Shear Strength of Joints in Precast Concrete Segmental Bridges
Shear Strength of Joints in Precast Concrete Segmental Bridges. Paper by Xiangming Zhou, Neil Mickleborough, and Zongjin Li
The authors present a great work, with an impressive number of experimental results, and should be congratulated. Experimental research on dry and epoxied multiplekey joints is very scarce, and to the discussers’ knowledge, it is the first time such tests have been performed on highstrength concrete specimens.
Nevertheless, the discussers have some comments and suggestions. It is the intention of this discussion to express some remarks based on previous research, just in case it could be useful to the authors and readers in general.
In the introduction of the article, it is stated that the shear keys serve three functions: aligning the segments during erection, transferring the shear force between segments during service, and ensuring durability of the tendons against corrosion. However, the crucial function of resisting shear during the construction of balanced cantilever bridges, when the epoxy has not hardened and acts like a lubricant, is not mentioned. Stating that keys help prevent corrosion of the internal tendons is not a very accurate assertion; the corrosion protection relies on other techniques such as the use of epoxy in the joints, the sealing of the ducts at the joints with compressed neoprene o-rings, and the duct injection.
Also in the introduction, the AASHTO formula for the design of the keyed joints is claimed to be empirical, whereas it is completely theoretical. From a presumed simple state of stresses within the key, when subjected to axial and shear forces, Roberts and Breen20 deduced the formula later adopted by AASHTO, stating that a key fails when the maximum principal tensile stress equals the concrete tensile strength. Regarding the content of the same paragraph, it is worth noting that a shearing-off failure along the keys only occurs when the shear span-depth ratio (a/d) is extremely low (a/d
It is very difficult to extract definite conclusions from the test program because the object of the research is very dependent on the concrete tensile strength. This magnitude can be derived from the concrete compressive strength with a significant scatter, which of course will be more important for concrete compressive strength in the range of 30 to 80 MPa, as those considered in the test program. In this manner, the comparison of the results is also difficult because compressive stresses for multiple-key specimens (ranging from 0.5 to 2 MPa) are systematically lower than in single-key specimens (ranging from 1 to 4.5 MPa). The compressive stresses observed in the tests seem to also be very low, especially for multiple-key specimens, where the most common service compressive stresses in a concrete box girder bridge is above an average of 0.15[function of]prime;^sub c^ .
Regarding the experimental results and analysis, some points should be discussed. The AASHTO code proposes Eq. (5) to estimate the shear capacity of the joints in PCSB (without safety factor). This formula is the one provided by Roberts and Breen20 and it depends on the tensile strength of the concrete. Actually, this formula was deduced for concrete with a compressive strength up to 55 MPa.20 In such concrete classes, the tensile strength was derived from the compressive strength through the following nondimensional formula (in psi)[function of]t = 7.5[radical][function of]’^sub c^ (8)
In Reference 5, Eq. (5) does not distinguish between strength levels. This formula, however, was not proposed for high-strength concrete. Hence, the fact that the grade of some test specimens is greater than 55 MPa should have been taken into account when checking the accuracy of Eq. (5). It could be wise to use the tests on the one hand for checking the accuracy of Eq. (5) for conventional strength concrete ([function of]prime;^sub c^ 55 MPa).
The generally accepted statement that the strength of an nkey joint will roughly be n-times the strength of a single-key joint relies on the plastic behavior of the joint. This plastic behavior depends on two main factors: the strength of the concrete and the compressive stresses acting at the joint. The higher the concrete compressive strength, the more brittle the material; thus, the high compressive strength of some concrete used in the test programs will also affect the behavior of the three-key specimens. At the same time, the higher the confinement stresses at the joint, the more plastic its behavior. Due to this fact, Roberts and Breen also limited the validity of their formula to joints where the actuating compressive stress is greater than 0.7 MPa. This stress level is generally lower than the one actuating in a real structure. The low confinement stress would explain the huge differences between the AASHTO predictions and the tests on multiple-key specimens. Actually, when a higher compressive stress is acting at the joint, the AASHTO formula proves to be very accurate for predicting the strength of panel tests with multiple-key joints (up to seven keys).3,22 Average compressive stresses in the mentioned panel tests range between 2.9 and 3.9 MPa (References 3 and 22, respectively).
