Analysis and Design of Reinforced Concrete Beams King Saud University University Civil Engineering Department Analysis and Design of Reinforced Concrete Beams

Concrete Properties 1. Uniaxial Stress versus Strain Behavior in Compression  Ec o 0.45f’c fc f’c 300 150 u

Concrete Properties The standard strength test generally uses a cylindrical sample. It is tested after 28 days to test for strength, fc. The concrete will continue to harden with time.

Concrete Properties Compressive Strength, f’c Normally use 28-day strength for design strength Poisson’s Ratio, n n ~ 0.15 to 0.20 Usually use n = 0.17

Modulus of Elasticity, Ec Corresponds to secant modulus at 0.45 f’c ACI 318-02 (Sec. 8.5.1): where w = unit weight 1500 kg/m3 < wc <2500 kg/m3 For normal weight concrete (wc  2300kg/m3)= 23 Kn/m3, for Reinforced Concrete Wc= 24 Kn/m3) E ( MPa ) = 0.043 w 1 . 5 f ' ( MPa ) c c E ( MPa ) = 4,700 , f ' ( MPa ) c c

Concrete strain at max. compressive stress,0 For typical  curves in compression  varies between 0.0015-0.003 For normal strength concrete, 0 ~ 0.002 Ec  o  u 0.45f’c fc f’c

Concrete Properties Maximum usable strain,  u ACI Code:  u = 0.003 Used for flexural and axial compression

Tensile Strength Tensile strength ~ 8% to 15% of f’c f = 0.7 f ' ( MPa Modulus of Rupture, fr For deflection calculations, use: Test: f = 0.7 f ' ( MPa ) ACI Eq. 9-10 r c P fr Mmax = P/2*a unreinforced concrete beam

Tensile Strength (cont.) Splitting Tensile Strength, fct Split Cylinder Test fct=2P/πDL P Concrete Cylinder Poisson’s Effect

Steel Reinforcement 1. General Standard Reinforcing Bar Markings

Steel Reinforcement Most common types for non-prestressed members: hot-rolled deformed bars welded wire fabric

Steel Reinforcement Areas, Weights, Dimensions

Steel Reinforcement 2. Types ASTM A615 - Standard Specification for Deformed and Plain-Billet Steel Bars Grade 420: fy = 420 MPa, Dia 6 to Dia50 most common in buildings and bridges Grade 300: fy = 300 MPa, Dia 6 to Dia 12 most ductile

Steel Reinforcement 3. Stress versus Strain Stress-Strain curve for various types of steel reinforcement bar.

Steel Reinforcement GR 420 (less ductile) Stress Strain 0.20 GR 300 GR 420 (less ductile) Es 1 Es = Initial tangent modulus = 200,000 MPa (all grades) Note: GR300 has a longer yield plateau