Civil Engineering Reference
In-Depth Information
Table 13.1
Variables of the deep bent cap example
A
s
mm
2
(in
2
)
A
′
mm
2
(in
2
)
b
w
mm
(in)
d mm
(in)
k
d
mm
(in)
d
′
mm
(in)
A
sh
mm
2
(in
2
)
L
mm (in)
j
d
mm (in)
L
/
j
d
α
N
h
ρ
T
ρ
L
η
1073
(42.25)
33.3° 4 396
(0.614)
L
, the beam length;
b
w
, the beam width;
d
, the effective depth of the beam from the extreme concrete compression iber to the centroid of the tension steel;
d
,
distance from extreme compression iber to the centroid of longitudinal compression reinforcement;
s
, the stirrup spacing;
j
, the internal lever arm coeficient, which,
in lieu of a more precise analysis, may be taken as
j
=
0.9;
A
s
, the area of longitudinal tension reinforcement;
A
′
, the area of compression reinforcement;
A
sh
, the area
of one set of stirrups;
ρ
L
, the volumetric ratio of longitudinal steel to concrete,
ρ
L
705
(27.76)
1.52
0.0030
0.0073
0.55
4813
(7.46)
4051
(6.28)
838
(33)
787
(31)
193
(7.6)
83
(3.25)
, where
A
L
is the area of longitudinal reinforcement contributing to the
=
A b d
/
L
w
tension tie;
ρ
T
the volumetric ratio of transverse steel to concrete over one hoop spacing
ρ
T
= /
;
η
, the arch breadth scalar, used to apportion the contribution
of arch-and-truss action deined as a function of the longitudinal and transverse reinforcement and the member's span-depth ratio, given by
A b s
sh
w
f
f f j
cot
k
, the elastic compression zone coeficient
ρ
η
L y
=
ρ
+
ρ
2
α
L y
T yh
′
d
d
′
ρ
2
L
k
(
′
)
n
2
2
n
(
′
)
n
=
ρ
+
ρ
+
ρ
+
+
ρ
+
ρ
;
L
L
L
L
L
N
h
, integer part of active hoops in truss mechanism
N
h
=
int(
L s
/ −
1);
α,
the corner-to-corner diagonal angle.
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