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RECENT DEVELOPMENTS IN SEISMIC ANALYSIS OF BRIDGE SUBSTRUCTURES. Mohiuddin A. Khan Ph.D., P.E. Manager Bridge Department, STV Inc., Trenton, NJ . What is an earthquake?
Mohiuddin A. Khan Ph.D., P.E.
Manager Bridge Department,
STV Inc., Trenton, NJ
and Richter Scales
The time periods varies from about three centuries in eastern states to slightly more than a century in some western states.
Date ----- Magnitude --- Intensity
Year Other Moment
California 1857 7.6MS 7.92 IX
1906 7.80MS 7.68 XI
Delaware 1871 VII
Georgia 1914 4.50Mfa V
Maine 1904 5.10Mfa VII
Maryland 1990 2.5Mn V
Massachusetts 1755 VIII
New Hampshire 1940 5.50Mn 5.25 VII
1940 5.50Mn 5.60 VII
New Jersey 1783 5.30Mfa VI
New York 1944 5.80Mn 5.52 VIII
North Carolina 1916 5.20Mfa VII
Pennsylvania 1998 5.2Mn VI
Rhode Island 1976 3.50Mn 2.07 VI
South Carolina 1886 6.70Mfa 7.02 X
Vermont 1962 4.2Mn V
Virginia 1897 5.60Mfa VIII
1. Chile 1960 05 22 9.5
2. Prince William
Sound, Alaska 1964 03 28 9.2
3. Aleutian Islands 1957 03 09 9.1
4. Kamchatka 1952 11 04 9.0
5. Off the Coast of
Ecuador 1906 01 31 8.8
6. Aleutian Islands 1965 02 04 8.7
7. India-China Border 1950 08 15 8.6
8. Kamchatka 1923 02 03 8.5
9. Banda Sea, Indonesia 1938 02 01 8.0
10. Kuril Islands 1963 10 13 8.5
Location Date Time Magnitude
1. New Madrid, Missouri 1811 12 16 8:15 8.1
2. New Madrid, Missouri 1812 02 07 9:45 ˜8
3. Fort Tejon, California 1857 01 09 16:24 7.9
4. New Madrid, Missouri 1812 01 23 15:00 7.8
5. Imperial Valley, California 1892 02 24 7:20 7.8
6. San Francisco, California 1906 04 18 13:12 7.8
7. Owens Valley, California 1872 03 26 10:30 7.6
8. Gorda Plate, California 1980 11 08 10:27 7.4
9. N Cascades Washington 1872 12 15 5:40 7.3
10. CA - Oregon Coast 1873 11 23 5:00 7.3
11. Charleston South Carolina1886 09 01 2:51 7.3
Strong earthquakes in 1638, 1661, 1663, and 1732 in the St. Lawrence Valley
First notable tremor centered within the State was recorded on December 18, 1737 (intensity VII).
Walls vibrated, bells rang, and objects fell from shelves (intensity VI) at Buffalo from a shock on
October 23, 1857.
A rather severe earthquake centered in northeastern New York area in 1877 (Intensity VII).
On August 10, 1884, an earthquake caused large cracks in walls at Amityville and Jamaica
A shock reported as severe (intensity VI), occurred in northeastern New York on May 27, 1897.
A very large area of the northeastern United States was shaken by a magnitude 7 earthquake on
February 28, 1925.
A maximum intensity of VIII was reached in the epicentral region, near La Malbaie, Quebec, Canada.
Extensive damage occurred in the Attica area from a strong shock on August 12, 1929.
On April 20, 1931, an earthquake centering near Lake George (intensity VII).
On September 4, 1944, an earthquake centered about midway between Massena, New York, and
Cornwall, Ontario, Canada, caused damage in the two cities. The shock was of Intensity VIII).
Earthquakes are linked to geologic conditions.
Precambrian Period is shown
Bridge curved in plan
Bridge curved in elevation
Bridge with Integral Abutment
Route U.S. 322/N.J. 50
PRECAST CONCRETE PIERS
Route U.S. 23/ U.S. 80 (NJ)
Route U.S. 80 (NJ)
Long Island R.R. Bridge (NY)
Seismic Study/ Literacy
A. Seismology B. Geotech Eng. C. Disaster Managment
D. Info. Links
E. Education F. Archives
G. US Coord. Agencies
H. International Coord. Agencies
I. Earthquake Engineering
J. Key Issues in Structural Engineering
K. Structural Engineers Role
a. Flow diagram for seismic study /seismic literacy
Draft LRFD Bridge Manual
Selection of method of analysis for bridges
For any supplied response spectrum (either acceleration vs. period or displacement vs. period), joint displacements, member forces, and support reactions may be calculated.
Time-History Analysis– This is an analysis of the dynamic responseof a structure when the base is subjected to a specific ground motion time history.
This analysis is performed using the modal superposition method. Hence, all the active masses should be modeled as loads in order to facilitate determination of the mode shapes and frequencies. In the mode superposition analysis, it is assumed that the structural response can be obtained from the "p" lowest modes.
