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Composite Slab to ACI 318's banner

Composite Slab to ACI 318

Verified by the CalcTree engineering team on October 3, 2024

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.


Summary Results

Construction_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
🟢


Calculation

Technical notes

  1. 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
    
    .
  2. The deck is assumed to act compositely with the concrete without the use of shear connectors
  3. Both the deck and concrete contribute to shear resistance (
    
    )

1. Properties

1.1 Metal Deck

1.1.1 Geometry



Deck Type
:1.5"x6"​



Deck Gage
:16​



Fyd
:33ksi​



Span Condition
:2-Span​



h
:5.00 in​



t
:0.00 in​



L
:6.00 ft​



1.1.2 Summary of Deck Properties


0.0229166667​
1.5​
6​
0.85​
2​
2.5​
2.25​
0.96​
0.4​
0.439​
0.434​


1.2 Concrete



f'c
:4.00 ksi​



Uwc
:150lb/ft3​




Wc
:0.35 psi​






1.3 Reinforcement



d1
:2.00 in​



L-rebar
:#4​



L-s
:1.00 ft​



fy
:60.00 ksi​



T-rebar
:#3​



T-s
:3.00 ft​



L-db
:0.5​



L-A
:0.2​



Asn
:0.20 in​



T-db
:0.375​



T-A
:0.11​



Ast
:0.04 in​




2. Applied Loads



W_ll
:1.39 psi​




W_dl
:0.38 psi​






W_lc
:0.14psi​




3. Design Checks for construction loads only

3.1 Flexural Strength

As per SDI Cl 2.4.2, the design sagging moment

and the design sagging stress

are given by:

Mu+={0.125(1.6min⁡(1.5Wc,Wc+30)+1.2Wd)L2+1.4Plc×Lfor one-way slabs0.096(1.6Wc+1.2Wd)L2+1.4Plc×Lfor two-way slabsfbu+=Mu+Sp+M_u^{+} =\begin{cases} 0.125\left( 1.6 \min(1.5 W_c, W_c + 30) + 1.2 W_d \right) L^2 + 1.4 P_{lc}\times L& \text{for one-way slabs}\\ 0.096\left( 1.6 W_c + 1.2 W_d \right) L^2 + 1.4 P_{lc}\times L& \text{for two-way slabs} \end{cases}\hspace{2cm} fb_u^{+} = \dfrac{M_u^{+}}{Sp^{+}}
Where:
  1. 
    
    is the section modulus for positive moments.
Additionally, the design hogging moment

and the design hogging stress

are given by:

Mu−=max⁡{0.063(1.6Wc+1.2Wd)L2+1.4Plc×L;0.125(1.6Wc+1.2⋅Wd+1.4Wlc)L2fbu−=Mu+Sp−M_{u} ^{-}= \max \begin{cases} 0.063\left( 1.6 W_c + 1.2 W_d \right) L^2 + 1.4 P_{lc}\times L; \\0.125\left( 1.6 W_c + 1.2 \cdot W_d + 1.4 W_{lc} \right) L^2 \end{cases} \hspace{2cm} fb_u^{-} = \dfrac{M_u^{+}}{Sp^{-}}
Where:
  1. 
    
    is the concentrated construction live load per unit width of the deck section.
  1. 
    
    is the uniform construction live load (combined with fluid concrete), not less than 20 psf (0.96 kPa).
  1. 
    
    is the section modulus for negative moments.
The flexural capacity of the composite deck is provided only by the metal deck, and is given by:

Fballow=0.95FydFb_{allow} = 0.95 F_{yd}
Where:
  1. 
    
    is the deck steel yield strength
  1. 
    
    is a safety reduction factor that accounts for uncertainties in material properties and load assumptions.



Fb_allow(+)
:31.35 ksi​




AISI S100 B3.2.2


Mu(+)_CL
:0.55 kip​




SDI 2.4.A.2.b


fbu(+)_CL
:15.04 ksi​






Utilisation(+)_CL
:0.48​






Mu(-)_CL
:0.51 kip​



SDI 2.4.A.2.b


fbu(-)_CL
:14.09 ksi​






Utilisation(-)_CL
:0.45​






3.2 Shear Strength

As per SDI Cl 2.4.2, the design shear action force

is given by:

Vu={(1.6min⁡(1.5Wc,Wc+30)+1.2wd+1.4W2)0.5Lfor one-way slabs(1.6Wc+1.2wd+1.4W2)0.625Lfor two-way slabsV_{u} = \begin{cases} \left( 1.6 \min(1.5 W_c, W_c + 30) + 1.2 w_d + 1.4 W_2 \right) 0.5 L& \text{for one-way slabs} \\ \left( 1.6 W_c + 1.2 w_d + 1.4 W_2 \right) 0.625 L& \text{for two-way slabs} \end{cases}
Where:
  1. 
    
    is a factor used to reflect the modified load distribution and increased moment capacity in a two-span system compared to a single-span.
Note,

for one-way slabs uses a

factor indicating the shear force is distributed over the length of the span, as the deck spans between two supports.

for two-way slabs assumes the deck is supported at three points, distributing the loads across two spans.
The beam shear capacity of the composite slab

is taken as per AISI S100 G.2.1.



