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Structural behavior of cable anchorage zones in prestressed concrete cable-stayed bridgeByung-Wan Jo, Yunn-Ju Byun, and Ghi-Ho Tae

Abstract: Since the cable anchorage zone in a prestressed concrete cable-stayed bridge is subjected to a large amount of concentrated tendon force, it shows very complicated stress distributions which can cause serious local cracks. Accordingly, it is necessary to investigate the parameters affecting the stress distribution, such as the cable inclination, the position of the anchor plate, the modeling method, and three-dimensional effects. The tensile stress distribution in the anchorage zone is compared to the actual design condition by varing the stiffness of spring elements in the local modeling, and an appropriate position for the anchor plate is determined. The results provide elementary data for the stress state in the anchorage zones and encourage more efficient designs. Key words: finite element analysis, bursting stress, spalling stress, cable anchorage zone, cable-stayed bridge. Rsum : Puisque la zone dancrage des cbles dun pont suspendu en bton prcontraint est sujette dimportantes forces concentres prs des cbles, cette zone prsente des distributions de contrainte trs compliques qui peuvent causer de srieuses fissures locales. Par consquent, il est ncessaire dtudier les paramtres affectant la distribution de contrainte, tel que linclinaison des cbles, la position de la plaque dancrage, la mthode de modlisation et les effets tridimensionnels. La distribution des contraintes de tension dans la zone dancrage est compare aux conditions relles de conception en variant la rigidit des ressorts dans la modlisation locale et une position approprie pour la plaque dancrage est dtermine. Les rsultats fournissent des donnes lmentaires pour ltat de contrainte dans les zones dancrage et encouragent une conception plus efficace. Mots cls : analyse dlments finis, contrainte dclatement, contrainte deffritement, zone dancrage des cbles, ponts suspendus. [Traduit par la Rdaction] Jo et al. 180

IntroductionFor the increased use of post-tensioning systems in largescale reinforced concrete structures, the development of a proper anchorage system that will contain a large concentrated load is necessary. Ordinary design methods for the anchorage zone of post-tensioned concrete members are very economical as yet. Localized failure or damage is frequently observed due to lack of knowledge in the areas of anchorage-zone design and construction method. The increased installation of cable-stayed bridges is a worldwide trend due to the recent development of design and construction methods. While the role of the anchorage zone of a cable-stayed bridge is critically important for load transmission and stability, this area requires more in-depth study. Since the concentrated load becomes much greater, and the load transfer pattern becomes must more complicated for the cable-stayedReceived 25 July 2001. Revised manuscript accepted 30 November 2001. Published on the NRC Research Press Web site at http://cjce.nrc.ca on 15 February 2002. B.-W. Jo1 and G.-H. Tae. Department of Civil Engineering, Hanyang University, Seoul, Korea. Y.-J. Byun. Sin-Sung Engineering, Seoul, Korea. Written discussion of this article is welcomed and will be received by the Editor until 30 June 2002.1

bridge anchorage zone than for an ordinary prestressed structure, the development of fitting analysis and design methods is required. This study explored the stress concentration of cable anchorage zones, load path, and transverse tension stress in the compression zone of the flexure cross section. This study also evaluated design parameters for the anchorage-zone stress, namely the angle of cable inclination, location of anchor plate, analysis modeling, and threedimensional effects.

Failure mechanism of anchorageFor cable anchorage zones, large tensile stresses may exist behind the anchor. These tensile stresses result from the compatibility of deformations ahead of and behind the anchorage. Figure 1 illustrates the distinction between the local and the general zone. The region subjected to tensile stresses due to spreading of the tendon force into the structure is the general zone. The region of high compressive stresses immediately ahead of the anchorage device is the local zone. In many cases, the general zone and the local zone can be treated separately. However, for small anchorage zones such as those in slab anchorages, local zone effects, such as high bearing and confining stresses, and general zone effects, such as tensile stresses due to the spreading of the tendon force, may occur in the same region. Three critical regions can be identified: (i) the region immediately ahead of the load that is subjected to large bearing and compressive 2002 NRC Canada

Corresponding author (e-mail: joycon@hanmail.net).

