Chapter 7 The ASCE 7-10 Design Provisions for Structures ...sharif.edu/~ahmadizadeh/courses/strcontrol/CIE626-Chapter-7-ASCE 7... · CIE 626 - Structural Control Chapter 1 - Introduction

CIE 626 - Structural Control Chapter 1 - Introduction

CIE 626 Structural Control Chapter 7 – ASCE 7-10 Design Provisions for Structures with

Passive Energy Dissipating Systems

Chapter 7 The ASCE 7-10 Design Provisions for

Structures with Passive Energy Dissipating Systems

1




CONTENT 1. Scope 2. Design Philosophy 3. Effective Damping 4. Types of Design Procedures 5. Equivalent Lateral Force (ELF) Procedure 6. Design of Damping System 7. Testing Requirements 8. Design Example 9. References

2




Major References • ASCE 7-10 Standard

– Chapter 18

3




1. Scope

• Building structures equipped with all types of damping systems: – Hysteretic, viscous, visco-elastic dampers.

4




2. Design Philosophy

• Seismic-Force-Resisting System (SFRS) that provides a complete load path is required.

• Damping of SFRS modified by damping devices. • Damping reduction applied at effective fundamental period

of SFRS (based on secant stiffness). • SFRS must be designed for not less than 75% of the base

shear of a conventional structure. • Damping devices must be designed and tested (prototypes)

for displacements, velocities, and forces corresponding to maximum considered earthquake (MCE).

5




SFRS Damping System

Damping Devices

6




3. Effective Damping

• Damping system reduces the response of SFRS based on effective damping

• Same approach as NEHRP provisions for base isolation systems

• Effective damping is a combination of 3 components: – Inherent Damping, βI - SFRS at or just below yield – Hysteretic damping, βh – hysteretic dampers + SFRS – Added viscous dampers, βv – viscous dampers

• Hysteretic and added viscous damping is amplitude dependent 7




≥

8

For when the period of the structure is greater than T0; otherwise, use linear interpolation between the value given in this table and value of 1.0 for zero period.




9

Subscripts:E: elastic, D: design, 1: first mode




4. Types of Design Procedures • Nonlinear procedures (static + dynamic)

– Permitted for all structures with damping devices. – Nonlinear dynamic procedure adopted for class retrofit project.

• Response spectrum procedure – At least 2 dampers in each story. – Effective damping in fundamental mode less than 35% of

critical. • Equivalent lateral force procedure

– At least 2 dampers in each story. – Effective damping in fundamental mode less than 35% of

critical. – SFRS does not have plan irregularity. – Rigid floor diaphragms. – Height of the structure does not exceed 100 ft. (30 m).

10




5. Equivalent Lateral Force Procedure (ELF)

• Response is defined by two modes: – The fundamental mode. – The residual mode.

• New concept used to approximate the combined effects of higher modes that may be significant to story velocity.

11




5. Equivalent Lateral Force Procedure (ELF) • Seismic Base Shear for SFRS

min22

1 VVVV R ≥+=V1 = Design base shear in fundamental mode VR = Design base shear in residual mode Vmin = Minimum design base shear

codeIv

codemin V75.0

BVV ≥=

+

Bv+I = Effective damping coefficient corresponding to the sum of viscous damping in fundamental mode + inherent damping in SFRS Note: if SFRS has less than 2 dampers in any floor level or is irregular, Vmin = Vcode

12

Mehdi

Text Box

Vcode calculated using the conventional equivalent static approach, V = C W





• Fundamental Mode Base Shear

111 WCV S=

CS1 = Fundamental mode seismic response coefficient. 1W = Fundamental modal weight (gravity load + portion of live load).

min22

1 VVVV R ≥+=

13




5. Equivalent Lateral Force Procedure (ELF) • Fundamental Mode Seismic Response Coefficient

DoD

D

dSSD

Do

DS

dSSD

BTS

CRCTT

BS

CRCTT

11

111

111

,For

,For

Ω

=≥

Ω

=<

T1D = Effective fundamental period at the design displacement R = Response modification coefficient associated with SFRS Ωο = Overstrength factor associated with SFRS Cd = Deflection amplification factor SDS = Short period design spectral acceleration SD1 = 1-second period design spectral acceleration B1D = Total effective first mode damping factor at the design displacement

