RAPID ASSESSMENT OF BONDED POST-TENSIONED CONCRETE BEAMS WITH RUPTURED TENDONS Amged O. Abdelatif1, John S. Owen2, Mohammed FM Hussein3 1
Department of Civil Engineering, Faculty of Engineering, University of Khartoum,
[email protected] 2 Department of Civil Engineering, Faculty of Engineering, University of Nottingham 3 Department of Civil and Architectural Engineering, Faculty of Engineering, Qatar University
ســت َْخـلـَص ْ ُمـ تقدم هذه الورق ة دراسة تحليلية تهدف إلي حساب قوة التحمل اإلنشائية المتبقية للعارضات الحقة الشد المحقونة والتي تعرضت أخذت الدراسة في اإلعتبار حدوث إنقطاع الوتر في.إلنقطاع في وتر الشد معتمدةً مساهمة الوتر المقطوع في قوة التحمل تم إنشاء منحنيات لعزوم التشقق علي طول الكمرة ومنها تم حساب قوة.أماكن مختلفة وكذلك عند مستوي أحمال متفاوتة المقارنة بين النتائج التحليلية والدراسات المعملية السابقة بينت إن الطريقة المقترحة.التحمل اإلنشائية المتبقية للعارضات خلصت الدراسة إلي أن الطريقة المقترحة يمكن إستخدامها في حاالت.تعطي نتائج معقولة لقوة التحمل اإلنشائية المتبقية فكرة أولية بشكل/التقييم اإلنشائي المبدئي للعارضات الحقة الشد المحقونة والتي بها وتر شد مقطوع للحصول علي نتائج .سريع ABSTRACT This paper presents an analytical study that aims to predict the residual structural capacity of bonded post-tensioned concrete beams with ruptured tendon. It considers the tendon reanchorage and hence its contribution toward the structural capacity. The study accounts for the occurrence of the rupture at different locations as well as different load level. Cracking moment profiles are generated and the residual structural capacity is predicted. The comparison of the analytical results with experimental investigation from literature shows that the proposed method gives reliable estimate of the residual structural capacity. The proposed method can be used in rapid structural assessment of bonded post-tensioned concrete beams with ruptured tendon. Keywords: post-tensioned concrete beams, rupture, tendon, re-anchorage, assessment, corrosion
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1 Introduction Many bonded post-tensioned concrete bridges have been reported to have ruptured tendons due to corrosion which led to structural failure in some extreme cases [1]. Further problems may occur as the corrosion protection begins to break down and moisture and chlorides gain access [2]. Previous studies revealed that the ruptured tendons are able to re-anchor after rupture and to contribute to the residual capacity of the structure. The contribution of ruptured tendon for the residual strength of bonded post-tensioned concrete structures is commonly assessed based on bond models for pre-tensioned concrete. However, this approach is inappropriate due to the inherent differences between the two forms of structure. Therefore, the authors developed an analytical and finite element (FE) re-anchorage models to simulate the re-anchorage of a ruptured tendon in order to be utilised in the prediction of the residual structural capacity of this type of damaged structure [3, 4]. In this paper, the developed linear analytical reanchorage model is incorporated in a full beam model to be utilised in rapid structural assessment in preliminary investigations. The influence of occurrence of the rupture at different load levels as well as different locations is discussed and the residual structural capacity is predicted. 2. Background The authors developed an analytical model based on the linear thick-wall cylinder theory and the Coulomb friction law to estimate the stress distribution in the tendon after the rupture and hence the re-anchorage length [3], Equation 1: r 1 1 B 1 s x s s 2 ln 1 f s s f s (1) 2 B Es B A Es BEs
Es : the Young’s modulus of steel. α : a factor to account for voids in the grout, ø: the coefficient of friction. The coefficient of friction in this study is taken as 0.4 [5-7]. A and B : are coefficients depending on geometry and material properties of steel, concrete, grout and duct that can be calculated as shown in [3]. Equation 1 estimates the re-anchorage length when the stress in the pre-stressing steel (fs) is substituted by the effective pre-stress (fse). The model has been verified using an axisymmetric FE model [3] and validated experimentally in the structural laboratory at the University of Nottingham [4]. 3 Analytical Methodology In order to assess a post-tensioned concrete beam with ruptured tendon the following procedure is proposed: a) Three locations of tendon rupture are considered: at support, near support (500 mm from the end), and at the mid-span. b) The re-anchorage model in Equation (1) is applied at the location of the rupture. c) Considering the pre-stressed concrete element Class 1 where cracking is not allowed [BS54004], the cracking moment capacity of a posttensioned concrete beam at each section can be calculated as follows (Equation 2):
M c x f ct Z
P x Z Px e p (2) A
where: : the cracking moment capacity at location x : the concrete tensile strength, : the elastic section modulus
Here:
: the prestress force at location x,
fs : tendon stress at distance x from the rupture point,
: the cross sectional area of the beam,
rs : radius of prestressing steel μs : the Poisson’s ratio of steel Sudan Engineering Society Journal
: the eccentricity of the tendon from the centre of gravity of the section. 2016, Volume 62; No.2
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RAPID ASSESSMENT OF BONDED POST-TENSIONED CONCRETE BEAMS WITH RUPTURED TENDONS
The first term in Equation 2 is the reinforced concrete contribution to the overall capacity while the second and third term are representing the prestress contribution. d) Taking into account the loading pattern (thereby the bending moment diagram) and the location of the rupture with the aid of Equation 2, the residual moment capacity can be assessed. e) To understand the influence of both rupture location and the level (i.e. magnitude) of the load at the time of rupture, the model presented in Equation 1 is utilised to calculate the prestress force at each section, P(x). f) The residual structural capacity is then estimated as a percentage of the capacity before tendon rupture (Equation 3). Residual capacity
Moment capacity after rupture 100% (3) Moment capacity before rupture
In this study, a laboratory sized beam was selected from previous literature [8] to be used. The analytical results using the proposed method are then compared with previous experimental results. The geometrical properties, steel reinforcement, and prestress are shown in Figure 1. The beam was prepared using concrete with tensile strength of 2.9 MPa and post-tensioned to 1500 MPa with eccentricity of 60 mm. The Young’s modulus and Poisson’s ratio for steel were taken as 200 GPa and 0.3, respectively [8]. The voids presence in the grout are not considered. g) Cracking moment capacity was estimated in previous experimental results at mid-span deflection of span/250 (i.e. 11.2 mm) according to the British Standard [3].
