Composite Slab to ACI 318

Verified by the CalcTree engineering team on October 3, 2024
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This calculator performs the structural analysis and design of composite slabs on metal decking for either one-way or two-way spans. It evaluates key parameters including flexural and shear capacity; and deflection limits. These key parameters are calculated for both the temporary case (construction loads) and permanent case. 
All calculations are performed in accordance with the ACI 318, the AISI S100, and the Steel Deck Institute (SDI) Design Handbook.
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Summary ResultsConstruction_Loads﻿
Design Check
Action
Resistance
Utilisation
Status
Positive Bending Stress Construction Loads
fbu(+) = 15.04 ksi
Fb_allow = 31.35 ksi
0.48
🟢
Negative Bending Stress Construction Loads
fbu(-) = 14.09 ksi
Fb_allow = 31.35 ksi
0.45
🟢
Beam Shear Construction Loads
Vu = 0.42 kips
ϕVd = 5.21 kips
0.08
🟢
Web Crippling (End Bearing)
Pu = 0.76 kips
ϕPd = 6.42 kips
0.12
🟢
Shear and Negative Moment Interaction Ratio for Construction Loads
S.R. = 0.46
S.R.≤ = 1.00 
0.46
🟢
Permanent_Loads﻿
Design Check
Action
Resistance
Utilisation
Status
Strong Axis Positive Moment
+Mu = 1.33 kips-ft
+Mno = 6.20 kips-ft
0.21 dimensionless
🟢
Strong Axis Negative Moment
-Mu = 1.87 kips-ft
-Mno = 2.00 kips-ft
0.93 dimensionless
🟢
Beam Shear
Vu = 1.44 kips
ϕVd = 5.21 kips
0.28 dimensionless
🟢
Shear and Negative Moment Interaction Ratio
S.R. = 0.96
S.R.≤ = 1.00 
0.96 dimensionless
🟢
Deflections﻿
Deflection Type
Parameter
Ratio (L / Δ)
Status
Construction Loads Deflection
L / 180
1277
🟢
Deflection
L / 180
1129
🟢
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CalculationTechnical notes
The topping layer does not contribute to the design depth of the composite slab, it is only used in the calculation of concrete weight. The design depth is taken as ﻿D=tc​+hc​
.
The deck is assumed to act compositely with the concrete without the use of shear connectors
Both the deck and concrete contribute to shear resistance (﻿ϕVd​+ϕVc​
)
1. Properties 1.1 Metal Deck
1.1.1 Geometry
﻿﻿Deck Type
:1.5"x6"​
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﻿﻿Deck Gage
:16​
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﻿﻿Fyd
:33ksi​
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﻿﻿Span Condition
:2-Span​
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﻿﻿h
:5.00 in​
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﻿﻿t
:0.00 in​
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﻿﻿L
:6.00 ft​
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1.1.2 Summary of Deck Properties
1.2 Concrete
1.3 Reinforcement
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﻿
2. Applied Loads ﻿﻿W_ll
:1.39 psi​
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﻿
﻿﻿W_dl
:0.38 psi​
﻿
﻿﻿Wdl​=Wd​+Wc​
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﻿﻿W_lc
:0.14psi​
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﻿
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3. Design Checks for construction loads only3.1 Flexural Strength
﻿﻿Fb_allow(+)
:31.35 ksi​
﻿
﻿﻿Fballow​=0.95Fyd​
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AISI S100 B3.2.2
﻿﻿Mu(+)_CL
:0.55 kip​
﻿
﻿﻿Mu+​={0.125(1.6min(1.5Wc​,Wc​+30)+1.2Wd​)L2+1.4P×L0.096(1.6Wc​+1.2Wd​)L2+1.4P×L​for one-way slabsfor two-way slabs​
﻿
SDI 2.4.A.2.b
﻿﻿fbu(+)_CL
:15.04 ksi​
﻿
﻿﻿fbu+​=Sp+Mu+​​
﻿
﻿﻿Utilisation(+)_CL
:0.48​
﻿
﻿﻿fbu+​≤Fballow​
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﻿﻿Mu(-)_CL
:0.51 kip​
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﻿﻿Mu−​=max{0.063(1.6Wc​+1.2Wd​)L2+1.4P×L0.125(1.6Wc​+1.2Wd​+1.4W2​)L2​
 
SDI 2.4.A.2.b
﻿﻿fbu(-)_CL
:14.09 ksi​
﻿
﻿﻿fbu−​=Sp−Mu+​​
﻿
﻿﻿Utilisation(-)_CL
:0.45​
﻿
﻿﻿fbu−​≤Fballow​
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3.2 Shear Strength
﻿﻿ϕVd_CL
:5210​
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﻿
AISI S100 G.2.1
﻿﻿Vu_CL
:0.42 kip​
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﻿﻿Vu​={(1.6min(1.5Wc​,Wc​+30)+1.2Wd​+1.4W2​)0.5L(1.6Wc​+1.2Wd​+1.4Wlc​)0.625L​for one-way slabsfor two-way slabs​
﻿
SDI 2.4.A.2.b
﻿﻿Utilisation shear_CL
:0.08​
﻿
﻿﻿Vu​≤ϕVd​
﻿
﻿
3.3 Shear and Negative Moment Interaction
﻿﻿SR_CL
:0.46​
﻿
﻿﻿S.R.=(ϕVnt​Vu​​)2+(Fballow​fbu−​​)2​≤1.0
 
