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Well foundation of pier: PCC and steel

Short answer

M20 concrete in steining is 612.61 m3 (upper 1 m thick 188.50 m3, lower 2 m thick 424.12 m3); adding two 1 m plugs gives 689.58 m3. Steel at 1.5% by volume is 72.13 tonnes.

A well foundation for pier of a bridge is to be constructed. It has 7 meters internal diameter and 15 metres depth from river bed level to top of well curb. Well steining of 1 meter thickness is to be constructed up to 7.5 metres depth and remaining of 2 m thickness with M20 RCC. There are two plugs of M20 concrete at top and middle of 1 m thickness. Find out i) Quantity of PCC for M20 RCC works ii) Steel reinforcement for M20 RCC work well steining (1.5% of PCC by volume)

Meaning of the data. The well steining is 1.0 m thick for the top 7.5 m of the 15 m depth and 2.0 m thick for the remaining 7.5 m (M20 RCC). Two 1.0 m thick M20 plugs are placed at the top and middle of the well.

i) Quantity of concrete in the steining

Annular volume = π4(Do2−Di2)×h\frac{\pi}{4}(D_o^2-D_i^2)\times h, with Di=7D_i = 7 m.

  • Upper steining (t=1t=1 m, Do=9D_o=9 m): π4(81−49)×7.5=188.496\frac{\pi}{4}(81-49)\times 7.5 = 188.496 m³
  • Lower steining (t=2t=2 m, Do=11D_o=11 m): π4(121−49)×7.5=424.115\frac{\pi}{4}(121-49)\times 7.5 = 424.115 m³

Total M20 concrete in steining = 188.496 + 424.115 = 612.61 m³.

Plugs (2 nos., 1.0 m thick, 7 m dia): 2×π4×72×1.0=76.972\times\frac{\pi}{4}\times 7^2\times 1.0 = 76.97 m³ of M20 plain concrete.

Total M20 concrete including the plugs = 612.61 + 76.97 = 689.58 m³.

ii) Steel reinforcement in steining (1.5 % by volume)

Volume of steel = 0.015 × 612.611 = 9.189 m³.

Weight = 9.189 × 7850 kg/m³ = 72,135 kg = 72.13 tonnes.

Answer: Steining concrete = 612.61 m³ (plus 76.97 m³ in plugs, 689.58 m³ in all); steel = 72.13 t.

✓ Answer checked by Claude Opus 5.5 (high effort)

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