Seismic Design Considerations for the
Thirty-Meter Telescope
Mike Gedig, Dominic Tsang, Christie Lagally
Dynamic Structures Ltd.
Dec 3, 2007
1
Outline
Overview of TMT configuration
Seismic performance requirements
Load determination
–
Tools and methodologies
Preliminary results
Restraint design
–
Criteria and considerations
2
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)
3
Model Refinement - Overview
Finite Element Model
M1 Cell
M2
Elevation journal
Elevation structure
Elevation bearings (4)
M3
Nasmyth deck
Instrument support
structure
Azimuth structure
Azimuth track
Azimuth bearings (6)
Foundation and soil
springs
Pintle bearing (Lateral
hydrostatic shoe bearing)
4
Seismic performance requirements
Two performance levels
1) 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.
5
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
6
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)
7
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
8
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 analysis
Based on D&M response spectra
Use 2% constant damping ratio
Transient analysis
Based 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
4.0%
Damping <= 2%,
between 2 & 10 Hz
3.5%
3.0%
Damping Ratio, zeta, %
–
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
0
5
10
Natural Frequency, Fn, Hz
15
9
20
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
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
13000 kN
7800 kN
2000 kN
N/A
N/A
9 mm
Displacement at M2
Restraint force*
Restraint plastic deformation
* For comparison, base shear ~ 13300 kN using ASCE 7’s equivalent lateral force procedure
10
Preliminary results
Time-history results
Below shows acceleration amplification from ground to top-end
Time-History Acceleration Results
2.5
Ground Motion
M2 Acceleration - Linear restraint
M2 Acceleration - Non-linear restraint
2.0
1.5
1.0
Acceleration, g
–
0.5
0.0
-0.5
-1.0
Max values:
Ground: 0.31g
M2 - linear: 2.3g
M2 - nonlinear: 1.6g
-1.5
-2.0
-2.5
0
2
4
6
8
Time, s
10
12
14
16
11
Preliminary results
Time-history results
Below shows displacement amplification from ground to top-end
Time-History Displacement Results
0.15
Ground Motion
M2 Displacement - Linear restraint
M2 Displacement - Non-linear restraint
0.10
0.05
Displacement, m
–
0.00
-0.05
Max values:
Ground: 0.067m
M2 - linear: 0.115m
M2 - nonlinear: 0.096m
-0.10
-0.15
0
2
4
6
8
Time, s
10
12
14
16
12
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.
13
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
14
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 timeconsuming 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
15
Seismic restraint design
Restraints with serial vs. parallel load path with lateral HSB
Serial
Force transmitted to structure
Parallel
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
16
Additional Slides
17
Damping
Damping is a major source of uncertainty in seismic design
Damping occurs through different mechanisms
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
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
18
Damping
Recommended design values for general steel structures
–
wide range of values
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
Survey of structural damping coefficients in telescope design
Telescope
Damping Ratio
Atacama Cosmology Telescope
1%
Keck I & II Telescopes
1%
Giant Magellan Telescope
Very Large Telescope (VLT)
OWL 100m Telescope
0.5%, 2.0%
1%, 5%
1%, 1.5%
19
Damping
Measured damping coefficients
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–
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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
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–
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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
20