Sagging Corridor Slab in a Bhopal Hostel Block: Strength versus Serviceability
A three-storey RCC hostel block in Bhopal has 4.5 m simply supported corridor slabs, 150 mm thick, M25 concrete with Fe500 steel: 12 mm bars at 150 mm centres at midspan, clear cover 20 mm. Imposed load for the corridor is 3.0 kN/m² and floor finish is 1.0 kN/m². After two monsoons the false ceiling shows a midspan sag of about 30 mm, and hairline soffit cracks run parallel to the supports. The original design note quotes a span/depth ratio of 30 and calls it acceptable. Site inspection finds no overloading, no fire damage and no corroded steel; the measured midspan steel is 0.50 per cent of the gross section. The department's specification requires deflection to be checked by IS 456 provisions, not thumb rules, and the block must be reoccupied within four months.
1. Check the 150 mm slab against the IS 456 span/depth and deflection requirements. Is the depth acceptable?
Read the worked answer
Effective depth d = 150 - 20 - 6 = 124 mm (12 mm bar, 20 mm cover).
L/d = 4500/124 = 36.3.
Basic ratio for a simply supported slab = 20. Modification factor depends on fs = 0.58 fy (Ast required/Ast provided) and on pt.
- Ast provided = 113/0.150 = 754 mm²/m; pt = 754/(1000 × 124) = 0.61%.
- Flexural Ast required is about 620 mm²/m, so fs ≈ 0.58 × 500 × 620/754 ≈ 238 N/mm² (~240).
- From IS 456 Fig. 4 at fs = 240 and pt ≈ 0.6%, the modification factor is about 1.35, giving an allowable L/d of about 27.
Required d ≈ 4500/27 ≈ 167 mm, i.e. an overall depth near 190 mm. The provided 36.3 is far above 27, so the span/depth check fails.
The measured sag of 30 mm is L/150. The code limit for total deflection is L/250 = 18 mm, and for members supporting brittle finishes it is stricter. The observed sag therefore also fails the explicit deflection limit and explains the ceiling distress. Conclusion: the slab is not code-compliant in serviceability, though this alone does not prove inadequate strength.
2. Is the slab's flexural capacity adequate for the actual loads? Interpret the result for the client.
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Flexural capacity (per metre width):
- xu = 0.87 fy Ast/(0.36 fck b) = (0.87 × 500 × 754)/(0.36 × 25 × 1000) = 36.5 mm; xu,max = 0.46 × 124 = 57 mm, so under-reinforced.
- Mu = 0.87 fy Ast (d - 0.42 xu) = 328,000 × (124 - 15.3) N·mm = 35.6 kN·m/m.
Applied: w = 1.5(3.75 + 1.0 + 3.0) = 11.6 kN/m (self weight 0.15 × 25 = 3.75). Mu = wl²/8 = 11.6 × 20.25/8 = 29.4 kN·m/m.
Utilisation = 29.4/35.6 = 0.83, leaving roughly 18 per cent margin, which is acceptable for a code-designed member of this age; shear and development length still need separate checks.
Interpretation for the client: strength is adequate, serviceability is not. The sag is not merely cosmetic because a 30 mm sag (L/150) damages brittle ceilings and partitions, can create ponding and vibration discomfort, and will keep increasing with creep. The slab should not be demolished, but it should not be treated as satisfactory; occupancy can be allowed with the imposed load restricted to the design 3.0 kN/m², no added partitions or water tanks, and a written monitoring record, while a retrofit is planned.
3. Recommend the cheapest code-compliant remedy, with calculations for the option you reject and the one you adopt.
Read the worked answer
Option 1 - plain soffit jacketing of 65 mm to reach d ≈ 189 mm. This fixes L/d (4500/189 × 0.8 ≈ 19 < 27) but adds 0.065 × 25 = 1.63 kN/m² dead load. New w = 1.5(5.38 + 1.0 + 3.0) = 14.1 kN/m, giving Mu = 35.6 kN·m - exactly the existing capacity. The jacket would consume all margin, so it is not acceptable as a plain jacket; it must contain added bottom reinforcement (say 10 mm at 150 mm = 524 mm²/m, total 1278 mm²/m, capacity about 57 kN·m) plus shear checks and shear keys. Cost is moderate but work is disruptive and must be done under full propping.
Option 2 - introduce a midspan beam (steel or RCC). Effective span halves to 2.25 m, so L/d = 2250/124 = 18 < 27, and deflection falls by well over an order of magnitude (span to the fourth power plus a change from simply supported to two-span behaviour). This is normally the cheapest compliant solution where corridor headroom allows.
Recommendation: adopt Option 2 if headroom permits, otherwise reinforced Option 1. In both cases repair the cracks with polymer-modified mortar, verify the result, and re-verify by a 24-hour load test with recovery of at least 75 per cent of the measured deflection before reoccupation.