Design Examples of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 419

determine the forces in the members of main trusses using the influence line
method as shown in the coming sections.

4.6.3.2 Calculation of Force in the Upper Chord Member L 4
To determine the force in the lower chord truss member L 4 (see
Figure 4.181 ) using the influence line method, we can follow the simple
procedures of putting a unit concentrated moving load at midspan
(point a), and using the sectioning method, we take a section s - s , as shown
in Figure 4.181 , and then take the moment at point a to calculate the force in
the member due to the applied unit load. After that, we can put the previ-
ously calculated dead and live loads acting on a main truss in the longitudinal
direction. The total force in the member will be the summation of the con-
centrated loads multiplied by the companion vertical coordinate in the influ-
ence line diagram and the summation of the distributed loads multiplied by
the companion areas in the diagram. Hence, the forces due to the dead and
live loads can be calculated as follows:
F D : L : L ðÞ¼ 0

: 5 40 2 : 5 77 : 1 ¼ 3855 kN

F L : L : L ð positive ¼ 450 2 ð : 5+2 : 35 Þ +0 : 5 40 2 : 5 45 : 65 ¼ 4465 kN

F L : L : L ð negative ¼ 7 : 5 2 ð : 5+2 : 35 Þ 0 : 5 40 2 : 5 2 : 45

¼ 158 : 9kN

s

a

4 m

A L 4

J 10

L 5

s

20 m

20 m
g vk = 77.1 kN/m

450 kN 450 kN

q vk = 45.65 kN/m

1.2 m

+

2.35

20 × 20/(40 × 4) = 2.5

Figure 4.181 Determination of the tensile force in lower chord member L 4 using the
influence line method.