Civil Engineering Reference
In-Depth Information
Figure 3.3
Equations 3.10 and 3.14
as shown in Fig. 3.2(d) and (e). The lever arm
z
is found by the approx-
imation shown by line EF in Fig. 3.3(b). This is clearly correct when
N
c,f
=
N
pa
,
because
N
ac
is then zero, so
M
pr
is zero. Equation 3.6 with
x
pl
=
h
c
then gives
M
Rd
. The lever arm is
z
=
d
p
−
0.5
h
c
=
h
−
e
−
0.5
h
c
(3.12)
as given by point F.
To check point E, we assume that
N
c,f
is nearly zero (e.g., if the concrete
is very weak), so that
M
pr
M
pa
.
The neutral axis for
M
pa
alone is at height
e
p
above the bottom of the sheet, and the lever arm for the force
N
c,f
is
z
=
h
−
e
p
−
0.5
h
c
(3.13)
as given by point E. This method has been validated by tests.
The line EF is given by
z
=
h
−
0.5
h
c
−
e
p
+
(
e
p
−
e
)
N
c,f
/
N
pa
(3.14)
(3) Partial shear connection
The compressive force in the slab,
N
c
, is now less than
N
c,f
and is deter-
mined by the strength of the shear connection. The depth
x
of the stress
block is given by
x
=
N
c
/(0.85
f
cd
b
)
≤
h
c
(3.15)
There is a second neutral axis within the steel sheeting. The stress blocks
are as shown in Fig. 3.2(b) for the slab (with force
N
c
, not
N
c,f
), and
Fig. 3.2(c) for the sheeting. The calculation of
M
Rd
is as for method (2),
except that
N
c,f
is replaced by
N
c
, and
h
c
by
x
, so that:
z
=
h
−
0.5
x
−
e
p
+
(
e
p
−
e
)
N
c
/
N
pa
(3.16)
