Civil Engineering Reference
In-Depth Information
This gives the maximum slip (when
x
0.45 mm.
This may be compared with the maximum slip if there were no shear
connection, which is given by Equation 2.6 as
=
±
5 m) as
±
wL
Ebh
3
. .
×
×× ×
35
10
3
=
.
=
81
mm
4
2
4
20
0 6
0 3
2
×
1000
The stresses at mid-span can be deduced from the slip strain and the
curvature. Differentiating Equation 2.28 and putting
x
=
0,
⎛
⎜
d
d
s
x
⎞
⎟
10
=
. .
1 05
−
0 0017
. .
×
1 36
=
1 05
4
x
=
0
so the slip strain at mid-span is 105
×
10
−6
. From Equation A.13,
d
d
x
.
=
464
s
.
−
65
×
10
4
−
x
Using Equation 2.28 for
s
and integrating,
10
6
φ
=
−
81.5
x
2
−
0.585 cosh(1.36
x
)
+
K
The constant
K
is found by putting
φ
= 0 when
x
=
L
/2, whence at
x
=0,
φ
=
0.0023 m
−1
The corresponding change of strain between the top and bottom faces of
a member 0.3 m deep is 0.3
10
−6
. The transformed
cross-section is symmetrical about the interface, so the strain in each
material at this level is half the slip strain, say 52
×
0.0023, or 690
×
10
− 6
, and the strain
distribution is as shown in Fig. 2.17. The stresses in the concrete, found
by multiplying the strains by
E
c
(20 kN/mm
2
), are 1.04 N/mm
2
tension
and 12.8 N/mm
2
compression. The tensile stress is below the cracking
stress, as assumed in the analysis.
The maximum compressive stress in the concrete is given by full-
interaction theory (Equation 2.7) as
×
3
16
wL
bh
2
. .
××
×× ×
=
3
35
100
σ
cf
=
=
.
12 2
N/mm
2
2
16
06
009
10
3
