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Concrete Two-way Slab Calculator to AS3600's banner

Concrete Two-way Slab Calculator to AS3600

Verified by the CalcTree engineering team on August 30, 2024
This calculator performs the analysis and design of reinforced concrete two-way spanning slabs supported on four sides by beams or walls. Design actions are calculated using simplified elastic analysis. Flexural capacity and deflection are then checked.
All calculations are performed in accordance with AS3600-2018.

Calculation

Technical assumptions

  1. Assumes the slab depth and reinforcement is known
  2. The support type is RC beams or walls. If the support type is RC columns, use our flat slab calculator
  3. Using
    
    means the results of
    
    and
    
    are per unit width strips of slab
  1. The calculation of
    
    and
    
    conservatively ignores the compressive force from
    
    
  1. The simplified slab analysis and deflection checks are valid if certain conditions have been satisfied as per Clause 6.10 and 9.4 respectively
  1. Axial capacity check, crack control, fire requirements and detailing requirements are not included.
  1. Prestress is not considered.
  2. Redistribution is not considered.
  1. This calculator assumes monolithic construction, that is, the supports are reinforced concrete and have been detailed (reinforcement provided) such that the slab-support interface is continuous (load transfer is enabled).


Slab Properties

RC slab cross-section

Geometry:


B
:1.00 m​



D
:150 mm​



Ly
:7.00 m​



Lx
:6.00 m​



Ly / Lx
:1.17​



Slab_type
:Two-way​


One- or two-way slab

Although not specified in the standards, it is typical to define a two-way slab as:

Ly/Lx≤2L_y/L_x \leq 2
Where:
  1. 
    
    is the length of the shorter slab span
  1. 
    
    is the length of the longer slab span
Otherwise, the slab is considered a one-way slab.

A one-way and two-way slab is designed in the same way. The difference is how you determine the design actions.

Concrete Properties:


fc
:32MPa​



Ec
:30,100​



Density_c
:25 kN / m^3​

Reinforcement Properties:


fsy
:500 MPa​



Es
:200 GPa​


Reinf in tension zone:


db_st
:16mm​



s_st
:250 mm​



c_st
:25 mm​



d_st
:117 mm​



Ast
:804 mm^2​

Reinf in compression zone:


db_sc
:10mm​



s_sc
:200 mm​



c_sc
:25 mm​



d_sc
:30 mm​



Asc
:393 mm^2​



Loads



SW
:3.75 kPa​



SDL
:0.50 kPa​



Q
:3.00 kPa​



Fd
:9.6 kPa​


ULS

This calculator computes the ULS design load as per AS1170.0:

Fd=1.2G+1.5QF_d=1.2G+1.5Q
where G = SW + SDL.



psi_s
:0.7​



psi_l
:0.4​



kcs
:0.97​



F_def, total
:11.7 kPa​



F_def, incr
:7.4 kPa​


SLS

Load combination factors for short-term,

and long-term,

are taken from Table 4.1 of AS 1170.0:
AS1170.0, Table 4.1

The SLS design load (service load), as per Clause 9.4.4, for total deflection, is given by:

Fd.ef, total=(1.0+kcs)G+(ψs+kscψ1)Q\small F_{\text{d.ef, total}}=(1.0+k_{cs})G+ (\psi_s+k_{sc} \psi_1)Q
And for incremental deflection (deflection that occurs after brittle finishes are attached) is given by:

Fd.ef, incremental=kcsG+(ψs+kscψ1)Q\small F_{\text{d.ef, incremental}}=k_{cs}G+ (\psi_s+k_{sc} \psi_1)Q
Where:
  1. 
    
    
  2. 
    
    is taken at midspan for simply supported and continuous slabs


Slab Analysis

For two-way slabs supported on four sides by walls or beams, as per Clause 6.10.3:


Short_edge
:One discontinuous​



Long_edge
:One discontinuous​



βx
:0.046​



βy
:0.036​


  1. At midspan:


+M*x
:15.8 kN m​



+M*y
:12.3 kN m​


+Mx∗=βx×FdLx2+My∗=βy×FdLx2+M^*_x=\beta_x \times F_d L_x^2 \\+M^*_y=\beta_y \times F_d L_x^2
  1. At a continuous edge:


-M*x_cont
:-21.0 kN m​



-M*y_cont
:-16.3 kN m​


−Mx∗=1.33×(+Mx∗)−My∗=1.33×(+My∗)-M^*_x=1.33 \times (+M^*_x) \\-M^*_y=1.33 \times (+M^*_y)
  1. At a discontinuous edge:


-M*x_discont
:-7.9 kN m​



-M*y_discont
:-6.1 kN m​


−Mx∗=0.5×(+Mx∗)−My∗=0.5×(+My∗)-M^*_x=0.5 \times (+M^*_x) \\-M^*_y=0.5 \times (+M^*_y)
Results are in

per

strip of slab, if

results are in

strip of slab.

