GENERAL REMARKS

As discussed in Section 1.2, in addition to strength, durability and fire resistance, serviceability is a design requirement specified in AS 3600-2009 (the Standard). Practical recommendations are given in Clauses 8.5, 8.6 and 8.9 of the Standard, for the treatments of beam deflection, crack control and slenderness limits for beams, respectively. The Standard also touches very briefly on the vibration of beams, stating qualitatively in Clause 8.7 (and in Clause 9.5 for slabs) that ‘vibration of beams shall be considered and appropriate action taken where necessary to ensure that the vibrations induced by machinery, or vehicular or pedestrian traffic, will not adversely affect the serviceability of the structure’.

Although vibration topics are not dealt with in this book, the reader may refer to articles published by Chowdhury and Loo (2001, 2006), and by Salzmann, Fragomeni and Loo (2003) for the damping characteristics of simple and continuous concrete beams.

In this chapter, details are provided on short- and long-term deflection calculations, and on alternative design requirements of maximum span/effective depth ratio, in accordance with the Standard. The analysis of the total deflection of beams under repeated loading is also introduced as an advanced topic. For completeness, crack control of beams is discussed in some detail. All the deflection topics are supplemented by worked out examples. Recommendations for computing effective flange width s have been presented in Section 3.7.2. The reader is referred to the Standard for discussions on slenderness limits and vibrations.

Introduction

For a traditional building or bridge structure, the vertical forces in the walls, columns and piers are carried to the subsoil through a foundation system. The most common system consists of footings. In soft soil, because the bearing capacity is low, piles are needed to transfer the forces from the superstructure to deeper grounds where stiffer clay, sand layers or bed rock exist. The wall or column forces are each distributed to the piles or group of piles through a footing-like cap – a pile cap.

In civil and structural engineering, slopes often need be to cut to provide level grounds for construction. To ensure stability at and around the cuts or to meet similar requirements, the use of retaining walls for the disturbed soil and backfill is sometimes necessary.

The design of reinforced concrete footings and pile caps is generally governed by shear or transverse shear for wall footings, and transverse or punching shear for column footings and pile caps. Retaining walls behave like a cantilever system, resisting the horizontal pressures exerted by the disturbed soil or backfill (or both) by bending action.

The analysis of the forces acting above and below typical wall footings and their design are presented in Section 11.2. The treatments for footings supporting single and multiple columns are given in Section 11.3 whereas Section 11.4 deals with pile caps. Illustrative and design examples are given to highlight the application of the analysis and design procedures.

The second edition retains all of the features of the original book on the explicit and implicit advice of our peers via the mandatory Cambridge University Press review process. To limit the volume size, the old Appendix C, ‘Development of an integrated package for design of reinforced concrete flat plates on personal computer’, has been removed, being of diminishing practical importance. To enhance the contents, new and important materials are added, some of which were also on the advice of the reviewers:

• updated tables and figures to reflect the amendments and addenda to AS3600-2009 promulgated by Standards Australia International since its first publication

• additional information on fire design, detailing and cover, long-term deflection, as well as aspects of partially prestressed concrete design; and

• an expanded Appendix on strut-and-tie modelling, encompassing the latest publications on the topic plus a numerical example.

Just as significant, another 37 tutorial problems have been added to the various chapters of the book. This makes a total of 108.

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.