Basic concepts of Prestressed Concrete per EC2

1.1 Introduction

F(caps) or the construction of mankind’s infrastructure, reinforced concrete is the most widely used structural material. It has maintained this position since the end of the nineteenth century and will continue to do so for the foreseeable future. Because the tensile strength of concrete is low, steel bars are embedded in the concrete to carry the internal tensile forces. Tensile forces may be caused by imposed loads or deformations, or by load-independent effects such as temperature changes and shrinkage.

Consider the simple reinforced concrete beam shown in Figure 1.1a, where the external loads cause tension in the bottom of the beam leading to cracking. Practical reinforced concrete beams are usually cracked under the day-to-day service loads. On a cracked section, the applied bending moment M is resisted by compression in the concrete above the crack and tension in the bonded reinforcing steel crossing the crack (Figure 1.1b). Although the steel reinforcement provides the cracked beam with flexural strength, it prevents neither cracking nor loss of stiffness during cracking. Crack widths are approximately proportional to the strain, and hence stress, in the reinforcement. Steel stresses must therefore be limited to some appropriately low value under in-service conditions in order to avoid excessively wide cracks. In addition, large steel strain in a beam is the result of large curvature, which in turn is associated with large deflection. There is little benefit to be gained, therefore, by using higher strength steel or concrete, since, in order to satisfy serviceability requirements, the increased capacity afforded by higher strength steel cannot be utilised.

Prestressed concrete is a particular form of reinforced concrete. Prestressing involves the application of an initial compressive load to the structure to reduce or eliminate the internal tensile forces and thereby control or eliminate cracking. The initial compressive load is imposed and sustained by highly tensioned steel reinforcement (tendons) reacting on the concrete. With cracking reduced or eliminated, a prestressed concrete section is considerably stiffer than the equivalent (usually cracked) reinforced concrete section. Prestressing may also impose internal forces that are of opposite sign to the external loads and may therefore significantly reduce or even eliminate deflection.

With service load behaviour improved, the use of high-strength steel reinforcement and high-strength concrete becomes both economical and structurally efficient. As we will see subsequently, only steel that can accommodate large initial elastic strains is suitable for prestressing concrete. The use of high-strength steel is therefore not only an advantage to prestressed concrete, it is a necessity. Prestressing results in lighter members, longer spans and an increase in the economical range of application of reinforced concrete.

Consider an unreinforced concrete beam of rectangular section, simply supported over a span l, and carrying a uniform load w, as shown in Figure 1.2a. When the tensile strength of concrete (f_ct ) is reached in the bottom fibre at mid-span, cracking and a sudden brittle failure will occur. If it is assumed that the concrete possesses zero tensile strength (i.e. f_ct = 0 ),then no load can be carried and failure will occur at any load greater than zero. In this case, the collapse load wu is zero. An axial compressive force P applied to the beam, as shown in Figure 1.2b, induces a uniform compressive stress of intensity P/A on each cross-section. For failure to occur, the maximum moment caused by the external collapse load wu must now induce an extreme fibre tensile stress equal in magnitude to P/A. In this case, the maximum moment is located at mid-span and, if linear-elastic material behaviour is assumed, simple beam theory gives (Figure 1.2b):