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Composite Slab Design

Effective Span = 5.8 m Slab depth = 175mm

Loads Imposed Load

= 2.5 kN/m2

Partitions

= 1.0 kN/m2

Finishes

= 0.70 kN/m2

Ceiling & services

= 0.25 kN/m2

Deck Profile

Holorib, steel grade S350, 1.2mm thickness.

Profile section structural properties: Self Weight

Effectiv e Area, As

Inertia, Ixx

Neutra l Axis, yna

Yield streng th

Moment of Inertia, Ip

Design Strength Py

Elastic Modulu s, E

0.17 kN/m2

2145 mm2/m

87.20 cm4

16.8 mm

350.0 N/mm2

75.0 mm4/m

325.5 N/mm2

205 kN/mm2

Moment Capacity

Web Capacity

Shear Bond

Positiv e, M+

Negativ e, M-

Residu al, M-r

Bucklin g, Pw

Shear, Pv

9.58 kNm/ m

9.69 kNm/m

5.92 kNm/m

125.68 kN/m

161.1 kN/m

mr

kr

Partial τ

228.6 0.004 N/m 8 2 m N/m m

358.4 kN/m2

Composite slab Slab Structural Section Properties: Nominal Slab Depth 175mm

Concrete

Type

Grade

Normal Weight

40 N/mm2

Inertia

Uncracke d, Iu

Cracke d, Ic

Averag e Ia

Dry self Weight

Effectiv e Depth, ds

Concret e Stress Block

Lever Arm, z

Moment Capacity ,M

4.22 kN/m2

158.20 mm

38.79 mm

138.8 1 mm

96.91 kNm/m

Modula r Ratio, m

Shear Span, Lv

Modula r Ratio,m

Shear

Trough Width , bb

Bond, Vs

Vertic al Vv

112 mm

3704.8 cm4

2468.2 cm4

3086.5 cm4

15.7

1.43

43.90 kN/m

121.8 6 kN/m

112mm

1.0 Construction Stage Design Span = Effective span - Beam Support Width + Profile Depth = 5.8 – 0.225 + 0.051 = 5.626 m Construction Span = Design Span/2 = 2.813 m Construction Load Allowance = 1.500 kN/m² for Nominal Span >= 3.0 m Unfactored Slab Self Weight, Wd (allowing for ponding + deck) = Density of concrete*9.81x10-3*depth of slab – (steel depth profile + (steel depth profile/2))+ load due to ponding Wd = 4.301 kN/m²

1.1 CHECK DECK DEFLECTION DUE TO WET CONCRETE Def = 33wl4384EI = 3 x (4.301) x 2.813^4 x 10^5 / (384 x 205 x 75.0) = 13.7mm (Allowable deflection with ponding = construction span/ 130 = 2.813 m / 130 = 21.6 mm 13.7mm OK!

1.2 CHECK WEB CRUSHING AT INTERMEDIATE SUPPORT OR CONSTRUCTION PROP Design Loading = 1.4Gk + 1.6Qk = 1.4 x 4.301 + 1.6 x 1.500 = 8.42 kN/m² Elastic Design Reaction, Fw = Design Loading x Construction Span x partial safety of resistance, ym = 8.42 x 2.813 x 1.25 = 29.61 kN/m Allowable reaction, Pw = 125.68 kN/m > 29.61kN/m OK!

1.3 CHECK COMBINED BENDING & WEB CRUSHING AT SUPPORT OR CONSTRUCTION PROPPING Negative Resisting Moment, Mc- = 9.690 kNm/m Steel yield strength, Py = 0.93 x 350 = 325.50 N/mm² Applied Elastic Moment, M = wl28 =8.42 x 2.813² x 0.125 = 8.33 kNm/m Fw / Pw = 29.61 / 125.68 = 0.236 > 0.168 M / Mc- = 0.860 For allowable Fw / Pw > 0.168, 1.151

(M / Mc-) + (0.901 x Fw / Pw) = 1.0726
30.44 kN/m Applied, OK!

2.5 CHECK APPLIED TOTAL ULTIMATE SHEAR AGAINST SLAB VERTICAL SHEAR CAPACITY

Applied ultimate vertical shear force = design ultimate loading x composite design span/2 = 12.83 x 5.733/2 = 36.78 kN/m 100.As/(Bs.ds) = 100 x 2145 / (1000 x 158.20) = 1.356 Using Table 3.8 BS8110-Pt.1,

vc = 1.032 N/mm² for Normal Wt concrete.

V = vc.bv.ds = 1.032 x 112.0 x 158.20 / 150.0 = 121.86kN/m >36.78kN/ Applied, OK!

2.6 DESIGN OF COMPOSITE FLOOR SLAB FOR 60 MINS. FIRE RATING (STEEL REINFORCEMENT) Slab dry self weight (ponded) = 4.22 kN/m² Total imposed load = Live Load x factor + Partitions+ Finished + Services = (2.50 x 1.0) + 1.00 + 0.70 + 0.25 = 4.45 kN/m² Applied Fire Moment, Mf = (total imposed load +slab dry s.w) x effective span2 x 0.125 = (4.45 + 4.215) x 5.800² x 0.125 = 36.44 kNm/m *From Steel Construction Institute Fire load/span table for 175mm slab depth using A393mesh ,Max span for 4.45kN/m2 imposed loading = 5.97 m. Notional Resisting Moment = (4.45 + 4.22) x 5.97² x 0.125 = 38.57 kNm/m > 36.44 kNm/m OK!

