Balcony Slab Upgrade with Corroded Top Reinforcement
An existing reinforced-concrete balcony slab cantilevers 1.40 m from a building face. It is 150 mm thick, made with C25/30 concrete, and has top reinforcement of 10 mm bars at 150 mm centres with an effective depth of 120 mm. The steel is specified as fyk = 500 MPa. The original finishes weigh 0.50 kN/m². The owner proposes to replace them with 30 mm granite (27 kN/m³) on a 40 mm mortar bed (20 kN/m³), plus 0.20 kN/m² for adhesive and waterproofing. The imposed load is 2.0 kN/m² and the reinforced-concrete unit weight is 25 kN/m³. Use γG = 1.35 and γQ = 1.50. A cover survey has found spalling along the front edge, and some bars may have lost section.
1. Calculate the ULS design load and the root bending moment per metre width.
Read the worked answer
Slab self-weight = 0.150 × 25 = 3.75 kN/m². New finishes = 0.030 × 27 + 0.040 × 20 + 0.20 = 0.81 + 0.80 + 0.20 = 1.81 kN/m². Total permanent G = 3.75 + 1.81 = 5.56 kN/m². ULS load w_u = 1.35G + 1.50Q = 1.35 × 5.56 + 1.50 × 2.0 = 7.51 + 3.00 = 10.51 kN/m². For a 1 m wide cantilever, M = w_u L²/2 = 10.51 × 1.40²/2 = 10.30 kN·m/m. This is the design moment at the root; the top bars must resist it in tension.
2. Using a rectangular stress block, calculate the design moment resistance of the existing top reinforcement and check it against the demand.
Read the worked answer
As = area of one 10 mm bar / spacing = (π × 10²/4)/0.150 = 78.54/0.150 = 524 mm²/m. f_yd = 500/1.15 = 435 MPa. f_cd = 25/1.5 = 16.7 MPa. x = As f_yd/(0.8 b f_cd) = 524 × 435/(0.8 × 1000 × 16.7) = 17.1 mm. z = d - 0.4x = 120 - 6.8 = 113.2 mm. M_Rd = As f_yd z = 524 × 435 × 113.2 = 25.8 × 10^6 N·mm/m = 25.8 kN·m/m. This exceeds 10.30 kN·m/m, with utilization about 0.40 in bending. The bending check therefore passes, but it does not prove shear, deflection, fire resistance or anchorage.
3. The measured residual bar diameter in the spalled zone is 8.5 mm. Recheck the bending capacity and state the action.
Read the worked answer
As = (π × 8.5²/4)/0.150 = 56.7/0.150 = 378 mm²/m. x = 378 × 435/(0.8 × 1000 × 16.7) = 12.3 mm. z = 120 - 0.4 × 12.3 = 115.1 mm. M_Rd = 378 × 435 × 115.1 = 18.9 × 10^6 N·mm/m = 18.9 kN·m/m, which is still above 10.30 kN·m/m. Bending is not the immediate governing failure, but 8.5 mm bars represent a significant loss and the anchorage and bond are suspect. The spalled concrete must be broken out, the bars cleaned and assessed, and a repair designed. Do not treat the calculation as permission to leave the corrosion; durability and fire cover must be restored.