111 WCV S=

ASCE 7-10 Design Spectrum

14

Mehdi

Text Box

Tabulated Values

Mehdi

Text Box

Tabulated Values

Mehdi

Text Box

Tabulated Values




Conservative since Cd ≤ R

15




5. Equivalent Lateral Force Procedure (ELF) • Effective fundamental period

DoD

D

dSSD

Do

D

dSSD

BTS

CRCTT

BS

CRCTT

11

111

1

111

,For

,For

Ω

=≥

Ω

=<

DD TT µ11 =T1 = Elastic fundamental period of SFRS. µD = Effective ductility demand of SFRS under Design Earthquake – DE.

k1

k1D

DD

D

D

Dy

D

D

D

yD

y

y

TT

TT

kk

DD

kk

DV

kDV

k

µ

µ

11

2

1

1

1

1

1

1

1

111 ;

=

=

==

==

Unknown

16




5. Equivalent Lateral Force Procedure (ELF) • Effective ductility demand at DBE

DD TT µ11 =

Y

DD D

D μ 1=

D1D = Fundamental mode design roof displacement at roof center of rigidity. DY = Yield roof displacement of SFRS.

k1

k1D

Unknown

Unknown

17





• Determination of fundamental mode design roof displacement E

D

D

DDDSD

E

DS

D

DDSDSD

BTS g

BTS gDTTFor

BTS g

BTS gDTTFor

1

1112

1

111211

1

21

121

21

1211

44,

44,

Γ

≥Γ

=≥

Γ

≥Γ

=<

ππ

ππ

Γ1 = Fundamental mode participation factor. B1E = Elastic first mode effective damping coefficient of SFRS.

Y

DD D

D μ 1=

18




5. Equivalent Lateral Force Procedure (ELF) • Determination of yield roof displacement

Y

DD D

D μ 1=

211124

TCRC gD s

doY Γ

Ω

=

π

k1

k1D

2111

02

110

11

1

11

12112

11

111212

1

211

2

1

11

4

;4

4;

TCRCgD

TTforCRC

BTS

BTSTgD

TTforB

TSgDT

TDD

TT

DD

Sd

y

sDSd

DD

D

DD

Dy

sDD

DDD

D

Dy

D

y

DD

Γ

Ω

=

≥

Ω

=Γ

=

≥Γ

==

==

π

π

π

µ

Note: Identical result if T1D < Ts 19





• Residual Mode Base Shear

RSRR WCV =CSR = Residual mode seismic response coefficient. = Residual modal weight.

min22

1 VVVV R ≥+=

RW Unknown

Unknown

20





• Residual Mode Seismic Response Coefficient

• Seismic Weight in Residual Mode:

Ro

DS

dSR B

SCRC

Ω

=

BR = Total effective residual mode damping factor at period.

RSRR WCV =

14.0 TTR =

1WWW R −=W = Total seismic weight of the structure (dead + live loads).

21




5. Equivalent Lateral Force Procedure (ELF) • Design lateral forces of SFRS

RR

RiRiiR

iii

iRii

VW

wF

VW

wF

FFF

Γ=

Γ=

+=

φ

φ 11

111

221

Fi = Design lateral force at level i. Fi1 = First Mode Design lateral force at level i. FiR = Residual Mode Design lateral force at level i. wi = Seismic weight at level i. φi1 = Amplitude of fundamental mode shape at level i. φiR = Amplitude of residual mode shape at level I. Γ1 = First mode participation factor. ΓR = Residual mode participation factor.

Unknown

Unknown 22





• Modal propertiesR

R

RiRiiR

iii

VW

wF

VW

wF

Γ=

Γ=

φ

φ 11

111

1

1

2

2

11

1

11

111

1

1

11

4.0

;;

:with1

11

1

TT

w

wW

w

Whh

R

n

ii

n

iii

n

iii

r

ii

R

iiR

i

=

==Γ=

Γ−=ΓΓ−

Γ−=

∑

∑

∑=

=

=

φ

φ

φφ

φφ

23

(alternative to the dynamic analysis using the elastic structural properties and deformational characteristics of the resisting elements)




Design Steps of Equivalent Lateral Force Procedure

24




25

Design Steps 1. Calculate minimum base shear:

