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)

Real behaviour of columns 73
settles down to an approximately steady value, which unfortunately cannot
be determined with precision (see Table 2.5-2). For practical concrete
mixes, the effective modular ratio for long-term loading may be two to
three times the short-term modular ratio; BS 8110: Clause 2.5.2 recommends
that the effective modular ratio should be taken as 15.
If the sustained load on a column is removed, there is an immediate
elastic recovery (see Fig. 2.5-3), and residual stresses are set up. The
reinforcement ends up in compression and the concrete in tension, as
demonstrated in Example 3.3-1 below. The residual tensile stress in the
concrete may sometimes be high enough to cause cracking.
The effect of shrinkage of concrete (see Section 2.5(c» causes further
redistribution of stresses. A plain concrete column undergoing a
(hypothetical) uniform shrinkage will experience no stresses; but in a
reinforced concrete column, the reinforcement bars resist the shrinkage
and set up tensile stresses in the concrete and compressive stresses in the
steel itself (See Example 3.3-2).
From the above discussion it is clear that the actual stresses in a column
may be quite different from the values predicted by eqns (3.3-3) and
(3.3-4). The difficulty of determining the creep and shrinkage with
precision means that the actual stresses in a column cannot be determined
precisely. If the column is subjected to a history of load applications and
removals, the residual stresses cconstitute further complications.
Example 3.3-1
A 400 x 200 mm rectangular concrete column is reinforced with six bars of
size 25 (Note: bar size refers to the nominal diameter of the bar in
millimetres; see 'detailing notation' in Example 3.6-3.) An axialload of
1000 kN is applied and sustained for a long time. For the level of concrete
stresses in question, the short-term modular ratio is 7.5 and the effective
modular ratio for the long-term loading is 15. Determine:
(a) the concrete and steel stresses immediately upon application of the
load;
(b) the long-term stresses; and
(c) the residual stresses when the sustained load is removed.
SOLUTION
A sc = area of six size 25 bars = 2945 mm 2 (see Table A2-1)
Ac = 400 x 200 mm 2 - 2945 mm 2 = 77 000 mm 2
(Note: In practical design, Ac is usually taken as the nominal concrete
area, 400 x 200 mm 2 , without allowing for the area taken up by the reinforcement.
)
ae(short term) = 7.5; a~(long term) = 15
Ac + aeAsc = 77000 + 7.5 x 2945
= 99100 mm 2
Ac + a~Asc = 77000 + 15 x 2945
= 121000 mm 2