F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Chapter4
Reinforced concrete beamsthe
ultimate limit state
Preliminary note: Readers interested only in structural design to BS 8110
may concentrate on the following sections:
(a) Section 4.4(c) and (d): BS 8110 stress blocks.
(b) Section 4.5: Use of BS 8110 design charts.
(c) Section 4.6: Use of BS 8110 simplified stress block.
(d) Section 4.8: Flanged beams.
(e) Section 4.10: Design details.
(f) Section 4.11: Design example.
4.1 Introduction
It was pointed out in Section 3.3 that the actual stresses in a reinforced
concrete column may bear little resemblance to the values calculated on
the basis of the elastic theory. In reinforced concrete beams, in addition to
the effects of shrinkage and creep and of loading history, there are the
uncertain effects of the cracking of the concrete in the tension zone; as in
columns, conventional calculations for the stresses in reinforced concrete
beams do not give a clear indication of their potential strengths.
Therefore, during the past several decades there has been a gradual move
in design from elastic stress calculations to ultimate strength methods
[1, 2]. For example, ultimate strength design for beams was introduced into
both the American and British design codes in the 1950s, and the limit state
design procedures in current British practice make specific requirements
for ultimate strength calculations.
Ultimate strength design is basically a return to forgotten fundamentals.
Though pronounced interest in the ultimate strength of structural members
dates back only 40 or 50 years. its beginnings may be traced further back
than the concepts of elasticity. In Europe the origin of systematic thought
regarding ultimate flexural strength of beams was due to G. Galilei [3]. His
work, devoted exclusively to ultimate strength, was published as early as
1638, 40 years before Robert Hooke made the statement 'ut tensio sic vis'
[4], which is now known as Hooke's law and which enabled Navier to
develop the fundamental theorems of the theory of elasticity some one and
a half centuries later.