A review of studies on the post-tensioned concrete beams Cite as: AIP Conference Proceedings 2404, 080011 (2021); https://doi.org/10.1063/5.0068963 Published Online: 11 October 2021 Taha K. Mohammedali, Kamaran S. Abdullah, Abbas H. Mohammed, et al. AIP Conference Proceedings 2404, 080011 (2021); https://doi.org/10.1063/5.0068963 © 2021 Author(s). 2404, 080011 A Review of Studies on the Post-Tensioned Concrete Beams Taha K. Mohammedali1), Kamaran S. Abdullah2), Abbas H. Mohammed1,a), Raad D. Khalaf1) and Ali K. Hussin1) 1 Department of Civil Engineering, University of Diyala, Diyala, Iraq Department of Civil Engineering, Tishk International University, Iraq 2 a) Corresponding author: abbas_Mohammed_eng@uodiyala.edu.iq Abstract. Post-tensioned method is a technique commonly used all over the world to prevent cracks and minimize deflections produced by externally applied loads. In post-tensioned, stress is added after concrete placement and appropriate hardness and strength are achieved. By a post-tensioned method greater loads, greater spans, control the cracks and smaller size of members can be achieved. This paper reviews some previous research studies on post-tensioned concrete beams. From this literature; it was concluded that the ultimate load capacity for a beam with a bonded tendon is higher if compared to the same beam with the unbonded tendon. The higher ultimate capacity for the bonded beam is due to the additive stiffness obtained by tendon-concrete bond. For external prestressed beam, the results showed that using draped tendon profile increases the flexural resistance as compared to straight tendon profile.. INTRODUCTION Concrete is a mainly used material in the construction of structural engineering in various ways. The concrete has strong strength in compression zone but tension zones are too weak. Concrete tensile strength is changed and differs between ranges from 8 to 14 percent of its strength in compression. Due to weakness of concrete in tension zone, the cracks appear after applied loadings. Some technics were appeared to avoid this cracks from increasing, one of them carried out high compressive force longitudinally along the axis of the structural elements, and this force can prevent cracks from growing by removing and significantly reducing the tension stress. Thus this force effects raising of shear, torsional and bending capacity of the sections of the element, the sections are then able to behave elastically. After load applications, concrete will have an all capacity which can be strongly used in the depth of the concrete sections. This proper technic was called prestressing force [1]. Fig. 1 shows the concrete beams response under service load and the impact of pre-stressing in structural concrete elements under stress. Post-Tensioned (PT) is a worldwide technique used to prevent cracking and minimize external load deflections. In this process, stress is applied after the concrete has been casting and hardening. After hardening, each tendon stressed by using stress jacks to the required load after the concrete casting has taken place. Both tendons must be anchored at the ends of the member to retain PT strength. This tendons force is counteracted by applied loads to minimize cracks and deflections [1]. By PT process, larger loads applied, larger span with the same depth of the members, crack controls and smaller members can be achieved. It can also be considered in the steel structures to increase seismic capability and can be used externally and internally. It can also be used to repair and strengthen existing buildings. Other structures such as PT slabs, beams with long span, bridges, parking, etc. are being designed using a PT system. The PT can be used both on-site cast and in precast. And this process enables the same member to combine both bonded and unbonded tendons which improves the clear period. Such examples are built in the US and in the South Korea [3]. 2nd International Conference on Engineering & Science AIP Conf. Proc. 2404, 080011-1–080011-8; https://doi.org/10.1063/5.0068963 Published by AIP Publishing. 