4 Results and discussions Figure 2 shows the cracking moment capacity with tendon rupture at different locations. Namely: at support, near support, at mid-span. For each case the reinforced concrete contribution (in dark grey), prestress contribution (in light grey), and the maximum possible bending moment diagram (in dashed line) are illustrated. In the case of the rupture at support (Figure 2a), highest cracking capacity was estimated as 99.2% compared to 95.5 % in the previous experiment [8]. This highest residual capacity is due to the fact that the rupture is located away from the high-moment-zone. For failure near support (500 mm from the beam end) the residual capacity was estimated 87.9% (Figure 2a) in comparison to 75.5% experimentally [8]. It is a fact that the loading influences the bending moment diagram and thereby the overall structural behaviour. For example, if the beam is subjected to applied load at the location of the rupture then the cracking capacity will reduce to 44% instead of 87.9% as demonstrated in Figure 2b. Both of these comparisons have shown a reliable closeness between the predicted and experimental residual structural capacity. The model is run further to test the influence of tendon rupture at the mid-span (not included in the literature we used here [8]). The results show that the predicted residual capacity in this case is about 44%, Figure 2c. This significant drop on the structural capacity because the rupture lies within high-moment-zone (i.e. between the loading points) as noted earlier. Generation of figures as in Figure 2 for structures with tendon rupture could be helpful especially in rapid preliminary structural assessment stages.
Figure 1: Properties of the beams used in the study [8]
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It is worth mentioning that structural decision in this type of damaged structure is also influenced largely by the magnitude of the applied load. Knowing the applied load could help in answering the questions regarding the structural safety.
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Figure 2: The cracking moment capacity of beams with ruptured tendon at: (a) support; (b) near support; (c) mid-span Sudan Engineering Society Journal
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RAPID ASSESSMENT OF BONDED POST-TENSIONED CONCRETE BEAMS WITH RUPTURED TENDONS
5 Conclusion The following conclusions are drawn: 1) The residual structural capacity of beams with a ruptured tendon and their structural behaviour is influenced by the location of the rupture and the loading at the occurrence of the rupture. 2) The proposed method provide an assessment tool to quantify the residual capacity and structural behaviour of post-tensioned concrete beams with a ruptured tendon. 3) The proposed method can be used in rapid structural assessment of bonded posttensioned concrete beams with ruptured tendon(s). 4) The work presented in this study provides valuable information however, there are still areas in which further research is needed in order to provide assessment guidelines for this type of the damaged structures considering both durability and uncertainty of materials.
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References 1.
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Concrete Society, Durable bonded posttensioned concrete bridges, in Technical Report 47 (TR47). 2002. Woodward, R.J. and F.W. Williams, Collapse of Ynys-Y-Gwas Bridge, West-Glamorgan.
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Proceedings of the Institution of Civil Engineers Part 1-Design and Construction, 1988. 84: p. 635-669. Abdelatif, A.O., J.S. Owen, and M.F.M. Hussein, Modeling the Re-anchoring of a Ruptured Tendon in Bonded Post-tensioned Concrete, in Bond in Concrete 2012: Bond, Anchorage, Detailing. 2012: Brescia, Italy. p. 233-240. Abdelatif, A.O., J.S. Owen, and M.F.M. Hussein, Re-Anchorage of a Ruptured Tendon in Bonded Post-Tensioned Concrete Beams: Model Validation. Key Engineering Materials, 2013. 569: p. 302-309. Janney, J.R., Nature of bond in pretensioned prestressed concrete. American Concrete Institute Journal, 1954. 26(4, Part 2): p. 736-1. Oh, B.H., E.S. Kim, and Y.C. Choi, Theoretical Analysis of Transfer Lengths in Pretensioned Prestressed Concrete Members. Journal of Engineering Mechanics, 2006. 132(10): p. 1057-1066. fib, Bond of reinforcement in concrete, in State of art report. 2000, International Federation For Structural Concrete. Coronelli, D., et al., Corroded posttensioned beams with bonded tendons and wire failure. Engineering Structures, 2009. 31(8): p. 1687-1697.
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