Can. J. Civ. Eng. 29: 171180 (2002)

DOI: 10.1139/L01-087

172 Fig. 1. (a) Local zone and (b) general zone.

Can. J. Civ. Eng. Vol. 29, 2002 Fig. 2. Anchorage failure mechanism.

stresses; (ii) the bursting zone that extends over some distance ahead of the anchorage and is subjected to lateral tensile stresses; and (iii) local tensile stress concentrations that exist along the loaded edge, known as spalling stresses, in spite of the fact that they do not cause any spalling of the concrete. At some distance from the anchor, the stresses on the cross section can be determined from ordinary bending theory. Within this distance bending theory is not valid, because the ordinarily assumed linear strain distribution is disturbed by the introduction of the concentrated anchorage force. The region affected by this disturbance is the anchorage zone. Common zone means the region where spalling stress and bursting stress are generated; beyond this region the specimen will have a linear stress distribution. From the results of analytical and experimental studies of many variables on the configuration of the plate and anchorage zone, a much improved study of failure mechanisms of the anchorage zone is available. This failure mechanism may be applied to the study of the failure mechanisms of conicalformed and bell-formed anchor devices. The failure mechanism can be divided into four steps. The first step begins with the development of tension stress forming longitudinal cracks in a region that is one plate width away from the application of force. The second step begins with spreading of inclined cracks to the end face and the side face from the rim of a rectangular anchor plate or from a circumference a radius distance away from a circular anchor. The third step occurs with the explosion of the side and commonly occurs when inclined cracks develop rapidly upon the application of the force. The fourth step comes after the failure when the concrete crumbles to pyramidal shape and shear failure occurs beneath the anchor plate. In this fourth instance, the failure or the stress condition of the shear failure mechanism can be obtained by calculating the bursting tension stress or strain and the maximum shear stress. A possible mechanism that generates failure in a conical- or bell-formed anchor can be classified as shown in Fig. 2. Traditionally, the end anchorage zones of a cable-stayed bridge have been designed using the results of elastic analysis. Thus the amount of reinforcement required to control bursting stresses has been determined from elastic stress distributions. The amount of transverse reinforcement is chosen so that it is capable of carrying the tensile force obtained by integrating the tensile stress distribution. Usually, the stress in the reinforcement is limited to one-half the yield stress and the reinforcement is uniformly distributed over the zone of significant tensile stresses. A simple expression recommended by Leonhardt (1964) to conservatively estimate the

total transverse tensile force, T, obtained by integrating the bursting stresses, is [1] T = 0.3 P(1 a / h) + 0.5

Pu sin

in which P is the maximum prestressing force due to posttensioning operation (kN), a is the anchor plate width (mm), h is the depth of member, Pu is the factored tendon force (N), and is the angle of inclination of a tendon force with respect to the centerline of the member.

The example structureThe example structure for this study is the cable-stayed bridge, which has some particular geometrical end configuration when compared with an ordinary post-tensioned flexure member, shown in Fig. 3. There are twelve cables on each end of the structure. These cables have inclinations varied between 23 and 66 to the horizontal. Also, the jacking force of each cable was found to be between 40.816 and 71.428 kN. Only the local effect was studied in the analysis of the anchorage zone, and the influence of the other features (such as the member with a box-shaped cross section) are omitted from the study. Figures 4a4c show the cable anchorage zone configuration and the inclination of the cables Stay 1, Stay 6, and Stay 12, respectively. The deck of Stay 6 was modeled with plane stress elements, each of which has eight nodes with three degrees of freedom at each node (Fig. 5). Boundary conditions at the vertical and the longitudinal directions of the model are shown in Fig. 7. 2002 NRC Canada

Jo et al. Fig. 3. General cable-stayed bridge: (a) Olympic Grand Bridge and (b) typical cross section. All dimensions are in millimetres.

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Anchorage analysis and resultsEffect of boundry condition The anchorage zone, the cable patterns, and the loading conditions have an intricate influence on the cross section of the structure and also on the overall structural system. At the same time an irregular vertical restraint develops due to the effect of the dead and live loads on the structure and the vertical component of the cable jacking force. Because the longitudinal girder of a cable-stayed bridge is supported by cables, and this in turn is connected to a pylon, the vertical behavior of a member is similar to a spring-supported one and is different from an ordinary rigidly supported one (Roverts 1990; Fenwick and Lee 1990). Therefore, the boundary condition on the top fiber of the floor, i.e., the upper edge of the anchorage cross section, varies with the jacking force and the longitudinal location of each cable. The vertical component of the stiffness also varies. To obtain more realistic and accurate stress behavior and load flow, this paper presents a complete two-dimensional structural analysis of the example structure to calculate the jacking forces of the cables and the vertical stiffness of the cables due to vertical displacement of each anchor caused by dead load. Figure 5 and Tables 1 and 2 show the jacking force, cable dimension, section properties, and structural model used in this analysis. Figure 6 shows the displacement aspect of the cable tension in Stay 6 as obtained in the analysis. Table 3 summa-