978-0-7354-4136-1/$30.00 080011-1 FIGURE 1. (a) Response of prestressed, reinforced and plain concrete to loading. (b) Internal stress designed to equilibrium external stress in PT members [2]. Prestressing method is define as concrete with embedded reinforcements in it to produce internal stress, this internal stress counteracts with external service loads to a preferred degree. This method is done by applying high stress to reinforced tendons in zones, which cracks takes place in it due to external loadings, and then it gives a section that has the ability to resist higher loads before cracking occurs. This system increases the external load capacity to crack [4]. The prestressed method has much application, especially in concrete constructions. A large part of bridges in the US is constructed by the prestressed system. Two methods were used for prestressing concrete system: pretensioned and PT [5]. In the pretensioned process, stress is applied to the tendons prior to the concrete placement. In this process, the tendon is tensioning in a stressed bed. Collecting the formwork is positioned with stressed anchorages at the ends, after that the concrete placement is finished. As soon as the concrete achieves sufficient strength, the tendons have to be released at the ends. This procedure produces great internal forces, and the tendon-produced forces are transferred to the concrete member by means of bonds between the tendon and the concrete. Typically this method is used in precast buildings where numerous identical elements are required [5]. In the PT method, stress is applied to the tendons after concrete placing. Ducts are used to obtain the desired profile and to allow free movement of tendons in the member. When concrete has gained sufficient strength, each tendon is stressed to the desired load by using a stressing jack and anchored at each end of the member to maintain the prestressing force in the concrete. This paper reviews some previous research studies on PT concrete beams. Bonding, unbonding and external PT reinforced concrete beams are considered in this study. This study focus on the strength and failure behaviour of PT beams. PREVIOUS RESEARCH WORKS ON POST-TENSIONED BEAMS There are three types of post-tensioned in beams which are bonded post-tensioned beams, unbounded posttensioned beams and external post-tensioning. 080011-2 Bonded Post-Tensioned Beams In bonded PT beams, the stressing force in PT system is held by bonds between tendons and surrounding concrete. The resistance of the PT members is greatly influenced by the adhesion between steel tendons and concrete. In the bonded PT system the tendons and the ducts have a void between them, cement mortar is added to fill this space, which greatly increases the strain compatibility and bond between the surrounding concrete and the tendons, and can also fully protect tendon from corrosion [5]. Bonded PT can be used in all environmental conditions. Bonded PT has not needed a large area of tendons to obtain the required strength as compared to unbonded PT. Due to sufficient bonds the tensile stress transfers between concrete and reinforcements. In 1962, Warwaruk et al. [6] experimentally tested eighty-two simply supported partially prestressed concrete beams. The purpose of their study was to indicate the effects of changing the concrete compressive strength, the amount of reinforcing steels and types of loading on stress in the prestressing tendons. Their results showed that in the case of using beams without using adequate reinforcements were failed with one major crack, while in beams with using adequate and developed reinforcements predict multiple cracks before failed, additionally, in the case of using tendons, the beams remained elastic ranges at ultimate stress in tendons. In 1985, Tao and Du [7] in their experimental study twenty-six prestressed concrete beams were tested, different amounts of bonded and unbonded steels were used. To predict the effects of changing amounts of non-prestressed reinforcements, concrete strength and prestressed steel on the prestressed stress of tendons. Their results showed that by decreasing the total amount of reinforcements (bonded and unbonded) the tendon stress increased at failure. In the case of using a low amount of reinforcement, the beams behave more ductile as compared with beams with a high amount of reinforcement used. The same results were obtained by Chakrabarti et al. [8] who reported that by increasing the total amount of reinforcements at ultimate load the stress changes in the unbonded steel tendons were smaller. In 1986, Rao and Vegh [9] experimentally tested three PT reinforced concrete beams and three bonded beams. All beams were simply supported and rectangular in sections. The aim of their tests was to predict the relationships between loads and deflection as well as to predict the growing cracks at nominal flexural capacity. Their results showed that the deflection behaviour of unbonded beams provided similar behaviour as that of bonded tendons, and flexural strength of unbonded tendons underestimated according to both Indian Code (1980) and ACI 318-77 equations which were 7.5 % and 5.0 % Respectively. In 1990, Seible et al. [10] performed tests of four pre-tensioned concrete beams under applying point loads. Tendons were harped under two-point loads with an angle of 4.8 degrees for each point load. Their results showed that by strengthened member, the average strength increased by 115 % when single strand was used. The deflections at