2. Design SFRS for Vmin.

codeIv

code VBVV 75.0min ≥=

+

Bv+I = Effective damping coefficient corresponding to the sum of the viscous damping in the first mode and the inherent damping in the SFRS. Note: If the SFRS has less than two dampers at any level or is irregular: Vmin = Vcode

25




26

Design Steps3. Determine fundamental and residual modal

properties:

1

1

2

2

11

1

11

111

1

1

11

4.0

;;

with :1

11

1

TT

w

wW

w

Whh

R

n

ii

n

iii

n

iii

r

ii

R

iiR

i

=

==Γ=

Γ−=ΓΓ−

Γ−=

∑

∑

∑=

=

=

φ

φ

φφ

φφ

26




27

Design Steps 4. Select a supplementary viscous damping in the first

mode (βv1 ) to satisfy the drift limits as if the SFRS responded elastically. For linear viscous dampers (for which the damping forces are linearly proportional to the velocities), βv1 can be written in terms of the damping constants:

∑

∑

=

===f

d

N

iii

N

iiiLi

es

vdV

kT

C

EE

1

211

1

221

1

cos

4ϕ

γϕπ

πβ

27




28

Design Steps5. Assume a value of µD (between 1.0 and 2.0) and

calculate β1D or T1D.

DD TT µ11 = HDDVID βµβββ ++= 11

βI = Inherent damping of the SFRS at or just below yield < 5% critical for all modes. βHD = Damping provided by the hysteretic dampers and/or the SFRS at the design displacement.

( )

167.05.0

1164.0

1

≤=<

−−=

TTq

q

SH

DIHHD µ

ββ

28




29

Design Steps 6. Calculate B1D, CS1 and V1.

DoD

D

dSSD

Do

DS

dSSD

BTS

CRCTT

BS

CRCTT

11

111

111

,For

,For

Ω

=≥

Ω

=<

111 WCV S=

29




30

Design Steps7. If V1 is approximately equal to Vmin, continue to Step

8, if not revise the value of µD and return to Step 5.8. Calculate DY, D1D, and µD.

211124

TCRC gD s

doY Γ

Ω

=

π

E

D

D

DDDSD

E

D

D

DDSDSD

BTS g

BTS g

For T ≥ T , D

BTS g

BTS g For T < T , D

1

1112

1

111211

1

211

121

21

1211

44

44

Γ

≥Γ

=

Γ

≥Γ

=

ππ

ππY

DD D

D μ 1=

30




31

Design Steps 9. Calculate BR, CSR and VR.

VRIR βββ +=

where βVR for linear viscous dampers can be obtained by:

∑

∑

=

===f

d

N

iiRiR

N

iiiRLi

es

vdVR

kT

C

EE

1

2

1

22 cos

4ϕ

γϕπ

πβ

Ro

DS

dSR B

SCRC

Ω

=

RSRR WCV =

31




32

Design Steps 10. Determine the design base shear V and lateral

design forces at all levels of the SFRS.

RR

RiRiiR

iii

iRii

VW

wF

VW

wF

FFF

Γ=

Γ=

+=

φ

φ 11

111

221

min22

1 VVVV R ≥+=

32




33

Design Steps 11. Design the elements of the SFRS for the design forces and

displacements. 12. Design the elements of the damping system (except for the

damping devices themselves) for the maximum forces generated by the damping devices and by the SFRS under the design earthquake (see next section). Three possible conditions to verify:

I. Condition at maximum displacements; II. Condition at maximum velocities; and III. Condition at maximum accelerations.

13. Design the damping devices for the forces, inter-story drifts and inter-story velocities corresponding to the Maximum Credible Earthquake (MCE). Forces at MCE are obtained by the same procedure as above except

that SDS is replaced by SMS and SD1 is replaced by SM1.

33




6. Design of Damping System

34




35

The elements of the damping systems (except for the damping devices themselves) must be designed for the maximum forces generated by the damping devices and by the SFRS under the design earthquake (Step 12 of ELF procedure ). Inter-story drifts caused by the design earthquake:

221 RDDD ∆+∆=∆

∆1D = Inter-story drifts in the fundamental mode caused by the design earthquake. ∆RD = Inter-story drifts in the residual mode caused by the design earthquake.

35




36

R

RDRD

D

DD

T

T∆

=

∆=

π

π

2v

2v1

11

• Inter-story velocities caused by the design earthquake:

221 RDDDv = v + v

1D = Inter-story velocities in the fundamental mode caused by the design earthquake.

