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)

2.5(d) Elasticity and Poisson's ratio
Elasticity and Poisson's ratio 37
Figure 2.5-8 shows a typical short-term stress/strain curve for concrete.
Up to about one-third of the maximum stress, the curve is approximately
straight; from that stress up to the maximum stress it is curved ascending,
and beyond that it is curved descending.
The term Young's modulus is only applicable to the initial straight part of
the curve. In fact, even the initial portion of the curve is slightly curved,
and the slope of the line OA, which is the tangent to the curve at the origin,
is called the initial tangent modulus. The slope of the tangent at an
arbitrary point B is the tangent modulus at that point. The initial tangent
modulus and the tangent modulus are not used in day-to-day structural
design, where the interest lies in knowing the strain corresponding to a
given stress. This information can be obtained from the secant modulus,
which is the slope of the chord OB, and its value depends on the stress at
B. As previously explained (Fig. 2.5-3), when a stress is applied to the
concrete, the observed strain is made up of two parts: the elastic strain and
the creep. Therefore, the secant modulus as determined from a laboratory
test depends on the rate of application of the load. BS 1881 :Part 121
recommends that standard cylinder specimens should be tested and
specifies that the stress should be applied at a rate of 0.6 ± 0.4 N/mm 2 per
second; the secant modulus shall be that corresponding to a stress equal to
one-third of the cylinder strength. These specifications may appear rather
arbitrary, but they have been chosen to yield a value which is of practical
use in structural design.
The secant modulus of concrete increases with the gel/space ratio and
decreases with an increase in the voids (Section 2.5(a) ). Broadly speaking,
the various factors that affect concrete strength have similar effects on its
modulus. It is therefore common practice to relate the secant modulus to
the strength. For example, BS 8110 gives the relations between strength
and modulus of elasticity shown in Table 2.5-6.
0 ·001 0·002 0·003 0·004 0·005 0.()()6
Strain
Fig. 2.5-8 Typical short-term stress/strain curve for concrete