Seismic Design Considerations v2 Mike Gedig

8/10/2019 Seismic Design Considerations v2 Mike Gedig

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Seismic Design Considerations for the

Thirty-Meter Telescope

Mike Gedig, Dominic Tsang, Christie LagallyDynamic Structures Ltd.

Dec 3, 2007


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Outline

Overview of TMT configuration

Seismic performance requirements

Load determination

Tools and methodologies

Preliminary resultsRestraint design

Criteria and considerations


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Overview of TMT configuration

TMT is a new generation ofExtremely 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 restrainlateral 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 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 elastically2) 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 withoutdamage, 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 withsimilar 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 frequencyDamping 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 & Moores 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

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

DampingRatio,zeta,

%

Damping


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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 agiven 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 1.6gM3 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 7s 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 16

Time, s

Acceleration,g

Ground Motion

M2 Acceleration - Linear restraint

M2 Acceleration - Non-linear restraint

Max values:

Ground: 0.31g

M2 - linear: 2.3g

M2 - 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 16

Time, s

Displacement,m

Ground Motion

M2 Displacement - Linear restraint

M2 Displacement - Non-linear restraint

Max values:

Ground: 0.067m

M2 - linear: 0.115m

M2 - 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 beutilized 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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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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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 thelateral 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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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 majorityof 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 tolerancerequirements 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 design

Telescope 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 ofEarthquake Engineering, Chopra

Working stress level 0.5 of yield stressAt 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

Documents

Seismic Design Considerations v2 Mike Gedig