ϕVd_CL
:5210​


AISI S100 G.2.1


Vu_CL
:0.42 kip​




SDI 2.4.A.2.b


Utilisation shear_CL
:0.08​






3.3 Shear and Negative Moment Interaction

Shear and negative moment interaction refers to the combined effect of shear forces and negative bending moments on the steel deck. In regions near the supports, the deck experiences negative moments (hogging) along with high shear forces. These forces must be evaluated together because they can lead to a combined failure mode where both shear and bending stresses interact and reduce the overall strength of the deck.
As per AISI S100 H2, the ratio for the shear and negative moment interaction to be satisfied is given by:

S.R.=(VuϕVnt)2+(fbu−Fballow)2≤1.0S.R. = \sqrt{\left( \dfrac{V_u}{\phi V_{nt}} \right)^2 + \left( \frac{f_{bu}^{-}}{F_{ballow}} \right)^2} \leq 1.0


SR_CL
:0.46​



AISI S100 H2


3.4 Web Crippling (End Bearing)

During construction, before the concrete hardens and composite action takes place, the steel deck must bear loads such as wet concrete, construction workers and equipment. These loads are often concentrated at the supports, making web crippling a potential failure mode.
Web crippling occurs when a steel deck experiences localized deformation or failure under concentrated loads near its supports, especially at the ends of the deck where the deck bears on the supports (like beams or walls). This failure mechanism is often referred to as end-bearing failure because it happens where the deck "bears" directly on its support. The design bearing action force

is given by:

Pu=ϕw(1.6Wc+1.2Wd+1.4W2)1.25LP_{u} = \phi_w \left( 1.6 W_c + 1.2 W_d + 1.4 W_2 \right) 1.25 L
Where:
  1. 
    
    is the safety reduction factor
  2. 
    
    is a factor representing a
    
    increase in allowable reaction, often used for temporary construction loads, which recognizes the temporary nature of the load.
  3. 
    
    is the uniform construction live load (combined with fluid concrete), not less than 20 psf (0.96 kPa).
The design capacity

is taken as per AISI S100 G5.



ϕPn
:6.42 kip​


AISI S100 G5


Pu
:0.76 kip​




AISI S100 Table G5-5


Utilisation bearing_CL
:0.12​






3.5 Deflection

As per the SDI Clause 2.4.5, deflection of the deck shall be limited to the lesser of 1/180 or the clear span of 3/4 inch. Keeping the deflection ratio within acceptable limits as

ensures that the deck maintains its structural integrity and prevents excessive deformation that could compromise the slab.

Δ(DL)=0.0054(Wc+Wd)L4EsId\Delta_{(DL)} = 0.0054 \dfrac{(W_c + W_d) L^4}{E_s I_d}
Where:
  1. 
    
    is the span length
  2. 
    
    is the deflection due to dead load


ΔDL
:0.056 in​






ΔDL_ratio
:L / 1277​






4. Design Checks for permanent loads

4.1 Flexural Strength

The strong axis positive moment refers to the bending moment that occurs in the steel deck as it supports the slab under uniform live loads. Positive moment typically occurs at the mid-span of the deck, where it bends downward (sagging) under the combined weight of the dead loads and live loads. The design sagging moment

and the sagging moment capacity

is given by:

Mu+={0.125(1.2DL+1.6LL)L2for one-way slabs0.096(1.2DL+1.6LL)L2for two-way slabsMno+=ϕsMyM_u^{+} =\begin{cases} 0.125(1.2 {\text{DL}}+ 1.6 {\text{LL}})L^2 & \text{for one-way slabs}\\ 0.096(1.2 {\text{DL}} + 1.6 {\text{LL}})L^2& \text{for two-way slabs} \end{cases} \hspace{2cm} M_{no}^{+} = \phi_s M_y
Where:
  1. 
    
    is the capacity reduction factor
  1. 
    
