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1
Seismic Design Considerations for the Thirty-Meter Telescope
Mike Gedig, Dominic Tsang, Christie Lagally
Dynamic Structures Ltd.
Dec 3, 2007
2
Outline
Overview of TMT configuration
Seismic performance requirements
Load determination– Tools and methodologies
Preliminary results
Restraint design– Criteria and considerations
3
Overview of TMT configuration
TMT is a new generation of Extremely Large Telescope with a segmented primary mirror diameter of 30m
Overall system mass is estimated to be 1700T– Including steel structural mass
of 1050T
System is supported on bearings which allow rotations about 2 axes and restrain lateral motions during operation
Fundamental frequency ~ 2.2 Hz (including soil and foundation)
4
Model Refinement - Overview
Finite Element ModelM1 Cell
Elevation journal
Instrument support structure
Nasmyth deck
Foundation and soil springs
Azimuth structure
Azimuth track
Elevation structure
M2
Elevation bearings (4)
Azimuth bearings (6)
M3
Pintle bearing (Lateral hydrostatic shoe bearing)
5
Seismic performance requirements
Two performance levels1) Operational Basis Survival Condition (OBS): After a 200-year average
return period earthquake (EQ) event, structure shall be able to resume astronomical observations and regular maintenance operations with inspection lasting no longer than 6 hours
• Structure is expected to behave elastically
2) Maximum Likely Earthquake Condition (MLE): After a 500-year average return period EQ event, structure shall be able to resume astronomical observations and regular maintenance operations within 7 days
• Minor damage at seismic load resisting elements are tolerated; the rest of the system remains elastic
– Telescope Structure System is required to sustain multiple OBS events without damage, and multiple MLE events with damaged seismic load resisting elements.
6
Load determination
Site-specific seismic hazard analysis– Seismic hazard analysis: uses information on local seismology and geology,
such as the location of surrounding faults, to calculate earthquake event probability
– Spectral matching: generates time histories that match a given design spectrum from input time histories; input should correspond to site with similar seismicity and geology, and matching should consider earthquake magnitude, distance and duration
– Site response analysis: generates a time history at surface using an input time history at bedrock level and a layered soil model
– Commercial software EZ-FRISK will be used
Reference to technical codes– American Society of Civil Engineers “Minimum Design Loads for Buildings
and Other Structures (ASCE7)– International Building Code (IBC)– Local building code
7
Load determination
FEA: perform both response spectrum and time-history analyses
Spectrum analysis is more straightforward but is restricted to linear elements
Time-history analysis can provide more realistic results but is computationally demanding– Solution: Create a simplified FE model representative of the full FEM
The complete telescope structure contains about 18,000 nodes and 35,000 elements
Apply substructuring techniques to reduce the number of DOF down to ~100 and cut computation time significantly– Stiffness distribution of original model is maintained– Mass distribution in the simplified model needs to be calibrated against
the that of the full model
Sensitivity analyses will be conducted to examine the effect of uncertainties in some parameters (e.g. bearing stiffness, damping, soil properties, etc)
8
Load determination
Other highlights of time-history analysis– Soil / foundation is included in the FEM to evaluate ground effects
– Rayleigh damping model will be used to define damping for time-history analyses
Involves mass- and stiffness-matrix multipliers (alpha & beta), which governs the damping ratio vs. modal frequency
Damping is a large uncertainty in seismic design, further discussion at the end of presentation if time permits
– Seismic restraint can be modeled with non-linear elements
Subsystem loads– There may be further load amplification for delicate components, e.g.
M2, M3, and Nasmyth instruments, which are modeled as lumped masses in the FEM
– Local response spectra will be generated to examine this effect in terms of support structure stiffness
9
Preliminary results
Analysis Assumptions– Based on 500-yr return-period spectral and time-history data from
Dames & Moore’s “Seismic Hazard Analysis” report for Gemini
– Seismic loads are applied to ground nodes in x-direction
– Spectrum analysisBased on D&M response spectra
Use 2% constant damping ratio
– Transient analysisBased on D&M “Modified Mauna Loa” time history @ 30 deg.