The second point of the conclusions is very controversial. There, it is stated that the dry joints had an ultimate strength of approximately 20 to 40% less than the epoxied joints. Comparing Fig. 11(a) and (b), completely different conclusions can be reached. In such figures, the normalized shear strength from the single-key dry joint specimens is systematically higher than the strength from the single-key specimens with a 1 mm epoxy joint. Also, from the comparison of these figures, similar conclusions can be obtained for the case of the normalized shear strength of the three-key specimens compressed up to 1 MPa.
Regarding the second point of the conclusions, another issue that is not sufficiently explained is the fact that specimens with a thicker epoxy layer (3 mm) have a worse behavior than specimens with a thinner one (2 mm). Common sense (and FEM analysis22) suggests that the softer the contact between two adjacent keys is, the more uniform the distribution of shear stresses among the keys is and, hence, the shear capacity of the joint should be higher. Shear transfer in a joint with several keys can be regarded as analogous to an elastic force transfer in a lap joint with several bolts; depending on the stiffness of the bolts, shear is transferred in a different way. If very stiff fasteners are provided, the shear flow will concentrate in the extreme bolts. On the other hand, flexible fasteners will lead to an equally distributed shear transfer among the bolts. In the same manner, the thicker the epoxy layer, the softer the connection, the more homogeneous the shear distribution, and the higher the shear capacity of the joint. The tests prove that this statement is true when comparing results from 1 and 2 mm-thick epoxy joints. Contrarily, tests results do not support this analogy when comparing results from 2 and 3 mm-thick epoxy joints. As test results show unexpected trends, some physical phenomenon should be counterbalancing the beneficial effect of a more equally distributed shear transfer along the 3 mm-thick epoxy joint. It is thought that it would be very convenient for the scientific and technical communities if the authors could explain such a physical phenomenon.
The authors thank the discussers for their meaningful comments and suggestions.
Rombach and Specker mainly discussed the issues involved in their design formula: 1) the derivation and applicability (Eq. (7)); 2) consideration of safety factor to take matching imperfections into account; and 3) single-keyed and multiple-keyed joint application.
There are mainly three methods to derive design formulas for concrete structural members of segmental bridges. One is purely from regression analyses of experimental results, such as those presented by Buyukozturk, Bakhoum, and Beattie;6 the second one is from numerical analyses with a finite element model calibrated by experimental work, such as those addressed by Rombach and Specker;10 the last one may be totally based on an analytical model, but this method is very limited. The authors did address that Rombach and Specker’s formula (Eq. (7)) was based on numerical analyses in the Introduction of the paper. The authors also stated in the Shear Capacity of Joints section of the paper that Rombach and Specker’s formula (Eq. (7)) is “mainly” based on their numerical simulations (third paragraph, left column of p. 9). Rombach and Specker have conducted a small number of tests on dry and epoxied joints in segmental bridges.23,24 They found that the models used in practical design, for instance, those of AASHTO,5 were obtained from experiments and described by simple analytical formulas.23,24 Due to the limitations in experimental measurements, they concluded that numerical calculations were required to investigate the shear capacity of the joints.23,24 From this point of view, they also built a finite element model and verified the model by their experimental results.23,24
In the discussed paper, the authors presented their experimental results and compared them with the predictions from design formulas proposed by AASHTO and Rombach and Specker,10 respectively, which were the only available formulas for design of shear capacity of joints in segmental bridges at that time according to the authors’ knowledge. The authors found that there was a significant difference in ultimate shear strength between measured and predicted results. Based on the observation of shear-off failure mode and analyses by separating the shear contribution of the contact flat parts in vertical direction from other parts of the joint, the authors pointed out that the shear capacity per key in multiple-keyed dry joints was systematically lower than that in single-keyed dry joints; in epoxied joints, the difference became smaller. The authors attributed the differences to the matching imperfections existing between the keys. As Rombach and Specker have pointed out in their discussion, both their formula (Eq. (7)) and the AASHTO formula (Eq. (5) or (6)) are based on a liner correlation between the number of keys and the shear capacity of the joint. Certainly it is difficult to consider the matching imperfection in numerical analyses, as well as in practical design formulas, but the matching imperfections may always occur in practice so that it leads to a lower shear capacity of joints than that predicted by most design formulas and analytical models. It is understandable that the model proposed by Rombach and Specker was intended for dry joints and could not accurately predict the loading-carrying capacity for epoxied joints.