1R = Inter-story velocities in residual mode caused by the design earthquake.

36

v

v




37

Three possible conditions to verify: Condition at maximum displacements:

QE = Total design seismic force for an element of the damping system. QmSFRS = Force for an element of the damping system corresponding to

the mode m of the SFRS under the design earthquake. QDSD = Force for an element of the damping system corresponding to

the forces caused by the hysteretic dampers at the maximum design displacements of the structure.

Ω0 = Overstrength factor of the SFRS per ASCE 7-10.

37




38

Three possible conditions to verify: Condition at maximum velocities:

QE = Total design seismic force for an element of the

damping system. QmDSV = Force for an element of the damping system

corresponding to the forces caused by the viscous dampers at the maximum design velocities of the structure.

38




39

Three possible conditions to verify: Condition of maximum accelerations:

HDDeff βββ −= 1

39

velocityexponent




7. Testing Requirements

• Prototype testing – Two full-size dampers of each type. – Wind tests (if applicable). – 5 fully reversed sinusoidal cycles at MCE

displacement and at frequency 1/T1M. – 3 different temperatures (minimum, ambient,

and maximum) if dampers are temperature-sensitive.

– 15% changes allowed in fore-displacement properties.

40





• Production testing – All dampers to be installed. – Verify force-velocity-displacement characteristics. – Protocol to be determined by engineer-in- record.

41




• Production testing at UC-San Diego of ALGA viscous dampers for the Rion-Antiron bridge in Greece.

Video


42




8. Design Example according to ASCE 7-10 ELF Procedure for a Two-Story Building

with Viscous Dampers.

43




Building Description • Regular two-story steel building.

– Torsional effects neglected.– Hospital building .

• Importance factor Ie = 1.5.• Square plan with 145 ft. (44.23 m) span in

each direction.• Roof and floors diaphragms (assumed

rigid) and composed of beams andlightweight concrete slab on a steel decks.

• SFRS composed of special steel moment frames (per ASCE 7-10) on the perimeter axes 1, 6, A and G.

– R = 8, Cd = 5.5, Ω0 = 3.• Linear viscous dampers in the frames of

the SFRS.– One type of dampers with constant CL.

44




• Seismic weight at the floor androof:– W1 = 1000 kips (4448 kN)– W2 = 1200 kips (5338 kN)

• Lateral stiffness of each storybased on a preliminary design:– k1 = k2 =374 k/in (65.5 kN/mm)

• Inherent damping: βI = 0.05 (5% of critical)

• Design seismic parameter at thesite (per ASCE 7-10):– SDS = 0.83 and SD1 = 0.58

Building Description

45




28.89o

1. Identify the elements of the SFRS and the elements of the damping system.

2. Determine the damping contact, CL, of each damper to obtain a supplemental viscous damping in the first mode of vibration, βv= 0.09.

3. Determine the design base shear for the SFRS.

4. Verify that the Elastic Lateral Force (ELF) procedure is applicable to this building.

5. Determine the design lateral forces for the elements of the damping system.

Design Requirements

46




47

1. Identification the elements of the SFRS and the elements of the damping system

SRFS Damping System

Certain elements of the SFRS and of the damping system overlap.

47




48

Mass matrix:

Stiffness matrix

2. Determine the damping constant, CL, of each damper

with ζ1 = βv= 0.09

k-s2/in

k/in

∑

∑

=

===f

d

N

iii

N

iiiLi

es

vdV

kT

C

EE

1

211

1

221

1

cos

4ϕ

γϕπ

πβ

ELF Procedure Step 4:

48




49

Natural periods:

Fundamental mode: Damping constant:

( )( ) ( )( )( )

s/mm)-kN(1.05 s/ink0.689.28cos5.04

5.0k/in3742s906.009.022

2

−=

=

L

oL

C

Cπ

2. Determine the damping constant, CL, of each damper

From Section 6.8:

49




50

Seismic weight in fundamental mode: Modal participation Factor in fundamental mode:

Effective fundamental period at design

displacement: Assume ductility demand of SFRS under design

earthquake, µD = 1.3.

