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

Effective Area, As

Inertia, Ixx

Neutral Axis, yna

Yield strengt

h

Moment of Inertia,

Ip

Design Strength Py

Elastic Modulus,

E0.17

kN/m22145

mm2/m87.20 cm4

16.8 mm 350.0 N/mm2

75.0 mm4/m

325.5 N/mm2 205 kN/mm2

Moment Capacity Web Capacity Shear BondPositive,

M+Negative,

M-Residual,

M-r

Buckling, Pw

Shear, Pv mr kr Partialτ

9.58 kNm/m

9.69 kNm/m

5.92 kNm/m

125.68 kN/m

161.1 kN/m 228.6 N/mm2

0.0048 N/mm

358.4 kN/m2

Composite slab

Slab Structural Section Properties:

Nominal Slab Depth

Concrete Dry self Weight

Effective Depth, ds

Concrete Stress Block

Lever Arm, z

Moment Capacity,M

175mm Type Grade 4.22 kN/m2

158.20 mm

38.79 mm 138.81 mm

96.91 kNm/mNormal

Weight40

N/mm2

Inertia Modular Ratio, m

Shear Span, Lv

Shear Trough Width

, bbUncracked,

Iu

Cracked, Ic

Average Ia

Modular Ratio,m

1.43

Bond, Vs Vertical Vv

112 mm

3704.8 cm4 2468.2 cm4

3086.5 cm4

15.7 43.90 kN/m

121.86 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 = 3 3w l4

384 EI

= 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 <= 30.0 mm (BS5950 part 4)

21.6mm > 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 = w l2

8

=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, (M / Mc-) + (0.901 x Fw / Pw) = 1.0726 < 1.151

Elastic resisting moment, Mr = (1.151 - (0.901 x 0.236)) x Mc- = 9.10 kNm/m

Applied M < allowable Mr therefore elastic design condition satisfied

1.4 CHECK BENDING IN CRITICAL FLANGE DUE TO POSITIVE MOMENT

Positive Resisting Moment, Mc+ = 9.580 kNm/m

py = 350 x 0.93 = 325.50 N/mm²

Applied moment, M = w l2

8

= 8.42 x 2.813² x 0.096 = 6.40 kNm/m < Mc+ = 9.580 kNm/m OK!

(Deck elastic over intermediate support or prop)

1.5 CHECK WEB BUCKLING AT END SUPPORT

Buckling resisting capacity = Pw / 2.5 = 125.7 / 2.5 = 50.27 kN/m

Design Reaction, Fw = 8.42 x 2.813 x 0.438 = 10.38 kN/m

(Deck elastic over intermediate support or prop)

Maximum Applied Reaction, Fw = 10.3 8kN/m < 50.27 kN/m OK!

1.6 CHECK WEB SHEAR AT INTERMEDIATE SUPPORT

Pv = 161.10 kN/m (at support)

Applied Shear, Fv = 8.42 x 2.813 x 0.625 = 14.81 <= 161.10 kN/m

Combined bending & shear check,

(Fv/Pv)² + (M/Mc-)² = 0.75 <= 1.0 OK!

2.0 Composite Stage

2.1 CHECK DEFLECTION DUE TO LIVE IMPOSED LOADING + PARTITION ALLOWANCE

Composite Design Span = Effective span + Slab Effective Depth - Beam Support Width

= 5.800 + 0.158 - 0.225

= 5.733 m

Floor Dry Self Weight = 4.215 kN/m2

Ixx = 0.5 x (Icracked + Iuncracked)

= 0.5 x (2468.2 + 3704.8)

= 3086.5 cm4

Deflection = 5/384 x (2.50 + 1.00) x 5.7334 x 105 / (205 x 3086.5)

= 7.78 mm

Allowable deflection = 5.733 m / 350

= 16.38 mm < 20.0 mm OK!

2.2 CHECK DEFLECTION DUE TO TOTAL IMPOSED SERVICE LOADING + CONSTRUCTION PROP REMOVAL

Uniformly Distributed load = Live load + partitions + finishes + service load

= 2.50 + 1.00 + 0.70 + 0.25 = 4.45 kN/m

Deflection caused by U.D.L = 4.45 / 3.50 x 7.78

= 9.89 mm

Deflection (propping removed) = 4.215 / 3.50 x 7.78 = 9.37 mm

Allowable deflection = 5.733 m / 250 = 22.93 mm > ( 9.89 + 9.37) mm OK!

2.3 CHECK POSITIVE ULTIMATE BENDING MOMENT IN COMPOSITE SLAB

Design Ultimate Loading = (4.22 +0.70 +0.25) x 1.4 + (2.50 +1.00) x 1.6

= 12.83 kN/m

Applied moment, Mw = wL²/8

= 12.83 x 5.733 x 5.733 x 0.125 = 52.72 kNm/m

Cover width of composite slab, Bs =1000mm

T = py x As = C = 0.45 x fcu x Bs x Xs = 698.20 kN/m

Effective Depth of slab to centroid of profile sheet, ds =175 - 16.8 = 158.20 mm Xs = 698.20 / (0.45 x 40) =38.79 mm

Moment Capacity, Mcs = (ds - Xs/2) x py x As

= 138.81 x (350 x 0.93) x 2145 / 106

= 96.91 kNm/m > 52.72 kNm/m Applied moment

2.4 CHECK ULTMATE HORIZONTAL SHEAR AGAINST SHEAR BOND CAPACITY AT END SUPPORT

Applied horizontal shear, Vhu = total composite shear - slab wt.shear + propping removed shear

= 36.78 - 4.215 x 1.4 x 5.733/2 + 15.10 x 1/2 x 1.4 = 30.44 kN/m

Slab self Wt.moment, Msw = 4.22 x 5.733² x 0.125 x 1.40

= 24.25 kNm/m

Propping removal moment, Mprp = Pfc x Nprops x Mselfweight

= 0.625 x 1 x 24.25

= 15.15 kNm/m

Lv = (Mw-Msw+Mprp)/ Vhu

= (52.72 - 24.25 + 15.15)/30.44

= 1.433 m

Shear Bond Resistance, Vs = Bs.ds/1.25 ( mr.Ap/(Bs.Lv) + kr )

= 1000 x 158.20/1.25 x (228.60 x 2145/(1000 x 1433) + 0.0048 )/1000

= 43.90 kN/m > 30.44 kN/m Applied, OK!

2.5 CHECK APPLIED TOTAL ULTIMATE SHEAR AGAINST SLAB VERTICAL SHEAR CAPACIT Y

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(Resistance) Composite Stage Applied(Resistance)

Deck Deflection 13.69 (21.64)mm Live load deflection

7.78 (16.38)mm

Intermediate Reaction Web Buckling

29.61 (125.68)kN Total imposed load deflection

19.27 (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 at End Support

10.38 (50.27)kN Composite Slab Shear

36.78 (121.86)kN

Web Shear Adjacent to support

14.81 (161.10)kN Fire Bending Moment

36.44 (38.57)kNm

Slab Section

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 self-weight 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.