Design Examples of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 283

produce a compressive or tensile force, respectively, while the dead loads
must be put on both triangles. Once again, the total force in the member
will be the summation of concentrated loads multiplied by the companion
vertical coordinate in the diagram and the summation of the distributed loads
multiplied by the companion area in the diagram. Hence, the forces due to
the dead and live loads can be calculated as follows:

A +ve D ðÞ¼ 0 : 5 33 : 34 0 : 641 ¼ 10 : 69

A ve D ðÞ¼ 0 : 5 26 : 66 0 : 512 ¼ 6 : 82

A net D ðÞ¼ 10 : 69 6 : 82 ¼ 3 : 87

F D : L : D ðÞ¼ 3 : 87 78 : 1 ¼ 302 : 2kN

F L : L : D ðÞ positive ð Þ 375 0 ð : 641 + 0 : 615 Þ +10 : 69 43 : 8+6 : 82 0 : 83

9kN
F Ed D ð maximum ¼F D : L : g g + F L : L : g q

¼ 944 :

F Ed D ð maximum ¼ 302 : 2 1 : 3 + 944 : 9 1 : 35

¼ 1668 : 5 kN Tension force ð Þ

F L : L : D ðÞ negative ð Þ ¼ 375 0 ð : 512 + 0 : 486 Þ 6 : 82 43 : 8 10 : 69

83 ¼ 681 kN
F Ed D ð minimum ¼F D : L : g g + F L : L : g q

0 :

F Ed D ð minimum ¼ 302 : 2 1 : 3 681 1 : 35

¼ 526 : 5 kN Compression force ð Þ

It should be noted that, from the equilibrium of joint J 5 (see Figure 4.60 ),
the force in the vertical truss member V 5 is equal to that of D 5 multiplied by
sin a but with a negative sign (a compression force of 1668.5 sin
51.34 ¼ 1302.9 kN).

4.3.3.8 Calculation of Force in the Diagonal Chord Member D 4
By repeating the procedures adopted for D 5 , the force in the diagonal truss
member D 4 can be calculated, as shown in Figure 4.61 , as follows:
A +ve D ðÞ¼ 0

: 5 40 0 : 769 ¼ 15 : 38

A ve D ðÞ¼ 0 :

5 20 0

:

384 ¼ 3

:

84

A net D ðÞ¼ 15 : 38 3 : 84 ¼ 11 : 54