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 |

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;

F

_{cu}= 35 N/mm

^{2}; F

_{yv}= 460 N/mm

^{2}; F

_{y}= 460 N/mm

^{2}

Concrete cover = 30 mm

Unit weight of concrete = 24 kN/m

^{3}

**Loading Analysis**

Load type = uniformly distributed loading

*Dead Load*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/m

^{2}

*Live Load*For grandstands with fixed seating = 4 kN/m

^{2}

Making allowance for dynamic magnification = 5 kN/m

^{2}

At ultimate limit state;

n = 1.4gk + 1.6qk

n = 1.4(6.32) + 1.6(5) = 16.848 kN/m

Design Moment M

_{max}@ 3.0m = (ql

^{2})/8 = (16.848 × 6

^{2})/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 – C

_{c}- ∅⁄2 - ∅

_{links}

Assuming Y16mm for main bars and Y8mm for links

d = 400 – 30 – 10 – 8 = 352 mm

b = b

_{w}= 150mm (since the flange is at the bottom)

k = M/F

_{cu}bd

^{2}= (78.816 × 10

^{6})/(35 × 150 × 352

^{2}) = 0.121

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

A

_{Sreq}= M/(0.95F

_{y}.la.d) = (78.816 × 10

^{6})/(0.95 × 460 × 0.8399 × 352) = 610 mm

^{2}

In the web, provide 2Y16mm + 2Y12mm (A

_{Sprov}= 628 mm

^{2})

Provide 2Y12mm (A

_{sprov}= 226 mm

^{2}) in the compression zone.

Spread the A

_{s,req}also along the width of the thread

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

^{2}/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

_{w }/ b

_{f }< 0.3)

In this case b

_{w}/b

_{f}= (0.15)/(0.95) = 0.157

Modification factor for tension reinforcement

Service stress F.S = (2F

_{y}A

_{sreq})/(3A

_{sprov}) = (2 × 460 × 610)/(3 × 628)

f.s = 297.9 N/mm

^{2}

m.f = 0.55 + (477 - Fs) / 120(0.9 + M/bd

^{2})

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 × 10

^{3}) / (150 × 352) = 0.957 N/mm

^{2}

0.957 N/mm

^{2}< 0.8 √35 < 5 N/mm

^{2}

Concrete resistance shear stress

v

_{c}= 0.632 × (100As/bd)

^{1/3}× (400/d)

^{1/4}

v

_{c}=0.632 × [(100 × 628)/(150 × 352)]

^{1/3}× (400/352)

^{1/4}

v

_{c}= 0.632 × 1.059 × 1.032 = 0.69 N/mm

^{2}

For concrete grades greater than 25 N/mm

^{2}

v

_{c}= v

_{c}(F

_{cu}/25)

^{1/3}= 0.69 × (35/25)

^{1/3}= 0.772 N/mm

^{2}

0.772 N/mm

^{2}< 0.957 N/mm

^{2}

0.5 v

_{c}< v < (v

_{c}+ 0.4)

provide minimum links with spacing

s

_{v}= (0.95A

_{sv}F

_{yv})/0.4b

_{v}

(Trying 2 legs of Y8mm bar)

s

_{v}= (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**

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?

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

DeleteNo...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

ReplyDeletesuch as occurs at pop concerts and events..Refer to BS 6399-1:1996...H.TURKAKIN

can we get a free pdf copy of the design

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

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

ReplyDelete