## Bhw

Effective depth, d = 115

Span 3.0m

Slope length of stairs = s/(32 + 5^) = 3.35 m Consider a I m width of stairs:

Weight of waist plus steps (0.14 x 3.35 + 0.26 x 1.5/2)25 = 16.60 kN Variable load = 3.0 x 3 = 9.0 kN Ultimate load, F = 1.35 x 16.60+ 1.5 x 9.0 = 35.91 kN

With no effective end restraint: ^ H 35.91x3.0 = 13 46kNm

Bending reinforcement M 13.46 x 106

bd2U 1000 x 1152 x 30

From the lever-arm curve, figure 4.5. /., - 0.95 (the maximum normally adopted in practice), therefore

Maximum allowable spacing is 3It 3 x 140 - 420mm with an upper limit of 400mm. Provide 1112 bars at 300 mm centres, area 377mnr/m. Span-effective depth ratio At the centre of the span lOOAypmv _ 100 x 377 bd 1000 x 115

which is greater than the minimum requirement of 0.15 for class C30 concrete (see Table 6.8).

From table 6.10 the basic span-effective depth ratio for a simply supported span with pra| - 0.5% is 20. Allowing for the actual steel area provided:

limiting span-effective depth ratio 20 x As.p„)V/As,req

actual span-effective depth ratio = 3000/115 = 26.09

Hence the slab effective depth is acceptable. (Note that the allowable ratio will actually be greater than estimated above since the required steel ratio is less than the 0.5% used with table 6.10.)

Secondary reinforcement

Transverse distribution steel > 0.2As,mm - 0.2 x 377 = 75.4mnr/m

This is very small, and adequately covered by H10 bars at the maximum allowable spacing of 400 mm centres, area = 174 mnr/m.

Continuity bars at the top and bottom of the span should be provided and, whereas about 50 per cent of the main steel would be reasonable, the maximum spacing is limited ^_to 400mm. Hence provide, say, H12 bars at 400 mm centres as continuity steel.__j

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