3. Determination of SFRS design base shear

(8866 kN)

50




51

Hysteretic damping from SRFS at design displacement: Total effective damping in the fundamental mode at

the design displacement:

( ) ( ) 07.03.1

1105.064.0517.01164.0

1517.0s906.0s699.067.067.05.0

s699.083.058.0

1

1

=

−−=

−−=

≤===<

===

DIHHD

SH

Ds

Ds

q

TTq

SST

µββ

569.11 =DB


51




52

Seismic coefficient in fundamental mode: Design base shear in fundamental mode:

Roof design displacement in fundamental mode:

32.114.009.005.0 11 =→=+=+= EVIE Bβββ

(116 mm)


52




53

Roof yield displacement: Effective ductility demand:

Less than 5% difference with the assumed value of 1.3. No iteration necessary.

(86 mm)


53




54

Modal properties in residual mode: Inter-story drifts in residual mode:


54




55

Equivalent viscous damping in residual mode:

( ) ( ) ( )[ ]( )( ) ( ) ( )[ ] 255.0

4.34.2k/in374s362.04.34.289.28cos2s/ink6

22

222

=+−

+−−=

o

VRπβ

=VRβ

815.1=RB


(Section 6.8)

55




56

Design roof displacement in residual mode: Seismic response coefficient and design base shear

in residual mode:

(2.54 mm)

(204 kN)


56




57

Design base shear: Verification of minimum design base shear:

(1556 kN)

( ) ( ) ( ) kN)(1527k2.343120010005.18

83.0=+=== W

IRSVV

e

DScode

(1556 kN)

32.1=+IVB

(1556 kN)


57




58

(1556 kN)

SFRS

RR

RiRiiR

iii

iRii

VW

wF

VW

wF

FFF

Γ=

Γ=

+=

φ

φ 11

111

221

( )( )

( )( )

( )( ) ( )

( )( ) ( )

( ) ( )( ) ( ) kN)(1107k1.2499.458.244

kN)(609k2.1378.91102

kN)(-204k9.45k9.45k9.206

1724.00.1k12002

kN)(408k8.91k9.45k9.206

1724.04.2k1000

kN)(1090k8.244k8.346k1.1993

1724.10.1k1200

kN)(454k102.0k8.346k1.1993

1724.15.0k1000

222

221

22

111

11

121221

11

111111

=−+=

=+=

−=−

=Γ

=

=−

−=Γ

=

==Γ

=

==Γ

=

F

F

VW

wF

VW

wF

VW

wF

VW

wF

RR

RR

RR

RRR

φ

φ

φ

φ

58




59

ELF procedure applicable if: At least two dampers at each level.

4. Verification of applicability of ELF Procedure

28.89o

Four dampers at each level in each principal direction.

59




60

ELF procedure applicable if : Effective damping in fundamental mode is less

than 35% of critical.


60




61

ELF procedure applicable if: SFRS does not have plan irregularities.

28.89o

Completely symmetric building in plan.


61




62

ELF procedure applicable if: Rigid roof and floor diaphragms. Assumed rigid.

Total height of the building does not exceed 30 m.

Design 1-sec spectral acceleration less than 0.6 g.

28.89o

32 ft = 9.8 m < 30 m

g60.0g58.01 <=DS

ELF procedure is applicable.


62




63

Inter-story drifts from design earthquake:

5. Design lateral forces for the elements of the damping system

(58 mm)

(59 mm)

63




64

Inter-story velocities from design earthquake :

(427 mm/s)`

(383 mm/s)

5. Design lateral forces for theelements of the damping system

64




65

Condition at maximum displacements: Condition at maximum velocities:

(4668 kN)

(3324 kN)

(593 kN)

(617 kN)


65




66

Condition of maximum accelerations: Fundamental mode

153.007.0223.01 =−=−= HDDeff βββ

0.11 =FDC 29.01 =FVC


66




67

Condition of maximum accelerations: Residual mode

0.1=RFDC 52.0=RFVC

5. Design lateral forces for theelements of the damping system

67




68

Condition of maximum accelerations :

(4844 kN)

(3510 kN)

Condition of maximum accelerations control.


68




69

Damping System

4844/2 kN 4844/2 kN

3510/2 kN 3510/2 kN


69




9. References

70




71

Questions/Discussions

Documents

Chapter 7 The ASCE 7-10 Design Provisions for Structures ...sharif.edu/~ahmadizadeh/courses/strcontrol/CIE626-Chapter-7-ASCE 7... · CIE 626 - Structural Control Chapter 1 - Introduction