Page 412 - Forensic Structural Engineering Handbook

CONCRETE STRUCTURES 12.3

cement reacts chemically with water to form a hard, inexpensive structural material. The
quality of the concrete improves inversely in proportion to the amount of water added.
Details of mix design and concrete properties are given in the book Design and Control of
Concrete Mixtures, published by the Portland Cement Association. 1
After hardening, concrete resists load by first responding elastically and then continuing
to deform or “creep” under sustained compressive or tensile loads. Figure 12.2 shows ideal-
ized stress versus strain relationships for concrete as load is applied over a short time.
Important properties for use in forensic investigation are the modulus of elasticity E and the
c
limiting compressive strain ε . For most cases, the value of modulus of elasticity can be taken
u
2
15 .
as the ACI 318 value of w ( 33) f ′ c (in pounds per square inch). The value of limiting
c
strains for unconfined concrete is generally assumed to be 0.003. Larger limiting strain may
be considered when confinement is present. Reference 3 gives guidance for calculating
increased strain capacities.
Inelastic
deformation

Elastic limit

f Recovery line
Stress,
Elastic range f
Load line

ε Modulus of elasticity = E = ε f

Permanent set Strain, ε
FIGURE 12.2 Stress-strain curve for concrete. (Courtesy of CTLGroup.)

Time-Dependent Properties
After concrete is hardened and load has been applied, two time-dependent effects begin to be
seen. First, concrete decreases in length as a result of continued chemical reaction and drying.
The curves in Fig. 12.3 show representative values for drying shrinkage strain in concrete
commonly used in structures. The lower curve represents good-quality concrete with a water-
to-cementitious-materials ratio w/cm of 0.4. The upper curve is representative of concrete
commonly used in residential construction. Shrinkage amounts that exceed these values can
cause excessive cracking or large deflections. As illustrated, most of the drying shrinkage
takes place in the first 12 months. After that time, increases in moisture in the concrete will
cause slight swelling while decreases will cause small amounts of additional shrinkage.
Another time-dependent phenomenon is creep. Under load, concrete changes length to
relieve load. When in compression, concrete shortens; but when in tension, concrete lengthens.
In general, creep is proportional to stress. Excessive creep can cause sag in beams and floors.