mid-span at the ultimate load were about 60 % of the corresponding beam deflections. Beams reach failure when concrete crushed. In 1994, Manalip et al. [11] experimentally studied five beams of high strength concrete. The beams were exposed to pure bending and studied to find the ductility and to realize the real strain-softening behaviour of compressed zones. The use of high-strength concrete instead of normal-strength concrete results were calculated by doubling the plastic rotation power for experimentally tested beams. In 2012, Hussien et al. [12] proposed the experimental program to research the behaviour of unbonded and bonded pre-stressed concrete beams. Their findings showed that by using prestressed concrete beams partially stressed with bonded tendons have good behaviour than those with unbonded tendons, and by raising the compressive strength between 72 MPa and 97 MPa for bonded pre-stressed beams, increase in the cracking loads and ultimate loads by 18 percent and 4 percent, respectively. Analytical work has been implemented and compared to findings of experimental work and makes strong predictions. In 2015, Nosrath et al.[13] proposed an experimental program to research the effect of various cable curvature and tendon profiles on the design of a bridge in order to gain greater strength while at the same time making the structure economical. The operation restriction states and the ultimate limitation states were used for the evaluation of optimisation. Their analysis showed that the parabolic profile is more economical when compared to the rectangular profile; similarly, the trapezoid profile is most economical than the parabolic profile. Unbonded Post-Tensioned Beams When mortar or grout not used to fill the spaces between tendons and ducts, then it is called unbonded PT system, instead, naturally filled with grease as a protection against corrosion. In unbonded PT may be avoided the 080011-3 expensive of time-consuming of grouting operation, it is an economical alternative to conventional to bonded prestressed. This system has some problems, which stopped it from being more widely used, the unbonded system cannot be used in corrosive environments due to disposed of corrosion like bridges (Nowak [16]), but may be used in parking structures with offering suitable protections against corrosion (Litvan [17]). This system requires a larger area of tendons to obtain the required strength because of the ultimate strength of unbonded tendons about ten to thirty percent lower than bonded members (Park and Paulay [18]). The behaviour of unbonded PT tendons does not wholly understand yet. Furthermore, it has not had a modest and accurate method for computing the tension stresses in unbonded tendon at failure. The tensile stress cannot be moved from surrounding concrete to the bar reinforcements because of the lack of bonds, thus the cracking pattern at failure characterized by single or little cracks in the maximum moment region. In 1967, Burns and Pierce [19] experimentally tested fifteen beams with prestressed unbonded tendons. Their tests focused on the relationship between loads and deflections, and growing cracks at ultimate load capacity. Their results showed that by using non-pretsressed unbonded tendons provide an acceptable performance for strengthening. Strands give a great role in controlling cracks and strength, for both shear strength and flexural. ACI Building Code (1963) equations provided very traditional predictions. In continuous beams when using sufficient shear reinforcements it can develop plastic hinging at the point of the highest moment before reaching ultimate load capacity. In 1971, Mattock et al. [20] experimentally observed that the plastic deformation happened in plastic regions in the prestressed reinforced concrete members, which affects the elongation of the prestressed steel between the anchorage ends. This is a contribution of the curvature distribution between zero and yield to the total elongation of the tendon. The stress in the unbonded tendons is constant along the length at the nominal flexural strength of the beams. According to the ACI Building Code (1983) assumptions, the strain on the concrete compressive zones at the top beams fibre, the total increase in the tendon elongation between the anchorages, and the strain increase in the tendons could be derived. In 1976, Tam and Pannell [21] experimentally used eight prestressed beams stressed partially with unbonded tendons. The span to the depth ratio, prestressing stress, and non-prestressing reinforcing steel amounts were fixed. Their results showed that diagonal cracks occurred, which cut across the flexural cracks in the case of using high reinforcement index. Furthermore predicts, at the ultimate load capacity a limit of small concrete strain appeared, the