Design Examples of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 427

s

a

4 m

Fsin a

A

s

5 35 m

g vk = 77.1 kN/m

450 kN

450 kN

q vk = 45.65 kN/m

1.2 m

+

1.6

1.352

1.4

Figure 4.188 Determination of the force in diagonal member D 1 using the influence
line method.

F L : L : D ðÞ positive ð Þ 450 1 ð : 4+1 : 352 Þ +28 45 : 65 ¼ 2516 : 6kN

F L : L : D ðÞnegative ð Þ¼ 7 : 5 1 ð : 4+1 : 352 Þ 28 2 : 45 ¼ 89 : 24 kN

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

F Ed D ð maximum ¼ 2158 : 8 1 : 3 + 2516 : 6 1 : 35

¼ 6203 : 9 kN Tension force ð Þ

F Ed D ð minimum ¼F D : L : g g + F L : L : g q

F Ed D ð minimum ¼ 2158 : 8 1 : 3 89 : 24 1 : 35

¼ 2684 : 9 kN Tension force ð Þ

4.6.3.10 Calculation of the Reactions at Supports
The reactions at supports can be also calculated using the influence line
method, as shown in Figure 4.189 , as follows:

A +ve ðÞ¼A net D ðÞ¼ 0 : 5 40 1 : 0 ¼ 20 : 0

F D : L : ðÞ¼ 20

: 0 77 : 1 ¼ 1542 kN

F L : L : ðÞ positive ð Þ 450 1 ð : 0+0 : 97 Þ +20 : 0 45 : 65 ¼ 1799 : 5kN

F Ed ðÞ¼F D : L : g g + F L : L : g q
F Ed ð maximum ¼ 1542 1 : 3 + 1799 : 5 1 : 35 ¼ 4433 : 9kN