FLOOR SYSTEM (PLATES)

FLOOR  SYSTEMS (PLATES)
1. Solid Slabs  - normally made of reinforced concrete but other materials are
called plates . Thickness  of PLATE depends on span ( refer span / depth ratio for
slabs BS8110 for RC design ) but 200 mm is common in residential houses or
buildings.
2. Other types of materials such as timber and steel can also be used to make on
floors. However they may have different spans and geometrical arrangement
due to properties of these materials ( refer to L/d ratios for timber , steel , plastics
etc ).
3. S.Slabs ( plates ) can be ONE WAY OR 2 WAY SPANNING .  One-way means that
loads are distributed in one direction  due to the aspect ration of slab.
                                                                                                                                                  Z
2
5m
Load
distributio
X
PLAN VIEW
4. The aspect ratio of above slab is 5/2  = 2.5  > 2 so its one way . if this ratio is less
than 2 then the distribution of loads is 2 way  ( in both directions  x & z ). 5. If a typical weight of slab is 24kN/m3 then a 200 mm slab will weigh  ; 24 x 0.2 =
4.8 kN/m2 . if the area of slab is 10m2 then a total load  of  ; 10 x 4.8 = 48 kN is
acting due to self load.
6. Each side of the slab ( if one way span ) will take  48/2 = 24 kN ( taken by beams
/ wall )
7. If  the slab is 2 way (5 m x 3m  ) then the sharing of loads is in both x and Z
directions . However the values of this distribution depend on end conditions and
has to be calculated from formulas (BS8110, Reynolds handbook design) , tables
or CAD.  
8. Slabs can have various end support conditions similar to beams  e.g  continuous
and simply supported or free.  If a slab is continuous then more loads will tend to
go to this side compared with simply support.  Continuous slabs means that there
is another slab adjacent to them and moments & other forces can be
transferred.
9. Example calc of 2 way slab formula  from BS 8110 ;
V sy = Bvy. n. lx ……………………………………. (1)
Vsx = Bvx.n.lx ………………………………….. (2)
Where Vx,y are the respective loads on supporting elements of slab.
Bvy, vx  are the shear coefficients UDL panels
Lx  is the shorter length of the panel
n is the uniform design load on the panel, kN/m2  From the table 3 of BS8110; if  ly = 5m and lx = 3.3m then ly/lx = 1.51 . If the slab
has 2 adjacent edges discontinuous, then  Bvx = 0.54 & 0.35 ( continuous &
discontinuous edges) and Bvy is 0.4 & 0.26 respectively for continue &
discontinue  edges.  If n = 6 kN/m2
   Continuous    continuous
  discontinuous
L
Lx
10. From equation (1) above  the  Vsy = 0.4 * 6 * 3.3 = 7.92 kN/ m  . Spread this load
on the whole length of side beam ; (if follow BS8110, spread only 0.75L )
7.92 kN/m
            3.3m
Therefore the maximum moment  is  wly2
 /8  = 7.92 * 3.3^2 * /8 = 10.78kNm
The above moment is used in the beam design to calculate its size & reinforcement .  11. Moments in 2 way slabs can be calculated from table 3.15 in BS8110 . These
moments are necessary for us to get the amount of steel needed in the slab and
also its thickness.  BS 8110 gives a simple formula for restrained slabs ;
Msx = Bsx . n.lx2    
 Msy = Bsy .n.lx2
Msx , Msy  - Moment per unit width in x , y direction
Bsx , Bsy – bending coeff from tables for x and y direction
Lx  - short length of the slab  
12. If  same slab above is considered then  Bsx = 0.078  ; 0.059 ( -ve moment at
continuous edge , positive moment at midspan ) ; Bsy = 0.045 ; 0.034 ( -ve
moment at  continuous edge , positive moment at midspan ).
Positive
moment
Negative
moment
Bending shape of the slab and moments at supports and mid span
12 .  Torsional action happens in slabs where corners are being restrained and sides
simple supported If a plate / slab  is restrained as above deflections at mid span are less . Bending at mid
span are also less compared to slabs which are not restrained . If  sides are rigid then
plate is more rigid . This is an advantage in normal house design since we want to
reduce deflections and steel in slabs .
Notes :  
• Boundary ( continuous, discontinuous, fixed , free ) conditions of slab can affect
the moment distribution.
• Maximum moments in slabs depends on the aspect ratio ( ly/lx )
• Negative moments and positive moments possible in slabs
• Torsional action in slabs can cause nearly 50 % of loads attracted to the supports
FLAT  SLABS 1. There are no beams under this type of slabs . There is large clearance for
services.  
2. There are columns supporting rectangular pieces of panels with each columns
taking the loads from the slab . Normally 2 way flat slabs.
3. The anaysis is similar to continuous slabs or can analyse as column frames. Refer
to BS8110 ; section 3.7 4. At each columns there may be a column head / widening of the column in
order to take up the punching shear stress . width and thickness of column head
is important and have to be designed.
5. The load transfer is in 2 directions just as in the 2 way S.Slab. Table 3.19 gives the
bending moment and shear force coeff  for flat slabs of 3 or more spans.
RIBBED SLAB WITH SOLID OR HOLLOW BLOCKS
  Structural topping
solid or
hollow
High
strength
reinforced
t
1. insitu slabs cast with reinforcement placed at distances which enable hollow
blocks to put in between them.
2. Slab is analyzed as ribbed one way spanning plate. Typical Span between ribs is
about 0.6m
3. Total Depth of  slab from 120 to 150 mm