Several points have brought up by discussers Turmo, Ramos, and Aparicio, which are: 1) the keys’ function; 2) the derivation of AASHTO formula, valid concrete strength range for the formula, and failure mode of different keys; 3) magnitude of the confining stress of specimens and its influence on shear behavior of multiply-keyed joints; 4) the comparison of shear strength of dry and epoxied joints; and 5) the influence of epoxy layer thickness.
The keys in segmental bridges may have many functions. Epoxy provides waterproofing of the joints for bridges.5 Thus, using epoxy, consequently epoxied joints, can reduce and/or prevent corrosion of the internal and external tendon in segment bridges. Certainly there are many other techniques that can achieve these targets, such as the sealing of the ducts at the joints and the duct injection. The authors agree that epoxy can also serve as a lubricant during placement of segments, behaves as a seal to avoid cross-over during grouting of internal tendons, and provides some tensile strength across the joint.5
AASHTO’s equation for shear design of keyed joints was derived with guidance from work by Mattock,25 and confirmed by test data from the experimental programs of Koseki and Breen,3 and Buyukozturk, Bakhoum, and Beattie.6 It is not to say that the formula is completely theoretical. Although web shear cracking and flexural shear cracking may occur in segmental bridges, it is well recognized that the most likely failure mode of keyed joints in precast concrete segmental bridges is the shearing-off of the keys along the joint plane.3,6 A keyed-joint can be considered under two-dimensional stresses. The stress along the longitudinal direction is sometimes called confining stress. For the authors’ experiments, due to the limitation of the testing facility and the relative large size of the specimens, the confining stresses applied on the specimens could only reach 5 MPa for single-keyed joints and 2 MPa for three-keyed joints. It should be noted that most of the specimens were tested under a confining pressure greater than 0.7 MPa, which was regarded as the valid lower-bound confining pressure when using Roberts and Breen’s design formula-the origin work of the AASHTO design formula (Eq. (5) or (6)).5 Based on observation of the large difference between the experimental and the predicted values by the AASHTO formula, it has been found that ultimate shear strengths of multiple-keyed joints can also be influenced by the fixing imperfections between multiple-keyed joints. As proof, the authors cite that the shear capacity per key in multiple-keyed dry joints is always lower than that in single-keyed dry joints. On the other hand, epoxy can largely reduce the fixing imperfections, so that the shear capacity per key in multiple-keyed epoxied joints is comparable to that in single-keyed epoxied joints.
Though AASHTO’s formula (Eq. (5)) is based on the work of Roberts and Breen,20 which was deduced for concrete with a compressive strength generally less than 55 MPa according to Turmo, Ramos, and Aparicio in their discussion, AASHTO5 does not distinguish between strength levels. In fact, if one takes the limit of the concrete strength, 55 MPa, as the design compressive strength ^sup -^f^sub ck^, and assume that the compressive strength has a normal distribution with mean value f^sub cm^ and standard deviation σ, it should exist f^sub cm^ = ^sup -^f^sub ck^ + 3σ, where s equates to 4 MPa, according to British standard. Therefore, the applicable mean compressive strength is 67 MPa. Besides, most of the specimens tested by the authors had a compressive strength of less than 55 MPa. Certainly, there were 16 specimens having a compressive strength between 55 to 60 MPa, and only two specimens had a compressive strength greater than 60 MPa. The authors did not intend to perform tests of keys made of high-strength concrete. Actually, most of the specimens were cast with commercial concrete, Grade 30 or 50 concrete widely used in Hong Kong. Only one specimen (M3-D-K11; refer to Table 1) was made of in-house high-strength concrete, which was deliberately tailored to achieve high strength and examine its shear behavior in segmental joints.
