Energy Dissipation

Energy Dissipation Techniques forEarthquake Resistance of Structures

Durgesh C. RaiAssistant Professor

Department of Civil EngineeringIndian Institute of Technology Kanpur

Kanpur 208 016

Single Degree of Freedom System

Equation of Motion

Multiply both sides by and integrate from initial rest state to any time t

Natural Frequency

Damping Ratioωωωω = k m

ξξξξ ωωωω= c m( )2

mu cu ku mug!! ! !!+ + = −

Seismic Energy

0 0 0mu cu dt F udt mug udt

t t! ! ! ( !! ) !+ + = −! ! !

KineticEnergy

ViscousDampingEnergy

Strain &HystereticEnergy

InputEnergy

W W W W IE D S H+ + + =( )

Dissipative Energy ComponentsW WD H+

Strategies for Earthquake Resistance

Enhance Energy Dissipation Capacity for Fixed Base Structures• Hysteretic Loss or Yielding• Viscous Damping

Ambient damping Cs and hysteretic capacity of Ks is inadequatefor earthquake resistance

Effect of Yielding & Hysteresis

Inelastic deformation permitted in specially detailed regions of structure provide energy dissipation potential. However,

• Results in damage to structural members• Large drifts required cause extensive non-

structural damage

��

-150 0 150

Roof Displn. (mm)

STMF (X-DIag.)

Effect of Damper

Energy Dissipation Device (EDD) will minimize/eliminateinelastic action in primary structural members and reduce non-structural damage

Three Types1) Viscous & Visco-elastic 2) Friction 3) Metallic

Effect of Viscous Damping

The response of higher damped system will be less as effect of individual earthquake pulses will damp out quickly and will not accumulate.

��

0 1 2 3 4 5

Frequency (Hz)

2% of CriticalDamping

��

0 0.05 0.1 0.15 0.2

5%Damping Ratio

Range of InherentAmbient Damping

��

Free Vibration

Harmonic Excitation

• Damping is effective when excitation frequency is in vicinity of natural frequency

��

0 0.5 1 1.5 2 2.5

Frequency Ratio

��

Effective Range

��

Supplemental damping can effectively reduce system response for earthquake type motions.

��

0 5 10 15

Frequency (Hz)

Sylmar Motion(Northridge 1994)

��

0 0.1 0.2 0.3 0.4 0.5

Damping Ratio

5% Normalization

Upper Bound

Lower Bound

22 ground motionsStructures with period 0.5 to 3 sAshour (1987)

Energy Dissipation Devices

Metallic System• Based on hysteresis behaviour of metals where

deformation in post-elastic range is used• Utilizes flexure, shear or extensional modes of

deformation

Desirable Features• Stable hysteretic behaviour• Long term reliability• Resistance to environmental factors

Orificed Viscous Fluid Damper

Dissipates energy through movement of a orificed piston in a highly viscous fluid.

Steel Bracing and Supplemental Damping

Cal Fed BuildingSherman Oaks, CA

Effect of Supplemental Damping

• Supplemental damping devices intend to dissipate seismic energy by acting either in parallel or in series with the primary structural system.

• As a result, the seismic energy demand is minimized on primary structural system thus reducing structural/non-structural damage

Shear-Link Braced Frame System

Collapse Mechanism

Configuration of SLBF

Aluminium Shear-Link as an EDD

Shear-Yielding of Aluminium• Ductile and large shearing

strains (up to 10%) without buckling or tearing.

• Low yield strength allows thicker web reducing the problem of web buckling

• Maximizes material participation in plastic deformation

YieldedShear-Link

Hysteresis of Shear-Link

Hysteretic Response• First yielding at 0.2% strain and stress at 20% strain is 2.6 times the

yield stress. No buckling until 10% strain• Stable response even after buckling due to tension field action.

