Lecture Notes on Reinforced Concrete Design

Lecture Notes on Reinforced Concrete Design

Professor Dr. Wail Nourildean Al-Rifaie

Properties of Reinforced Concrete

Compressive Strength

The values obtained for the compressive strength of concretes, f ‘c, is determined by testing to failure 28-day-old cubes, 150/ 100 mm on each side or by 150x300/ 100x200 mm cylinder. The testing of 150x300 mm cylinders provides compressive strengths equal to about 80% of the values determined with the cubes, i.e., the measured values of compressive strength using cubes are equal to 1.2 x the measured values of compressive strength determined with cylinders.

The stress–strain curves of Fig. 1 represent the results obtained from compression tests of sets of 28-day-old standard cylinders of varying strengths.

(a) The curves are roughly straight while the load is increased from zero to about one-third to one-half the concrete’s ultimate strength.

(b) Beyond this range the behavior of concrete is nonlinear. This lack of linearity of concrete stress–strain curves at higher stresses causes some problems in the structural analysis of concrete structures because their behavior is also nonlinear at higher stresses.

(c) Of particular importance is the fact that regardless of strengths, all the concretes reach

their ultimate strengths at strains of about 0.002.

(d) Concrete does not have a definite yield strength; rather, the curves run smoothly on

to the point of rupture at strains of from 0.003 to 0.004. It will be assumed for the

purpose of future calculations in this text that concrete fails at 0.003.

(e) Many tests have clearly shown that stress–strain curves of concrete cylinders are almost identical to those for the compression sides of beams.

(f) It should be further noticed that the weaker grades of concrete are less brittle than the

stronger ones, that is, they will take larger strains before breaking.

Static Modulus of Elasticity

The following expression can be used for calculating the modulus of elasticity of concretes weighing from 90 lbs./ft3 to 155 lb/ft3:

In this expression, Ecis the modulus of elasticity in psi, wcis the weight of the concrete in pounds per cubic foot, and f ‘c is its specified 28-day compressive strength in psi.

For normal-weight concrete weighing approximately 145 lb/ft3, the ACI Code states that

the following simplified version of the previous expression may be used to determine the

modulus:

wc is the weight of the concrete varying from 1500 to 2500 kg/m³.

For normal crushed stone or gravel with a mass approximately 2320 kg/m³ be used,

Concretes with strength above 6000 psi (42 MPa) are referred to as high-strength concretes. The expression to follow has been recommended for normal-weight concretes with f ‘c values greater than 6000 psi (41 MPa) and up to 12,000 psi (82 MPa) and for lightweight concretes with f ‘c and up to9000 psi (62 MPa).

Dynamic Modulus of Elasticity

The dynamic modulus of elasticity, which corresponds to very small instantaneous strains, is generally 20% to 40% higher than the static modulus. When structures are being analyzed for seismic or impact loads, the use of the dynamic modulus seems appropriate.

Poisson’s Ratio

As a concrete cylinder is subjected to compressive loads, it not only shortens in length but also expands laterally. The ratio of this lateral expansion to the longitudinal shortening is referred to as Poisson’s ratio. Its value varies from about 0.11 for the higher-strength concretes to as high as 0.21 for the weaker-grade concretes, with average values of about 0.16. There does not seem to be any direct relationship between the value of the ratio and the values of items such as the water–cement ratio, amount of curing, aggregate size, and so on.

Shrinkage

When the materials for concrete are mixed, the paste consisting of cement and water fills

the voids between the aggregate and bonds the aggregate together. This mixture needs to be sufficiently workable or fluid so that it can be made to flow in between the reinforcing bars and all through the forms. To achieve this desired workability, considerably more water (perhaps twice as much) is used than is necessary for the cement and water to react (called hydration). After the concrete has been cured and begins to dry, the extra mixing water that was used begins to work its way out of the concrete to the surface, where it evaporates. As a result, the concrete shrinks and cracks. The resulting cracks may reduce the shear strength of the members and be detrimental to the appearance of the structure. In addition, the cracks may permit the reinforcing to be exposed to the atmosphere or chemicals, thereby increasing the possibility of corrosion. Shrinkage continues for many years, but under ordinary conditions probably about 90% of it occurs during the first year. The amount of moisture that is lost varies with the distance from the surface. Furthermore, the larger the surface area of a member in proportion to its volume, the larger the rate of shrinkage;