rizes the stiffness at each anchorage as computed. As regards the boundary conditions of the top of the anchorage section, the distribution of stress and variation of the value developed within the cross section due to the different stiffness were explored from zero stiffness to complete fixity in the vertical direction without reference to the computed full rigidity. Figure 8 shows the results for Stay 1 and Stay 12. The stress examined in this test is the rupture tensile stress developed through the cable path. Figure 7 shows a twodimensional model of the anchorage area, which ignores the influence made by the passage of the cable and the continuity made by the rear end of the anchor block. Through the above, it can be seen that as the rigidity increased the bursting tensile stress decreased; also, at a certain large level of rigidity the tensile stress did not develop at all, or rather a compressive stress was observed. This can be interpreted such as the bursting tensile stress acting perpendicular to the cable path varies, the uppermost fiber of the anchorage cross section is checked and this brings about the modification of the main stress direction and a decrease of its value. Through the above, it can be seen that through the proper application of a restraint in the anchorage area, a considerable reduction of the concrete tensile force is achieved in the cross section during the erection. After the completion, this insures the integrity of the structure. Therefore, it can be seen that a certain degree of integrity in concrete can be achieved without exploding the stiffness of the anchorage top fiber during the design stage and that amount varies with 2002 NRC Canada

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Fig. 4. Cable anchorage zone for (a) Stay 1, (b) Stay 6, and (c) Stay 12. All dimensions are in millimetres.

Fig. 5. Finite element modeling of the cable-stayed bridge system.

the location of cable stays and the inclination angles of the cables. Effect of cable inclination Generally, the post-tensioned tendon has an inclination angle at the anchorage in most of the flexure members that have a shape like a girder that is usually 20 or less. But in the instance of a cable-stayed bridge where the top flange (or deck) of the member is supported by cables, the crosssectional configuration is very complicated and thereby the inclination angle between the longitudinal cross-sectional axis and the tendon can be greater. The studies conducted heretofore were mainly based on an inclination angle of 20 or less. The edited data used in the design can give a distorted outlook when the initial inclination angle becomes greater. However, these facts are regarded as on the safe side during the design computation. For example, the effect of an 2002 NRC Canada

Jo et al. Table 1. Jacking force at Stay 1, Stay 6, and Stay 12. Stay No. 1 6 12 () 66.26 37.64 23.52 Tendon force (kN) 81.55 109.89 132.62 X-direction force (T cos ) 322.07 853.63 1192.91 Y-direction force (T sin ) 732.31 658.33 519.19 Area (mm2) 5550 7950 9150

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Dimension 37T15 53T15 61T15

Table 2. Section properties. Area (mm2) 1783.5 1158.2 1311.3 601.5 Inertia moment (mm4) 244 254 191 50 550 260 210 170 Torsional constant (mm4) 665 239 199 47 950 020 740 170

Fig. 7. Two-dimensional modeling (Stay 1 anchorage).

Division Deck (concrete box) Pylon 1 (el. 0-2500 mm) Pylon 2 (el. 2500-24 200 mm) Pylon 3 (el. 24 300-77 600 mm)

Fig. 6. Deformed shape of cable-stayed bridge loaded by unit load in Stay 6.

Table 3. Vertical stiffness at Stay 1, Stay 6, and Stay 12. Stay No. 1 6 12 Deflection (mm) 0.0084 0.604 0.1 Vertical force (kN) 4.354 1.186 4.661 Stiffness (kN/mm) 51.935 1.962 13.609

inclination angle of the tendon is corrected as is eq. [2] (AASHTO 1994), when the bursting stress is calculated with an inclination angle of a tendon of 5 - 20. That is a safety factor of 10-15%, but the case of an inclination angle larger than 5 - 20 is not studied sufficiently. [2] T burst = 0.25 Pu (1 a / h) + 0.5 Pu sin

Figure 9 shows a diagram for eq. [2]. To explore the effects when the inclination angle becomes greater than that in general practice, analyses were made on five selective locations on anchorage zones. Bearing area and load sizes varied slightly in each sample location of the actual structure examined. To keep the variable number consistent, the bearing plate area Stay 12 was used consistently. An identical load was used throughout the test for each location. In light of the above, the boundary condition was established where the upper fiber of the anchorage was not restrained to secure the required safety from the analysis. Figure 10 shows the bursting stress developed in the cable tendon through its path in this analysis. From Fig. 10, it can be learned that as the cable inclination angle increased, the maximum bursting stress increased as did the slope of variation in tensile stress. From Fig. 10 it can be seen that the variation in tensile stress was largely between 20 and 50. Beyond that it became moderate. The tensile stress was twice the value at 70 as that at 20. This force was obtained by integrating the stresses perpendicular to a line going from the middle of the anchor to a point located in a section at a distance h/cos from the anchor. In general, the transverse force increases with the increased inclination of the tendon. Figure 11 also shows the values given by a conservative estimate using the proposed simplified formula, eq. [3], in which the effect of the inclina 2002 NRC Canada

176 Fig. 8. Bursting stresses for various vertical stiffnesses at Stay 1 and Stay 12.

Can. J. Civ. Eng. Vol. 29, 2002

expansion of stress toward the interior of the cross section as the cable inclination angle decreases.

