Question

The ring beam of a Intze tank carries a hoop tension of 120 kN.The beam cross-section is 250 mm wide and 400 mm deep, and it is reinforced with 4 bars of 20 mm dia of Fe – 415 grade. The modular ratio of concrete is 10. The tensile stress (N/mm²) in the concrete is
1. 1.02
2. 1.07
3. 1.20
4. 1.32

Answer 1

Correct Answer - Option 2 : 1.07

Concept:

The tensile stress in concrete (σ_T) is given by

\({{\bf{\sigma }}_{\bf{T}}} = \frac{{\bf{T}}}{{{\bf{b}} \times {\bf{d}} + \left( {{\bf{m}} - 1} \right) \times {{\bf{A}}_{{\bf{st}}}}}}\)

T - Hoop tension in the ring beam

b - Width of ring beam

d – Depth of ring beam

A_st - Area of tensile reinforcement

\({{\rm{A}}_{{\rm{st}}}} = {\rm{n}} \times \frac{{\rm{\pi }}}{4} \times {{\rm{d}}^2}\)

m - Modular ratio of concrete

n – Number of bars

d – Diameter of bars

Calculation:

Given:

T = 120 kN, d = 400 mm

m = 10, b = 250 mm

n – Number of bars

d – Diameter of bars

\({{\rm{A}}_{{\rm{st}}}} = {\rm{n}} \times \frac{{\rm{\pi }}}{4} \times {{\rm{d}}^2} = 4 \times \frac{{\rm{\pi }}}{4} \times {20^2} = 1256{\rm{\;m}}{{\rm{m}}^2}\)

\({{\rm{\sigma }}_{\rm{T}}} = \frac{{120}}{{250 \times 400 + \left( {10 - 1} \right) \times 1256}} = 1.07\;{\bf{N}}/{\bf{m}}{{\bf{m}}^2}\)