The equilibrium equations are written as
Recent Developments in Methods of Analysis, Seismic Codes and Computer Software
220.127.116.11 CAPACITY DESIGN
Capacity design principles require that those elements not participating as part of the primary energy
dissipating system (flexural hinging in columns), such as column shear, joints and cap beams, spread
footings, pile caps and foundations be “capacity protected”. This is achieved by ensuring the maximum
moment and shear from plastic hinges in the columns (overstrength) can be dependably resisted by
18.104.22.168 SDAP C – CAPACITY SPECTRUM DESIGN METHOD
22.214.171.124.1 Capacity Spectrum Design Approach
SDAP C combines a demand and capacity analysis, including the effect of inelastic behavior of ductile
earthquake resisting elements. The procedure applies only to bridges that behave essentially as a single
degree-of-freedom system. SDAP C is restricted to bridges with a very regular configuration
and with the recommended earthquake resisting systems (ERS) as described in Section 2.
Similar to the Caltrans procedures.
Table 3.10.1-1 Design Earthquakes and Seismic Performance Objectives
Table 3.10.3-2 - Seismic Design and Analysis Procedures (SDAP) and Seismic Detailing
Flow Diagram for seismic Codes
a. There are significant physical differences, such as multi-bay, multi-frame action in a building, compared to the use of Continuous Beam, with alternate fixed and free bearing supports, in a bridge.
b. Magnitude of live load is considerably higher in a bridge, compared to building live load. AASHTO Code requires a tributary live load to be added to vertical dead load reaction, depending on the seismic zone, when calculating horizontal design connection force.
c. International Building Code (IBC) 2000 is composed of 3 model code organizations ICBO, BOCA and SBC. Erstwhile, NEHRP and ASCE 7 Codes were based on USD unlike UBC & SEAOC.
d. IBC uses “Seismic Design Category”, which is based on contours representing mapped spectral response acceleration, at short periods of 0.2 seconds. It is a function of three parameters: probable ground motion defined by spectral response accelerations (Site Class A to F), soil class, and building occupancy (Seismic Use Groups I, II, III).
e. AASHTO LRFD Code uses “Seismic Zones” 1 to 4 (Acceleration Coefficient 0.09 to 0.29) to establish design earthquake ground motion.
f. AASHTO uses Importance category (Critical bridge, Essential bridge or Other categories) and Soil Profiles I to IV. In addition, AASHTO uses separate Response Modification Factor (R Factor varies between 0.8 to 5.0) depending on Substructure type and Connection detail.
g. The method of analysis in AASHTO code (Uniform Load, Single Load, Multimode elastic methods or Time History method) is directly related to Importance Category.
h. The scale and magnitude of each of the parameters is different in the two codes. Hence, it is not easy to correlate each parameter for building and bridge seismic analysis.
MAXIMUM TRUCK LOADS DURING AN EARTHQUAKE.
LENGTH OF NJ PERMIT VEHICLE =
1/2 OF COOPER TRAIN LENGTH
MAXIMUM TRAIN LOADS DURING AN EARTHQUAKE
1. Railway bridges have more conservative design approach
2. Have historically performed well in seismic events with little or no damage.
3. Railway Bridges are traversed by track structure that functions very effectively as a restraint against longitudinal and transverse movement during earthquakes.
4. Spans are smaller.
5. Heavy concrete decks are not present and dead load inertia forces are smaller.
6. Types of damage that are permissible are very limited compared to highway bridges.
7. Post-seismic event operation guidelines put restrictions on train traffic and speeds of train, depending on the intensity of earthquake, until proper inspection has been carried out.
8. Ground Motion Level for level 1 has smaller earthquake return period for railway bridges 100 years as compared to 450 years for highway bridges. Acceleration coefficients are expressed as % of gravity, for 50, 100, 250, 475 and 2400 year return periods.
9. Risk factor parameter is included as an integral part of seismic design for railway bridges.
1. Modeling of superstructure
2. Modeling of substructure
3. Modeling of bearings- Guided, Unguided and Fixed
Placing fixed bearing on shorter abutment or on shorter pier to minimize seismic moments
4. Selection of methods of analysis
5. Selection of numerical method- SRSS, CQC
6. Sub-models for connections- Alternates
7. Determine pile-bent height from pile programs,such as COM624P or L-pile.
Route U.S. 322/N.J. 50
Elastic seismic response coefficient Cs = (1.2AS)/(Tm^23) was computed, by hand calculations. A limiting value of 2.5 A was used.
The simplified equation Tm = 2 (W/gK)^ 0.5 from AASHTO Sec. 4.7.4 was used.
For single mode analysis, using Deck weight Vs and , , factors,
from Section 5.3 of AASHTO Code
Equivalent static earthquake loading pe (x) = Cs/ w(x) Vs (x) was then computed and modified by the response modification factor R.
Seismic force = pe (x). L/R Comparison was made with the results obtained from the two methods. Results were found to be within 5 % of the hand computed values.
Acceleration Coefficient A was modified due to energy dissipation.
2. Elastic Dynamic Analysis Method (Multi-mode Spectral method):
Multimode method of analysis is selected based on irregular geometry.