Influence of anchor plate locationBecause it is difficult to develop sufficient prestress force with a single tendon, it is a general practice to place several anchorages or to move around anchorage position to obtain a desired force. The stress developed inside the cross section shows rather a complex form depending on the pile up or dispersion of various stresses developed by the number and (or) location of anchorage site(s). Accordingly, this study looked into the variation of stress conditions in a sample with two anchorages in horizontal directions by varying the anchor plate locations. The cross section of the analysis model is the section cut at the anchorage in the anchor block thickness direction (Fig. 12). Figure 13 shows the analysis result of the internal stress when the distance, s, between the center line of the cross section and the center line of the anchorage is 550 cm. Figure 14 shows the bursting stress developed in the section through the center line of the anchor plate from the above analysis. Figure 15 shows the spalling stress between the anchor plates that develops through the center line of the cross section. Each tensile stress is expressed as the ratio to the applied stresses and is dimensionless. The change in stresses is shown by varying the centerline distances of the anchor plates. The height of the section is 1800 mm. Figure 16 shows the changes in the maximum bursting stress and the maximum spalling stress relative to the distance from the anchor plates. Figure 14 shows variation in the bursting stress within the anchor plate cross section. It can be seen from this that, as the distance between s lessens, the value of the maximum bursting stress decreased and the slope of the stress variation flattened. The variation of the tensile stress between the two extremes of s was observed to be 40%. Meanwhile, the increase in the bearing stress at the edge of the bearing plate was seen with the decrease of the s distance. From the above, it can be inferred that as the distance between s increased, the tensile stress would increase and the bearing stress would decrease. Therefore, it is important to consider both the values of the maximum bursting stress and the bearing stress when positioning the anchorages. Figure 15 shows spalling stress developed between the anchor plates. It can be seen that as the distance between the anchor plates widened, the tensile stress increased and the magnitude was about 30%. It can be learned that as it moved farther away from the anchor plate, tensile stress diminished rapidly. At a point a plate distance away, the variation in the tensile stress became gradual, and the distribution of stress within the cross section became uniform. The variation in spalling stress directly under the anchor plate was intense depending on the spacing of the anchorages, but at one tenth of a plate distance away essentially no variation was observed. It is evident from the study that the optimum spacing of the bearing plate should be approximately the plates size apart or slightly less. When there are several anchorages, the value of spalling stress becomes much greater than that of bursting stress, and the range of the variation also becomes greater. Therefore a close examination of the spalling stress at the 2002 NRC Canada

tion of the tendon on the transverse (bursting) force is estimated as one-half the transverse component of posttensioning force. Figure 11 indicated that variations of the tensile stress were increased in a cable inclination angle with 20 - 50, the augmentation of tensile stress was rather decreased by over 50. Also, tensile stress value was more than twice that under 20 or 70. [3] T burst = 0.15 P(1 a / h) + 2 P sin

It can be ascertained that the increase of bursting stress is affected by the increase of moment developed by the amplification of distance between the cable jacking force application point and the load application point of the restrained surface. Also, it can be thought that the shifting location of the maximum bursting stress is due to the

Jo et al. Fig. 9. Notations for an inclined tendon.

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Fig. 10. Bursting stresses due to the cable inclinations.

Fig. 11. Maximum bursting stresses due to the cable inclinations and proposed simplified formula.

