1 Seismic Design Considerations for the Thirty-Meter Telescope Mike Gedig, Dominic Tsang, Christie Lagally Dynamic Structures Ltd. Dec 3, 2007.

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Seismic Design Considerations for the Thirty-Meter Telescope

Mike Gedig, Dominic Tsang, Christie Lagally

Dynamic Structures Ltd.

Dec 3, 2007

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Outline

Overview of TMT configuration

Seismic performance requirements

Load determination– Tools and methodologies

Preliminary results

Restraint design– Criteria and considerations

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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)

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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)

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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.

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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

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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)

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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

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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

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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

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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

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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

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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.

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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

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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

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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

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Additional Slides

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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

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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

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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