Design Examples of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 284

s

a

D 4

V 4

F sin α

B

s b

A

18 m 6 m 36 m

g vk = 78.1 kN/m

375 kN

375 kN

q vk = 43.8 kN/m

1.2 m

375 kN

375 kN

q vk = 43.8 kN/m

1.2 m 1.281

0.384

0.358

-

+

0.769

0.743

2 m 4 m

1.281

Figure 4.61 Determination of the force in diagonal member D 4 using the influence line
method.

F D : L : D ðÞ¼ 11 : 54 78 : 1 ¼ 901 : 3kN

F L : L : D ðÞ positive ð Þ 375 0 ð : 769 + 0 : 743 Þ +15 : 38 43 : 8+3 : 84 0 : 83

8kN
F Ed D ð maximum ¼F D : L : g g + F L : L : g q

¼ 1243 :

F Ed D ð maximum ¼ 901 : 3 1 : 3 + 1243 : 8 1 : 35

¼ 2850 : 8 kN Tension force ð Þ

F L : L : D ðÞ negative ð Þ ¼ 375 0 ð : 384 + 0 : 358 Þ 3 : 84 43 : 8 15 : 38

0 : 83 ¼ 459 : 2kN

F Ed D ð minimum ¼F D : L : g g + F L : L : g q
F Ed D ð minimum ¼ 901 : 3 1 : 3 459 : 2 1 : 35

¼ 551 : ð Þ

8 kN Tension force

It should be noted that, from the equilibrium of joint J 4 (see Figure 4.61 ),
the force in the vertical truss member V 4 is equal to that of D 4 multiplied
by sin a but with a negative sign (a compression force of

2850.8 sin 51.34 ¼ 2226.1 kN).