Analytical investigation and monitoring of end-zone

109PCI Journal | Spr ing 2014

Precast, prestressed concrete bridge girders are widely used in the United States. Longitudinal web cracks, often called end zone cracks, at the ends of

pretensioned concrete girders are commonly observed at the time of strand detensioning, an event generally referred to as prestress transfer or release. During the past two decades, especially with the use of high-strength concrete, deep girders, and high prestressing forces, these cracks have become more prevalent.1,2 Many states, such as Cali-fornia, Nebraska, Florida, Texas, Virginia, and Washington, have developed new I-shaped girders for spans exceeding 200 ft (60 m). These new girders can be as deep as 100 in. (2500 mm) and accommodate in excess of ninety 0.6 in. (15 mm) diameter strands. As a result, end zone cracking has become more prevalent and has received more atten-tion from bridge owners, design engineers, and precast concrete producers. As long as the vertical splitting stresses generated by prestress transfer exceed the tensile capacity of the concrete, end zone cracks will develop and end zone reinforcement will be required to control the width of these cracks, especially at time of prestress transfer. After girders are installed on the bridge many factors help to close the end zone cracks, such as the weight of the deck, barriers, and wearing surface, as well as prestress losses. Also, embed-ding girder ends in the abutment and pier diaphragms helps to cover the majority of the end zone cracks and minimize the potential for reinforcement corrosion.

■ The finite element method was used to investigate the behavior of the end zone reinforcement of 210 ft (64 m) long, 100 in. (2500 mm) deep super girders used in construction of the Alaskan Way viaduct in Seattle, Wash.

■ End zone reinforcement of eight girders was instrumented for this purpose.

■ he finite element analysis accurately predicted the measure-ments collected from the instrumented girders.

Analytical investigation and monitoring of end-zone reinforcement of the Alaskan Way viaduct super girders

Amir Arab, Sameh S. Badie, Majid T. Manzari, Bijan Khaleghi, Stephen J. Seguirant, and David Chapman

Spr ing 2014 | PCI Journal110

In addition to the disagreement on the distribution of end zone reinforcement, some highway authorities require a specific method of anchoring it. For example, the Illinois Department of Transportation requires that the end zone reinforcement consist of 3/4 in. (19 mm) diameter threaded rods welded to a 1 in. (25 mm) thick plate embedded in the bottom flange. The threaded rods are bolted at the top surface of the girder through a 3/4 in. thick plate. The nuts are manually snug tight. Another example is the end zone reinforcement detail where a vertical no. 8 (25M) bar through the center of the girder is bent back into the beam at top and bottom. This bar is installed as close as possible to the end of the girder.

Due to lack of experimental investigations, most decisions by bridge owners to adopt a new end zone reinforcement detail are based on the experience of the design engineers and local precast concrete producers. Because so many pa-rameters potentially affect end zone cracking, experimental investigations can be too expensive for individual state departments of transportation. As a result, some theoretical approaches have been developed to supplement the experi-mental data with the aim of enhancing the effectiveness of end zone reinforcement.

In 1967, Gergely and Sozen developed a method of analysis based on the equilibrium of the cracked end zone.9 This equilibrium analysis procedure is equally applicable to pretensioned and posttensioned concrete members. It can be used as a valuable guide to identify where splitting cracks are expected to be initiated. Nevertheless, it requires assuming a distance for the lever arm between the tension and compression resultants formed at the elevation of the crack.

Castrodale et al.10 have used the strut-and-tie method to analyze pretensioned member end zones for potential cracking. Although the strut-and-tie method is based on strength limit state, which does not contemplate service-ability concerns such as crack width, it can be useful in as-sessing the flow of stresses in the end zone and in locating zones of relatively high tension. Because the strut-and-tie method does not require strain compatibility and because a large number of truss models can be generated for the same problem, the strut-and-tie method typically provides upper-bound solutions, predicting relatively high splitting forces. Castrodale et al.10 found the splitting force to be as high as 12% of the prestress force, compared with the 4% recommended by AASHTO LRFD specifications8 and 3% recommended by Tuan et al.6 In applying the strut-and-tie method to prestressed concrete beam end zones, designers must maintain the steel stress below the limit that would result in undesirable crack widths, about 20 to 24 ksi (140 to 170 MPa). The strut-and-tie method is used qualitatively by many designers. Application of the strut-and-tie method depends on designer knowledge and experience and the rules used for detailing the end zone reinforcement.

In an attempt to address end zone cracking in the 1960s, Marshall and Mattock reported that end zone cracks were consistently observed near the centroidal axis of the member as well as at the interface between the web and the bottom flange.3 At that time, end zone cracking was attributed to the smaller horizontal cross sections of the concrete resisting the vertical tensile forces at release. Their research emphasized that end zone cracks would not likely widen or lengthen during the service life of the member.

Many factors may increase or decrease the likelihood of longitudinal end zone cracking in pretensioned concrete girders. Based on a literature review and survey, Na-tional Cooperative Highway Research Project (NCHRP) report 6542 suggested that factors such as method of de-tensioning, release of the top straight or draped strands before the bottom straight strands, order of release of bottom strands with the flame-cutting method, length of the free strand in the prestressing bed, friction with the bottom form of the prestressing bed, heat concentra-tions during flame cutting, use of lightweight concrete, and radial expansion of the strand following release.1,4–7

Conventional reinforcement is generally placed to limit the cracks to an acceptable width.2 Design of end zone reinforcement details is typically done by estimating the splitting force (vertical tensile force developed at ends of pretensioned precast concrete girders during prestress release) as a percentage of the total prestress-ing force just before release, setting a limit on the stress in the required end zone reinforcement to maintain the crack widths within acceptable limits, and providing a distribution scheme for the end zone reinforcement.

