DESIGN OF SLABS

                      DESIGN OF SLABS

SLABS

A slab is a flat two dimensional planar structural element having thickness small compared to its
other two dimensions. It provides a working flat surface or a covering shelter in buildings. It
primarily transfer the load by bending in one or two directions. Reinforced concrete slabs are
used in floors, roofs and walls of buildings and as the decks of bridges. The floor system of a
structure can take many forms such as in situ solid slab, ribbed slab or pre-cast units. Slabs may
be supported on monolithic concrete beam, steel beams, walls or directly over the columns.

Concrete slab behave primarily as flexural members and the design is similar to that of beams.

              CLASSIFICATION OF SLABS

Slabs are classified based on many aspects

1) Based of shape: Square, rectangular, circular and polygonal in shape.
2) Based on type of support: Slab supported on walls, Slab supported on beams, Slab
supported on columns (Flat slabs).
3) Based on support or boundary condition: Simply supported, Cantilever slab,
Overhanging slab, Fixed or Continues slab.
4) Based on use: Roof slab, Floor slab, Foundation slab, Water tank slab.
5) Basis of cross section or sectional configuration: Ribbed slab /Grid slab, Solid slab,
Filler slab, Folded plate
6) Basis of spanning directions :
One way slab – Spanning in one direction

Two way slab _ Spanning in two direction

In general, rectangular one way and two way slabs are very common


METHODS OF ANALYSIS

The analysis of slabs is extremely complicated because of the influence of number of factors
stated above. Thus the exact (close form) solutions are not easily available. The various methods
are:
a) Classical methods – Levy and Naviers solutions(Plate analysis)
b) Yield line analysis – Used for ultimate /limit analysis
c) Numerical techniques – Finite element and Finite difference method.
d) Semi empirical – Prescribed by codes for practical design which uses coefficients.

SPECIFICATIONS 

a. Effective span of slab :
Effective span of slab shall be lesser of the two
1. l = clear span + d (effective depth )
2. l = Center to center distance between the support
b. Depth of slab:
The depth of slab depends on bending moment and deflection criterion. the trail depth
can be obtained using:
• Effective depth d= Span /((l/d)Basic x modification factor)
• For obtaining modification factor, the percentage of steel for slab can be assumed
from 0.2 to 0.5%
• The effective depth d of two way slabs can also be assumed using cl.24.1,IS 456
provided short span is
3.5m and loading class is < 3.5KN/m2

Load on slab:

The load on slab comprises of Dead load, floor finish and live load. The loads are calculated

per unit area (load/m2).

Dead load = D x 25 kN/m2 ( Where D is thickness of slab in m)

Floor finish (Assumed as)= 1 to 2 kN/m2

Live load (Assumed as) = 3 to 5 kN/m2 (depending on the occupancy of the building)

DETAILING REQUIREMENTS AS PER IS 456 : 2000

Nominal Cover :

For Mild exposure – 20 mm

For Moderate exposure – 30 mm

However, if the diameter of bar do not exceed 12 mm, or cover may be reduced by 5 mm.

Thus for main reinforcement up to 12 mm diameter bar and for mild exposure, the nominal

cover is 15 mm

Minimum reinforcement : The reinforcement in either direction in slab shall not be less

than

• 0.15% of the total cross sectional area for Fe-250 steel

• 0.12% of the total cross sectional area for Fe-415 & Fe-500 steel.

Spacing of bars : The maximum spacing of bars shall not exceed

• Main Steel – 3d or 300 mm whichever is smaller

• Distribution steel –5d or 450 mm whichever is smaller

Where, ‘d’ is the effective depth of slab.

Note: The minimum clear spacing of bars is not kept less than 75 mm (Preferably 100 mm)

though code do not recommend any value.

d. Maximum diameter of bar: The maximum diameter of bar in slab, shall not exceed D/8,

where D is the total thickness of slab.