plane sections before loading remains after loading. In 1978, Mojtahedi and Gamble [22] their study was focused on the effect of the span to the depth ratio of the ultimate stress of unbonded tendons. Their results showed that at ultimate nominal resistance, the stress in prestressing steels has been significantly affected by span to the depth ratio. Increasing the span to the depth ratio, effects on the stress of unbonded tendons, which reduced at ultimate. Conclusions supported by using the analytical model of the truss, the analysis showed that the strain in a tie at mid-span decreased suddenly as the span-to-depth ratio increased. To continue the same result were verified on a parametric study on externally PT concrete beams by (Harajli [23]). In 1989, Chakrabarti and Whang [24] experimentally published the cracking and ultimate strength behaviour of simply supported reinforced concrete beams with partially prestressing of unbonded tendons. Eight beams have been tested. Their results showed that at the ultimate load the tensile steel bars reach yielding, failure occurs by concrete crushing at the ultimate load. By decreasing of partially prestressed ratio the stress in the steel bars increased. To predict the stress in the unbonded tendons at ultimate, the non-prestressed and compressive reinforcements should be taken into account in the ACI 318-83 equation. Test results were reported with specific conclusions and recommendations for future design and code revisions. In 1990, Harajli [23] presented a theoretical model for unbonded prestressed concrete members to evaluate the influence of the effect of the span-depth ratio parameters on the stress in prestressed steels. Harajli showed that the increase in stress in unbonded prestressing steels mainly depends on the geometry of the applied loads and depends on the plastic region length relative to the span length. By increasing span to the depth ratio decreases the predicted stress. In 1991, Bums et al. [25] experimentally tested two continuous PT concrete beams with internally unbonded tendons to predict change in the prestressing force in tendons. The results showed that the tendon forces under cycle service loads did not change up to the compressive stress level of (12√fc-). When the beams overloaded in just single span, tendons are tended to slide into a loaded span, this causes stress in tendons decreases on the end of the loaded beam span and increases stress in the unloaded span at the end. In the case of applying two spans loaded, the distributed stress in tendons did not change significantly. Furthermore predicted that by using of draped tendon profiles, the change in tendon stress for a given deflection was larger than the corresponding beam with less of severing draped profiles. 080011-4 In 1991, to determine the impact of parameters on the magnitude of the prestressing stress of steel, Harajli and Kanj [26] tested twenty-six simply supported concrete beams with rectangular cross-sections, prestressed with unbonded tendons and without and with reinforcing steels. Their results showed that the application of the load types has no significant influence on the stress in prestressed tendons. Also, their results showed that the stress in prestressed tendons in single concentrated load was same in two third-point loads. By increasing the span to depth ratio from 8 to 20 effects in decreasing the stress in the tendons by 35 %. It means the load application was not significantly affected. Also in 1991, Campbell and Chouinard [27] experimental used six partially unbonded prestressed concrete beams with rectangular cross-sections, their results showed that by increasing the amount of non-prestressed bonded steels decreases the stress in the prestressing tendons at ultimate loads. Their test results were compared with predictions from two related design codes and identified some limitations of these code application to construction of prestressed concrete with unbonded tendons. In 1991, Naaman and Alkhair [28] suggested a methodology leads the strain reduction coefficients to provide the necessary correlations between the member and section behavior, inelastic uncracked, cracked ranges, ultimate resistance, and nominal resistance. In their study, tests were done on simply supported beams included symmetrically tendon profiles. Effects of diagonal shear cracks were neglected. The analysis of a concrete beam stressed with unbonded tendons is converted to the analysis of a concrete beam stressed with bonded tendons, by using the strain reduction coefficients. They predicted that when only one crack has occurred in the elastic cracked region the strain reduction coefficient must be used. In 1993, Alkhairi and Naaman [29] developed nonlinear models for forecast of moment versus deflection response of reinforced