A literature search2 has shown that most design meth-ods require end zone reinforcement to resist up to 4% of the total prestressing force at transfer at a stress not exceeding 20 ksi (140 MPa). However, there is no agreement on how to distribute this reinforcement in the end zone. For example, article 5.10.10.1 of the AAS-HTO LRFD Bridge Design Specifications8 states that it should be located within 1/4 of the depth h of the girder measured from the end of the girder, while research conducted by the University of Nebraska6 and adopted by the Alberta Ministry of Transportation in Canada has recommended that 50% of this reinforcement be placed within h/8 and the remainder between h/8 and h/2 from the member end. Some highway authorities specify limits on the bar size and spacing of the end zone reinforcement. For example, the Washington State Department of Transportation specifies that end zone reinforcement shall not be larger than no. 5 (16M) bars, spacing shall not be less than 21/2 in. (64 mm), and the remaining end zone reinforcement not fitting within the h/4 zone may be placed beyond the h/4 zone at a spac-ing of 21/2 in. (64 mm).


for the Seattle metropolitan area. Span 2C of this project is 210 ft (64 m) long and consists of an 8 in. (200 mm) thick cast-in-place concrete slab supported on seventeen WF100G precast, pretensioned concrete girders. Phase 1 of the construction included eight girders spaced at 6 ft 5 in. (1.96 m) on center, and phase 2 included nine girders spaced at 6 ft (1.8 m) on center. Span 2C has an 11-degree skew and includes four cast-in-place concrete diaphragms at the quarter points in addition to the end diaphragms.

The WF100G girders are each 205 ft (62 m) long and 100 in. (2500 mm) deep. Each girder was pretensioned us-ing eighty 0.6 in. (15 mm) diameter, 270 ksi (1860 MPa), low-relaxation seven-wire strands (Fig. 1). Forty-six straight strands were provided in the bottom flange, twen-ty-six harped strands in five groups were provided in the web, and eight temporary straight strands were provided in the top flange (Fig. 1). The temporary strands were used to control shipping and handling stresses. They were debond-ed over the length of the girder except for a distance of 10 ft (3 m) from each end. These strands were cut through pockets provided in the top flange after the girders were in-stalled on the bridge. All strands were fully pretensioned to a stress of 202.5 ksi (1396 MPa) during jacking. All girder ends were skewed at 11 degrees to conform to the bridge pier geometries and provided with a shear key pattern to provide for shear transfer. Ten no. 7 (22M) bars, marked as item 701 in Fig. 1 and 2, were embedded in the web about 12 ft (300 mm) from both ends of the girder and extended into the cast-in-place concrete pier diaphragm. These bars, along with the shear key pattern, are used to transmit loads from the girder to the piers. No. 3 (10M) cross ties, marked as item 301 in Fig. 1 and 2, are used in the end zone to tie the end zone reinforcement across the web thickness. Fig-ure 2 shows the distribution of the no. 5 (16M) web shear reinforcement including the end zone reinforcement. The bottom flange has no. 3 confinement stirrups. The distribu-tion of these stirrups matches the distribution of the no. 5 web shear reinforcement.

Because precast concrete girders of such magnitude and pretensioning force had not been cast before in the United States, there was moderate concern regarding the response at the time of release, most specifically related to end zone cracking. Therefore, all eight girders of phase 1 were instrumented and monitored to observe and investigate the potential and patterns of end zone cracking at time of release.

The prestressing bed was provided with hydraulic movable abutments that allow gradual transfer of the prestressing force. During prestress release, the girders were lifted from the bed 8 ft (2.4 m) from the girder ends to preclude any binding of the girder to the form. This practice helps to eliminate the friction between the bottom of the girder and the prestressing bed during prestress release. This practice introduced new temporary boundary conditions with a con-

With the advent of supercomputers and efficient com-mercial software packages, many researchers have applied the finite element method to analyze the end zones of pretensioned members.5,11–15 The finite element method pro-vides many advantages over other theoretical approaches. It accurately models concrete and steel behavior using constitutive models that are calibrated against experimen-tal data, recognizes the elastic-plastic behavior of cracked concrete, accurately addresses the transfer length and bond stress distribution along pretensioned strands (that is, linear versus parabolic), and addresses many of the fabrication parameters that affect end zone cracking.

Arab et al.16 used two finite element techniques for the numerical simulation of behavior of pretensioned con-crete girders immediately after the release of prestressing: extrusion and embedment. The analytical results indicated that both techniques are viable methodologies for the finite element modeling of pretensioned concrete members. The extrusion technique provides more detail at the interface of the concrete and released strands (including slippage, transfer length, stress distribution within the transfer length), but it is usually complex and computationally expensive. The embedment technique is generally less complicated and computationally much less expensive. While embedded simulation gives results with acceptable convergence to the extruded simulation, the interaction of the released strands with the concrete matrix within the transfer length is treated as input data and can only be sim-ulated and controlled during the initial conditions through stepwise stressing of the strands. In addition to the model-ing techniques used for the simulation of the pretensioning mechanism, material nonlinearity with proper calibration of the key parameters can affect the response. Depend-ing on the objectives of the analysis, unless the material response remains elastic, accuracy of the finite element analysis is significantly affected and governed by mate-rial nonlinearity and hence the reliability of the selected constitutive models.

This paper presents findings on the analysis of end zone cracking of deep pretensioned concrete I-girders based on nonlinear finite element analysis. It compares the results obtained from the traditional elastic analyses, including the Gergely-Sozen method,9 strut-and-tie method,10 and finite element method.16 Also, the paper provides an alternative closed-form solution that was developed based on shear-friction theory to estimate the tensile stresses in the end zone reinforcement at the web and bottom flange interface.

The finite-element analysis performed in this study was applied to the super girders used to replace a portion of the Alaskan Way viaduct in downtown Seattle, Wash. The project consists of several sub-tasks, including the total replacement of the State Route 99 double-deck viaduct.17 The Alaskan Way viaduct is a vital factor for economic sustainability while serving as a major transportation artery


• At about 69 in. (1750 mm) from the bottom surface of the girder: this height was used after fabrication of the first and second girders because end zone cracks were observed at this height.

