Municipal checks
In a municipality in South Holland, I was assisting a client who had to obtain municipal approval again to install a staircase. I found that the previously approved reinforcement was inadequate. See the calculation below.
Floor span l = 5.15 + 0.125 + 0.09 = 5.365 m
Design load per m²
pd = 1.2 × 0.22 × 25 + 1.3 × 1.75 = 8.9 kN/m²
Span moment per m = Mv/m = (9/128)pl² = 18 kNm
Fixed-end moment per m = Mi/m = pl²/8 = 32 kNm
concrete cover = 30 mm; assuming ø10 bars, the internal lever arm is 0.9 × (220 – 30 – 5) = 166 mm
Required span reinforcement without opening trimming bars, per m
Av/m = 18/{0.435 kN/mm² × 0.166 m} = 249 mm²/m = 125 mm²/0.5 m
Minimum span reinforcement without opening trimming bars
0.15% × 220 = 330 mm²/m = 165 mm²/0.5 m
Required hogging reinforcement without opening trimming bars
Ai/m = 32/{0.435 kN/mm² × 0.166 m} = 443 mm² = 222 mm²/0.5 m
Because the opening is larger than 400 × 400 mm, two strips of 0.5 m carry
the load that cannot be carried across the 0.7 × 1.2 m opening.
These strips therefore carry 0.35/0.5 = 70% extra load1.
The total required span reinforcement per 0.5 m then becomes
Av/0.5 m = 1.7 × 125 mm²/0.5 m = 213 mm²/0.5 m > 165 mm²/0.5 m
so 213 mm²/0.5 m governs.
Provided: 2ø10 + ø7.5-150 = 157 + 147 = 304 mm²/0.5 m, so the bottom reinforcement is adequate.
The total required top reinforcement per 0.5 m then becomes
Av/0.5 m = 1.7 × 222 = 377 mm²/0.5 m
Provided: 434 mm²/m = 217 mm²/0.5 m, i.e. only 65% of what is needed. For the top reinforcement, a wider load spread could in practice be assumed.
Assuming, for example, a 2 m load spread, 70%/4 = 17.5% extra reinforcement is needed. This is not present either, but because of the higher safety factors it will not lead to failure. Moreover, the loads on the second-floor slab will remain limited.
Whereas the engineers who submitted the calculation needed many pages within a document of over a hundred pages, a single A4 sheet was enough for me. The unclear presentation is probably also why the municipality concerned did not spot the error.