Balcony Cantilever with the Main Steel Laid at the Bottom
On a five-storey apartment project, the 1.2 m cantilever balconies are 110 mm thick, M25 concrete, Fe 415 steel, with a floor finish of 1.5 kN/m² and a service live load of 4.0 kN/m². Site inspection shows the specified 8 mm bars at 250 mm c/c lying on the bottom of the slab: the contractor removed the bar chairs before concreting. Clear cover is 20 mm. Hairline cracks have appeared along the slab–wall junction and the free edge has deflected 6 mm. The contractor argues that the steel area is 'the same as the interior slabs, which have performed well', and offers to inject the cracks with epoxy and hand over. The client wants a written opinion on whether the balconies may be accepted as they stand.
1. Compute the design hogging moment per metre width and the reinforcement required at the support. Compare with the reinforcement provided, and comment on the contractor's argument.
Read the worked answer
Step 1 - Service load. Self weight = 0.110 x 25 = 2.75 kN/m²; finish 1.5; live 4.0. w = 8.25 kN/m².
Step 2 - Hogging moment at the support (cantilever). M = wL²/2 = 8.25 x 1.2²/2 = 5.94 kN·m/m. Factored Mu = 1.5 x 5.94 = 8.91 kN·m/m.
Step 3 - Effective depth for top steel. d = 110 − 20 − 4 = 86 mm.
Step 4 - Required steel (Fe 415, M25). Mu,lim = 0.138 fck b d² = 0.138 x 25 x 1000 x 86² = 25.5 kN·m, so the section is singly reinforced. 4.6 Mu/(fck b d²) = 4.6 x 8.91 x 10⁶/(25 x 1000 x 7396) = 0.222 Ast = 0.5 x (25/415) x (1 − √0.778) x 1000 x 86 = 305 mm²/m. Cross-check: with Ast = 305, Mu = 0.87 x 415 x 305 x 86 x (1 − 415 x 305/(25 x 1000 x 86)) = 8.9 kN·m ✓.
Step 5 - Provided. 8 mm @ 250 = 201 mm²/m - and that is at the bottom, where for a hogging moment it sits near the compression face and contributes almost nothing. At the tension face, the top, the provided steel is zero, against a requirement of 305 mm²/m.
Judgement. The contractor's comparison is invalid. Interior slab panels carry sagging moments of the order of wL²/8 over long spans and are supported all round; a cantilever has one support, the tension face is the top, and the steel must be there. Even if the bars had been placed correctly at the top, 8 mm @ 250 would have been inadequate (201 < 305 mm²/m); 10 mm @ 200 (393 mm²/m) or 8 mm @ 125 (402 mm²/m) would be required. There are two independent errors, not one.
2. Assess the actual safety margin of the as-built slab and explain how it would fail.
Read the worked answer
The as-built section behaves as plain concrete in hogging. With the steel at the bottom (24 mm from the soffit), the tension face at the support is unreinforced concrete, so the governing capacity is the cracking moment.
Step 1 - Modulus of rupture. fcr = 0.7√fck = 0.7 x √25 = 3.5 MPa.
Step 2 - Section modulus. Z = bD²/6 = 1000 x 110²/6 = 2.017 x 10⁶ mm³/m.
Step 3 - Cracking moment. Mcr = 3.5 x 2.017 x 10⁶ = 7.06 x 10⁶ N·mm = 7.06 kN·m/m.
Comparison. Service moment 5.94 kN·m gives a factor of only 7.06/5.94 = 1.19 against first cracking, whereas the required factor is 1.5, i.e. the factored moment of 8.91 kN·m exceeds Mcr. The section therefore cracks at or before the design ultimate load.
Failure mode. Once the top fibre cracks, there is no tension reinforcement, so the section snaps through - a brittle, sudden failure with no yielding, no deflection warning and no moment redistribution. The 6 mm free-edge deflection and the junction cracks show that cracking has already begun; the observable ductility that would normally signal distress is absent.
Additional checks the contractor omitted. The 6 mm tip deflection is roughly L/200 and will grow with creep; the epoxy injection is cosmetic and does nothing to the capacity, and injecting before strengthening would hide the very crack that must be monitored. The supporting beam must also be checked for the additional torsion and for the anchorage of any new top bars into it.
3. Recommend a remedial scheme and state how you would verify it.
Read the worked answer
Design intent. The slab geometry cannot be changed cheaply, so the remedy must put tension steel where hogging moment demands it, and develop it into the supporting beam.
Preferred scheme - structural topping over the cantilever.
- Prop the cantilever at the free edge and remove the cracked, loose screed; chip the top surface to a sound, roughened profile (10–15 mm aggregate exposure).
- Place the new top steel, 10 mm @ 200 (393 mm²/m, > 305 mm²/m required), with an anchorage/development length into the supporting beam of at least Ld, and U-bars or drilled-and-grouted dowels into the beam face.
- Cast a 50 mm minimum structural topping in M30 with a bonding agent; the increased D also raises d and reduces the steel demand.
- Alternatively, provide a structural steel or RCC edge beam and columns at the free edge to convert the cantilever into a propped slab - acceptable where the elevation allows.
What not to do. Do not accept epoxy injection alone, and do not simply plaster over the cracks: the section still has no top steel.
Verification.
- Recheck the strengthened section for Mu ≥ 1.5 x 5.94 = 8.91 kN·m/m and for deflection under total load.
- Check the supporting beam for the added torsion from the new topping and dowels.
- Before concreting, confirm by cover-meter or by opening up that no existing top steel exists elsewhere along the cantilever.
- After the specified curing period, carry out a load test on one representative balcony with 1.5 x service load for 24 hours, measuring tip deflection and recovery; residual deflection should be small and no new cracks should appear.
- Issue a written structural stability certificate only after the load test and a physical check that all other balconies have been treated.