Civil Engineering Reference
In-Depth Information
crete (different for lightweight concrete, as per Section 9.5.2.3 of the Code),
M
a
is the
maximum service-load moment occurring for the condition under consideration, and
I
cr
is
the transformed moment of inertia of the cracked section.
You will note that the values of the effective moment of inertia vary with different
loading conditions.
This is because the service load moment,
M
a
, used in the equation for
I
e
, is different for each loading condition. Some designers ignore this fact and use only
one
I
e
for each member, even though different loading conditions are considered. They
feel that their computed values are just as accurate as those obtained with the different
I
e
values. It is true that the varying conditions involved in constructing reinforced concrete
members (workmanship, curing conditions, age of members when loads were first ap-
plied, etc.) make the calculation of deflections by any present-day procedure a very ap-
proximate process.
In this chapter the authors compute
I
e
for each different loading condition. The work
is a little tedious, but it can be greatly expedited with various tables such as the ones pro-
vided in the
ACI Design Handbook
.
3
6.6
LONG-TERM DEFLECTIONS
With
I
e
and the appropriate deflection expressions, instantaneous or immediate deflections
are obtained. Long-term or sustained loads, however, cause significant increases in these
deflections due to shrinkage and creep. The factors affecting deflection increases include
humidity, temperature, curing conditions, compression steel content, ratio of stress to
strength, and the age of the concrete at the time of loading.
If concrete is loaded at an early age, its long-term deflections will be greatly in-
creased. Excessive deflections in reinforced concrete structures can very often be
traced to the early application of loads. The creep strain after about five years (after
which creep is negligible) may be as high as four or five times the initial strain when
loads were first applied seven to ten days after the concrete was placed, while the ratio
may only be two or three when the loads were first applied three or four months after
concrete placement.
Because of the several factors mentioned in the last two paragraphs, the magnitudes
of long-term deflections can only be estimated. The Code (9.5.2.5) states that to estimate
the increase in deflection due to these causes, the part of the instantaneous deflection that
is due to sustained loads may be multiplied by the empirically derived factor
at the end
of this paragraph and the result added to the instantaneous deflection.
4
(ACI Equation 9-11)
1
50
In this expression, which is applicable to both normal and lightweight concrete,
is a
time-dependent factor that may be determined from Table 6.2.
3
American Concrete Institute, 1997,
ACI Design Handbook
(Farmington Hills, MI), Publication SP-17 (97),
pp. 110-124.
4
Branson, D. E., 1971, “Compression Steel Effect on Long-Time Deflections,”
Journal ACI
, 68(8), pp. 555-559.
