CE421 REINFORCED CONCRETE

STRUCTURE DESIGN

SLAB DESIGN

SLABSShell Members: The thickness of shell members is very small compared to itsother two dimensions and the loads are applied vertical to its surface.

Example: Slabs!

Slabs mainly transfer the distributed vertical gravity loads to the beams or directlyto the columns/shear walls. But another important duty of slabs (together withbeams) is to distribute the lateral earthquake forces between the columns/shearwalls. For a proper distribution of these lateral forces, slabs should be rigid(thickness should be enough to behave rigidly under lateral forces).

x

y

zDistributed

Loads

SLABSTypes of Slabs:

1. Slabs with beams

a. One-way slabs (for m=ll/ls>2)

b. Two-way slabs (for m=ll/ls<2)

The most common solution for slab systems. Both vertical and

horizontal loads may be transferred from one member to another

properly (if the beams and slabs are designed succesfully).

SLABSTypes of Slabs:

2. Slabs without beams (In cases where beams are not required: beams reduces storey height)

a. Flat Plate

a. Flat Slab

For short span lengths and light distributed weight (e.g.

in ordinary buildings) flat plates may be used. The

gravity loads of the slabs are directly transferred to the

columns. There is a risk for PUNCHING

In industrial structures, where heavy loads may be the

case, flat slabs may be used.

SLABSTypes of Slabs:

3. Waffle slabs: has «tiny» beams (joists) supporting the slab.

The empty spaces between the joists may be filled with blocks (block joist floors).

For large spans, the thickness of the slab may become

to be excessive and not economical. In these cases,

waffle slabs may be a solution.

Block joist floor systems are not successful in

terms of rigidity along its surface (small

thickness of the slab and beams). Therefore, it

is not appropriate for structures those may be

subjected to lateral earthquake forces.

SLABSNotes for Slabs:

Generally, there occurs no problem related to the ultimate limit state design. But the problems are generally observed related to the serviceability limit state (excessive deflections/vibrations and excessive cracking). Excessive deflections/vibrations are caused by insufficient slab thickness. Excessive cracking is caused by insufficient reinforcement.

Definition of ls, lsn, ll and lln.

lsn ls

ll

lln

m=ll/ls

If m<2 : Two-way slab

If m>2 : One-way slab

SLABS As «m» ratio increases, the percentage of the load resisted as bending along short direction

increases. When m>2 (one way slabs), it may be assumed that bending only takes place along short direction (no bending along long direction).

Bending of one-way slab (m>2) Bending of two-way slab (m<2)

Bending of slabs along both

x and y directions

SLABSSupport conditions of slabs

• Continuous (interior) edge : supported by a beam and there is a neighboring slab (similar to fixed support)

• Discontinous (exterior edge : supported by a beam and there is no neighboring slab (similar to pin support)

• Free edge : not supported by a beam and no neighboring slab (similar to free end)

D1 D2BD1 D3

D4 D5BD2 D6

D7 D8 D9

D1

D5

D7

BD3

Continuous

edge

Discontinuous

edge

BD1

Free

edge

D7

BD3

SLABSThe loads on slabs: Uniformly distributed dead (g) and live (q) loads.

Load

Sla

b

Marble floor (2 cm.)

Concrete topping (5 cm.)

Slab concrete (10 cm.)

Plaster (2 cm.)

Marble floor: 0.02 m.× 27 kN/m3 = 0.54 kN/m2

Concrete topping: 0.05 m.× 22 kN/m3 = 1.10 kN/m2

Slab concrete: 0.10 m.× 25 kN/m3 = 2.50 kN/m2

Plaster: 0.02 m.× 20 kN/m3 = 0.40 kN/m2 +

Dead load (g) = 4.54 kN/m2

Live Load (q) = 2.00 kN/m2

Note: 1. If dropped ceiling exists, this should also be taken into account.

2. The characteristic unit weight of the materials, should be obtained from TS ISO 9194-1997.

3. The live load for different types of usage should be taken from TS 498-1997.

4. If there is an infill wall on the slab (not on the beam), this should be taken as a distributed (line) load on the slab or added

to the distributed (area) live load (add 1.5 kN/m2 if total live load is below 5.0 kN/m2)

SLAB DESIGNThe slabs are designed according to bending moment, shear and torsion.

• In case of two-way slabs, the reinforcement against bending is estimated for both short and long directions for two-way slabs.

SLAB DESIGN• In case of one-way slabs, the reinforcement against bending is estimated only for short

direction; and a percentage of this reinforcement is placed along long direction.

• Generally, thickness of slab is sufficient to resist shear stresses, so there is no need for extra shear reinforcement.

• No torsional reinforcement is required for the slabs according to the codes; but special torsional reinforcement may be placed at the corner regions only.

SLAB DESIGN• The bending moment along short direction (Mshort) results in tension cracks along long direction;

the bending moment along long direction (Mlong) results in tension cracks along short direction.

• At span, the tension cracks are at the bottom (positive moment; reinforcement at the bottom). Whereas, at support, the tension cracks are at the top (negative moment; reinforcement at the top). Maximum moment occurs at the span, support moments are smaller.

Mshort

Mlong

Before bending

After bending

Larger crack width

along long direction

(Mshort>>Mlong)

[Mshort]

[Mlong]

SLAB DESIGN• The bending moment distribution for different support conditions.

Four sides are continuous

(fixed supported)

Four sides are discontinuous

(pin supported) Two sides are continuous

Two sides are discontinuous

Three sides are continuous

One side is discontinuous

One side is continuous

Three sides are discontinuous