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 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)

5. Seismic performance requirements
Two performance levels
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
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 analysis
Based on D&M response spectra
Use 2% constant damping ratio
Transient analysis
Based on D&M “Modified Mauna Loa” time 30 deg.
Set 2% damping for frequency range of 2 to 10 Hz by applying appropriate alpha & beta damping values

10. Results (Maximum values)
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
Restraint force*
13000 kN
7800 kN
2000 kN
Restraint plastic deformation
N/A
9 mm
* For comparison, base shear ~ kN using ASCE 7’s equivalent lateral force procedure

11. Preliminary results Time-history results
Below shows acceleration amplification from ground to top-end

12. Preliminary results Time-history results
Below shows displacement amplification from ground to top-end
Ref. C:\Work\TMT_Telescope\FEA\Rev10.1\Run1\SUP\substructure\maunaloa\071127_k-lin_8HzM2_2%alpha&beta

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:
Serial or parallel (or combination) load path with lateral hydrostatic bearing (HSB)
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
Lower
Analysis complexity
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
Downtime
Short, since no damage
Longer, to repair/replace components
Relative cost
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
Greater precision is required
Installation tolerance requirements
Greater effort required to align components so they are loaded as intended
Downtime
Short, since no damage
Longer, to repair/replace components
Relative cost
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 design
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
Telescope
Damping Ratio
Atacama Cosmology Telescope 1%
Keck I & II Telescopes
Giant Magellan Telescope
0.5%, 2.0%
Very Large Telescope (VLT)
1%, 5%
OWL 100m Telescope
1%, 1.5%

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 Hz, 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