Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 546

800
700
600
500
400
300
200
100

120

100

80 0°

30°

0°
30°

60

40

2 3 4

2 3 4

(a) (b) Pier number

Pier number

1000
900
800
700
600
500
400

0°
30°

2 3 4

(c) Pier number

Figure 17.27 Maximum amplitude of internal forces at bottom of piers under oblique
incidence SV waves: (a) shear force ( V ); (b) axial force ( N ); (c) moment ( M y ).

Table 17.10 Indices of nonuniform effects for piers under oblique incidence waves at 30 °

η P η SV

Internal
forces Pier 2 Pier 3 Pier 4 Pier 2 Pier 3 Pier 4

V

552 % 874 % 477 %

- 53.28 % - 62.39 % - 62.80 %

N - 13 % - 24 % - 27 % 118.86 % 274.26 % 259.41 %

M y 359 % 319 % 344 % - 44.76 % - 29.41 % - 56.02 %

Considering ratio of the values computed from vertical and oblique inci-
dence input, an index can be calculated as follows:

η = max

F − max F

0

(17.27)

max

F

0

where:
F 0 is the internal force of the piers including shear forces, axial forces,
and moment computed by vertical input
F is the internal force computed by oblique incidence wave

The indices of nonuniform effects for piers in valley under oblique inci-
dence waves at 30° are shown in Table 17.10. It is shown that the oblique
incidence waves have great effect on the piers of bridges in valley.