Design Characteristics of Shear-Links

Force-Deformation Behaviour

• Shear force

• Shear deformation

• Stress-Strain relationship

R Aw= ⋅ττττ

∆∆∆∆ = ⋅γγγγ d

ττττ σσσσ γγγγavg,max ...= ⋅ ⋅2 6 0 2

Three Limit States• Yield Limit of 0.2% strain• Design Limit of 10% strain• Ultimate Limit of 20% strain

Design Characteristics of Shear-Links

Cyclic Plastic Web Buckling

• Plastic web buckling stress

• Elastic web buckling stress

• Plastic reduction factor (Gerard 1948)• Experimental value

ττττ ηηηη ττττ ττττ= ⋅( ) E

ττττ ππππυυυυ ββββ

ββββE s w wk E d t=−"#$%&' =

( ); /

Stiffener spacing

ηηηη ττττ ττττ= b E

ττττ ττττbs

= ⋅3 76.

γγγγ ττττββββ

Gk= =3 76 9 37 2. .

Inelastic Activities for Miyagi Motion

Response due to Groundmotions

Shear-Link Braced Frame SystemR

Benefits of Aluminium Shear-Link as an EDD

• Shear-links have very ductile shear-yielding and can dissipate large amount of energy effectively and reliably even at large strains

• Energy dissipation capacity of TMFs can be improved significantly with Aluminium shear-links

• TMFs with shear-links showed significant reduction in – Seismic energy input– Base shear– Storey drift

• Shear-links can be easily replaced after extreme earthquakes and can be deployed in existing TMFs for seismic strengthening.

Truss Moment Frames

Framing for Large Span Areas• Open large span areas for factories,

warehouses and shopping malls • Main Truss Girders support secondary

triangular roof trusses running in perpendicular direction.

• Truss moment frames (TMF) resist lateral forces from wind and earthquakes

Seismic Resistance of TMF• Codes specify a Strong Girder - Weak

Column yield mechanism• Designed as SMRF or OMRF• Poor response in Mexico City

earthquake.

Special Truss Moment Frames

Yield Mechanism• Strong column - weak girder• Inelastic activities contained

in truss girderSpecial Segment• Located at mid-span where

vertical shear is high• Inelastic activities in this

segment only

Energy Dissipation• Through Yielding and Buckling of diagonals arranged in X-pattern• Through Moment hinging of chords in Vierendeel configuration

X-Diagonal Vierendeel

Shear-Link Truss Moment Frames

Shear-Link in TMF

• Shear-Link inside the special segment at mid span

Yield Mechanism• Strong column - weak girder• Aluminium Links yield in

vertical shear due to lateral loads

• Inelastic activities predominately in Links

• Easy link replacement after extreme events of earthquakes

Pushover Analyses of TMFs

• Yielding in shear-link only and reaches its max. strength at 1.1% drift.• Buckling, yielding and chord hinging for X-Diagonal system.

Yield-MechanismsSystem Capacity Curve

��

0 50 100 150 200

Roof Displn. (mm)

Shear-link TMF

STMF (X-Diag.)

��

Design Base Shear

��

Yielding of Shear-Link

�� Shear-Link at 0.2 strain

��

Buckling of X-diag.

Yielding of X-diag.Moment hingingof chords

Time History Analyses of TMFs

Shear-Link TMF• Strain-hardening of

shear-link ensured good post-yielding stiffness & strength

• Stable hysteresisenergy loss in shear-link only

X-Diagonal STMF• Drifting response for

X-Diagonal STMF following yield mechanism.

• Pinching & degradinghysteretic behaviour

Miyagi-ken-Oki (0.51g)

Northridge, Sylmar (0.84g)

��

0 5 10 15 20

Time (s)

��

-150 0 150Roof Displn. (mm)

Shear-Link TMF

��

-150 0 150

Roof Displn. (mm)

STMF (X-DIag.)

