Answer :
The stress in the steel and the concrete is 71.67 MPa and 0.215 MPa, respectively.
Width of concrete beam, b = 600 mm
Depth of concrete beam, d = 700 mm
Reinforcement provided, diameter of bars = 20 mm,
Distance from the bottom face of the beam = 60 mm
Load on the beam = w = 16 kN/m
Modular ratio = m = 15
The cross-sectional area of one bar = (π/4) × (20)² = 314.16 mm²
Total area of steel = 6 × 314.16 = 1884.96 mm²
Area of concrete = Width × Depth - Area of steel
= 600 × 700 - 1884.96
= 414.04 × 10⁴ mm²
Stress in steel (σ_s) can be calculated using the following relation:
σ_s/E_s = σ_c/E_c×m
Where σ_c = Stress in concrete
E_c = Modulus of elasticity of concrete
E_s = Modulus of elasticity of steelσ_s
= (σ_c × m × E_s)/E_cσ_c
= (w × L)/[(b × d) - A_s] + ((σ_s × A_s)/A_c)σ_c
= (16 × 6)/[600 × 700 - 1884.96] + [(σ_s × 1884.96)/(414.04 × 10⁴)]σ_c
= 0.215 MPaσ_s = (σ_c × E_c)/[m × E_s]σ_s
= (0.215 × 10⁶)/(15 × 200 × 10³)σ_s
= 71.67 MPa
Learn more about Modular ratio from the given link
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