Figure 7.25. Flat slab, unit quantities: (a) reinforcement; (b) concrete.

Figure 7.25. Flat slab, unit quantities: (a) reinforcement; (b) concrete.

7.3.2. Materials Post-Tensioning Steel

The basic requirement for post-tensioning steel is that the loss of tension in the steel due to shrinkage and creep of concrete and the effects of stress relaxation of the tendon should be a relatively small portion of the total prestress. In practice, the loss of prestress generally varies from a low of 15 ksi (103.4 MPa) to a high of 50 ksi (344.7 MPa). If mild steel having a yield of 60 ksi (413.7 MPa) were employed with an initial prestress of, say, 40 ksi, it is very likely that most of the prestress, if not the entire prestress, would be lost because of shrinkage and creep losses. To limit the prestress losses to a small percentage of, say, 20% of the applied prestress, the initial stress in the steel must be in excess of 200 ksi (1379 MPa). Therefore, high-strength steel is invariably used in prestressed concrete construction.

Although high-strength steel is generally produced using alloys such as carbon, manganese, and silicon, prestressing steel achieves its high-tensile strength by virtue of the process of cold-drawing, in which high-strength steel bars are drawn through a series of progressively smaller dyes. During this process, the crystallography of the steel is improved, because cold-drawing tends to realign the crystals.

High-strength steel in North America is available in three basic forms: 1) uncoated stress-relieved wires; 2) uncoated stress-relieved strands; and 3) uncoated high-strength steel bars. Stress-relieved wires and high-strength steel bars are not generally used for post-tensioning. High-strength strands are fabricated by helically twisting a group of six wires around a slightly larger center wire by a mechanical process called stranding. The resulting seven-wire strands are stress-relieved by a continuous heat treatment process to produce the required mechanical properties.

ASTM specification A416 specifies two grades of steel, 250 and 270 ksi (1724 and 1862 MPa), the higher strength being more common in the building industry. A modulus of elasticity of 27,500 ksi (189,610 MPa) is used for calculating the elongation of strands. To prevent the use of brittle steel, which would result in a failure pattern similar to that of an overreinforced beam, ASTM A-416 specifies a minimum elongation of 3.5% at rupture.

A special type of strand called low-relaxation strand is increasingly used because it has a very low loss due to relaxation, usually about 20 to 25% of that for stress-relieved strand. With this strand, less post-tensioning steel is required, but the cost is greater because of the special process used in its manufacture.

The corrosion of unbonded strand is possibile, but can be prevented by using galvanized strands. This is not, however, popular in North America because: 1) various anchorage devices in use for post-tensioned systems are not suitable for use with galvanized strand because of low coefficient of friction; 2) damage can result to the strand because the heavy bite of the anchoring system can ruin the galvanizing; and 3) galvanized strands are more expensive.

A little-understood and infrequent occurrence of great concern in engineering is the so-called stress corrosion that occurs in highly stressed strands. The reason for the phenomenon is little known, but chemicals such as chlorides, sulfides, and nitrates are known to start this type of corrosion under certain conditions. It is also known that high-strength steels exposed to hydrogen ions are susceptible to failure because of loss in ductility and tensile strength. This phenomenon is called hydrogen embrittlement and is best counteracted by confining the strands in an environment having a pH value greater than 8. Incidentally, the pH value of concrete is ±12.5. Therefore, it produces a good environment. Concrete

Concrete with compressive strengths of 5000 to 6000 psi (34 to 41 MN) is commonly employed in the prestress industry. This relative high strength is desirable for the following reasons. First, high-strength concrete is required to resist the high stresses transferred to the concrete at post-tensioning anchors. Second, it is needed to develop rapid strength gain for productivity. Third, high-strength concrete has higher resistance in tension, shear, bond, and bearing, and is desirable for prestressed structures that are typically under higher stresses than those with ordinary reinforced concrete. Fourth, its higher modulus of elasticity and smaller creep result in smaller loss of prestress.

Post-tensioned concrete is considered a self-testing system because, if the concrete is not crushed under the application of prestress, it should withstand subsequent loadings in view of the strength gain that comes with age. In practice it is not the 28-day strength that dictates the mix design, but rather the strength of concrete at the transfer of prestress.

Although high-early-strength (type III) Portland cement is well-suited for posttension work because of its ability to gain the required strength for stressing relatively early, it is not generally used because of higher cost. Invariably, type I cement conforming to ASTM C-150 is employed in buildings.

The use of admixtures and fly ash is considered good practice. However, use of calcium chlorides or other chlorides is prohibited because the chloride ion may result in stress corrosion of prestressing tendons. Fly ash reduces the rate of strength gain, and therefore increases the time until stresses can be transferred, leading to loss of productivity.

A slump of between 3 to 6 in. (76 to 127 mm) gives good results. The aggregate used in the normal production of concrete is usually satisfactory in prestressed concrete, including lightweight aggregates. However, care must be exercised in estimating volumetric changes so that a reasonable prestress loss can be calculated. Lightweight aggregates manufactured using expanded clay or shale have been used in post-tensioned buildings. Lightweight aggregates that are not crushed after burning maintain their coating and therefore absorb less water. Such aggregates have drying and shrinkage characteristics similar to the normal-weight aggregates, although the available test reports are somewhat conflicting. The size of aggregate, whether lightweight or normal weight, has a more profound effect on shrinkage. Larger aggregates offer more resistance to shrinkage and also require less water to achieve the same consistency, resulting in as much as 40% reduction in shrinkage when the aggregate size is increased from, say, % to 1)2 in. (19 to 38 mm). It is generally agreed that both shrinkage and creep are more functions of cement paste than of the type of aggregate. Lightweight aggregate has been gaining acceptance in prestressed construction since about 1955 and has a good track record.

7.3.3. Design Considerations

The design involves the following steps:

1. Determination of the size of concrete member.

2. Establishment of the tendon profile.

3. Calculation of the prestressing force.

4. Verification of the section for ultimate bending and shear capacity.

5. Verification of the serviceability characteristics, primarily in terms of stresses and long-term defections.

Deflections of prestressed members tend to be small because under service loads they are usually uncracked and are much stiffer than nonprestressed members of the same cross section. Also, the prestressing force induces deflections in an opposite direction to those produced by external loads. The final deflection, therefore, is a function of tendon profile and the magnitude of prestress. Appreciating this fact, the ACI code does not specify minimum depth requirements for prestressed members. However, as a rough guide, the suggested span-to-depth ratios given in Table 7.7 can be used to establish the depth of continuous flexural members. Another way of looking at the suggested span-to-depth ratios is to consider, in effect, that prestressing increases the span range by about 30 to 40% over and above the values normally used in nonprestressed concrete construction.

Table 7.7 Approximate Span Depth Ratios3 for Post-Tensioned Systems

Floor system Simple spans Continuous spans Cantilever spans

Table 7.7 Approximate Span Depth Ratios3 for Post-Tensioned Systems

Floor system Simple spans Continuous spans Cantilever spans

One-way solid slabs

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