Case Study:: Supplemental Damping

San Francisco City Hall

• Renaissance architecture located in SF Civic Center National Historic Landmark District

• Built in 1913 at the same site where previous city hall was destroyed in 1906 earthquake

• 5-storey office building, 94 by 124 m in plan with central dome rising 90 m above main floor

• 27.5 m in diameter, the massive dome acts as a pendulum for seismic loads

• Damaged in 1989 Loma Prieta earthquake

GroundMain

SecondThirdFourthPediment

OctagonDrum

Lantern

Building Characteristics

• Non-uniform distribution of lateral strength and stiffness• Second storey is soft storey: its stiffness is 12% of the first storey

GroundMainSecondThirdFourthPediment

OctagonDrum

Lantern

Stick Model (9-story)

38,01633,284

24,89229,782

24,768

5,0779,013

Floor Weight (Kips)

204,00025,800

38,00057,500

45,625

Story Stiffness (Kips/In.)

Lateral Strength

• Storey Shear Strength ~0.11W of which only 10% is due to ductile steel frame

Dynamic Characteristics

Supplemental damping is required to control both office and dome response

��

-1 0 1

Mode 1��

��

-1 0 1

��

Mode 2

��

-1 0 1

Mode 3��

��

-1 0 1

Mode 4��

��

-1 0 1

Mode 5��

��

-1 0 1

Mode 6��

��

-1 0 1

��

��Mode 8

��

-1 0 1

Mode 7��

��

-1 0 1

Mode 9��

��

5.718.30.11.30.46.87.368.6

0.130.130.150.180.240.270.480.9887654321Mode

Period (sec)

Base shear (MN)

Strengthening with Viscous EDDs

Independent support system for EDDs13 to 30% damping in dominant modesExpected reduction in response is about 25-50%

Location Of EDDs (Typ)

GroundMainSecondThirdFourthPediment

OctagonDrum

Lantern

Dome & Drum Strenghening

New Drag Beams (Typ)New Grade Beams

Strengthening with Viscous EDDs

40 EDDs with each to carry max. dissipation force of 2000 kN in main floor level and 20 with a force capacity of 1400 kN at second floor

Verification Analysis

El Centro Ground Motion

Effectiveness of EDDs

��

0 10 20 30 401

9Relative Floor Displn. (mm)

��

without suppl. damping

with suppl. damping

��

0 50 100 150 2001

9Elastic Story Shear (MN)

��

without suppl. damping

with suppl. damping

• 40% reduction in storey drift for the ‘soft’ main storey• Significant reduction in shear resisted by building components• Acceleration at lantern level were only 0.3g for El Centro motion• Proposed strengthening with supplemental damping satisfactorily

meets and exceeds current Code requirements

Supplemental Damping

Cal State Univ. LA

Building Configuration

• 8 Storey RC Frame with Shear Walls

19.4 m X 46.7 m

34.7 m high (6.7 m first storey; 4 m typical)

• No Shear Wall in Ground Storey

• Deep transfer girders at First Floor Level

Retrofit Objective

• Performance Objective:Life Safety for DBE and MCE

• Under DBE, first storey columns would undergo excessive nonlinear deformations posing life safety hazard.

• Viscous dampers at the first storey level to reduce ductility demand

Base Shear :: before and after

Soft Storey Displacement :: before and after

Retrofit Scheme

Dampers6 transverse8 longitudinal

Each1000 kN Max. ForceWith Cv=15,000 kN/ (m/sec)

Retrofit Scheme :: Details

Viscous Dampers at the tip of Chevron Braces

Strengthening of first floor girders

Steel Jackets in columns to transfer vertical component of brace forces

Closing Remarks

EDDs have also been used to reduced the strength and ductility demand on the seismically deficient primary structural members such as columns in open ground storeys

Earthquake Ground Motion

Characteristics:PGA, PGV, PGDFrequency distributionDuration

Response Spectra

Flexible systemsLarge displacementSmall accelerationDisplacement controlled

Stiff systemsSmall displacementLarge acceleration Force controlled

Intermediate systemsVelocity controlled

Controlling Motion Variables

Accn.Vel.