• At the interface between the web and the bottom flange: these gauges were installed only on girders 7 and 8 after preliminary results of the finite element analysis showed high shear stresses at this location.

The live and dead end zones of all eight girders exhibited similar cracks during release (Fig. 4). The end zone cracks were concentrated in three specific locations:

• top one-third of the web, where the cracks had 30-de-gree slope and extended about 36 in. (900 mm) from

sequent reversal of stresses during fabrication, which was accounted for in the finite element simulations conducted in this study.

Monitoring end zone reinforcement

Electric resistance gauges were used to monitor the end zone reinforcement of eight WF100G girders of the Alaskan Way viaduct. The strain gauges were mounted on the end zone vertical reinforcement at three different heights (Fig. 3):

• At about 51 in. (1300 mm) from the bottom surface of the girder: the Gergely-Sozen procedure9 was used to determine this height, where splitting cracks are expected to initiate.

Figure 1. Typical cross sections of WF100G girder used on Alaskan Way viaduct. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m.

4 ft 1 in.

1 ft 1 in. 6 in.4 in.

2 in

.

Eight 0.6 in. diameter

4 in

.

at 2

in.

2 in.

21/4 in.

No. 3 (302)

No. 3 (301) cross tie

No. 6 (601)

at 2

in. 41/2 in.

at 2 in.

3 in.

41/8 in. to centroid of six 0.6 in.


Ten

no. 7

(701

) bar

s sp

aced

at 6

in. o

n ce

nter

41/2 in.

31/2 in. 1 ft 1 in.

1 ft

6 in

.

No. 5 (503)

No. 5 (502)

1 in

.

3 in

.3

in.

3 in

.

1 ft 61/2 in.

3 in.

6 ft

6 3 / 8 i

n.3

in.

51 / 8 in.41 / 2 i

n.

61/8 in.

No. 5 (501)



85/8 in. to centroid ofone 0.6 in. diameter strand

1 ft

1 ft 11/8 in.

3 in.

1 in. clear

1 in. clear

3 ft 23/8 in.


the member end face; their orientation is opposite that of regular shear cracks

• bottom one-third of the web, where cracks were almost horizontal and extended about 20 in. (500 mm) from the member end

• at the web and bottom flange junction, where the cracks had very mild slope and extended about 24 in. (600 mm) from the end (Fig. 5)

The width of these cracks ranged from 0.006 to 0.012 in. (0.15 to 0.30 mm).

Table 1 gives the locations of the gauges and the corre-sponding stresses during release. The stresses were calcu-lated using the measured strains in the end zone reinforce-ment and a modulus of elasticity of 29,000 ksi (200 GPa).

Analyzing the information in the table, the following observations were made:

• The strain measured in the end zone reinforcement was greater than the strain capacity of the concrete. This shows that end zone cracking is inevitable and that any numerical procedure used to analyze stresses in this part of the girder should recognize nonlinear (that is, elasto-plastic) behavior of concrete.

• The greatest stress observed at 52 in.(1300 mm), which is the height calculated using the Gergely-Sozen procedure,9 was about 16.9 ksi (117 MPa). This was reported in girder 1 at 6.625 in. (168 mm) from the member end, which is the location of the second row of end zone reinforcement. Girders 2 through 8 showed lower stresses, ranging from 9.3 to 14.2 ksi (64 to 98 MPa).

Figure 2. Longitudinal profile of WF100G girder used on Alaskan Way viaduct. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m.

1 ft 10 in. No. 5 (501)

with no. 5(502) and

pairedno. 3 (302)

No. 5 (501) with

102 ft 71/4 in.

No. 5 (502) and pairedno. 3 (302)

No. 5 (503)

No. 5 (501) with

No. 5 (502) and pairedno. 3 (302)

No. 7 (701) splay tocenterline of harped strands

No. 6

3 in. at 21/2 in. =2 ft 1 in.

No. 3 (301) cross ties not shown for clarity

5 in. = 7 ft 11 in. 6 in.

19 spaces at 5 in. 60 spaces at 1 ft 6 in. = 90 ft

1 ft 41/2 in.

21 ft


• The greatest tensile stresses in the first row of end zone reinforcement was observed at a higher eleva-tion in the web (69.875 in [1775 mm]) and was about 15.6 ksi (108 MPa).

• The Gergely-Sozen procedure9 was not able to predict the high tensile stresses observed at the web and bot-tom flange interface (about 37.3 ksi[257 MPa]). This observation is consistent with the end zone crack pat-tern observed at the web and bottom flange interface (Fig. 5) and with the findings of Dunkman et al.18

• The occurrence of the greatest stress at the web and bottom flange interface should be expected with deep girders having thin webs. Because the bulky bottom flange houses a large number of pretensioned strands and is well confined, it tends to act separately from the web, generating high shear stresses across the interface with the web. According to the shear friction theory, the end zone reinforcing bars crossing the interface act as shear dowels clamping the web and the bottom flange together, producing high stresses at the interface. The following section presents a simple procedure to determine the stresses in the end zone reinforcement using the shear friction theory.

• The greatest stresses close to the bottom of the web demonstrate the importance of anchoring the web rein-forcement in the bottom flange. To reduce the required development length of the end zone reinforcement, the standard hook detail may be used and the develop-

Figure 3. Strain gauges mounted on end zone reinforcement. Note: no. 5 = 16M; no. 7 = 22M.

Figure 4. Web cracks observed in WF100G girders. Note: 1 in. = 25.4 mm.

Figure 5. Web and bottom flange interface cracks observed in WF100G girders. Note: 1 in. = 25.4 mm.


Girder Gauge numberGauge height from bottom surface, in.

Distance from member end, in.

