Effect of unbonded prestressing steel in terms of serviceability

The stress in bonded prestressing tendon varies along their length due to prestress losses. In areas where crack form, the bonded tendons directly contribute to tensile force transfer because of their bond with the surrounding concrete. In contrast, unbonded tendons are not connected to concrete in any way, so after cracking, tensile forces cannot be smoothly transferred from the concrete into the tendons. Once cracks appear, the stress tends to concentrate in one or a few cracks, which may open significantly. In bonded systems, by comparison, stress is redistributed among multiple narrower cracks. The concrete in the cross-section near a localized crack thus quickly exhausts its compressive reserve, and localized crushing in the compression zone occurs earlier (i.e., concrete failure in compression). This behavior has been observed in tests on beams with unbonded tendons, where collapse often occurred due to concrete crushing, while the increase in tendon stress before and after failure was relatively small. As a result, the full strength of the prestressing steel was not utilized, because the tendon strain was insufficient, unlike in the case of bonded tendons (Alkhairi, 1991). From the serviceability limit states (SLS) perspective, this implies that initial cracks in unbonded systems may be wider and cause larger local and global deformations. For this reason, design code (e.g., EN 1992-1-1) requires that structures with exclusively unbonded tendons meet the minimum reinforcement criteria using bonded passive reinforcement, to prevent cracking.

In unbonded prestressing systems, particularly in external tendons, geometrical changes in the position of the tendon relative to the beam’s centroid of gravity can occur during loading. As the beam deforms, the cable profile relative to the concrete centroid of gravity slightly shifts, which alters the effectiveness of the prestressing force on the structure. This phenomenon can adversely affect both the load-carrying capacity and stiffness of structure. For example, as shown in Figure 3, the eccentricity of the tendon relative to the beam axis decreases under load, which reduces the prestressing effects. At the same time, this slight geometric relaxation decreases the tendon length and results in a reduction in prestressing force.

Figure 3:

Effect of beam deflection on tendon eccentricity

These secondary effects are typically considered in more advanced nonlinear analyses. In conventional design practice, they are accounted for through safety margins, since linear analysis assumes a fixed tendon geometry. For slender beams, it is advisable to verify whether large deformations could lead to a reduction in prestressing force.

A saddle is an element that changes the direction of the tendon’s profile and transfers radial forces from the tendon into the structure. The curvature radii of saddles are selected as the smallest possible very often, primarily due to spatial constraints. At the interface between the tendon and the saddle, friction develops, which has two main consequences: (1) Losses in prestressing force, as part of the force is consumed in overcoming friction, and (2) Restriction of tendon movement under loading. In the case of an ideally unbonded tendon, the tendon would be free to slip and redistribute stress along its length. However, friction in the saddles inhibits this movement. As loading progresses, the tendon may gradually overcome the frictional resistance, resulting in minor stress redistributions along the tendon, accompanied by slight tendon slips within the saddle. Similarly, under asymmetric or dynamic loading, stress redistribution may occur progressively in the unbonded tendon. Under ideal conditions, a state could be achieved in which the tendon stress becomes uniform along the entire length due to redistribution. However, this tendon movement within the saddle may damage the protective system, and repeated movement can eventually lead to a loss of corrosion protection. The degree of wear on the protective sheathing is strongly influenced by the magnitude of the prestressing force and the surface roughness of the saddle (see Chapter 4).

It follows that the behavior of structures with unbonded tendons is complex and sensitive to various factors, particularly friction in saddles, changes in tendon geometry due to structural deformations, and crack formation. These factors significantly influence both stress distribution and deformation behavior, and therefore require special attention during design, especially with respect to the serviceability limit state. Accurate representation of these effects is only possible through the use of advanced analytical methods, often involving geometric and material nonlinearity.

