slab
Click here to load reader
description
Transcript of slab
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.