Question 12.P.11: If the concrete in the composite beam in P.12.10 has a reduc...
If the concrete in the composite beam in P.12.10 has a reduced strength of 15 N/mm² determine its resulting moment of resistance.
The available compressive force in the concrete is
0.4 × 15 × 2 × 10^{3} × 175 × 10^{-3}=2100 kN
The available tensile force in the steel is
0.87 × 350 × 9490 × 10^{-3}=2890 kN
Since the available compressive force in the concrete is less than the available tensile force in the steel the neutral axis of the composite beam section lies within the steel beam. Then, from Eq. (12.30) 0.4 \sigma_{\mathrm{cu}} b h_{\mathrm{c}}+2 \times\left(0.87 \sigma_{\mathrm{Y}}\right) A_{\mathrm{sc}}=0.87 \sigma_{\mathrm{Y}} A_{\mathrm{s}}
0.4 × 15 × 2 × 10^{3} × 175+2 × 0.87 × 350 A_{sc}=0.87 × 350 × 9490
which gives
A_{sc} = 1297 mm²
From Steel Tables the flange thickness of the steel beam is 17 mm so that, by inspection, the neutral axis lies within the flange of the beam. Then
152 h_{f}=1297
from which
h_{f} = 8.5 mm
and
h_{sc} = 175 + 8.5 = 183.5 mm
From Eq. (12.31) M_{\mathrm{u}}=0.87 \sigma_{\mathrm{Y}} A_{\mathrm{s}}\left(d-\frac{h_{\mathrm{c}}}{2}\right)-2 \times\left(0.87 \sigma_{\mathrm{Y}}\right) A_{\mathrm{sc}}\left(h_{\mathrm{sc}}-\frac{h_{\mathrm{c}}}{2}\right)
M_{u}=0.87 × 350 × 9490(405.5-87.5)-2 × 0.87 × 350 × 1297(183.5-87.5)
which gives
M_{u} = 843 kN m