Structural Concrete - Hassoun

2.13 Models for Predicting Shrinkage and Creep of Concrete 27
8. Type, Fineness, and Content of Cement. The amount of cement greatly affects the final creep
of concrete, as cement creeps about 15 times as much as concrete.
9. Water–Cement Ratio. Creep increases with an increase in the water–cement ratio.
10. Type and Grading of Aggregate. Well-graded aggregate will produce dense concrete and consequently
a reduction in creep.
11. Type of Curing. High-temperature steam curing of concrete, as well as the proper use of a
plasticizer, will reduce the amount of creep.
Creep develops not only in compression but also in tension, bending, and torsion.
The ratio of the rate of creep in tension to that in compression will be greater than 1 in the
first 2 weeks, but this ratio decreases over longer periods [5].
Creep in concrete under compression has been tested by many investigators. Troxell, Raphale,
and Davis [10] measured creep strains periodically for up to 20 years and estimated that of the total
creep after 20 years, 18 to 35% occurred in 2 weeks, 30 to 70% occurred in 3 months, and 64 to
83% occurred in 1 year.
For normal concrete loaded after 28 days, C r = 0.13 3 √
t,whereCr = creep strain per unit stress
per unit length. Creep augments the deflection of reinforced concrete beams appreciably with time.
In the design of reinforced concrete members, long-term deflection may be critical and has to be
considered in proper design. Extensive deformation may influence the stability of the structure.
Sustained loads affect the strength as well as the deformation of concrete. A reduction of up
to 30% of the strength of unreinforced concrete may be expected when concrete is subjected to a
concentric sustained load for 1 year.
The fatigue strength of concrete is much smaller than its static strength. Repeated loading
and unloading cycles in compression lead to a gradual accumulation of plastic deformations. If
concrete in compression is subjected to about 2 million cycles, its fatigue limit is about 50 to 60%
of the static compression strength. In beams, the fatigue limit of concrete is about 55% of its static
strength [11].
2.13 MODELS FOR PREDICTING SHRINKAGE AND CREEP OF CONCRETE
Seven models were described in this chapter for the prediction of shrinkage and creep of concrete.
These include ACI 209R-92, B3, GL-2000, CEB 90, CEB MC 90–99, fib MC 2010, and AASHTO.
2.13.1 ACI 209R-92 Model
The American Concrete Institute recommends the ACI 209R-92 as one of four models [12].
Branson and Christianson [13] first developed this model in 1970. The ACI 209 model was used
for many years in the design of concrete structures. The model is simple to use but limited in its
accuracy.
Shrinkage Calculation. Calculation of shrinkage using the ACI 209R-92 model can be performed
if the following parameters and conditions are known: curing method (moist-cured or
steam-cured concrete), relative humidity, H, type of cement, specimen shape, ultimate shrinkage
strain, ε shu , age of concrete after casting, t, age of the concrete drying commenced, usually taken
as the age at the end of moist curing, t c .
The shrinkage strain is defined as
t − t
ε sh (t, t c )= c
f +(t − t c ) K ssK sh ε shu (2.10)