Displ.

Force or Displacement ?

Demand Response SpectrumAccelerationDisplacementNatural periodDamping

Increasing Period (flexible isolator)and damping (energy dissipator)

can reduce seismic response

Effect of Isolation and Damping

Isolation lengthens the time-period of the structure reducing force response at the cost of increased displacement.Additional damping to control excessive displacement

Various energies

Kinetic energy Viscous Damping energy

Hysteretic energy

Energy Distribution

Hysteretic Energy

Viscous Damped Energy

Rubber Bearing Isolator

• Laminated rubber bearing (LRB) for isolation and damping

• Lead-plug LRB for increased stiffness and damping

Arrangement of LRB Isolator

Friction Pendulum Isolators

• Pendulum of long period• Energy dissipation

through friction

Friction Pendulum Isolator

Capacity = 265 kLShell thick. = 150 mm, Diameter = 4.5 mLong. Steel = 0.283%

Friction Pendulum Isolator

Rocker Isolator and Damper

Orificed Viscous Fluid Damper

Dissipates energy through movement of a orificed piston in a highly viscous fluid.

Energy Dissipation

Documents

Transcript of Energy Dissipation

«Renewable Energy Sources & Energy Efficiency, New Challenges» · 2018. 10. 12. · 8 9 1-2NOVEMBER2018 6th International Conference on Renewable Energy Sources & Energy Efficiency

Parlebas. La Dissipation Sportive

High-Energy-Density Physics: A Developing Frontier · High-Energy-Density Physics: A Developing Frontier ... high-energy-density physics E12543 “Frontiers in High Energy ... Questions

Viscoelastic Energy Dissipation: Some Constraints from ... · Viscoelastic Energy Dissipation: Some Constraints from Materials Physics Reid F. Cooper Department of Geological Sciences

LLow Energy Neutrino Physics ow Energy Neutrino Physics at ...taup2009.lngs.infn.it/slides/jul1/smy.pdf · LLow Energy Neutrino Physics ow Energy Neutrino Physics at Super-Kamiokande.

ΣχολήΠολιτικώνΜηχανικών ∆ΠΜΣ Επιστήµη ... · BUCKET TYPE ENERGY DISSIPATORS ( SecondRevision) 3. Chanson, H. (Editor) 2015. Energy Dissipation

Cascade and dissipation from MHD to electron scales in …€¦ · Cascade and dissipation from MHD to electron scales in the solar wind ... 2. e-Acceleration & Heating 3.

By Vishnu Engineer R&D - · PDF fileThe loss angle is usually expressed as the tangent of delta, or just tan delta(dissipation factor) ... the dissipation factor (tan δ) ... PFC correction

Chapter 5: Work & Energy The Work/Energy Relationship.

Save energy

Contribution Of Riparian Areas To Flash Floods Events Occurence Energy Dissipation

Dissipation of Dark Matter - uni-bielefeld.de · 2013. 4. 26. · Bulk Viscous fluid and the (Unified) Dark Sector Dark matter and Dark energy would be different manifestations

Energy Balance Energy in = Energy out + Δ Storage Bio 164/264 January 11, 2007 C. Field.

Electromagnetic energy density in metalsoptics.hanyang.ac.kr/~shsong/8-EM energy density in metals.pdf · Electromagnetic energy density in metals R. Ruppin, “Electromagnetic energy

Solar Photovoltaics & Energy Systems · Solar Photovoltaics & Energy Systems Lecture 2. Thermodynamics of solar energy conversion and solar thermal energy conversion ChE-600 Kevin

Gibbs Energy

Improvement of Thermal Dissipation by Nanomaterial addition

Energy Maneuvering

Magnetic Dissipation in the Photosphere and Heating of the Corona

Biochimica et Biophysica Acta - University of Illinois at ... · the harmless dissipation of excess excitation energy, as heat, in the thylakoids (see e.g. [14,15] for review). The