Structural Concrete - Hassoun

78 Chapter 2 Properties of Reinforced Concrete
SUMMARY
Section 2.1
The main factors that affect the strength of concrete are the water–cement ratio, properties and
proportions of materials, age of concrete, loading conditions, and shape of tested specimen.
Sections 2.2–2.6
f ′ c(cylinder) =0.85f ′ c(cube) =1.10f ′ c(prism)
1. The usual specimen used to determine the compressive strength of concrete at 28 days is a 6 ×
12-in. (150 × 300-mm) cylinder. Compressive strength between 3000 and 6000 psi is usually
specified for reinforced concrete structures. Maximum stress, f c, ′ is reached at an estimated
strain of 0.002, whereas rupture occurs at a strain of about 0.003.
2. Tensile strength of concrete is measured indirectly by a splitting test performed on a standard
cylinder using formula f sp ′ = 2P∕πLD. Tensile strength of concrete is approximately 0.1f c.
′
3. Flexural strength (modulus of rupture, f r ) of concrete is calculated by testing a 6 × 6 × 28-in.
plain concrete beam, f r = 7.5λ √ f c ′ (psi), where λ is a modification factor related to unit
weight of concrete.
4. Nominal shear stress is 2λ √ f c ′ (psi).
Sections 2.7–2.9
The modulus of elasticity of concrete, E c for unit weight w between 90 and 160 pcf, is E c =
33w 1.5√ f ′ c (psi) =0.043w 1.5√ f ′ c MPa.
For normal-weight concrete, w = 145 pcf.
E c = 57,600 √ f ′ c or E c = 57,000 √ f ′ c = 4700 √ f ′ c MPa
The shear modulus of concrete is G c = E c /2(1 + μ) = 0.43 E c for a Poisson ratio μ = 1 6 . Poisson’s
ratio, μ, varies between 0.15 and 0.20, with an average value of 0.18.
Section 2.10
Modular ratio is n = E s ∕E c = 500∕ √ f ′ c,wheref ′ c is in pounds per square inch.
Section 2.11
1. Values of shrinkage for normal concrete fall between 200 × 10 −6 and 700 × 10 −6 .Anaverage
value of 300 × 10 −6 may be used.
2. The coefficient of expansion of concrete falls between 4 × 10 −6 and 7 × 10 −6 / ∘ F.
Section 2.12–2.13
The ultimate magnitude of creep varies between 0.2 × 10 −6 and 2 × 10 −6 per unit stress per unit
length. An average value of 1 × 10 −6 may be adopted in practical problems. Of the ultimate
(20-year) creep, 18 to 35% occurs in 2 weeks, 30 to 70% occurs in 3 months, and 64 to 83% occurs
in 1 year.