6. BEHAVIOR OF ONE WAY SLAB

When a slab is supported only on two parallel apposite edges, it spans only in the direction

perpendicular to two supporting edges. Such a slab is called one way slab. Also, if the slab is

supported on all four edges and the ratio of longer span(ly) to shorter span (lx) i.e ly/lx > 2,

practically the slab spans across the shorter span. Such a slabs are also designed as one way

slabs. In this case, the main reinforcement is provided along the spanning direction to resist one

way bending.

BEHAVIOR OF TWO WAY SLABS

A rectangular slab supported on four edge supports, which bends in two orthogonal directions

and deflects in the form of dish or a saucer is called two way slabs. For a two way slab the ratio

of ly/lx shall be
2.0 .

Since, the slab rest freely on all sides, due to transverse load the corners tend to curl up and lift

up. The slab looses the contact over some region. This is known as lifting of corner. These slabs

are called two way simply supported slabs. If the slabs are cast monolithic with the beams, the

corners of the slab are restrained from lifting. These slabs are called restrained slabs. At corner,

the rotation occurs in both the direction and causes the corners to lift. If the corners of slab are

restrained from lifting, downward reaction results at corner & the end strips gets restrained

against rotation. However, when the ends are restrained and the rotation of central strip still

occurs and causing rotation at corner (slab is acting as unit) the end strip is subjected to torsion.

Types of Two Way Slab

Two way slabs are classified into two types based on the support conditions:

a) Simply supported slab

b) Restrained slabs

Two way simply supported slabs

The bending moments Mx and My for a rectangular slabs simply supported on all four edges

with corners free to lift or the slabs do not having adequate provisions to prevent lifting of

corners are obtained using

Where, x and y are coefficients given in Table 1 (Table 27,IS 456-2000)

W- Total load /unit area

lx & ly – lengths of shorter and longer span.

Table 1 Bending Moment Coefficients for Slabs Spanning in Two Directions at

Right Angles, Simply Supported on Four Sides (Table 27:IS 456-2000)

Two way Restrained slabs

When the two way slabs are supported on beam or when the corners of the slabs are prevented

from lifting the bending moment coefficients are obtained from Table 2 (Table 26, IS456-2000)

depending on the type of panel shown in Fig. 3. These coefficients are obtained using yield line

theory. Since, the slabs are restrained; negative moment arises near the supports. 

The bending moments are obtained using;

Detailing requirements as per IS 456-2000

a. Slabs are considered as divided in each direction into middle and end strips as shown

below

b. The maximum moments obtained using equations are apply only to middle strip.

c. 50% of the tension reinforcement provided at midspan in the middle strip shall extend in

the lower part of the slab to within 0.25l of a continuous edge or 0.15l of a discontinuous

edge and the remaining 50% shall extend into support.

d. 50% of tension reinforcement at top of a continuous edge shall be extended for a distance

of 0.15l on each side from the support and atleast 50% shall be provided for a distance of

0.3l on each face from the support.

e. At discontinuous edge, negative moment may arise, in general 50% of mid span steel

shall be extended into the span for a distance of 0.1l at top.

f. Minimum steel can be provided in the edge strip

g. Tension steel shall be provided at corner in the form of grid (in two directions) at top and

bottom of slab where the slab is discontinuous at both the edges . This area of steel in

each layer in each direction shall be equal to ¾ the area required (Ast) for maximum mid

span moment. This steel shall extend from the edges for a distance of lx/5. The area of

steel shall be reduced to half (3/8 Astx) at corners containing edges over only one edge is

continuous and other is discontinuous.

ONE WAY CONTINUOUS SLAB

The slabs spanning in one direction and continuous over supports are called one way

continuous slabs.These are idealised as continuous beam of unit width. For slabs of uniform

section which support substantially UDL over three or more spans which do not differ by

more than 15% of the longest, the B.M and S.F are obtained using the coefficients

available in Table 12 and Table 13 of IS 456-2000. For moments at supports where two

unequal spans meet or in case where the slabs are not equally loaded, the average of the two

values for the negative moments at supports may be taken. Alternatively, the moments may

be obtained by moment distribution or any other methods.

Bending moment and Shear force coefficients for continuous slabs

( Table 12, Table 13, IS 456-200)