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
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
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
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
Major References • ASCE 7-10 Standard
– Chapter 18
3
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
1. Scope
• Building structures equipped with all types of damping systems: – Hysteretic, viscous, visco-elastic dampers.
4
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
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
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
SFRS Damping System
Damping Devices
6
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
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
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
≥
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.
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
9
Subscripts:E: elastic, D: design, 1: first mode
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
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
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
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
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
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
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
5. Equivalent Lateral Force Procedure (ELF)
• 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
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
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
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
Conservative since Cd ≤ R
15
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
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
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
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
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
5. Equivalent Lateral Force Procedure (ELF)
• 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
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
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
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
5. Equivalent Lateral Force Procedure (ELF)
• Residual Mode Base Shear
RSRR WCV =CSR = Residual mode seismic response coefficient. = Residual modal weight.
min22
1 VVVV R ≥+=
RW Unknown
Unknown
20
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
5. Equivalent Lateral Force Procedure (ELF)
• 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
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
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
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
5. Equivalent Lateral Force Procedure (ELF)
• 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)
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
Design Steps of Equivalent Lateral Force Procedure
24
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
6. Design of Damping System
34
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
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
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
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
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
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
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
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
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
39
Three possible conditions to verify: Condition of maximum accelerations:
HDDeff βββ −= 1
39
velocityexponent
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
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
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
7. Testing Requirements
• Production testing – All dampers to be installed. – Verify force-velocity-displacement characteristics. – Protocol to be determined by engineer-in- record.
41
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
• Production testing at UC-San Diego of ALGA viscous dampers for the Rion-Antiron bridge in Greece.
Video
7. Testing Requirements
42
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
8. Design Example according to ASCE 7-10 ELF Procedure for a Two-Story Building
with Viscous Dampers.
43
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
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
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
• 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
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
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
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
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
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
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
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
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
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
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
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
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
3. Determination of SFRS design base shear
51
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
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)
3. Determination of SFRS design base shear
52
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
53
Roof yield displacement: Effective ductility demand:
Less than 5% difference with the assumed value of 1.3. No iteration necessary.
(86 mm)
3. Determination of SFRS design base shear
53
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
54
Modal properties in residual mode: Inter-story drifts in residual mode:
3. Determination of SFRS design base shear
54
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
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
3. Determination of SFRS design base shear
(Section 6.8)
55
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
56
Design roof displacement in residual mode: Seismic response coefficient and design base shear
in residual mode:
(2.54 mm)
(204 kN)
3. Determination of SFRS design base shear
56
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
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)
3. Determination of SFRS design base shear
57
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
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
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
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
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
60
ELF procedure applicable if : Effective damping in fundamental mode is less
than 35% of critical.
4. Verification of applicability of ELF Procedure
60
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
61
ELF procedure applicable if: SFRS does not have plan irregularities.
28.89o
Completely symmetric building in plan.
4. Verification of applicability of ELF Procedure
61
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
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.
4. Verification of applicability of ELF Procedure
62
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
63
Inter-story drifts from design earthquake:
5. Design lateral forces for the elements of the damping system
(58 mm)
(59 mm)
63
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
64
Inter-story velocities from design earthquake :
(427 mm/s)`
(383 mm/s)
5. Design lateral forces for theelements of the damping system
64
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
65
Condition at maximum displacements: Condition at maximum velocities:
(4668 kN)
(3324 kN)
(593 kN)
(617 kN)
5. Design lateral forces for the elements of the damping system
65
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
66
Condition of maximum accelerations: Fundamental mode
153.007.0223.01 =−=−= HDDeff βββ
0.11 =FDC 29.01 =FVC
5. Design lateral forces for the elements of the damping system
66
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
67
Condition of maximum accelerations: Residual mode
0.1=RFDC 52.0=RFVC
5. Design lateral forces for theelements of the damping system
67
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
68
Condition of maximum accelerations :
(4844 kN)
(3510 kN)
Condition of maximum accelerations control.
5. Design lateral forces for the elements of the damping system
68
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
69
Damping System
4844/2 kN 4844/2 kN
3510/2 kN 3510/2 kN
5. Design lateral forces for the elements of the damping system
69
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
9. References
70
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
71
Questions/Discussions