Set 2% damping for frequency range of 2 to 10 Hz by applying appropriate alpha & beta damping values
Damping Ratio vs. Natural Frequency
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
0 5 10 15 20Natural Frequency, Fn, Hz
Dam
ping
Rat
io, z
eta,
%
Damping <= 2%,between 2 & 10 Hz
10
Preliminary results
Three sets of results– #1: Spectrum analysis, all-linear system including seismic restraint– #2: Transient analysis, all-linear system including seismic restraint– #3: Transient analysis, all-linear structure with non-linear seismic restraint
For this third set of results, restraint is modeled as a bilinear spring with a force limit of 2000 kN, i.e. behaves plastically if force limit is exceeded at a given time
Item Results (Maximum values)
#1 #2 #3
Displacement at M2 90 mm 115 mm 96 mm
M2 support acceleration with stiff support 2.5g 2.3g 1.6g
M3 support acceleration with stiff support 1.7g 1.8g 1.8g
Restraint force* 13000 kN 7800 kN 2000 kN
Restraint plastic deformation N/A N/A 9 mm
* For comparison, base shear ~ 13300 kN using ASCE 7’s equivalent lateral force procedure
11
Preliminary results
Time-history results– Below shows acceleration amplification from ground to top-end
Time-History Acceleration Results
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 2 4 6 8 10 12 14 16Time, s
Ac
ce
lera
tio
n,
g
Ground MotionM2 Acceleration - Linear restraintM2 Acceleration - Non-linear restraint
Max values:Ground: 0.31gM2 - linear: 2.3gM2 - nonlinear: 1.6g
12
Preliminary results
Time-history results– Below shows displacement amplification from ground to top-end
Time-History Displacement Results
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0 2 4 6 8 10 12 14 16Time, s
Dis
pla
cem
ent,
m
Ground MotionM2 Displacement - Linear restraintM2 Displacement - Non-linear restraint
Max values:Ground: 0.067mM2 - linear: 0.115mM2 - nonlinear: 0.096m
13
Seismic restraint design
Restraint design criteria and strategies– The restraints must not interfere with normal telescope operations
– The restraints are the primary lateral-motion resisting devices during a survival-level earthquake and protect the rest of the structure from damages
Lateral load-resisting ability of lateral hydrostatic shoe bearing may be utilized to a limited degree
– The structure and restraints should both behave elastically during an operational-level earthquake
– The restraints may behave inelastically during a survival-level earthquake to keep the structural loads within the elastic level
– The restraints should retain sufficient stiffness and strength to also protect the structure against aftershocks
– Telescope downtime in order to “reset” the seismic restraint must be compatible with the observatory requirements with operational considerations included in the design for repair and replacement, structural re-alignment, and equipment re-calibration, etc.
14
Seismic restraint design
Design considerations– Two fundamental restraint design choices:
1) Serial or parallel (or combination) load path with lateral hydrostatic bearing (HSB)
2) Linear or Non-linear restraint– Type of non-linearity: friction, yielded component, buckling-restrained braces
– Factors that drive the restraint scheme choices:Amount of forces transmitted to structure
Required load capacity of the lateral HSB
Analysis complexity
Analysis accuracy
Fabrication tolerance requirements
Installation tolerance requirements
Relative cost
Downtime
– The goal is to protect the telescope structure with the simplest and most economical restraint design
15
Seismic restraint design
Linear vs. non-linear restraints
Linear Non-linear
Force transmitted to structure Higher Lower, since seismic load is limited by non-linear behaviour
Required load capacity of the lateral HSB
Higher Lower
Analysis complexity Lower Higher, requires use of time-consuming transient analysis
Analysis accuracy Use standard analysis methods with confidence
More work is needed to verify result accuracy
Fabrication tolerance requirements
Similar
Installation tolerance requirements
Similar
Downtime Short, since no damage Longer, to repair/replace components
Relative cost Lower Higher repair/replacement costs
16
Seismic restraint design
Restraints with serial vs. parallel load path with lateral HSB
Serial Parallel
Force transmitted to structure Same if linear behaviour
Required load capacity of the lateral HSB
Higher, since lateral HSB takes the same load as the restraint
Lower, since the restraint can be designed to take the majority of loads
Analysis complexity Lower Higher; need to be concerned about load sequence
Analysis accuracy Use standard analysis methods with confidence
More work is needed to verify result accuracy
Fabrication tolerance requirements
Lower Greater precision is required
Installation tolerance requirements
Lower Greater effort required to align components so they are loaded as intended
Downtime Short, since no damage Longer, to repair/replace components
Relative cost Lower Higher
17
Additional Slides
18
Damping
Damping is a major source of uncertainty in seismic design
Damping occurs through different mechanisms
Structural damping (complex-stiffness damping)– proportional to vibration amplitude
– different damping levels for different design earthquakes
– range of 0.5% to 2% will be considered for TMT as conservative values
Damping Type Energy Absorption Mechanism
Base/soil damping Frictional interactions or movement between soil particles and/or the foundation
Frictional damping Friction between bolted joints, restraints, attached walkways, cables and hoses, etc.
Viscous damping Drag from air or wind as the structure vibrates in a medium
Control system damping Mechanical, magnetic or hydraulic damping mechanisms (active or passive)
Structural damping Inter-molecular interactions in the material from which the structure is made
19
Damping
Recommended design values for general steel structures– wide range of values
Survey of structural damping coefficients in telescope designTelescope Damping Ratio
Atacama Cosmology Telescope 1%
Keck I & II Telescopes 1%
Giant Magellan Telescope 0.5%, 2.0%
Very Large Telescope (VLT) 1%, 5%
OWL 100m Telescope 1%, 1.5%
Source Recommended Use Damping Ratio
U.S. Nuclear Regulatory Commission
Operating Basis Earthquake (OBE) Safe Shutdown Earthquake (SSE)
3% 4%
Theory and Applications of Earthquake Engineering, Chopra
Working stress level 0.5 of yield stress At or just below yield stress
2-3% 5-7%
Handbook of Structural Engineering, Chen & Lui
Unclad welded steel structures* Unclad bolted steel structures*
0.3% 0.5%
*recommended for low amplitude vibration
20
Damping
Measured damping coefficients– damping can be calculated by instrumenting a structure with
accelerometers
– structure can be excited by instrumented hammer or by existing loads such as wind
– damping values are typically low because vibration amplitude is low, and are too conservative for design
Statistical analysis of damping coefficients– Bourgault & Miller evaluated damping coefficients for 22 space-based
structures
– For frequency range 0.14-9.99Hz, damping coefficient has mean 1.9% and standard deviation 1.58%
– Gamma probability density function for space-based structures may be used for other structures, such as buildings