Tensile stress, ksi Gauge location

G1

R1 52.000 3.000 5.5 W

R2 52.000 5.625 16.9 W

R3 52.000 8.375 12.9 W

R4 52.000 11.250 15.4 W

R5 52.000 13.875 14.2 W

R6 52.000 19.375 9.1 W

R7 52.000 24.750 0.7 W

R8 52.000 30.312 4.7 W

G2

R1 52.000 3.000 10.3 W

R2 52.000 5.6250 12.9 W

R3 52.000 8.375 11.5 W

R4 52.000 11.250 10.5 W

R5 52.000 13.875 9.8 W

R6 52.000 19.375 4.1 W

R7 52.000 24.750 1.6 W

R8 52.000 30.312 1.2 W

G3

R1 69.500 3.000 14.0 W

R2 63.000 5.500 13.1 W

R3 52.000 8.375 14.2 W

R4 52.000 10.375 13.9 W

R5 52.000 12.625 12.7 W

R6 52.000 13.250 10.1 W

R7 52.000 22.375 8.8 W

R8 52.000 28.000 7.2 W

G4

R1 69.875 2.000 15.6 W

R2 63.000 5.000 13.5 W

R3 52.000 7.500 12.5 W

R4 52.000 9.750 13.1 W

R5 52.000 12.000 11.7 W

R6 52.000 17.875 6.2 W

R7 52.000 22.500 9.1 W

R8 52.000 28.250 NA W

G5

R1 69.000 2.250 13.7 W

R2 63.500 5.250 13.2 W

R3 57.500 7.750 12.6 W

R4 51.000 10.750 10.1 W

R5 51.000 13.500 10.7 W

R6 51.000 18.500 10.1 W

R7 51.000 23.750 7.9 W

R8 13.500 2.750 19.5 W/BFI

Table 1. Location of gauges installed on the end zone reinforcement and measured stress during release


Girder Gauge numberGauge height from bottom surface, in.

Distance from member end, in.

Tensile stress, ksi Gauge location

G6

R1 69.000 3.250 8.8 W

R2 63.000 5.750 12.6 W

R3 56.75 9.500 9.5 W

R4 52.000 12.500 9.7 W

R5 52.000 15.500 9.6 W

R6 52.000 21.750 10.3 W

R7 52.000 27.750 8.3 W

R8 52.000 33.750 5.0 W

R9 12.250 3.500 37.7 W/BFI

R10 12.500 5.750 30.6 W/BFI

R11 12.500 9.000 NA W/BFI

R12 11.750 12.000 7.1 W/BFI

G7

R1 69.25 3.250 9.9 W

R2 63.000 5.500 10.9 W

R3 57.000 7.250 12.7 W

R4 51.000 10.500 11.7 W

R5 51.000 13.250 9.0 W

R6 51.000 18.500 9.4 W

R7 51.000 23.500 6.6 W

R8 51.000 29.250 6.3 W

R9 12.000 3.250 25.7 W/BFI

R10 12.500 5.500 23.9 W/BFI

R11 13.000 8.000 14.6 W/BFI

R12 12.500 10.500 24.9 W/BFI

R13 49.000 11.500 1.1 CT

R14 49.000 21.500 1.1 CT

R15 25.000 11.500 0.6 CT

R16 25.000 22.000 1.3 CT

G8

R1 69.000 4.000 9.8 W

R2 63.000 6.500 11.4 W

R3 57.000 9.500 13.6 W

R4 51.000 12.500 12.3 W

R5 51.000 15.000 12.4 W

R6 51.000 21.000 10.0 W

R7 51.000 26.500 6.5 W

R8 51.000 32.000 NA W

Note: CT = cross ties; W = web; W/BFI = web and bottom flange interface. 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.

Table 1. Location of gauges installed on the end zone reinforcement and measured stress during release (cont.)


to reduce the number of the cross ties by 50% in future projects. Also, electric resistance gauges were mounted on one strand in the bottom flange for a distance of 36 in. (900 mm) from the end face of the girder to investigate the distribution of strand stress and the actual transfer length of the 0.6 in. (15 mm) strands (Fig. 6). The stress-es reported by these gauges indicated that pretensioning transfer occurs along a parabolic path instead of linearly as prescribed by the AASHTO LRFD specifications.8 About 34% of the pretensioning force was transferred to the girder at 6 in. (150 mm) from the member ends. Sub-sequently, 80% and finally 100% of the transfer occurred at 18 in. (460 mm) and 34 in. (910 mm) from the mem-ber ends, respectively (Fig. 7). Therefore, linearization of transfer length as recommended by AASHTO LRFD specifications and widely assumed in the current practice may result in significant underestimation of the tensile stresses developed in the end zone immediately after release. Also, the gauge measurements showed that actual transfer length of the 0.6 in. (15 mm) strands is smaller than 60 times the strand diameter, 60db, recommended by the AASHTO LRFD specifications.

ment length can be prorated to develop about 40 ksi (280 MPa) rather than the full yield strength of the steel.

• The greatest stress, observed at the web and bottom flange interface, is about 85% higher than the 20 ksi (140 MPa) recommended by the AASHTO LRFD specifications.8

• The greatest stress observed in the end zone reinforce-ment is at about 6 in. (150 mm) from the end face of the girder, which is about 6% of the girder height. This observation is consistent with the findings of Tuan et al.6 and NCHRP 6542, which recommend that 50% of the end zone reinforcement be provided within 1/8 of the depth of the girder (h/8) from the end and the remainder between h/8 and h/2 from the end.

Low tensile stresses were observed in the web cross-tie bars (0.6 to 1.3 ksi [4 to 9 MPa]), demonstrating that these ties have no structural significance while complicat-ing placement of the reinforcement in this congested area of the girder. Based on this observation, WSDOT decided

Figure 6. Strain gauges mounted on one of the strands of the bottom flange.


the concrete. The basic concrete properties at the time of release were provided by the fabricator (Table 2). The con-stitutive model was calibrated through an iterative process to obtain the simulation parameters.