critical area is required (see Fig. 16). A three-dimensional modeling of the anchorage zone was carried out in order to supplement deficiencies found in the two-dimensional modeling and to more accurately access the internal characteristics of the member. The three-dimensional modeling was carried out for Stay 1 and Stay 6 as was done for the twodimensional modeling. Due consideration was taken for the opening, for the tendon and the boundary condition of the backside of the member was treated as a hinge. From the results of the two-dimensional analysis, it is evident that a restraint on the top surface would bring about a decrease in the internal tensile stress. This would portray a safe side of the structure when obtaining data for design purposes. For these reasons, the boundary condition was set so the restraint acted only on the back face as in the two-dimensional case. Figure 17 shows an example of the three-dimensional analysis as applied to Stay 1. The anchorage internal stress pattern

and the center of the tendon spalling stress distribution obtained from the three-dimensional analysis for Stay 1 and Stay 6 are shown respectively in Fig. 18 and Fig. 19. From the above it was learned that the three-dimensional analysis produced slightly more moderate values. In the case of Stay 1, the maximum bursting stress for the two-dimensional analysis was found to be 0.225 versus 0.172 from the threedimensional analysis. The two-dimensional value was 24% greater. In the case of Stay 6, the two-dimensional value of 0.18 versus 0.17 from the three-dimensional analysis puts the two dimensional 6% greater. From the above, it can be concluded that in order to avoid extra bother in the design and to obtain the safety of the anchorage area the twodimensional analysis alone is quite satisfactory. 2002 NRC Canada

178 Fig. 12. Modeling geometry of anchor block in thickness direction.

Can. J. Civ. Eng. Vol. 29, 2002 Fig. 14. Bursting stresses due to the different positions of the anchor plate.

Fig. 13. Maximum principal stress contour (s = 5500 mm).

Fig. 15. Spalling stresses due to the different positions of the anchor plate.

ConclusionsThe following are the conclusions reached from the studies of the stress properties of the cable- stayed prestress concrete bridge made above. (1) In an analysis of the anchorage area, while conscious of the specific qualities of the cable-stayed bridge, it is found that the vertical directional stiffness increased as the bursting stress lessened. When the stiffness attained a certain level, the cross section showed no tensile stress or some compressive stress. (2) The internal stress in the block region will give slight variance with the shift in the cable inclination angle, bearing plate area, and its position. If the stiffness of the upper edge is not taken into consideration in the design, that would only throw off the computation of stress by 10% and hence is considered safe. (3) The maximum bursting stress value varies with the vertical stiffness. When the stiffness becomes 10.194 kN/mm, the bursting stress falls off rapidly until it reaches 101.937 kN/mm and then the variance tends to taper off. Therefore, it can be concluded that vertical directional stiffness should be held at 10.194 kN/mm or above in order to effectively regulate the tensile stress developed within the anchorage cross section. (4) The stress configuration within the member is influenced by the cable inclination angle at the anchorage. When the inclination angle becomes acute, the maxi 2002 NRC Canada

Jo et al. Fig. 16. Transverse stresses due to the relative distances from the anchor plate. Fig. 18. Variation of bursting stresses for Stay 1.

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Fig. 19. Variation of bursting stresses for Stay 6.

Fig. 17. Three-dimensional modeling for Stay 1.

(6) The three-dimensional analysis showed slightly less values for the anchorage than the two-dimensional one. Therefore, to avoid the hassle in the analysis and to ensure the safety in the design, it was concluded as sufficient to adopt the two-dimensional results only.

Referencesmum bursting stress increases; when the inclination angle is moderate, the maximum stress falls off and the rate of the drop is rapid. (5) The placement of the bearing plates should be such that it will minimize the tensile stress developed within the anchorage. The spacing should be a bearing plate size apart or slightly less.AASHTO. 1994. LRFD bridge design specifications. American Association of State Highway and Transportation Officials, Washington, D.C. Burdet, O. 1990. Analysis and design of post-tensioned anchorage zones concrete bridges. Ph.D. thesis, Unversity of Texas at Austin, Austin, Tex. Fenwick, R.C., and Lee, S.C. 1990. Anchorage zones in prestressed concrete members. Magazine of Concrete Research, 38(135): 5560. 2002 NRC Canada

180 Leonhardt, F. 1964. Prestressed concrete, design and construction. Wilhelm Ernst & Sohn, Inc., Berlin and Munich. Roverts, C. 1990. Behavior and design of local anchorage zones in post-tensioned concrete. M.Sc. thesis, University of Texas at Austin, Austin, Tex. ky LE n P Pu s Tburst

Can. J. Civ. Eng. Vol. 29, 2002 vertical stiffness length of bridge (mm) stay number maximum prestressing force due to post-tensioning operation (kN) factored tendon force (N) distance from section center to anchorage zone center line tensile force in the anchorage zone acting ahead of the anchorage device and transverse to the tendon axis (N) angle of inclination of a tendon force with respect to the center line of the member the angle between horizontal surface and cable stay member

List of symbolsa the anchor plate width (mm) dburst distance from anchorage device to the centroid of bursting force, Tburst (mm) e eccentricity of the anchorage device or group of devices in the direction considered (mm) h depth of member

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