❗Ensure these conditions have been met

For two-ways slabs with two or more spans, the simplified elastic analysis as outputted above is valid if:
  1. loads are uniformly distributed
  2. no big slab opening (that adversely affects the slab stiffness)
  1. 
    
    at supports are only caused by loads applied to the beam or slab, not from the columns


Flexural (ULS) Design Check



phi
:0.85​


Capacity reduction factor

Capacity reduction factor

shall be taken from Table 2.2.2. For pure bending:
  1. 
    
    for Normal (N) ductility reinforcement, which is when
    
    
  2. 
    
    for Low (L) ductility reinforcement
AS3600-2018, Table 2.2.2



ku
:0.15​



Check ku
:< 0.36 ✅​


Ductility check

It is universal practice to ensure your concrete section is ductile. A ductile section means the reinforcement will yield before the concrete crushes, which is deemed a less dangerous failure mechanism since the failure occurs relatively slow compared to a sudden brittle failure. As per Cl 8.1.5, the code ensures ductile failure by checking:

kuo≤0.36k_{uo} \le 0.36
Where

for a section in pure bending.
The

factor is the depth ratio of the neutral axis from the extreme compressive fibre to the bottom reinforcement, at ultimate strength. Therefore

represents the depth to the neutral axis.
Factor

is not defined explicitly in the standards and must be computed via force equilibrium.

Cc=Tsα2fc′γbd=Astfsy→ku=Astfsyα2fc′γbdWhere:α2=0.85−0.0015fc′≥0.67γ=0.97−0.0025fc′≥0.67C_c=T_s\\ \alpha_{2}f'_c\gamma bd = A_{st}f_{sy} \\\rightarrow k_u = \dfrac{A_{st}f_{sy}}{\alpha_{2}f'_c\gamma bd}\\\text{Where:}\\\alpha_2=0.85-0.0015f'_c \ge 0.67 \\ \gamma = 0.97-0.0025 f'_c \ge 0.67


Ast,min
:248 mm^2​



Check Ast
:> Ast,min ✅​


Minimum reinforcement check

Clause 8.1.6 specifies minimum strength requirements. Clause 9.1.1 specifies an adjustment to this for two-way slabs.
Therefore, for reinforced concrete sections, the minimum strength requirement is deemed to be satisfied if

satisfies the following:

Ast≥[αb(D/d)2fct.f′/fsy]bwdA_{st}\geq [\alpha_b(D/d)^2f'_{ct.f}/f_{sy}]b_wd
Where:
  1. 
    
    for one-way slabs
  1. 
    
    for two-way slabs supported by columns at their corners
  1. 
    
    for two-way slabs supported by beams or walls on four sides


α2
:0.80​



γ
:0.89​



Mu
:37.3 kN m​



+M*_max
:15.8 kN m​



-M*_max
:-21.0 kN m​


Moment capacity check

Slab moment capacity is calculated the same way as a beam.
The strain and equivalent rectangular stress block of a typical RC section

Using the Rectangular Stress Block as per Cl. 8.1.2, the moment capacity is given by:

Mu=ϕAstfsy×lever armM_u=\phi A_{st}f_{sy}\times \text{lever arm}
Where the lever arm is given by

.
Substituting in the equation for

, the moment capacity equation becomes:

Mu=ϕAstfsyd(1−Ast/bdfsy2α2fc′)M_u=\phi A_{st}f_{sy}d(1-\frac{A_{st}/bdf_{sy}}{2\alpha_2f'_c})


Check +M*
:= 16kNm ≤ Mu = 37kNm, OK ✅​



Check -M*
:= 21kNm ≤ Mu = 37kNm, OK ✅​


Note

  1. For sagging moment
    
    ,
    
    is on the bottom &
    
    on the top
  1. For hogging moment
    
    ,
    
    is on the top &
    
    on the bottom


Deflection (SLS) Check

  1. 
    
    Slab type
    :Ly/Lx = 1.17 ∴ Two-way slab supported by Beams or walls​
  2. 
    
    Edge condition
    :Two adjacent edges discontinuous​


k3
:1.00​



k4
:2.65​



Lef / d
:51​


Simplified approach

As per Clause 9.4.4, slab deflections are deemed to conform to code requirements if the following is satisfied:

Lef/d≤k3k4[(Δ/Lef)1000EcFd.ef]1/3L_{ef} / d \leq k_3 k_4 \left[ \dfrac{(\Delta/L_{ef})1000 E_c}{F_{d.ef}}\right]^{1/3}
For total deflection:


Deflection_limit_total
:1/250​



(Lef / d)_limit
:58​



Check
:Lef/d ≤ limit ✅​



Min D
:137 mm​

For incremental deflection:


Deflection_limit_incr
:1/500​



(Lef / d)_limit (1)
:53​



Check (1)
:Lef/d ≤ limit ✅​



Min D (1)
:146 mm​


❗Ensure these conditions have been met

As per Clause 9.4.4.2, for RC slabs, the simplified approach for two-way slab deflection is valid if:
  1. loads are uniformly distributed
  2. 
    
    
    check
    :Q = 3.0kPa ≤ G = 4.2kPa, simplified analysis is valid ✅.​