Acceleration factor = 0.18 was used for all cases.
Route U.S. 23/ U.S. 80 (NJ)
Route U.S. 80 (NJ)
Case study 3-Multispan vertically curved girders, supported on transverse frames:Existing bridge was evaluated for seismic adequacy in order to provide rehab. to the existing bridge structure. Three-dimensional modeling was carried out using STAAD-PRO program.
Two sub-models were tried to simulate the highly eccentric connection between the 3.5 feet deep longitudinal girders and the 4.0 feet deep pier cap.
The first was a Tee shaped rigid link in the plane of longitudinal girders.
The alternate was a Vee shaped rigid link and the vertical member was replaced by two inclined members. The longitudinal girders were connected to horizontal members of the rigid link.
The second model gave an improved transfer of forces from superstructure to substructure.
Due to discontinuity between adjacent transverse frames SEISAB could not be applied.
Complete Quadratic Combination (CQC) method was used for elastic dynamic analysis
with 5 % damping.
Seismic Response Coefficients Cs were computed for various periods T.
For a range of values of T = 0.05, 0.45, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0 the computed values were
Cs = 1.59, 0.37, 0.34, 0.22, 0.17, 0.14, 0.10, 0.09. using the Equation for period T.
Site Coefficient was taken as unity.
BSDI program (Bridge Software Development International Ltd.) modeled vertically curved
girders for computing deflections and dead load camber.
Centerlines of beams were curved upwards by maximum 8 inches at the midspan.
A comparison of dead load analysis with alternate STAAD-PRO analysis showed a difference of
up to 5 % in vertical deflection values.
Seismic isolation bearings were not required.
Long Island R.R. Bridge (NY)
Multispan girders supported on column bentsfor railroad bridge
Three continuous spans were planned for the Railroad bridge.
Steel girders were supported on transverse bents.
The geometry of Continuous transverse column bents was simplified by using repeated single bent with cantilever beams.
Spectral acceleration values with 5% damping for OBE level design were for
T =0, 0.04, 0.1, 0.2,0.5, 1.0, 2.0 and 5.0,
the computed values for site class D were 0.12, 0.29, 0.29, 0.29, 0.20, 0.10, 0.05, 0.02.
T = 0, 0.04, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0
the computed values were 0.37, 0.87, 0.87, 0.87, 0.59, 0.30, 0.15 and 0.06.
Group Load = 1.0 (D + LL + PS + B + SF + E + EQM);
LL = Cooper E-80 train loads Live load acting on one track only;
EQM = Elastic seismic force (MDE and ODE) modified by dividing by the appropriate
R-factor. For foundations and for ODE R = 1.
For connections design R = 0.8.
For MDE multiple column bent R =4.
Although AREMA does not require live loads to be combined with D + EQ, project
design criteria required seismic forces resulting from both dead and live loads,
due to a higher importance classification factor for the railroad bridge.
1. Equivalent Static Analysis method is suitable only for preliminary design. For final design moments and forces should be checked by Spectral methods.
2. Computer models: 3 standard softwares, SEISAB, STAAD-PRO, and BSDI were used for the 4 case studies. For discontinuous frames within the same bridge, STAAD-PRO was found to be more suitable than SEISAB. Within the STAAD program, either self weight analysis or equivalent density method for composite beam can be used. The two methods gave identical results.
3. Comparisons of BSDI line girder dead load analysis with STAAD analysis, to account for camber, showed a difference of about 7%. BSDI program appears to model vertical curvature more accurately than STAAD.
4. Idealization of longitudinal and deep beam connections in computer model is sensitive to magnitudes of lateral forces and moments. Vee shaped rigid link was found more accurate.
5. To comply with all aspects of bridge analysis procedures, additional to those prescribed in AASHTO and AREMA seismic codes, are considered necessary. Familiarity with numerous computer programs, modeling techniques, selection and locations of guided, unguided and fixed bearings is necessary.
6. Use of supporting software, such as for dead load camber analysis or for computation of seismic pile capacities, will lead to an accurate analysis, and improved connections design.
7. Laboratory models of important (Essential) bridges with complex geometry need to be tested by simulating earthquakes, using shake-tables displacements and forces.
8. AASHTO LRFD Code specifies R Factors which are rounded off figures 1 to 4 which appear to be approximate. Since this factor scales down the design moments future research should focus on arriving at a more accurate assessment of the R Factors.
9. An independent Code Committee should also verify the suitability/accuracy of each of the standard software. Such a comparative study is beyond the capacity of most consulting firms.
10. Application of 3 state seismic codes from NJ, PA and NY has shown refinements of AASHTO code with emphasis on different aspects.
NJ addresses seismic retrofit aspects, PA on seismic detailing and NY on multimode analysis and soil behavior.
AASHTO, “Standard Specifications for Highway Bridges,” Sixteenth Edition, 1996
AREMA, “Manual for Railway Engineering,” 1999
NJDOT, “Bridges and Structures Design Manual,” Third Edition, 1998
spectral acceleration (SA)