The second point of the conclusions summarizes the “apparent” experimental results-the overall shear capacity-of dry joints and epoxied joints, that is, the ultimate shear strength of the joints, in the unit of kN, including the contributions of both the contact flat part in vertical direction and the keys. This point is based on the ultimate strength values in Table 1. However, in Fig. 11, the normalized shear capacity per key is obtained by subtracting the contribution of the contact flat part in vertical direction from the ultimate shear strength. This part has a high percentage for epoxied joints, and a lower percentage for dry joints.
During testing, the authors found that epoxied joints with 3 mm-thick epoxy bonding layers showed lower shear capacity than those with 1 or 2 mm-thick epoxy layers (refer to Table 1). Based on these data, the authors drew the conclusion that a 3 mm-thick epoxy layer may bring worse behavior than a thinner (1 or 2 mm) epoxy layer. Buyukozturk, Bakhoum, and Beattie6 have also found that the epoxied keyed joints exhibit different shear strength in the presence of a different epoxy layer thickness. This may be because that the variation of epoxy layer thickness increases as the thickness of epoxy layer increases, especially if this could lead to an accumulation of geometric errors. The variation of epoxy layer thickness can lead to more matching imperfections and, thus, a lower shear capacity of epoxied joints. Epoxy normally has a lower elastic modulus (around 6 GPa) and brittle failure mode. Also, the shear stress increases with the epoxy thickness at a horizontal portion of the joint. Thus, more deformation will be generated in the epoxy layer that can lead to fracture of the specimen. It is questionable to treat epoxy layers as ductile springs in numerical analyses.
Though a lot of segmental bridges have been built and are open for traffic, there is still very limited research, especially experimental work, on the design of keyed joints in such bridges. From the authors’ point of view, there is still far from adequate research in this area. Certainly there are many controversial points on the available research. The authors believe that these points will be clarified as more and more research is done on shear behavior of joints in segmental box bridges.
20. Roberts, C. L., “Measurement Based Revisions for Segmental Bridge Design and Construction Criteria,” PhD dissertation, The University of Texas at Austin, Austin, Tex., Dec. 1993.
21. Ramírez-Aguilera, G., “Behavior of Unbonded Post-Tensioning Segmental Beams with Multiple Shear Keys,” master’s thesis, The University of Texas at Austin, Austin, Tex., Jan. 1989.
22. Turmo, J., “Flexure and Shear Behavior of Segmental Concrete Bridges with External Prestressing and Dry Joints,” PhD dissertation, ETSICCP de Barcelona, Dept. Ing. de la Construcción, July 2003. (in Spanish)
23. Rombach, G. A., and Specker, A., “Numerical Modelling of Segmental Bridges,” Proceedings of the European Conference on Computational Mechanics, W. Wunderlich, ed., Munich, Germany, Aug. 31 to Sept. 3, 1999.
24. Rombach, G., and Specker, A., “Finite Element Analysis of Externally Prestressed Segmental Bridges,” Proceedings of the Fourteenth Engineering Mechanics Conference, J. L. Tassoulas, ed., Austin, Tex., May 21-24, 2000.
25. Mattock, A. H., “Design Proposals for Reinforced Concrete Corbels,” PCI Journal, V. 21, No. 3, May-June 1976, pp. 18-42.
Discussion by José Turmo, Gonzalo Ramos, and Ángel C. Aparicio
Civil Engineering School, Castilla-La Mancha University, Spain; Visiting Faculty at Indian Institute of Technology, Madras, India; Civil Engineering School, Technical University of Catalonia, Barcelona, Spain
Copyright American Concrete Institute Nov/Dec 2005
Provided by ProQuest Information and Learning Company. All rights Reserved