A hub for civil engineering related designs, analyses, discussion, information, and knowledge...

## Saturday, June 30, 2018

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 2: Double L Precast Seating Deck

 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

1. if i may ask, i also wish you respond, why isnt the trend designed as an entity? lets presume the section is a a flat trend with no beam (150*400). would the section still satisfy deflection?

1. If properly designed, it will be able to satisfy limit state requirements.

2. No...not really... you should consider the principal axis of L shaped seat section and take into consider the dynamic loading. That is, you should consider synchronized movement of occupants, s
such as occurs at pop concerts and events..Refer to BS 6399-1:1996...H.TURKAKIN

3. can we get a free pdf copy of the design

4. Great designs! what is the the best types of precast compound wall designs to choose my residential compound wall installation.

5. Great blog! the precast compound walls is one of the best option to make our construction process in an effective way.

6. You have shared a nice article here about the Precast Seating Decks. Your article is very informative and useful to know more about the process of manufacturing the Seating Decks for stadiums. If anyone looking for the Precast Structural Engineering Design services, SLABS is the best choice.