Most of the contents of this book were originally developed in the late 1980s at the University of Wollongong, New South Wales. The contents were targeted towards third-year courses in reinforced and prestressed concrete structures. The book was believed useful for both students learning the subjects and practising engineers wishing to apply with confidence the then newly published Australian Standard AS 3600-1988. In 1995 and following the publication of AS 3600-1994, the contents were updated at Griffith University (Gold Coast campus) and used as the learning and teaching material for the third-year course, ‘Concrete structures’ (which also covers prestressed concrete). In 2002, further revisions were made to include the technical advances of AS 3600-2001. Some of the book’s more advanced topics were used for part of the Griffith University postgraduate course, ‘Advanced reinforced concrete’.

In anticipation of the publication of the current version of AS 3600, which was scheduled for 2007, a major rewrite began early that year to expand on the contents and present them in two parts. The effort continued into 2009, introducing in Part 1 ‘Reinforced concrete’, inter alia, the new chapters on walls, as well as on footings, pile caps and retaining walls, plus an appendix on strut-and-tie modelling. In addition, a new Part 2 has been written, which covers five new chapters on prestressed concrete. The entire manuscript was then thoroughly reviewed and revised as appropriate following the publication of AS 3600-2009 in late December 2009.

Introduction

Columns exist in all conventional building structures. Whereas beams, slabs or even trusses may be used to span the floors, columns carry loads vertically, floor by floor, down to the foundations. Even in specialised systems such as shear-wall, shear-core and framed-tube structures, columns are used to support parts of the floor areas.

Figure 9.1(1)a shows a portion of a three-dimensional building frame. For the purposes of discussion on the role of columns, the frame may be taken as representative of other popular building systems, such as multistorey flat slabs, as well as beam/slab and column structures. At each level, the floor spans in both the x and z directions. As a result, bending occurs in both the x–y and y–z planes. Thus, for a typical column AB, the forces acting at the top end, or joint A, include:

• N, the axial force equal to the portion of the vertical load (from the floor immediately above) to be carried by column AB plus the axial load transmitted by the column above (i.e. column CA)

• Mx, the bending moment about the z-axis

• Mz, the bending moment about the x-axis.

ASSUMPTIONS

By definition, a fully prestressed beam sustains neither tensile cracking nor overstress in compression, under any given service load. Achieving these no-crack and no-overstress conditions throughout the working life of a beam – when prestress losses occur instantaneously and continuously – is a complicated problem. The critical stress state (CSS) approach presented in this chapter provides a fool-proof solution to this otherwise intractable problem. It is a linear–elastic method and is valid subject to the following assumptions:

• The plane section remains plane after bending.

• The material behaves elastically.

• The beam section is homogenous and uncracked.

• The principle of superposition holds.

Note that the CSS approach is suitable for partially prestressed beams sustaining tensile stresses below the concrete cracking strength (see Section 12.5).

NOTATION

Figure 13.2(1)a illustrates a typical section of a prestressed I-shaped bridge beam. It may be idealised as shown in Figure 13.2(1)b in which the resultant H of the individual prestressing forces is located at the effective centre of prestress, or with an eccentricity (eB) from the neutral axis (NA). The effective centre is the centre of gravity (action) of the individual prestressing forces. Its location, or the value of ℯB, can be determined by simple statics.

GENERAL REMARKS

Prestressing may be seen as an elaborate and active way to reinforce concrete when it is weak in tension. Whereas the traditional reinforcement becomes active mainly after the concrete has exceeded its cracking strength, the purpose of prestressing is to prevent cracking from occurring. This is done by introducing compressive stress in the concrete to neutralise the anticipated tensile stress developed under load.

In a traditional reinforced concrete design, the safety margin can always be increased by providing more reinforcement. The same may not be true in prestressed concrete, as over-prestressing can cause cracking or perhaps failure before even any external loading is applied. As a result, prestressed concrete analysis and design are more complicated and mechanics-based than for reinforced concrete, which relies more on empirical formulas. In practice, prestressed concrete also requires a higher level of technology in its construction.

By nature, prestressing is more efficient than the traditional reinforcement in that the stress in concrete, either tensile or compressive (caused by self-weight or other forms of dead load), can be neutralised before any additional (live) loading is applied. Consequently, for a given design, the maximum permissible prestressed concrete span can be considerably larger than a reinforced one. Following some fundamentals given in this chapter, Chapter 13 presents the bending theory of fully prestressed concrete beams based on the critical stress state criteria (which ensures that no cracking or overstressing in tension or compression would ever occur throughout the life of the beam under service load). The design of beams in bending using the critical stress state approach is given in Chapter 14. To comply with the Australian Standard (AS) 3600–2009 (the Standard), in practice, all prestressed beams must have the required strength. The bending strength analysis of fully and partially prestressed concrete beams is discussed in Chapter 15. The last chapter, Chapter 16, reviews the analysis and design of end blocks for prestress anchorage.

INTRODUCTION

Origin and nature of torsion

Torsion is a three-dimensional action; it is the moment about the longitudinal axis of the structural member. Occasionally, torsional moment is also referred to as twisting moment or torque.

In a three-dimensional structure, there are numerous situations in which torsion occurs. Figure 6.1(1) shows two typical cases.

For the case of the cantilever bent beam or bow girder in Figure 6.l(l)a, the torsional moment (T) is produced by the transverse load (P) acting eccentrically with respect to the axis of the beam. As it is a statically determinate structure, adequate design for torsion is vitally important – collapse of the system will result if failure in torsion occurs.

The grillage system shown in Figure 6.1(l)b is often used for beam-and-slab floor structures. The system is statically indeterminate. Torsion of the girder is a result of the unbalanced end moments at C of the two cross beams spanning in the z-direction. Note that, for convenience, torsional moments may be indicated in the x – y plane by doubleheaded arrows following the right-hand screw rule. As the system is statically indeterminate, failure of beam AB in torsion would not automatically mean collapse of the grillage. However, serious serviceability problems of the beam (torsional cracking) can be expected as well as the redistribution of bending moments in the two cross beams (DC and CE).

GENERAL REMARKS

It is recognised in Section 12.1 that prestressing tendons (either in the form of wire or strands of wire) reinforce the weaknesses of concrete in an active manner. Because of this, considerable concentrated forces are exerted at the extremities of a prestressed beam. At the end zones, these forces in pretensioned beams translate into intensive bond stresses in the steel concrete interface. In post-tensioned beams, they induce acute lateral tensile stresses and the anchor heads (see Figure 12.4(3)a) create high bearing stresses on the concrete ends.

These stresses need to be fully considered and carefully designed for, to prevent cracking and even premature failure in the end zones. A properly reinforced end zone is referred to as an end block.

The nature and distribution of the bond stress in the end zones of a pretensioned beam are given in Section 16.2, which also includes the design method recommended in AS 3600-2009 (the Standard). Section 16.3 identifies the three types of stresses induced by a post-tensioned anchorage system. These are the bursting stress and the spalling stress, both of which are tensile, and orthogonal or transverse to the axis of the post-tensioned tendon. There is also the bearing (compressive) stress on the concrete behind the steel anchor head. The design for the bursting, spalling and bearing stresses is discussed in Section 16.4. Finally, the distribution and detailing of the end-block reinforcement are presented in Section 16.5.