Archive Conversion on an Existing Flat-Plate Floor
A 1998 flat-plate office building in Mohandeseen, Cairo, has 220 mm slabs, 400 × 400 mm columns on a 6.0 × 6.0 m grid, fcu = 30 MPa, 20 mm cover and 16 mm bottom bars. The owner is converting the third floor into a compact archive. Superimposed dead load rises by 1.2 kPa for mobile shelving tracks and the live load rises from 2.5 to 7.5 kPa. The contractor wants to install shelving within two weeks and asks you to confirm that the floor is adequate. You also note a 0.25 mm crack running diagonally from the corner of an edge column, which supports a 6 m span plus a 2.0 m cantilever balcony on one side. The building has no shear walls, only moment frames, and the original design drawings are available but the as-built reinforcement was never verified. The architect argues that because the slab was designed for 2.5 kPa live load with a 1.6 factor, 'there is spare capacity'.
1. Estimate the factored load and the punching shear demand at a typical interior column. State the assumed effective depth and critical perimeter, and say whether punching or flexure governs the strengthening decision.
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Loads. Slab self-weight 0.22 × 25 = 5.50 kPa; finishes and suspended services about 1.2 + 1.0 = 2.2 kPa; new shelving tracks 1.2 kPa, giving DL ≈ 8.9 kPa. LL = 7.5 kPa. Factored w = 1.4(8.9) + 1.6(7.5) = 12.5 + 12.0 = 24.5 kPa.
Effective depth. With 20 mm cover, a 16 mm bottom bar and an assumed 10 mm top mat, d ≈ 220 − 20 − 16 − 8 = 176 mm; adopt 175 mm.
Critical perimeter at 0.5d from the column face: b0 = 4(400 + 175) = 2300 mm. The area inside the perimeter is 0.575² ≈ 0.33 m², so V = 24.5 × (36.0 − 0.33) ≈ 874 kN.
Stress. v = 874,000/(2300 × 175) ≈ 2.17 MPa. For fcu = 30 MPa, ECP 203 punching capacity without shear reinforcement is of the order of 1.0–1.3 MPa for a slab of this depth and reinforcement ratio. Demand exceeds capacity by roughly 1.7–2.0.
Which governs. Flexure is far less critical: the sagging moment is about 24.5 × 6²/8 ≈ 110 kNm/m, comfortably carried by the existing bottom bars. Punching governs, so the floor cannot be loaded as proposed and the solution must address the column regions, not the mid-span steel.
2. Explain why the edge column with the cantilever needs a separate check, and how the unbalanced moment changes the punching stress distribution. What would you require before accepting the archive load?
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The edge column carries a 6 m interior span on one side and a 2.0 m cantilever on the other, so it has a permanent unbalanced moment that grows with the archive loading. Two things change relative to an interior column. First, the critical perimeter is effective on only three sides, so b0 is smaller and the average shear stress rises. Second, part of the unbalanced moment is transferred by eccentric shear rather than by flexure alone, giving v = V/(b0d) + γv·M·c/J, where γv is typically 0.3–0.4 for a near-square column and must be taken from ECP 203 rather than assumed.
The diagonal crack at the column corner is consistent with high local shear stress, or with yielding of the top bars over the cantilever; it cannot be dismissed as shrinkage. Before accepting the load I would: verify the top reinforcement over the cantilever by cover meter and a small opening; check the cantilever tip deflection and crack width against code limits; recover the original edge-column design moment; and confirm the slab's ability to redistribute moment into the adjacent panels. If calculations remain marginal, require a monitored trial loading with deflection readings rather than a paper approval.
3. Recommend a strengthening and load-sequencing plan. Rank the options by cost, downtime and reliability, and explain the sequence.
Read the worked answer
Options. (1) Reduce the demand: specify high-density compact shelving with fewer aisles, or limit storage height, cutting the live load to about 4–5 kPa. Cheapest and fastest, but it depends on the owner's operational discipline. (2) Add punching shear reinforcement: drilled-in shear studs or a steel collar bolted around the column, designed for the full V and the unbalanced moment. Moderate cost, moderate downtime, high reliability if the anchorage is verified. (3) Enlarge the columns with a reinforced concrete jacket, which also helps the edge column's moment transfer. Higher cost and longer downtime because of propping and curing. (4) A drop panel or new transfer beams is rarely economic in an existing building.
Sequence. Prop the slab adjacent to the critical columns; strip finishes and confirm bar positions; install the shear reinforcement from the top where possible; allow the anchorage or jacket to reach strength; then load in stages, with levelling of the shelving and deflection readings at 0, 50 and 100 per cent load. Do not permit shelving installation before the strengthened zones are released by a signed inspection.