Civil Engineering Reference
In-Depth Information
B
A
Influence line for
M
D
E
C
D
FIGURE 5.15
Influence line for bending moments at location D in three-hinged arch rib.
can be developed from influence lines for directly loaded arches in a manner analo-
gous to simple spans with transverse members (floorbeams) (see Sections 5.2.1.1.2
and 5.2.1.1.4).
For example, with a pin at location C, the influence line for bending moment at
D will be of the general form shown in Figure 5.15. The influence lines for other
internal forces can be determined in a similar manner.
5.2.1.2.3.3 Maximum Axial Forces with Moving Loads on a Statically Deter-
minate Trussed Arch
Long-span steel railway bridges can be economically
constructedofthree-hingedarcheswiththearchribreplacedbyatruss.Thetechniques
used in Section 5.2.1.2.3.1 to determine maximum effects are useful for the construc-
tion of influence lines for trussed arches. The crown hinge is designed to achieve
static determinacy with a bottom chord pin and top chord sliding arrangement
∗
as
shown in Example 5.7 and
Figure E5.8.
Example 5.7
DeterminetheinfluencelineformemberU1-U2inthe400 fteight-paneldeck
trussed arch in Figure E5.8.
The force in the chord U1-U2 can be determined using Equation 5.20 by
considering Section 1.1 and taking moments about L2.
M
D
y
D
=
R
A
(a
D
)
−
H
A
(h
D
)
y
D
R
A
(a
D
)
−
(L/
4
h)(h
D
)
y
D
F
U1
-
U2
=
=
.
The ordinate of the influence line at L2 provides
R
A
(a
D
)
=
(
6
/
8
)(
100
)
=
75.
This component of the influence line is related to vertical reaction,
R
A
.
The ordinate of the influence line at L4 provides
(L/
4
h)(h
D
)
=
(
400
/
4
(
150
))(
45
66.67. This component of the influence line is related to
horizontal thrust reaction,
H
A
.
+
55
)
=
∗
Thereby, rending the force in one central top chord member as zero.