Design Summary Construction Stage

Applied(Resista nce)

Composite Stage

Applied(Resista nce)

Deck Deflection Intermediate Reaction Web Buckling

13.69 (21.64)mm

29.61 (125.68)kN

Live load deflection

7.78 (16.38)mm

Total imposed 19.27 load deflection (22.93)mm

-ve Support Moment

8.33 (9.10)kNm

Composite Bending Moment

52.72 (96.91)kNm

+ve Bending Moment

6.40 (9.58)kNm

Composite Shear Bond

30.44 (43.90)kN

Web Buckling 10.38 at End Support (50.27)kN

Composite Slab Shear

36.78 (121.86)kN

Web Shear Adjacent to support

Fire Bending Moment

36.44 (38.57)kNm

Slab Section

14.81 (161.10)kN

RISK ASSESSMENT AND MITIGATION OF COMPOSITE SLAB A composite slab comprises steel decking, reinforcement and cast in situ concrete which is normally supported by a steel beam. Risk associated with using a composite slab: 1) Excessive ‘ponding’, occurs especially in the case of long spans

during construction stage. The profiled sheet deflects considerably at the centre due to loads arising from the weight of the wet concrete and steel deck, construction loads (operatives and equipment). This requires additional wet concrete, as the central depth of the slab is decreased which will cause increase weight. 2) Cracking of concrete. The lower surface of the slab is protected by

the sheeting. Cracking will occur in the top surface where the slab is continuous over a supporting beam, and will be wider if each span of the slab is designed as simply-supported, rather than continuous, and if the spans are propped during construction. 3) Breakdown of shear bond. The ultimate moment resistance of

composite slabs is determined by the breakdown of bond and mechanical interlock between the decking and the concrete, known as

shear bond. Composite slabs are usually designed as simply supported members, and the slip between the decking and the concrete usually occurs before the plastic moment resistance of the composite section is reached. The bond between the steel deck and concrete may not be fully effective and longitudinal slip may occur before the steel deck yields. As a result, two primary failure modes are possible; flexural failure and shear-bond failure. Flexural failure occurs not due to cracking but due to slip of concrete and steel. Shear-bond failure occurs when lateral load exceeds the ultimate longitudinal shear load resistance at the steel concrete interface. 4) Misalignment of the structural diaphragm. During construction

the steel decking is often assumed to provide adequate lateral bracing to resist in-plane forces arising from wind loading. The ability of the decking to function as a stressed-skin diaphragm is dependent on the fixing details in place at the time of the applied loading. Initially the deck will only be secured to the beams with shot fired pins. Through deck welding of shear connectors is likely to occur soon after but there could be a delay of a few days. This is when the building is at its most vulnerable. 5) Failure due to low fire resistance period of the metal deck, which is

usually unprotected, heats up rapidly and loses strength and stiffness. Each floor slab can be designed for up to 4 hours of fire protection period by increasing the thickness of the slab and its reinforcement. Risk of prolonged period of fire longer than the designed period can cause severe slab cracking around the column, reinforcement fracture and exposed shear studs. A major reason for this separation of the shear studs is when the composite slab is connected to each beam by limited number of shear studs. Local buckling in the lower beam flange and web may also occur due to partial end plates incapable of transferring high internal force from the beam to the adjacent columns.

Slab may move downwards at its connection with column due to excess deflection of slab caused by fire.

Mitigation measures: 1) Composite deck slabs were shown to be adequately strong in fire and

crack if reinforced with mesh. Providing a minimum depth of slab also satisfies insulation requirements. For crack prevention, longitudinal reinforcement should be provided above internal supports. The minimum amounts are given by British Standard BS 5950: Part 4: 1994 as 0.2% of the area of concrete above the sheeting for unpropped construction, and 0.4% if propping is used. These amounts may not ensure that crack widths do not exceed 0.3 mm. If the environment is corrosive (i.e. de-icing salt on the floor of a parking area), the slabs should be designed as continuous with cracking controlled. 2) For

‘ponding’, longer spans will require propping to eliminate

substantial deflection or need significant quantities of concrete. The British Standard recommends that where the deflection exceeds one tenth of the slab depth, the additional weight of concrete due to the deflection of the sheeting should be taken into account in the selfweight of the slab. 3) Shear connectors between beam and slab also influence the failure mode. Where shear studs are provided to ensure composite action between the beam and slab the anchorage provided by the studs will enhance the longitudinal shear capacity and hence the load carrying capacity of the slab. 4) To resist wind load, the decking can be fixed to the supporting steel

beams using 4 mm shot fired pins are used at 300 mm spacing, self-

tapping screws or welding. Lateral restraint to the steel framed structure can be achieved by ensuring that sufficient fixings are used.