Figure 9 shows the compressive and tensile stress-strain model used in this study. Calibration of the constitutive model was performed by analyzing the response of a 2 × 8 in. (50 × 400 mm) prism to uniaxial compressive and tensile straining. Figure 9 also shows the convergence of the response of the calibrated models toward the theoreti-cal uniaxial compressive and tensile stress-strain curves, respectively, after several iterations.

Transfer length

As described earlier, one characteristic of the embedment technique is that the transfer length and distribution of the strand stress within the transfer length are treated as model inputs. In the finite element model developed by the authors for the girders of the Alaskan Way viaduct, the elements simulating the strands were subjected to an initial condition (prestressing) in accordance with a parabolic relationship (Eq. [1]). This equation was developed based on the measurements taken from strain gauges on the

Numerical simulation

The finite element simulations were performed using a commercial software package. Due to the complexity of the reinforcement and the geometry of the girder, the embedment technique was used for the numerical simula-tion. Figure 8 shows a typical finite element simulation of the girders using the embedment technique. The concrete girder was modeled and analyzed using three-dimensional continuum brick elements, while the prestressing strands were modeled as truss members. Nonprestressed reinforce-ment, such as end zone, shear, and confinement bars, was modeled using three-dimensional beam elements with shear stiffness. The finite element model accounted for the skewed end faces of the girder. This was achieved by con-structing the model with the corresponding end skew and embedding the end zone reinforcing bars in conformance with the splayed reinforcement details as indicated on the shop drawings. More details on the finite element model can be found in Arab et al.16

Calibration of constitutive model

The concrete damage plasticity constitutive model16 was used for the simulation of the elasto-plastic response of

Figure 7. Normalized measured strand stress. Note: 1 in. = 25.4 mm.


study conducted earlier by the authors on a 12 × 12 in. (300 × 300 mm), 12 ft (3.7 m) long concrete prism rein-forced with a single concentric 0.6 in. (15 mm) diameter strand modeled using the extrusion technique.19 The study showed that the transfer relationship follows a parabolic pattern rather than the bilinear simulation recommended by the current specifications and that the transfer length of the strand is significantly affected by the input value of the coefficient of friction between the strand and the surround-ing concrete.

Simulation of pretensioning

Pretensioning of the strands and the release mechanism is simulated based on the strain compatibility between strand and concrete. The strain-compatibility technique includes the following steps:

monitored girders of the Alaskan Way viaduct, as discussed earlier (Fig. 7).

fx = (0.000006x3 - 0.0013x3 + 0.0667x)fpi (1)

where

fx = strand stress at distance x at release

fpi = maximum strand stress at release

x = distance measured from the end of the pretensioned member

Deviation from the bilinear transfer relationship and the 60db transfer length recommended by the AASHTO LRFD specifications8 were detected in a separate finite element

Figure 8. Typical components of finite element model of WF100G girders using embedment technique. Note: no. 5 = 16M; no. 7 = 22M.

No. 5 (502)No. 5 (503)

No. 5 (501) paired

No. 3 (302)

No. 5

No. 5

No. 7

No. 6No. 6

Table 2. Summary of concrete constitutive parameters used in finite element analyses

Parameter Value

Compressive strength at release 'cif 8.00 ksi

Modulus of rupture at release fri = 0.24 'cif 0.679 ksi

Unit weight wc: Plain concrete Reinforced concrete

0.157 kip/ft3

0.165 kip/ft3

Modulus of elasticity at release Eci = 33,000(wc)1.5 'cif 5784 ksi

Poisson’s ratio νc 0.20

Note: 1 ft = 0.305 m; 1 kip = 4.448 kN; 1 ksi = 6.895 MPa.


compares it with end zone cracking reported from the monitored girders (Fig. 11). The finite element results indicate that the lower two-thirds of the web down to the interface with the bottom flange experienced principal stresses higher than the modulus of rupture at release (red area in Fig. 10), which resulted in material softening and subsequent stress redistribution within the end zone. This area extends from the member end face up to approximate-ly 24 in. (610 mm) inside the girder, which is about h/4. The stress distribution shows perfect correlation with the AASHTO LRFD specifications8 requirements of distribut-ing the end zone reinforcement within a distance equal to h/4 from the girder end. However, the stress distribution shows that relatively high stress concentration extends be-yond h/4 to about h/2 (orange and yellow areas in Fig. 10), where no end zone reinforcement is provided according to the AASHTO LRFD specifications recommendation. This observation is consistent with the end zone cracking reported in the monitored girder (Fig. 11).

The authors believe that the recommendation of Tuan et al.6 to place 50% of the end zone reinforcement within h/8 and the remainder of the end zone reinforcement between h/8 and h/2 would better match the stress distribution obtained by the finite element analysis. Figure 10 also indicates the potential for end zone cracking at the web and bottom flange interface close to the member end (red,

1. Deactivate the strain compatibility to decouple the strands and concrete host.

2. Apply the pretension to the strands as initial condi-tions.

3. Apply the boundary constraints to the concrete host.

4. Activate the strain compatibility, which simulates the release of the strands.

Model verification

Table 3 compares the theoretical top- and bottom-fiber stresses at midspan with the corresponding values obtained by the nonlinear finite element analysis. Comparison of the results indicates acceptable convergence between the theoretical and numerical results. It also shows that the in-clusion of the end zone, shear, and confinement reinforce-ment does not significantly affect the longitudinal stresses at the top and bottom fibers at midspan, consistent with the assumptions of beam theory.

Numerical analysis results

Figure 10 shows the maximum principal stress distribu-tion at the member end along the length of the girder and

Figure 9. Comparison of stress-strain relationships of concrete obtained by constitutive model and theoretical stress-strain curves. Note: positive values correspond to compression. 1 in. = 25.4 mm; 1 psi = 6.895 kPa.


