Design Guide: Concrete Slabs to AS3600



Different slab behaviour

One-way vs Two-way Slabs

1. 
   

   $L_x$
   is the length of the shorter slab span

1. 
   

   $L_y$
   is the length of the longer slab span





Simplified Slab Analysis

One-way Slab Analysis

1. coefficient depends on the location of the
   

   $M^{\ast }$
   under consideration, see figures below
2. 
   

   $F_d$
   is the factored ULS design load per unit length
   

   $(kN/m)$
   
3. 
   

   $L_n$
   is the clear span length



Simplified analysis of one-way slabs - two spans



Simplified analysis of one-way slabs - more than two spans

Two-way slab analysis

1. 
   

   ${\beta }_x,{\beta }_y$
   are moment coefficients, taken from Table 6.10.3.2(A)
2. 
   

   $F_d$
   is the factored ULS design load per unit area
   

   $(kN/m^2)$
   
3. 
   

   $L_x$
   is the shorter span length



AS3600-2018, Table 4.10.3.2(A)

The code talks about edges of a two-way slabs supported on four sides by beams or walls as either continuous or discontinuous:

1. continuous edge means the slab is able to transfer load to the adjacent slab through that edge
2. discontinuous edge means the slab is unable to transfer load to the adjacent slab through that edge, either because it is not detailed as continuous or it is the outside edge of a slab



Edge conditions of a two-way slab

1. at a continuous edge:

1. at a discontinuous edge:

Flat slab analysis

1. 
   

   $F_d$
   is the uniformly distributed design load per unit area (
   

   $kPa)$
   
2. 
   

   $L_t$
   is the width of the design strip, which for an interior design strip is taken as
   

   $L_t=L_x$
   in the longer span and
   

   $L_t=L_y$
   in the shorter span. For edge design strips, it is taken as
   

   $L_t=L_x/2$
   in the longer span and
   

   $L_t=L_y/2$
   in the shorter span.
3. 
   

   $L_o$
   is the effective span, which is taken as
   

   $L_o=L_y$
   in the longer span and
   

   $L_o=L_x$
   in the shorter span, for simplicity



AS3600-2018 Commentary, Figure C6.10.4.2



AS3600-2018, Table 6.10.4.2(A) & (B)



AS3600-2018, Table 6.9.5.3



Flat slab analysis for the longer span



$L_y$





Flat slab analysis for the shorter span



$L_x$





Example of flat slab analysis with



$M_o=408\text{ kNm}$

for the sagging moment in an interior design strip, distributed to the column strip and middle strip

1. 3x
   

   $M_{\text{end span in interior design strip}}^{\ast }=\{-M_{\text{exterior}}^{\ast },-M_{\text{interior}}^{\ast },+M^{\ast }\}$
   for the end spans in the interior design strip, which are then each distributed to the column strip and half of a middle strip, making 6x unique moments
2. 2x
   

   $M_{\text{interior span in interior design strip}}^{\ast }=\{-M^{\ast },+M^{\ast }\}$
   for the interior spans in the interior design strip, which are then each distributed to the column strip and two halves of a middle strip, making 4x unique moments
3. 3x
   

   $M_{\text{end span in edge design strip}}^{\ast }=\{-M_{\text{exterior}}^{\ast },-M_{\text{interior}}^{\ast },+M^{\ast }\}$
   for the end spans in the edge design strip, which are then each distributed to the column strip and half of a middle strip, making 6x unique moments
4. 2x
   

   $M_{\text{interior span in edge design strip}}^{\ast }=\{-M^{\ast },+M^{\ast }\}$
   for the interior spans in the edge design strip, which are then each distributed to the column strip and two halves of a middle strip, making 4x unique moments
5. 2x
   

   $M_{\text{total}}^{\ast }=\{M_x^{\ast },M_y^{\ast }\}$
   for each direction (shorter and longer span direction), making 2x20 unique moments

Design Checks

Flexure (ULS)

1. moment capacity check
2. ductility check
3. minimum reinforcement check (i.e. minimum strength check)



The strain and equivalent rectangular stress block of a typical RC slab section, without top reinforcement



The strain and equivalent rectangular stress block of a typical RC slab section, with top reinforcement

1. 
   

   $\varphi$
   is the capacity reduction factor, taken from Table 2.2.2.
2. 
   

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

   $k_{u}d$
   represents the depth to the neutral axis.

1. 
   

   ${\alpha }_2=0.85-0.0015f_c^{\prime }\ge 0.67$
   
   
2. 
   

   $\gamma =0.97-0.0025f_c^{\prime }\ge 0.67$
   
   
3. 
   

   ${\sigma }_{sc}=\min (f_{sy},E_s{\epsilon }_{sc})$
   is the stress in the reinforcement in the compressive zone
4. 
   

   ${\epsilon }_{sc}={\epsilon }_{cu}(1-\frac{d_{sc}}{k_{u}d})$
   is the strain in the reinforcement in the compressive zone, and is derived from similar triangles in the figure above
5. 
   

   ${\epsilon }_{su}=0.003$
   is the maximum strain in the extreme compressive concrete fibre as per Clause 8.1.3

1. 
   

   ${\alpha }_b=0.2$
   for one-way slabs

1. 
   

   ${\alpha }_b=0.24$
   for two-way slabs supported by columns at their corners

1. 
   

   ${\alpha }_b=0.19$
   for two-way slabs supported by beams or walls on four sides

Shear (ULS)

Deflection (SLS)

1. 
   

   $\Delta /L_{ef}$
   is the deflection limit, chosen by the user, as per Table 2.3.2
2. 
   

   $L_{ef}$
   is the effective span, where
   

   $L_{ef}=L_y$
   in one-way slabs or two-way flat slabs, and
   

   $L_{ef}=L_x$
   in two-way slabs supported on four sides
3. 
   

   $d$
   is the slab effective depth
4. 
   

   $F_{d.ef}$
   is the effective design service load
   

   $(kPa)$

1. 
   

   $k_{cs}=(2-1.2A_{sc}/A_{st}]\ge 0.8$
   where
   

   ${\psi }_s,{\psi }_l$
   is from Table 4.1 in AS1170.0 and
   

   $A_{sc}/A_{st}$
   is taken at midspan for simply supported and continuous slabs
2. 
   

   $k_3=1.0$
   for one-way slab and two-way slabs supported on four sides,
   

   $=0.95$
   for multi-span two-way flat slab without drop panels,
   

   $=1.05$
   for multi-span two-way flat slab with drop panels
3. 
   

   $k_4=1.4$
   for simply support slabs,
   

   $=1.75$
   for an end span of a continuous slab,
   

   $=2.1$
   for an interior span in a continuous slab



AS3600-2018, Table 2.3.2

1. uniform slab depth
2. fully propped during construction
3. loads are uniformly distributed and
   

   $Q\le G$
4. for two-way flat slabs with drop panels, drop panels must extend at least
   

   $L/6$
   in each direction on each side of the support centre-line, and have an overall depth not less then
   

   $1.3\times$
   slab thickness beyond the drops
5. for continuous one-way slabs or two-way flat slabs, in adjoining spans, the ratio of the longer span to the shorter span does not exceed
   

   $1.2$
   , and no end span is longer than an interior span