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 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

Positive, 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/m

Normal Weight

40 N/mm2

Inertia Modular Ratio,

m

Shear Span,

Lv

Shear Trough Width

, bb

Uncracked, Iu

Cracked, Ic

Average Ia

Modular

Ratio,m

Bond, Vs

Vertical Vv

112 mm

1.433704.8 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 = 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 <= 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 PROP PING

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, (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 = wl28

= 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 ULTIM ATE 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 ULTM ATE 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.