TO LRFD specifications.8 The finite element simulations predicted the location of the highest tensile stresses in the end zone bars consistent with observations obtained from the monitored girders.

Horizontal shear

Figure 13 shows the horizontal shear stress contour at the member end along the length of the girder. The transfer of the axial pretensioning from the bottom flange upward into the web resulted in significant concentration of shear stress at the interface between the web and the bottom flange. This shear transfer mechanism is anticipated to be due to the shear-lag caused by the difference in the magnitude of pretensioning in the bottom flange and web. The maxi-mum planar shear stress was observed at a height of 14 in. (360 mm) from the bottom of the bottom flange, 13/8 in. (35 mm) above the web and bottom flange interface. Be-yond the optimum height of 14 in., the planar shear stress significantly decreased as the height along the member web increased. The shear concentration was eventually resolved into the web over a distance approximately equal to the member height h.

The shear lag is believed to be a strong contributor to the cracking in the vicinity of the web and bottom flange, increasing the tensile stresses in the end zone reinforce-ment along the corresponding zone. The area where the greatest shear stresses were detected (gray area in Fig. 13) started at about h/8 and extended to 0.7h from the end of the girder. This observation detected by the finite element analysis is consistent with the cracks observed in the moni-tored girders (Fig. 5). Also, it is consistent with the high tensile stresses measured in the end zone reinforcement bars at the interface (Table 1).

In accordance with article 5.8.4 of AASHTO LRFD specifications,8 the interface shear transfer comprises two

orange, yellow, and green areas). This observation is con-sistent with the high tensile stresses measured in the end zone bars at the interface and end zone cracks (Fig. 5).

Figure 12 shows the distribution of the axial tensile stresses in the end zone bars provided by the finite ele-ment analysis and compared it with the stresses reported from the monitored girders as well as those obtained from the Gergely-Sozen procedure.9 The axial tensile stress distribution provided by the finite element analysis is ob-tained at 3.5, 5.25, and 10.75 in. (90, 134, and 273 mm) from the member end, respectively. The finite element analysis shows that the highest tensile stress is observed close to the web and bottom flange interface and at a lower height than that computed by the Gergely-Sozen procedure.9 Figure 12 also shows that the highest tensile stress detected by the finite element analysis occurs at the first row of end zone bars (at 3.5 in. [90 mm]) and is about 20 ksi (140 MPa), as recommended by the AASH-

Figure 10. Principal stress distribution in concrete along end zone at release. Note: h = depth of girder.

Table 3. Comparison of results obtained by the finite element analysis versus the closed-form solutions based on elastic beam theory

Nonlinear finite element analysis Closed-form solution (elastic theory analysis)

, %

With reinforcing bars

Without reinforcing bars

With reinforcing bars

Without reinforcing bars

Stress in extreme top fiber at midspan, ksi* 1.490 1.490 1.502 -0.80 -0.80

Stress in extreme bottom fiber at midspan, ksi* 4.188 4.188 4.124 1.53 1.53

Deflection at midspan, in.† 2.736 2.736 2.356 16.13 16.13

* Positive stresses correspond to the state of compression† Positive deflection indicates upward displacementNote: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.


Pc = permanent net compressive force

Upon the formation of the crack, the contribution by cohe-sion has already been overcome by the magnitude of the planar shear and can therefore be ignored. Also, because the girders were lifted from the bed during the process of detensioning, the entire contribution by weight of the girder above the interface level Pc can be ignored. There-fore, Eq. (2) is rewritten as Eq. (3):

(3)

where

(fEZR,S)average = average allowable end zone reinforcement stress

ΔVshear = difference between the pretensioning force generated by bonded strands below and above the web and bottom flange interface

Equation (3) can be used to estimate the average stress in the end zone reinforcing bars due to the anticipated shear lag, if Avf is known. Also, Eq. (3) can be used to estimate the required amount of the end zone reinforcement, assum-ing that the allowable stress fEZR,S equals 20 ksi (140 MPa)and the friction factor µ equals 1.4 for normalweight con-crete placed monolithically.

Confinement reinforcement

Figure 14 shows the distribution of the lateral stress in concrete in the bottom flange at two elevations, 1.5 and 12.625 in. (38 and 321 mm) from the bottom surface of the girder. The figure shows that relatively high lateral tensile stresses are generated close to the member end and extend a distance about 1.5h from it. This observa-tion indicates the importance of providing confinement reinforcement within this distance as stipulated by the AASHTO LRFD specifications. Fig. 14 shows that mini-mum confinement reinforcement is also needed at the draping point.

Figure 15 shows the distribution of the axial tensile stress in the confinement reinforcement. The largest recorded tensile stress was about 6.5 ksi (45 MPa) at 25.5 in. (650 mm) from the member end. This low tensile stress shows that no. 3 (10M) steel bars are sufficient to confine the bottom flange even with a large number of strands.

Cross ties

The finite element analysis also shows that the tensile stresses detected in the no. 3 cross ties were low. The

important parameters: cohesion at the interface and the friction resistance (Eq. [2]):

Vni = cAcv + µ(Avf fy + Pc) (2)

where

Vni = nominal interface shear resistance

c = cohesion factor

Acv = area of concrete section resisting shear transfer

µ = coefficient of friction

Avf = area of shear-friction reinforcement

fy = specified minimum yield strength of reinforcing bars

Figure 11. Region at end of beam monitored for end zone cracking. Note: h = depth of girder.


little role in the performance of the end zone of the girder. The authors recommend eliminating these ties.

Conclusion

This paper presents some key results of the analytical investigation and monitoring of end zone reinforcement of eight super girders during prestress release in the casting yard. All eight were production girders for the Alaskan Way viaduct in Seattle, Wash. Field observations indicated that the super girders responded to the release of pretensioning similarly to other I-girders commonly used in practice. They experienced end zone cracking immediately after release, including a typical network of splitting cracks along the web height and the web and bottom flange interface.

