# Design of Precast Seating Decks for Stadium One of the most common construction concept of sports stadiums today normally involves having precast concrete terrace units (seating decks) span between inclined (raker) steel or reinforced concrete beams and rest on each other, thereby forming a grandstand. The raker beams are usually formed in-situ with the columns of the structure, and forms part of the structural frame of the grandstand. It is also feasible to construct precast raker beams as was done in the Corinthians Arena Sao Paolo, Brazil for the 2014 FIFA world cup. Fig 3: Structural Section of a grandstand

Precast seating decks are usually of L-shaped reinforced concrete units of length usually between 7-8 meters spanning between the raker beams. The seating decks also rest on each other. The role of the third (resting support) is to stop the units from undergoing excessive twisting, and in general, provide extra stability. Seating units are used to span between raker beams, and form the exposed surface which the seats are bolted onto. The seating units are fabricated in moulds depending on the length of the span, angle of inclination/curve, and support conditions. Fig 4: Triple L Seating Deck being installed at Cape Town Stadium SA

Seating units can be easily installed on site, and when the joints between units have been sealed, form an effective barrier against external elements. Precast seating units can also be easily installed in steel structures.

Design Example
Let us design a 6m long precast seating deck for a stadium with a section shown below;

Fcu = 35 N/mm2; Fyv = 460 N/mm2; Fy = 460 N/mm2
Concrete cover = 30 mm
Unit weight of concrete = 24 kN/m3

Self weight of the unit = (24 × 0.15 × 0.25) + (24 × 0.15 × 0.95) = 4.32 kN/m
Make allowance for stair units and railings = 2 kN/m2

For grandstands with fixed seating = 4 kN/m2
Making allowance for dynamic magnification = 5 kN/m2

At ultimate limit state;
n = 1.4gk + 1.6qk
n = 1.4(6.32) + 1.6(5) = 16.848 kN/m

Design Moment Mmax @ 3.0m = (ql2)/8 = (16.848 × 62)/8 = 75.816 KN.m
End shears = ql/2 = (16.848 × 6)/2= 50.544 KN

Design of the section to resist the applied moment
M = 78.816 KN.m
Effective depth d = h – Cc – ∅⁄2 – ∅links

Assuming Y16mm for main bars and Y8mm for links
d = 400 – 30 – 10 – 8 = 352 mm

b = bw = 150mm (since the flange is at the bottom)
k = M/Fcubd2 = (78.816 × 106)/(35 × 150 × 3522) = 0.121

la = 0.5 + √[0.25- 0.121/0.9] = 0.8399

ASreq = M/(0.95Fy.la.d) = (78.816 × 106)/(0.95 × 460 × 0.8399 × 352) = 610 mm2

In the web, provide 2Y16mm + 2Y12mm (ASprov = 628 mm2)
Provide 2Y12mm (Asprov = 226 mm2) in the compression zone.

Provide Y12 @ 175mm c/c Top and Bottom (Asprov = 646 mm2/m)

Distribution bars
Provide Y10 @ 200mm c/c as closed links

Check of Deflection
Basic span/effective depth ratio = 16 (for simply supported beams of b/ b < 0.3)

In this case bw/bf = (0.15)/(0.95) = 0.157

Modification factor for tension reinforcement
Service stress F.S = (2FyAsreq)/(3Asprov) = (2 × 460 × 610)/(3 × 628)
f.s = 297.9 N/mm2
m.f = 0.55 + (477 – Fs) / 120(0.9 + M/bd2)
m.f = 0.55 + (477 – 297.9) / 120(0.9 + 1.1445) = 1.28

Limiting span/effective depth = 1.28 × 16 = 20.48
Actual span/effective depth = 6000/352 = 17.045
Actual < Limiting, therefore deflection is satisfied

Design of the section to resist shear
Critical end shear = 50.544KN
Shear stress v = V/bd = (50.544 × 103) / (150 × 352) = 0.957 N/mm2

0.957 N/mm2 < 0.8 √35 < 5 N/mm2

Concrete resistance shear stress
vc = 0.632 × (100As/bd)1/3 × (400/d)1/4
vc =0.632 × [(100 × 628)/(150 × 352)]1/3 × (400/352)1/4
vc = 0.632 × 1.059 × 1.032 = 0.69 N/mm2

For concrete grades greater than 25 N/mm2
vc = vc(Fcu/25)1/3 = 0.69 × (35/25)1/3 = 0.772 N/mm2

0.772 N/mm2 < 0.957 N/mm2
0.5 vc < v < (vc + 0.4)

sv = (0.95AsvFyv)/0.4bv
(Trying 2 legs of Y8mm bar)
sv = (0.9 5 × 107 × 460)/(0.4 × 150) = 735.62mm

Maximum spacing of links = 0.75d
0.75 × 352 = 264m
Provide Y8 @ 250mm c/c links

Detailing Sketches

3. Anonymous