Before the formation of cracks, structures with unbonded and bonded prestressing tendon behave similarly, and their deflections are comparable. Significant differences only emerge after cracking, as illustrated in Figure 4. Deformations and crack widths increase more rapidly in structures with unbonded tendons due to the lack of bond between the tendons and the surrounding concrete. Since the stress increase in unbonded tendons is smaller, the deflection of the structure grows faster compared to bonded tendons, where the tensile stress is concentrated at the crack locations. This leads to lower stiffness and wider but fewer cracks in unbonded systems. Brenkus et al. (2017) already pointed this out in the early stages of research, and Alkhairi and Naaman (1993) found that, after exceeding the elastic limit, deflection in beams with unbonded tendons increases significantly faster, see Figure 4. For practical design, this means either increasing the amount of prestressing or increasing the amount of non-prestressed reinforcement to prevent excessive cracking and deflections.

Figure 4:

Behavior of different types of prestressing steel during loading (Alkhairi, 1991)

As already mentioned at Figure 1, unbonded prestressing tends to result in fewer cracks, but with greater crack widths. Virlogeux (1983) pointed out that the lack of bond can lead to the formation of a single dominant crack, which may compromise the durability of the structure. Therefore, Alkhairi (1991) recommended combining prestressing steel with an appropriate amount of conventional reinforcement to ensure better crack distribution. Design standards reflect this by requiring a minimum area of conventional (non-prestressed) reinforcement. Codes also limit the allowable crack width, which compels the designer to add either more prestressing steel or conventional reinforcement to prevent cracking.

Due to dynamic, asymmetric, or cyclic loading, minor displacements of the tendon relative to the beam may occur at the saddles, as local static friction is overcome and tendon slip is allowed. If this phenomenon is not considered during design, it may lead to excessive deformation. In the case of external prestressing, friction losses can be significantly lower due to the absence of unpredictable angular changes, since tendons between saddles are straight. Tendon slip depends on the saddle radius, friction between the sheath and saddle, and the type of protective sheath. This slip is accompanied by an increase in tendon stress and minor movements, which can damage the tendon’s protective sheath. Harajli (1990) observed in his experiments that repeated loading leads to degradation of the sheath material at stress concentration zones (specifically, where the tendon contacts the saddle). As will be discussed in one of the following chapters, measurements were conducted to determine the reduction in sheath thickness as a function of saddle radius and prestressing force. In some cases, the material loss reached up to 6% of the original thickness (Klusášek & Svoboda, 2017). These effects can compromise the primary corrosion protection much earlier than in bonded prestressing systems. All these findings highlight the importance of careful detailing of saddle components and rigorous inspection of the entire structure throughout its service life.

To verify the actual behavior of prestressing tendons in saddle with various radii of curvature, a series of short-term experiments was conducted at the Department of Concrete and Masonry Structures at Brno University of Technology (BUT), Faculty of Civil Engineering. These tests focused on the behavior of monostrands (seven-wire strand Y1860-S7-15.7, with an HDPE sheath approximately 2.0 mm thick) in saddles with small radii. The aim of the tests was to examine how radial forces in the saddles affect the monostrand itself, including both the steel cross-section and its protective sheath. For the experiment, a reinforced concrete L-shaped specimen was designed with openings for tendon guidance and an integrated saddle (see Figure 5). The specimen was conceived in such a way that the curvature radius could be changed simply by replacing the saddle. The saddle itself was made of steel strip bent to the required radius. To measure the relevant parameters, several instruments were used: inductive sensors to monitor displacements, strand flattening, and elongation; magnetoelastic sensors to measure mechanical stress in the tested strands; and feeler gauges to assess the thinning of the HDPE sheath (Svoboda et al., 2016).

Figure 5:

Test specimen (Svoboda & Klusáček, 2018)

The test specimen consists of two concrete parts (L-shaped part and saddle segment) to enable measurements at different radii of curvature of the prestressing tendons. The first part of specimen is a reinforced concrete L-shaped segment with dimension 1375×900 mm and a constant thickness of 120 mm. This part serves as the base for the saddle segment. The second part is an additionally cast saddle segment with a thickness of 120 mm, which fills the inner space of the main base part and, with its curved shape, allows the installation of the saddle. The saddle part permits changes in the radius of curvature by removing and recasting a new segment of the required shape. The test specimen was designed for measuring monostrands at curvature radii of 600, 1000 and 1500 mm. The saddle of the test specimen is made of flat structural steel strips and is in the UHPC saddle part of the test specimen. The strip steel has length of 700 mm, a width of 50 mm and thickness of 5 mm. Monostrands are guided on the saddle by welded steel bars with a diameter of 8 mm and length of 50 mm, at regular intervals of 100 mm (Svoboda et al., 2016).

