Civil Engineering Reference
In-Depth Information
substituted in Equation (9.43) to determine
-values for column and middle
strips followed by Equation (9.44) or (9.45) to obtain the de
δ
fl
ection at the
centre of two-way slab panels. This gives a basic de
ection value
D
basic
which
does not account for the reinforcement, creep or cracking. The true de
fl
fl
ection
can be much higher than the value
D
basic
(
fi
ve to eight times), as will be
discussed in the following subsection.
Table 9.2
8
may be employed to
ection value
D
basic
at the
centre of an interior panel and at the centre of column strips for two-way slab
systems with or without beams. It should be noted that the de
fi
nd the basic de
fl
ection values
given in this table are based on elastic analysis of an interior panel. Exterior
panels usually have larger de
fl
fl
ection. Other limitations of Table 9.2 are
mentioned with the table.
9.9.3 Effects of cracking and creep
In this subsection an approximate procedure is presented to account for the
e
ff
ect of the reinforcement ratio, cracking and creep on the de
fl
ection at the
centre of panels of two-way slab systems. The e
ff
ect of shrinkage will be
discussed in the following subsection.
The de
fl
ection at the centre of a panel can be considered as the sum of
de
for column and middle strips (see Equation (9.44) or
(9.45) and Fig. 9.11(c) ). The symbol
fl
ection values,
δ
δ
represents the de
fl
ection at the middle
of a strip relative to its ends. First, basic
-values are determined using Equa-
tion (9.43) and curvature values based on gross concrete sections, without
consideration of cracking or creep. The basic
δ
δ
-values may also be extracted
from Table 9.2 or from alternative sources.
The de
fl
ection
δ
of a strip is largely in
fl
uenced by the curvature at its mid-
span. Thus, the reinforcement ratio,
ρ
at mid-span section of the strip is used
to determine coe
cients
κ
s1
and
κ
φ1
and also
κ
s2
and
κ
φ2
when cracking
occurs. These coe
cients are employed as multipliers to the basic
δ
-values to
approximately account for the e
ects of creep and cracking in the same way
as discussed for beams in Section 9.4.
The suggested procedure is more clearly explained in steps given below.
The steps are to be followed after the bending moments and the reinforce-
ments in the middle and column strips have been determined.
(1) Calculate curvatures at ends and at mid-span for a column strip running
in the
x
or
y
direction and for a middle strip running in the perpendicular
direction. In this step use the moment values corresponding to the service
load for which the de
ff
ection is required. Ignore the reinforcement, creep,
shrinkage and cracking (Equations (9.46-49) ).
(2) Use the curvatures to determine basic de
fl
fl
ection
δ
basic
of the two strips
relative to their ends (by Equation (9.43) ).
Alternatively, steps 1 and 2 may be replaced by a design aid which gives
δ
-values such as Table 9.2.
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