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Concrete structures miscellaneous

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The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are M25 and Fe415, respectively. The total area of reinforcing bars (As) is 4000 mm2. At the ultimate limit state, xu denotes the depth of the neutral axis from the top fibre. Treat the section as under-reinforced and flanged (xu > 100 mm).

  1. The value of xu (in mm) computed as per the Limit State Method of IS 456: 2000 is
    1. 200.0
    2. 223.3
    3. 236.3
    4. 273.6
Correct Option: C

Cw = 0.362 fck

Take xu
7 × Df
3

Cf = 0.447 fck. (bf – bw) Φf.
T = 0.87fy Ast
Total compressive force = total tensile force
Cw + Cf = T
0.362 fck + 0.447. fck (bf – bw) Df = 0.87 fy Ast
∴ xu =
(0.87 × 415 × 4000) - (0.447 × 25 × 675 × 100)
(0.362 × 25 × 325)

=
1444200 - 754312.5
= 234.55 mm
2941.25



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