    Yield moment for the composite slab, considering a cracked cross-section.
The negative moment occurs at the supports of the slab where the slab bends upwards (hogging). This negative moment is critical as it could cause failure near the slab’s edges or supports if it exceeds the allowable moment capacity. The design sagging moment

and the hogging moment capacity

is given by:

Mu+={0.125(1.2Wdl+1.6Wll)L2for one-way slabs0.096(1.2Wdl+1.6Wll)L2for two-way slabsMno−=0.90AsnFy((h−d1)−a2)M_u^{+} =\begin{cases} 0.125(1.2 W_{dl}+ 1.6 W_{ll})L^2& \text{for one-way slabs}\\ 0.096(1.2 W_{dl} + 1.6 W_{ll})L^2& \text{for two-way slabs} \end{cases} \hspace{2cm} M_{no}^{-} = 0.90 A_{sn} F_{y} \left( (h - d_1) - \frac{a}{2}\right)
Where:
  1. 
    
    is the area of longitudinal reinforcement per foot.
  2. 
    
    is the distance from top of slab to neutral axis of cracked section.
  3. 
    
    is the total slab thickness.


Mno(+)
:6.20 ft kip​




SDI A.3.3.2


Mu(+)
:1.33 ft kip​




SDI 2.4.A.2.b


Utilisation(+)
:0.21​






Mno(-)
:2.22 ft kip​




SDI A3.3.3


Mu(-)
:1.87 ft kip​






Utilisation(-)
:0.84​






4.2 Shear Strength

As per SDI Clause 2.4.2, the design shear force

due to the combined dead; and as per SDI Clause 2.4.7, the total shear capacity

of the composite section (steel deck + concrete) is given by:

Vu={0.5(1.2DL×L+1.6LL×L)for one-way slabs0.625(1.2DL×L+1.6LL×L)for two-way slabsϕVn=min⁡{ϕsVD+ϕvVc4×ϕsfc′AcV_{u} = \begin{cases} 0.5(1.2 DL\times L + 1.6 LL\times L)& \text{for one-way slabs}\\ 0.625(1.2 DL\times L + 1.6 LL\times L)& \text{for two-way slabs}\end{cases} \\\phi V_{n} = \min\begin{cases} \phi_s V_D + \phi_v V_c \\ 4\times \phi_s \sqrt{f'_c} A_c \end{cases}
Where:
  1. 
    
    is a capacity reduction factor
  2. 
    
    is a capacity reduction factor
  3. 
    
    where concrete density exceeds 130 lbs/ft3 (2100 kg/m3);
    
    where concrete density is equal to or less than 130 lbs/ft3
  4. 
    
    is the shear capacity of the steel deck alone, obtained from AISI Clause G.2.1 for the deck profile being used
  5. 
    
    is the effective area of concrete for shear, calculated based on the slab thickness and rib dimensions
  6. 
    
    is the shear capacity of the concrete, which depends on its compressive strength and effective area for shear. Note, the concrete's contribution is capped at 4 times its basic shear capacity to ensure safety.


ϕsVD
:5.21 kip​


AISI S100 G.2.1


Ac
:28.33 in^2​


SDI 2.4.B.7 Fig 2.1


Vc
:3.58 kip​




SDI 2.4.B.7


ϕVn
:6.09 kip​




SDI 2.4.A.7


Vu
:1.44 kip​




SDI 2.4.A2.b


Utilisation shear
:0.28​






4.3 Shear and Negative Moment Interaction

The shear and negative moment interaction equation checks the combined effects of shear forces and negative bending moments on the slab. As per AISI S100 H2, the ratio for the shear and negative moment interaction to be satisfied is given by:

S.R.=(VuϕVnt)2+(Mu−Mno−)2≤1.0S.R. = \sqrt{\left( \dfrac{V_u}{\phi V_{nt}} \right)^2 + \left( \dfrac{M_u^{-}}{M_{no}^{-}} \right)^2} \leq 1.0


SR
:0.88​




AISI S100 H2


4.4 Deflection

Deflection under uniform live loads must be calculated to ensure that the slab will not experience excessive sagging, which could affect performance and comfort.

Δ(LL)=0.0054LL×L4EsIav\Delta_{(LL)} = 0.0054 \dfrac{LL\times L^4}{E_s I_{av}}
Where:
  1. 
    
    average inertia of a non-cracked and cracked section



Iav
:11.28 in^4​




ΔLL
:0.007 in​






ΔLL_ratio
:L / 9741​






Related Resources

  1. Concrete One-way Slab Designer to ACI318
  2. Concrete Slab-on-grade Calculator to ACI 360R-10
  3. Concrete One-Way Slab Designer to EC2
  4. Concrete Slabs to AS3600