SLABS

Prepared by: Engr.Ayaz Waseem

Lecture # 1

ONE-WAY SLABS

BEHAVIOR OF ONE-WAY SLABS

Simple supports on two long edges only

lxly

h

h

lx

Main reinforcement in shorter direction

ly

1 m strip

Distribution steel in longer direction

Span

ONE-WAY SLABS

Span

Unit strip

1m (SI units) 12 in.(FPS units)

Unit strip

TWO-WAY SLABS

BEHAVIOR OF TWO-WAY SLABS

Simple supports on all four edges

lxly

h

Figure shows two center strips of

rectangular plate with short span lx and

long span lyIf uniform load is w per m2 of slab, each of

two strips acts like a simple beam,

uniformly loaded by its share of w

As deflection at the intersection point of

these two strips is same, so we have

EI

lw

EI

lw yyxx

384

5

384

544

Larger share of load is carried in shorter

direction as the ratio of the two portions of

the total load is inversely proportional to

the fourth power of the ratio of spans

Remember that this expression is

approximate because we have only

considered deflection due to bending. No

effect of torsion is taken into account

4

4

x

y

y

x

l

l

w

w

.

Ly/Lx wx/wy wx wy1 1 1/2 w 1/2 w1.5 81/16 81/97 w

16/97 w1.8 21/2 21/23 w 2/23 w

2 16 16/17 w 1/17 w2.5 39 39/40 w 1/40 w

One-Way Slab

Two-Way Slab

Shorter direction strips

Longer direction strips

Bending + Torsion Bending

ADDITIONAL STIFFNESS

Beam axis

Due to Poisson’s ratio bending causes lateral expansion

lxly

h

STRIP AS A BEAM

ANTI-ELASTIC BENDING

Neutral axis

ADDITIONAL STIFFNESS

We can assume slab to be a combination

of number of unit width beams

If we consider Poisson’s ratio then actual

bending of the beam causes lateral

expansion and the actual curvature of the

beam after bending is called anti-elastic

curvature If each beam tries to expand in lateral

direction, it will induce extra stiffness in

slab which is not considered in our design

calculations to avoid complexity

CONTINUITY

SUPPORT CONDITIONS

Supports on all four sides

APPROXIMATE METHODS FOR DESIGN OF TWO-WAY SLABS

ACI Direct Design Method (DDM)

ACI Equivalent Frame Method

Strip method

Yield Line Theory

ACI coefficient method

ACI COEFFICEINT METHOD

Moments and shears coefficients used for

the design of slabs by coefficient method

are determined by combining the moment

and shear diagrams for different load

cases to obtain the maximum values along

each spanThe resulting diagrams obtained by

combining all moment and shear diagrams

are called Envelope Moment Diagram and

Envelope Shear Diagram respectively

Dead load

live load

This loading condition will result in the maximum positive moments in the exterior span, the minimum positive moment in the center span, and the maximum negative moments at the interior faces of the exterior columns

LOADING CASE # 1

This loading condition will result in maximum positive moment in the center span and the minimum positive moments in the exterior span

LOADING CASE # 2

Dead load

live load

This loading condition will result in maximum negative moment at the at both faces of the interior columns

LOADING CASE # 3

live load

Dead load

Loading 1

Loading 3

Loading 2

Loading 3

Loading 1 Loading 3

Loading 3

ENVELOPE MOMENT DIAGRAM

ENVELOPE SHEAR DIAGRAM

SUPPORTS CONDITION FOR NEGATIVE MOMENT COEFFICIENTS

For dead load negative moments full fixity at the interior supports is considered

For live load moments full fixity at the interior supports where negative moment is to found is considered is considered

For dead load positive moments full fixity at the interior supports is considered

For live load negative moments partial fixity at the interior supports is considered

SUPPORTS CONDITION FOR POSITIVE MOMENT COEFFICIENTS

There is one set of coefficients for negative moments (Dead or Live) at the supports. (derived with full fixity at continuous supports)

There are two different sets of positive moments coefficients separately for Dead and Live Loads (full fixity for dead load and partial fixity for live loads)

ACI MOMENT PROFILE

ACI ASSUMED PROFILE

Edge stripMiddle strip (L/2)

Edge strip

M M

M/3M/3

EDGE STRIP (ES)

Edge strip moment = 2/3 (Mmax)

Steel spacing (ES) = 1.5 Steel spacing (MS)But steel spacing should not exceed maximum spacing limit provided by the code

Edge strip steel = 2/3 (Middle strip steel)

MAXIMUM STEEL SPACING

Maximum spacing is smaller of the following;

450 mm

5 times the slab thickness

CORNER STEEL

Bottom cracks Top cracks

At corners of the slab unbalanced twisting moment is resulted. Therefore cracks occur at the bottom and top of the slab at corners

REINFORCEMENT OPTION # 1

Bottom steel Top steel

Bottom steel Top steel

l /5

REINFORCEMENT OPTION # 2

TABLE FOR SLAB DESIGN

Slab Pane

lLx Ly

Case

Thickness,h

d1 d2 wuCxD

+

CxL+

m m mm mm

mm kN/m

Cx- Mx

+ Mx- CyD

+ CyL+ Cy

- My+ My

- Asx+

kN-m kN-m kN-m kN-m mm2/m

Asx- Asy

+ Asy-

mm2/m mm2/m mm2/m

CONCLUDED