Civil Engineering Reference
In-Depth Information
5.2.1.2.3 Influence Lines for Maximum Effects in Statically
Determinate Arch Spans
Many steel railway arches are designed as three hinged to impose statically deter-
minate conditions
(Figure 5.10a).
Statically determinate arches are often simpler
to fabricate and erect, and are not subjected to temperature or support displace-
ment induced stresses. The construction of influence lines for statically determinate
arches can be made efficient by understanding the relationships between arch reac-
tions, internal forces (shear, bending, and axial), and the influence lines obtained in
Section 5.2.1.2.1 for shear and bending in simply supported spans.
5.2.1.2.3.1 Maximum Bending Moment, Shear Force, and Axial Force (with
Moving Loads Applied Directly to the Arch)
For the moving concentrated
load,
P
=
1, a distance
x
P
from support A in Figure 5.10a,
−
L
x
P
R
A
=
,
(5.18a)
L
x
P
L
.
R
B
=
(5.18b)
E
P
=1
a
D
C
D
ϕ
D
h
h
D
H
A
H
B
B
A
x
P
L
R
B
R
A
1
Influence line for
R
A
L
/(4
h
)
Influence line for
H
A
FIGURE 5.10a
Three-hinged arch rib with concentrated moving loads applied directly to
the rib.