concrete beams with unbonded and bonded prestressed tendons and non-prestressed reinforcements. As well as the verification has been carried out by using fifteen experimental test results investigated from 1962-1990 and good correlation was observed between experimental and analytical results. Also in 1993, Dall'Asta and Dezi [30] studied the Ritz approximation method to solve the stress in the unbonded PT tendons. And they suggested that using the concept of total potential energy minimization. In 1994, Chakrabati et al. [31] experimentally tested thirty-three unbonded prestressed reinforced concrete beams. Their results showed that beams with enough reinforcement index and enough partial prestressing ratio have better load caring capacity, better ductility, and performance in the post-cracking range. Using the high amount of partial prestressing ratio caused sudden large cracking in the tension zones and high amount of combined reinforcing index cause crushing in the compression zones. To improve ductility, deflection, and cracking control the partial prestressing ratio should be reduced gradually. In the case of span-depth ratio above 35, post-cracking behaviour and deflection control were enhanced. The tendon initial stress had no effect on overall beam behavior, however, the ultimate strength of prestressing steel increased. In 1995, Picard et al. [32] studied the efficiency of tendon profiles for both external and internal prestressing tendons of statically in-determined structures for both parabolic and linear tendon profiles. The results showed that the linear profiles were more effective in support regions in counteracting gravity moments, their efficiency within the spans can be considerably reduced. The optimization of the effective eccentricity was more difficult along all members. They recommended that by using internally prestressed with parabolic tendons gives more uniform efficiency through the structures and recommended using linear draped tendons and localized tendons. In 1996, the comprehensive flexural behaviour of pre-stressed beams with external as well as internal unbonded tendons has predicted in the study by Srinivasa and Mathew [33]. They outlined a detailed theoretical study for forecast the behaviour of the externally pre-stressed concrete beams over the entire loading range up to failure load. In addition, this procedure is valid for the general polygonal shaped tendon profile for any number of deviators. In 2010, Vu et al. [34] calculated the structural response of unbonded PT beams, including both the ultimate bearing capacity and deflections under the service loading. They predicted overall unbonded wires lengthening at all levels of loading: serviceability, cracking and ultimate. The bearing ability and deflection calculations were extremely significant at failure. In 2020, Fu et al.[35] suggested a method of evaluating stiffness based on the actual pattern of cracking. Internal force equilibria are used to overcome the top strain and neutral axis problems. Based on the solution, the lengthening of the unbonded tendons is calculated by using an iterative algorithm, and the inertias of the key sections are calculated to assess the beam stiffness. Using a clearly assisted beam and four two-span continuous beams, the proposed approach was experimentally validated. The proposed method has been demonstrated to accurately simulate the change in inertias, assess beam stiffness, and reflect the stiffness dependence on the cracking pattern. 080011-5 External Post-Tensioning Another method was introduced which was externally PT system, used in many parts of engineering structures, such as in segmental bridge constructions, rehabilitations, strengthening of existing structures, and also used to replace the damaged tendons. By this method, the dimensions of the member sections and member self-weight can be reduced (Allouche [5]). In 1993, Harajli [38] experimentally studied the strengthening flexural members by external prestressing. For this purpose, he tested sixteen simply supported beams with rectangular cross-sections. The results of his tests showed that nominal flexural strength of the beams was increased about 146 % by applying externally prestressing tendons, without a reduction in ductility, and the service load deflections were reduced by about 75 % under cyclic fatigue loading. Harajli found that by using draped tendon profile increases the flexural resistance as compared to straight tendon profile. Furthermore, he assumed that by an increase in elongation of the tendon between the ends the strain in the external prestressing steel increases under applied loads, and the proportional between strain in strands and deflections were linear. In 1995, AI-Gahtani et al. [39] reported an effective creation for optimum design of