Civil Engineering Reference
In-Depth Information
(3) For the cross-section at the middle of the two strips, determine the
curvature coe
κ
φ
1
for a non-cracked section, using graphs of
Figs. F.1, F.3-5 or Equations (F.1) and (F.2). For each of the two strips,
calculate the instantaneous plus creep value of
cients
κ
s1
and
δ
in the uncracked state 1:
δ
1
=
δ
basic
κ
s1
(1
+
φ
κ
φ
1
)
(9.50)
Calculate the value
M
r
of the bending moment which produces cracking. If
the bending moment at the centre of a strip is less than or equal to
M
r
, no
cracking occurs and
ection at the middle of the strip
relative to its ends, a value to be used in step 5.
(4) When cracking occurs at the mid-span section of any of the two strips,
determine the curvature coe
δ
=
δ
1
; where
δ
is the de
fl
κ
φ
2
for a fully cracked section,
using graphs of Figs. F.2, F.6, F.7 and F.8 or Equations (F.1) and (F.2) and
calculate the instantaneous plus creep de
cients
κ
s2
and
fl
ection for a fully cracked strip:
δ
2
=
δ
basic
κ
s2
(1
+
φ
κ
φ
2
)
(9.51)
Calculate the interpolation coe
cient using Equation (9.24) and determine
the
δ
-value including e
ff
ects of creep and cracking.
δ
=
(1
−
ζ
)
δ
1
+
ζδ
2
(9.52)
-values of a column and a middle strip according to Equation
(9.44) or (9.45) to obtain the de
(5) Add the
δ
ection at the centre of the panel. For a more
reliable answer, two possible patterns of strips may be used and the probable
de
fl
ection considered equal to the average of the answers from the two
patterns.
When the column strips running in one direction have di
fl
-values, an
average value is to be used in Equations (9.44) and (9.45), as shown in Fig.
9.11(c).
ff
erent
δ
Example 9.5 Interior panel
Figure 9.12 is a top view of an interior square panel of a two-way slab
supported directly on columns. It is required to calculate the long-term
de
ection due to a uniform load 8.40 kN/m
2
(175 lb/ft
2
), which repre-
sents the dead load plus a part of the live load. The bending moments
9
due to this load are indicated in Fig. 9.12(b) for a section at mid-span of
a column and a middle strip. The reinforcement cross-section areas
10
at
these two locations are given in Fig. 9.12(a). Other data are: slab thick-
ness,
h
fl
=
0.20 m (8 in); average distance from top of slab to centroid of
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