For measuring prestressing force was used magnetoelastic sensor, which are placed in openings in L-shaped segment of test specimen. This measuring method is based on utilization of changes in the physical properties of ferromagnetic materials under load. In the half of curvature of test specimen was point where flattening (loss of cross-sectional circularity) of monostrands and thinning of HDPE sheath was measured. In his point was sheath from strand removed and an inductive sensor with a spring-loaded tip with a range of 5 mm was installed (see Figure 6). With this sensor it was able to measure displacement, flattening and elongation of monostrand. Together with flattening was thinning of HDPE sheath measured. On the strand where was sheath removed it was possible to measure the thinning of sheath with steel leaf gauge with an accuracy of one hundredth of a millimeter (Svoboda et al., 2016).

Figure 6:

Three inductive sensors for measuring strand displacement and flattening (Svoboda & Klusáček, 2018)

So far, measurements have been carried out on saddle with a curvature radius of 1.50 m and on two series of prestressing tendons from different suppliers, result of tendon from first supplier are shown in red in figures and labeled with numbers 01, 02 and 04 and from second supplier are shown in blue and labeled with numbers 1701, 1702 and 1703, there are no main difference between that type of tendon. The loading step by prestressing force was chosen value of 20 kN up to maximum force 200 kN, for typical process see Figure 7 (Svoboda et al., 2016).

Figure 7:

Typical tensioning of monostrand and sensor displacement under load (Svoboda & Klusáček, 2018)

The flattening of strand (loss of cross-sectional circularity) can be numerically derived from the data measured by the three inductive displacement sensors. The sensors measured the displacement of the strand in two mutually perpendicular planes (see Figure 8). The sensors labeled Def_1 and Def_2 measured the displacement of the prestressing tendon against each other in a plane parallel to the plane of the saddle contact surface. The Def_3 sensor measured the displacement of the monostrand in a plane perpendicular to the plane of the saddle contact surface. From the known displacement values, it is possible to quantify the resulting flattening of the monostrand as: (1) Δd||=dDef_1-dDef_2 \Delta d_{||} = d_{Def\_1} - d_{Def\_2} Where:

• Δd_|| - flattening of the strand in the plane parallel to the plane of the saddle contact surface,

• d_{Def_1} - displacement value of Def_1 sensor

• d_{Def_2} - displacement value of Def_2 sensor.

Figure 8:

Scheme of measuring flattening and HDPE sheath thinning (Svoboda et al., 2016)

The evaluation was performed by substituting values at corresponding times and searching for the maximum flattening values (Svoboda et al., 2016).

At smaller saddle curvature radii, the strand cross-section may become flattened, potentially compromising the integrity of the HDPE sheath. The measured values indicate the extent of flattening under corresponding prestressing force. The maximum observed flattening was around 1–2%, see Figure 9. In addition to cross-sectional deformation, the deformation of the HDPE sheath was also examined. Due to the radial forces generated by prestressing, which are directly related to the curvature radius of the saddle, the HDPE sheath, which serves as the primary corrosion protection for the strand, becomes thinned. At a maximum force of 200 kN, the thinning was measured to be in the range of 0.123–0.253 mm, which corresponds to approximately 6% of the original sheath thickness, see Figure 10. These measurements highlight the stringent requirements for the quality of the saddle contact surfaces. Even the slightest inaccuracy or unevenness can lead to the degradation of the primary protective function of the prestressing system.

Figure 9:

Result of experimental measurements of flattening of monostrands in saddles with radius of curvature 1500 mm (Svoboda & Klusáček, 2018)

Figure 10:

Result of experimental measurements of thinning of the protective HDPE sheath of monostrands in saddles with radius of curvature 1500 mm (Svoboda & Klusáček, 2018)