Applied Loads and Stability of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 142

simply supported bridges with only longitudinal line beam or simple plate
behavior with negligible skew effects on rigid supports. A dynamic analysis
is required where the frequent operating speed of a real train equals a reso-
nant speed of the bridge. For bridges with a first natural frequency n 0 within
the limits given by Figure 3.15 and a maximum line speed at the site not
exceeding 200 km/h, a dynamic analysis is not required. For bridges with
a first natural frequency n 0 exceeding the upper limit (1) in Figure 3.15 ,a
dynamic analysis is required. For a simply supported bridge subjected to
bending only, the natural frequency may be estimated using the following
formula as specified in EC1:

17 : 75

d 0

n 0 ¼ p ð 3 : 19 Þ

where n 0 is in Hz and d 0 is the deflection at midspan due to permanent
actions in millimeters and is calculated, using a short-term modulus for

n 0 (Hz)

150

100

80

60

40

20

15

(1)

10

8

6

4

(2)

2

1.5

1.0 L (m)

2 4 6 8 10 15 20 40 60 80 100

Key
(1) Upper limit of natural frequency
(2) Lower limit of natural frequency

Figure 3.15 Limits of bridge natural frequency n 0 (Hz) as a function of L (m)

recommended by EC1 [ 3.1 ] .