Structural Concrete - Hassoun

234 Chapter 6 Deflection and Control of Cracking
Table 6.2
Multipliers for Long-Time Deflections
Period
(months) 1 3 6 12 24 36 48
ζ 0.5 1.0 1.2 1.4 1.7 1.8 1.9 2.0
60 and
over
The factor λ Δ is used to compute deflection caused by the dead load and the portion of the live
load that will be sustained for a sufficient period to cause significant time-dependent deflections.
The factor λ Δ is a function of the material property, represented by ζ, and the section property,
represented by 1 + 50ρ ′ . In Eq. 6.14, the effect of compression reinforcement is related to the area
of concrete rather than the ratio of compression to tension steel.
The ACI Code Commentary, Section 24.2.4.1.3, presents a curve to estimate ζ for periods
less than 60 months. These values are estimated as shown in Table 6.2.
The total deflection is equal to the immediate deflection plus the additional long-time deflection.
For instance, the total additional long-time deflection of a flexural beam with ρ ′ = 0.01 at a
5-year period is equal to λ Δ times the immediate deflection, where λ Δ = 2/(1 + 50 × 0.01) = 1.33.
6.4 ALLOWABLE DEFLECTION
Deflection shall not exceed the following values according to the ACI Code, Section 24.2.2:
• L/180 for immediate deflection due to service roof live load, snow loads, and rain loads for
flat roofs not supporting elements that are likely to be damaged by large deflections.
• L/360 for immediate deflection due to live load for floors not supporting elements likely to
be damaged by large deflections.
• L/480 for the part of the total deflection that occurs after attachment of elements, that is, the
sum of the long-time deflection due to all sustained loads and the immediate deflection due
to any additional live load, for floors or roofs supporting elements likely to be damaged by
large deflections.
• L/240 for the part of the total deflection occurring after elements are attached, for floors or
roofs not supporting elements not likely to be damaged by large deflections.
6.5 DEFLECTION DUE TO COMBINATIONS OF LOADS
If a beam is subjected to different types of loads (uniform, nonuniform, or concentrated loads)
or subjected to end moments, the deflection may be calculated for each type of loading or force
applied on the beam separately and the total deflection calculated by superposition. This means
that all separate deflections are added up algebraically to get the total deflection. The deflections
of beams under individual loads are shown in Table 6.3.