The most severe tensile stresses were measured along the web and bottom flange interface. Similar observations were made at both dead and live ends of the girder. These cracks were generally observed to originate at the end face extending approximately 2 ft (600 mm) toward the mid-span of the member. The maximum tensile stresses in the end zone bars were measured at 16.9 and 37.7 ksi (117 and 260 MPa) along the web height and at the web and bottom

greatest tensile stress was 0.9 ksi (6 MPa). This observa-tion is comparable to the tensile stresses detected in the monitored girders and demonstrates that the cross ties have

Figure 12. Axial tensile stress in end zone reinforcement bars obtained from finite element analysis compared with measured stresses from monitored girders. Note: EZR = end zone reinforcement. 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.

Figure 13. Horizontal shear stress contour in concrete at member end immediately after prestress release. Note: h = depth of girder.


of 0.6 ksi (4 MPa) to a maximum of 1.3 ksi (9 MPa) im-mediately after release. Therefore, it was concluded that the web tie bars do not significantly contribute to the resistance against lateral stresses.

The analytical stresses correlate well with the results obtained from the monitored girders. The finite element analysis showed that material nonlinearity should be con-sidered to accurately predict the behavior of the end zone. In addition to nonlinear finite element simulation, three closed-form solutions were used to analyze the end zone stresses immediately after the release of pretensioning: the Gergely-Sozen method, the strut-and-tie procedure, and the shear-friction analogy. The latter method is proposed based on the findings of this research, indicating that significant planar shear transfer occurs at the web and bottom flange interface. The concentration of the straight strands in the bottom flange in combination with the relatively narrow web is anticipated to cause a shear lag at the web and bot-tom flange interface, which can potentially cause cracking along the member end zone. The following observations were made:

• Per the current AASHTO LRFD specifications recom-mendation, the end zone reinforcement should be

flange interface, respectively. The tensile stresses (16.9 ksi maximum) in the web height conformed to the allowable stress recommended by AASHTO LRFD specifications. However, the maximum tensile stresses at the web and bottom flange interface (37.7 ksi) were approximately 85% higher than the allowable tensile stress.

The electric resistance gauges mounted on some of the strands in the bottom flange indicated that pretension-ing transfer occurs along a parabolic path instead of the linear transfer length prescribed by the AASHTO LRFD specifications. It was observed that 34% of the pretensioning force was transferred to the girder within 6 in. (150 mm) of the member ends. Subsequently, 80% and finally 100% of the transfer occurred within 18 and 36 in. (460 and 910 mm) from the member ends, respectively. Therefore, linearization of transfer length as recommended by AASHTO LRFD specifications and widely assumed in current practice may result in signifi-cant underestimation of the tensile stresses developed in the member end zone immediately after the release of pretensioning.

The experimental observations also indicated that the tensile stresses in the web tie bars vary from a minimum

Figure 14. Distribution of lateral stress in bottom flange along length of girder. Note: h = depth of girder. 1 in. = 25.4 mm; 1 psi = 6.895 kPa.


inaccurately predicts its vertical location.

• The maximum tensile stress in the end zone reinforce-ment estimated by shear-friction analogy is consistent with experimental observations.

As shown in this research, the current AASHTO LRFD specifications for the design of splitting reinforcement may not adequately address the shear-lag phenomenon along the web and bottom flange interface. Therefore, the pro-posed closed-form solution based on shear friction theory may offer another alternative for estimating the tensile stresses in the end zone reinforcement along the web and bottom flange interface.

Acknowledgments

This study was conducted to complement the results of the National Cooperative Highway Research Program 18-14 project, “Evaluation and Repair Procedures for Precast/Prestressed Concrete Girders with Longitudinal Crack-ing in the Web.” This study was sponsored by the Civil and Environmental Engineering Department of George Washington University in Washington, D.C.; Concrete Technology Corp. in Tacoma, Wash.; and the Washington State Department of Transportation (WSDOT). Many

distributed within a distance of h/4 from the girder end, and no end zone reinforcement is required beyond h/4. However, based on the findings observed from the presented study, 50% of the end zone reinforcement should be placed within h/8 and the remainder of the end zone reinforcement should be placed between h/8 and h/2.

• The maximum tensile stress (20.2 ksi [140 MPa]) in the end zone reinforcement detected by the nonlinear finite element solution corresponds to the mean of the experimental data.

• The strut-and-tie procedure results in a maximum tensile stress in the end zone bars near the end of the member, in agreement with the corresponding maxi-mum experimental measurement.

• The Gergely-Sozen method and shear-friction analogy result in similar maximum tensile stresses but at differ-ent heights along the member, 51 and 125/8 in. (1300 and 320 mm) in the web and the interface between web and bottom flange, respectively.

• The Gergely-Sozen method overestimates the maxi-mum tensile stress in the end zone reinforcing bar and

Figure 15. Distribution of tensile stress in confinement reinforcement obtained from the finite element analysis. Note: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.


10. Castrodale, R. W., A. Lui, and C. D. White. 2002. “Simplified Analysis of Web Splitting in Pretensioned Concrete Girders.” Proceedings, PCI Annual Conven-tion/National Concrete Bridge Conference, Nashville, TN, October 6-9.

11. Kannel, J., K. French, and H. Stolarski. 1997. “Re-lease Methodology of Strands to Reduce End Zone Cracking in Pretensioned Concrete Girders.” PCI Journal 42 (1): 42–54.

12. Stephen, E. 2006. “Simulation of the Long-Term Behavior of Precast/Pretsressed Concrete Bridges.” Master of Science Thesis, University of Cincinnati, Department of Civil and Environmental Engineering.

