisions do not reflect actual beam behavior. And the pretensioned strand can be developed in shorter distances than required by the code. 2. Development lengths decrease as concrete cover size in these tests 3. The development of fully bonded strand is approximately proportional to the sum of transfer length and local flexural length for the strand from the moment distribution. ANKNOWLEDGMENT This research was supported by a grant(06-CIT-A02: Standardization Research for Construction Materials) from Construction Infrastructure Technology Program funded by Ministry of Construction & Transportation of Korean government. REFERENCES Cousins, T. E., Francis, L. H., Stallings, J. M., and Simmons, M. B., “Reduced Strand Spacing in Pretensioned, Prestressed Members”, ACI Structural Journal, May-June 1994, pp. 277-286. Deatherage, H. J., and Burdette, E. G., and Chong, K., “Development Length and Lateral Spacing Requirements of Prestressing Strand for Prestressed Concrete Bridge Girders”, PCI Journal, Vol. 39, No. 1, January-February 1994, pp. 70-83. Mitchell, D., Cook, W. D., Khan, A. A., and Tham, T., “Influence of High Strength Concrete on Transfer and Development Length of Pretensioning Strand”, PCI Journal, May-June 1993, pp. 52-66. Russell, B. W., and Burns, N. H., “Measurement of Transfer Lengths on Pretensioned Concrete Elements”, Journal of Structural Engineering, May 1997, pp. 541-549.

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