Structural Design of Reinforced Concrete Members
This domain tests strength design to ACI 318: whether you can carry out flexure, shear, development, serviceability and seismic detailing checks with the correct assumptions and resistance factors.
Flexure
Factored load combinations begin with U = 1.2D + 1.6L. For a singly reinforced rectangular section, a = As fy / (0.85 f'c b) and Mn = As fy (d - a/2). The strength reduction factor is 0.90 when the strain in the extreme tension steel at nominal strength is at least 0.005 (tension controlled); it drops toward 0.65 for compression-controlled sections.
Shear and detailing
Vc is about 0.17 times lambda times the square root of f'c times bw times d; Vs = Av fyt d / s with phi = 0.75, and Vs has an upper limit. Minimum shear reinforcement is required once Vu exceeds half of phi Vc. Minimum flexural steel is the greater of 0.25 times the square root of f'c divided by fy and 1.4/fy, times bw d. Development length and cover follow the applicable ACI 318 tables.
Serviceability and seismic
Deflection limits are commonly l/360 for live load and l/240 for total load. Special moment frames need strong-column weak-beam ratios, confinement and joint shear checks.
Worked example
b = 300 mm, d = 500 mm, As = 1200 mm2, f'c = 30 MPa, fy = 420 MPa. a = 1200 times 420 divided by (0.85 times 30 times 300) = 65.9 mm. Mn = 1200 times 420 times (500 - 33) = 235 kN m, so phi Mn = 212 kN m. Neutral axis depth c = 65.9/0.85 = 77.5 mm gives tensile strain 0.016, well above 0.005, confirming phi = 0.90.
Traps
Using h instead of d; forgetting phi; applying the rectangular stress block without the beta1 reduction for high-strength concrete; omitting minimum shear reinforcement.