118 For periods less than or equal to, the elastic
seismic coefficient for the mth mode of vibration, C
sm, shall betaken as
πΆπΆ
π π ππ
= π΄π΄
π π
+ (ππ
π·π·ππ
β π΄π΄
ππ
)(
ππ
ππ
ππ
0
) Equation 8-1) Where As
= F
pga
PGA.
S
DS
= F
a
S
s.
PGA = Peak ground acceleration coefficient on rock (Site Class BS s Horizontal response spectral acceleration coefficient at sec period on rock (Site Class B. Tm Period of vibration of mth modes. T Reference period used to define spectral shape = 0.2T
s
(s). Ts
= Corner period at which spectrum changes from being independent of period to being inversely proportional to period = S
D1
/S
DS
(s). For periods
greater than or equal to T0
and less than or equal to Ts, the
elastic seismic coefficient, C
sm, shall betaken as
πΆπΆ
π π ππ
= Equation 8-2) For periods greater than Ts the elastic seismic coefficient, C
sm, shall betaken as
πΆπΆ
π π ππ
= Equation 8-3) Where SD F
v
S
1.
S
1
= Horizontal response spectral acceleration coefficient at 1.0 sec period on rock (Site Class B
). The elastic seismic response coefficient can then be used to determine the equivalent static force using Equation 8-4 (Hannigan et al. 2016).
ππ
ππ
(π₯π₯) = πΆπΆ
π π ππ
ππ Equation 8-4) Where
P
e
(x) = Equivalent static horizontal seismic force acting on superstructure.
C
sm
= Elastic seismic response coefficient (dimensionless. W = Equivalent weight of the superstructure. Once the equivalent
static force is determined, the structural engineer applies the force to the superstructure following the procedure described in AASHTO (2014) Section 4.7.4.3. Table 8-1 presents the seismic zone of abridge depending on the coefficient S
D1
(Hannigan et al. 2016). For multispan bridges with a seismic zone of 2 through 4, a liquefaction assessment is required.
119 The factored loads resulting from the seismic analysis should be applied to the foundation and analyzed as outlined in Chapter 5. Methods described in Chapters 6 and 7 can be used as appropriate for individual and group analyses.
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