13. Rabczuk, T., and J. Eibl. 2004. “Numerical Analy-sis of Prestressed Concrete Beams Using a Coupled Element Free Galerkin/Finite Element Approach.” International Journal of Solids and Structures 41: 1061–1080.

14. Ayoub, A., and F. Filippou. 2010. “Finite-Element Model for Pretensioned Prestressed Concrete Girders.” Journal of Structural Engineering (ASCE) 136 (4): 401–409.

15. Okumus, P., and M. G. Oliva. 2013. “Evaluation of Crack Control Methods for End Zone Cracking in Prestressed Concrete Bridge Girders.” PCI Journal 58 (2): 91–105.

16. Arab, A. A., S. S. Badie, and M. T. Manzari. 2011. “A Methodological Approach for Finite Element Model-ing of Pretensioned Concrete Members at the Release of Pretensioning.” Engineering Structures 33 (6): 1918–1929.

17. Washington State Department of Transportation (WSDOT). 2012. Alaskan Way Viaduct Replacement Program. http://www.wsdot.wa.gov/projects/Viaduct/.

18. Dunkman, D. A., C. G. Hovell, A. M. Moore, A. Avendano, O. Bayrak, and J. O. Jirsa. 2010. “Bursting and Splitting in Pretensioned Concrete Beams.” In 3rd fib International Congress, May 29 – June 2, 2010, Gaylord Resort, Washington, DC. Chicago, IL: PCI. DVD-ROM.

19. Arab, A.A. 2012. “A Methodological Approach for Finite Element Modeling of Pretensioned Concrete Members at the Release of Pretensioning.” PhD diss., The George Washington University, Department of Civil and Environmental Engineering.

thanks are due to Anthony Mizumori of WSDOT; Cameron West of Concrete Technology Corp.; William Nickas and Roger Becker of PCI; and Mark Wagner, Katherine Farley, and James Swanson of George Washington University, who provided valuable support through different stages of the study. Special thanks are due to Maher Tadros of e-construct in Omaha, Neb., who provided valuable guidance early in this study.

References

1. Koyuncu, Y., R. Birgul, T. M. Ahlborn, and H. M. Aktan. 2003. “Identifying Causes for Distress in Prestressed Concrete (PC).” Proceedings of TRB 2003 Annual Meeting. Washington, DC: Transportation Research Board.

2. Tadros, M. K., S. S. Badie, and C. Y. Tuan. 2010. “NCHRP (National Cooperative Highway Research Program) Report 654: Evaluation and Repair Proce-dures for Precast/Prestressed Concrete Girders with Longitudinal Cracking in the Web.” Washington, DC: Transportation Research Board.

3. Marshall, W. T., and A. H. Mattock. 1962. “Control of Horizontal Cracking in the End of Pretensioned Pre-stressed Concrete Girders.” PCI Journal 7(5): 56–74.

4. PCI. 2003. Manual for the Evaluation and Repair of Precast, Prestressed Concrete Bridge Products. MNL-137-06. Chicago, IL: PCI.

5. Mirza, J. F., and M. E. Tawfik. 1978. “End Cracking of Prestressed Members during Detensioning.” PCI Jour-nal. 23 (2): 67–78.

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7. Collins, M. P., and D. Mitchell. 1997. Prestressed Concrete Structures. 1st ed.:Prentice Hall College Div. (March 1991), ISBN-13: 978-0136916352 .

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Notation

Acv = area of concrete section resisting shear transfer

Avf = area of shear-friction reinforcement

c = cohesion factor

db = nominal diameter of prestressing strand

Eci = modulus of elasticity of concrete at release

= compressive strength of concrete at release

fEZR,S = allowable end zone reinforcement stress

(fEZR,S)average = average allowable end zone reinforcement stress

fpi = maximum strand stress at release

fri = modulus of rupture of concrete at release

fx = strand stress at distance x from girder end at release

fy = specified minimum yield strength of reinforc-ing bars

h = overall depth of the girder

Pc = permanent net compressive force

νc = Poisson’s ratio of concrete

Vni = nominal interface shear resistance

wc = unit weight of concrete

x = distance from the end of pretensioned member

ΔVshear = difference between the pretensioning force generated by bonded strands below and above the interface

µ = coefficient of friction


About the authors

Amir Arab, PhD, PE, is an associate vice president and Mid-Atlantic district manager at T. Y. Lin International in Alexan-dria, Va. Arab conducted this research as part of the require-ments of his doctorate at The

George Washington University in Washington, D.C.

Sameh S. Badie, PhD, PE, is an associate professor in the Civil and Environmental Engineering Department at The George Washington University.

Majid T. Manzari, PhD, is a professor and chair of the Civil and Environmental Engineering Department at The George Washington University.

Bijan Khaleghi, PhD, PE, SE, is a state bridge design engineer for the Bridge and Structures Office at the Washington State Depart-ment of Transportation in Olym-pia, Wash.

Stephen J. Seguirant, PE, is vice president and director of engineer-ing at Concrete Technology Corp. in Tacoma, Wash.

David Chapman, PE, is chief engineer at Concrete Technology Corp.

Abstract

End zone cracking of pretensioned concrete girders has been become more prevalent due to the increased use of high-strength concrete, deep girders, thin webs, and high prestress forces. This paper provides a methodology for analytically simulating the behavior of pretensioned concrete members. The finite element method approach developed in this study was used to investigate the behavior of the end zone reinforcement of the 210 ft (64 m) long, 100 in. (2500 mm) deep super girders used in construction of the Alaskan Way Viaduct replacement in Seattle, Wash. End zone rein-forcement of eight girders was instrumented for this purpose. The finite element analysis accurately predict-ed the measurements collected from the instrumented girders. The results of the finite element are compared with those of several other methods.

Keywords

Bridge, cracking, end zone, girder, pretensioned, rein-forcement, repair.

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This paper was reviewed in accordance with the Precast/Prestressed Concrete Institute’s peer-review process.

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