AISI S100 H2
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3.4 Web Crippling (End Bearing)
﻿﻿ϕPn
:6.42 kip​
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AISI S100 G5
﻿﻿Pu
:0.76 kip​
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﻿﻿Pu​=ϕw​(1.6Wc​+1.2Wd​+1.4Wlc​)1.25L
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AISI S100 Table G5-5
﻿﻿Utilisation bearing_CL
:0.12​
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﻿﻿Pu​≤ϕPn​
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3.5 Deflection
﻿﻿ΔDL
:0.056 in​
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﻿﻿Δ(DL)​=0.0054Es​Id​(Wc​+Wd​)L4​
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﻿﻿ΔDL_ratio
:L / 1277​
﻿
﻿﻿Δ(ratio)​=Δ(DL)​L​
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4. Design Checks for permanent loads4.1 Flexural Strength
﻿﻿Mno(+)
:6.20 ft kip​
﻿
﻿﻿Mno+​=ϕs​My​
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SDI A.3.3.2
﻿﻿Mu(+)
:1.33 ft kip​
﻿
﻿﻿Mu+​={0.125(1.2Wdl​+1.6Wll​)L20.096(1.2Wdl​+1.6Wll​)L2​for one-way slabsfor two-way slabs​
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SDI 2.4.A.2.b
﻿﻿Utilisation(+)
:0.21​
﻿
﻿﻿Mu+​≤Mno+​
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﻿﻿Mno(-)
:2.22 ft kip​
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﻿﻿Mno−​=ϕs​Asn​Fy​((h−d1​)−2ycc​​)
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SDI A3.3.3
﻿﻿Mu(-)
:1.87 ft kip​
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﻿﻿Mu−​=0.125(1.4Wdl​×L2+1.7Wll​×L2)
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﻿﻿Utilisation(-)
:0.84​
﻿
﻿﻿Mu−​≤Mno−​
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4.2 Shear Strength
﻿﻿ϕsVD
:5.21 kip​
﻿
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AISI S100 G.2.1
﻿﻿Ac
:28.33 in^2​
﻿
﻿
SDI 2.4.B.7 Fig 2.1
﻿﻿Vc
:3.58 kip​
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﻿﻿Vc​=2λfc′​​Ac​
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SDI 2.4.B.7
﻿﻿ϕVn
:6.09 kip​
﻿
﻿﻿ϕVn​=min{ϕs​VD​+ϕv​Vc​4×ϕs​fc′​​Ac​​
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SDI 2.4.A.7
﻿﻿Vu
:1.44 kip​
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﻿﻿Vu​={0.5(1.2DL×L+1.6LL×L)0.625(1.2DL×L+1.6LL×L)​for one-way slabsfor two-way slabs​
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SDI 2.4.A2.b
﻿﻿Utilisation shear
:0.28​
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﻿﻿Vu​≤ϕVn​
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4.3 Shear and Negative Moment Interaction
﻿﻿SR
:0.88​
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﻿﻿S.R.=(ϕVnt​Vu​​)2+(Mno−​Mu−​​)2​≤1.0
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AISI S100 H2
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4.4 Deflection
﻿﻿Iav
:11.28 in^4​
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﻿
﻿﻿ΔLL
:0.007 in​
﻿
﻿﻿Δ(LL)​=0.0054Es​Iav​LL×L4​
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﻿﻿ΔLL_ratio
:L / 9741​
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﻿﻿Δ(ratio)​=Δ(LL)L​
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Related ResourcesConcrete One-way Slab Designer to ACI318
Concrete Slab-on-grade Calculator to ACI 360R-10
Concrete One-Way Slab Designer to EC2 
Concrete Slabs to AS3600
Design Check	Action	Resistance	Utilisation	Status
Positive Bending Stress Construction Loads	fbu(+) = 15.04 ksi	Fb_allow = 31.35 ksi	0.48	🟢
Negative Bending Stress Construction Loads	fbu(-) = 14.09 ksi	Fb_allow = 31.35 ksi	0.45	🟢
Beam Shear Construction Loads	Vu = 0.42 kips	ϕVd = 5.21 kips	0.08	🟢
Web Crippling (End Bearing)	Pu = 0.76 kips	ϕPd = 6.42 kips	0.12	🟢
Shear and Negative Moment Interaction Ratio for Construction Loads	S.R. = 0.46	S.R.≤ = 1.00	0.46	🟢
Deflection Type	Parameter	Ratio (L / Δ)	Status
Construction Loads Deflection	L / 180	1277	🟢
Deflection	L / 180	1129	🟢