The Ingenieur Vol 59 July-Sept 2014 The Ingenieur Vo. 59, July-Sept 2014 | Page 32

INGENIEUR
Bridge Stiffness Element Calculation
i) Piers
The piers effective stiffness for seismic analysis
is estimated initially and is checked after the
design of the pier reinforcement. For both piers the
stiffness is assumed to be 40% of the un-cracked
stiffness.
ii) Deck
The un-cracked bending stiffness of the prestressed concrete deck is considered. The
torsional stiffness considered is the 50% of the
uncracked stiffness.

called “Response 2000”. Figure 4 shows the
geometric and material properties of the column
used in this bridge model.

Figure 4: The geometric and material properties of
column provide by RESPONSE 2000

Permanent load for the design seismic situation
The loads applied in the bridge deck for the
seismic situation (WE) are the sum of self weight
(G), additional dead (G2) and the effective seismic
live load. The sum of self weight (G) and additional
dead (G2) are computed qG = 17,919 kN. The
effective seismic live load (qLE) is 20% of the
uniformly distributed traffic load (qL = 7,014 kN)
are 0.20qL = 1,403 kN. And the final total load
applied in the bridge deck for the seismic situation
(WE) are 19,322 kN.
Fundamental Mode Analysis in the Longitudinal
Direction
The fundamental mode and period is estimated based
on a simplified SDOF cantilever model of the bridge.
The mode corresponds to the oscillation of the bridge
along its longitudinal axis, assuming both ends of the
piers are fixed. For octagonal columns of 2m in diameter,
the un-cracked moment of inertia, Jun = 0.8758 m4.
The assumption made for effective moment of inertia
of piers is Jeff/Jun = 0.40, when both ends of the piers
are fixed with concrete grade C40 (fcm = 48) with Ecm =
22 [fcm /10]0.3 GPa. The calculated Ecm is 31.68GPa
and the horizontal stiffness of each pier in longitudinal
direction, Kpier are 12EJeff/H3 = 12 x 31,680MPa x (0.40
x 0.8758m4) / (6.18 m) 3 = 564.24 MN/m (per pier) or
1,128 MN/m (per bent). From this calculation, the total
horizontal stiffness, Kpier is 1,128 x 2 Bent = 2,257
MN/m with the total seismic weight , WE is19,322 kN,
then the fundamental period T is 0.1857 sec.

Analytical model
The material nonlinearity is evaluated by using
a programme developed by University of Toronto
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ingenieur 2014-July-FA.indd 30

O operational, IO immediate occupancy, LS life safety, CP collapse
prevention (FEMA 356)

Figure 5: Conceptual plastic hinge states. 
The hinge sections are located at several
points of the column section to study nonlinearity
behaviour. Any failures are expected to develop
at the lower or upper points of the column. The
serviceability behaviour factor was evaluated
and superimposed onto the nonlinear Force
Displacement (F-D) curve to indicate overall
structural
performance.
However, property
owners and the public are more interested in
performance measures which are easier to
understand. Performance measures describe ‘on
limit states’, understanding immediate-occupancy
(IO), life-safety (LS), and collapse-prevention (CP),
which indicate the correlation between material
nonlinearity and deterministic projections for any
structural damage sustained (FEMA356, 2005.
The static-pushover analysis is a nonlinear method
which generates a idealised monotonic response
curve shows in Figure 5.

VOL 59 JULY –2013
VOL 55 JUNE SEPTEMBER 2014

7/9/14 10:37 AM