design of 2-way slabs
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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
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