two-span continuous concrete beams with partially prestressed. Different forces on prestressed tendon profiles have been used along the beam length, tendons are anchored at the both beam ends with flexibility in the overlapping location. Their results showed that the design of partially prestressed concrete beams was economic as compared to the designing of fully prestressed concrete beams in two span continuous concrete beams, moreover, the same conclusion was verified by (Colin and MacRae [39]) for simply supported concrete beams. In 1997, Tan and Ng [41] tested six reinforced concrete beams with external prestressing tendons, the cross sections were T-section for all beams, and all beams were strengthened in flexure using external strands. Their test results showed that by using deviators for beam sections of maximum deflection had a significant effect on satisfactory service load behaviors (cracking, deflection, and steel stress) and had a higher load- carrying capacity as compared to the case where no deviators were used. Their results showed that by increasing eccentricity of straight tendons with a correspondingly smaller prestressing force had a significant effect on makes a larger internal steel stresses, service load deflections, and crack widths with a higher ductility. In the case of using draped tendon profile, significantly effects on stiffness, which was reduced, increase tendon stresses, makes more ductile behaviour near failure. Also, the service load behaviour was not changed by using a larger tendon area, which gives a lower ductility with higher ultimate strength. In 2010, Naghipour et al. [42] experimentally and numerically studied the concrete beams behaviour stressed with the externally prestressed tendons. They used a finite element method program such as ANSYS to modeling PT reinforced concrete beams. They concluded that for lower bending reinforcement beams, the strengthening approach was very successful. Additionally, the increasing in the flexural strength resulting from the use of unbound external PT reinforcement bars is predicted to be in the opposite proportion to the percentage of internal bending reinforcement. In 2020, Kwon et al. [43] investigated the bending action of external lightweight aggregate beams. The eccentricity of prestressing strands and the setup of deviators for harped strands are variable under various loading conditions. In comparison with the internal PT lightweight aggregate concrete one-way members, the flexural capacity, stress increases (Δfps) of the unbundled strands in the ultimate state and the displacement ductility ratio (μ) of current strains are measured. The comparisons showed clearly that the Δfps and μ calculated in external PT beams were smaller than those of internal one-way reinforcement members of the same reinforcing index. CONCLUDING REMARKS 1. 2. 3. 4. Prestressing is a technic used for constructions like (bridges, buildings, offshore structures and towers …etc.) widely all over the world, because of their cost and efficiency in meeting requirements such as long span with a small depth of the member. Prestressing used for flexural strengthening of reinforced concrete structures for improving cracking loads and decrease deflection at service loads. Three methods for prestressing which are post-tensioning, pre-tensioning and external post-tensioning. When external pre-stressed tendons are applied to the composite cantilever beam, the failure load can be substantially increased and the deflection of the beam decreased. 080011-6 5. The ultimate post-tensioned beam load capacity is improved by the use of parabolic tendon profiles. The cable curvature exists in parabolic profiles to balance the tension forces with the concrete. The tendons are located with eccentricity to counteract sagging bending moments due to transverse loads. As a result, when the prestress is applied, the prestressed beams deflect upward. Since the bending moment is the product of pre-stressing force and eccentricity, the tendon profile itself will reflect the shape of the bending moment diagram. 6. The ultimate load capacities for bonded tendon beam are higher than the same unbonded tendon beam. The highest ultimate bonding potential is due to the additive rigidity obtained from a tendon-beton bond. 7. The results showed that the deflection behaviour of unbonded beams provided similar behaviour as that of bonded tendons. 8. The results showed that by using PT concrete beams with bonded tendons providing better behaviour than PT concrete beams with unbonded tendons. 9. The results found out that a parabolic profile of tendons is most economical when compared to rectangular profile, similarly, a trapezoidal profile is most economical than a parabolic profile. 10. 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