Dan Abrams + Magenes Course on Masonry

1. Seismic Design and Assessment of
Seismic Design and Assessment of
Masonry Structures
Masonry Structures
Lesson 11: Performance-Based Seismic
Evaluation and Rehabilitation of
Masonry Buildings
Notes Prepared by:
Daniel P. Abrams
Willett Professor of Civil Engineering
University of Illinois at Urbana-Champaign
October 25, 2004
Masonry Structures, lesson 11 slide 1
NEHRP Guidelines
FEMA 273, FEMA 356
first national consensus document for
rehabilitation
performance-based design
ductility-based rehabilitation
displacement-based analyses
For free copy of FEMA 356 call:
1-800-480-2520
Masonry Structures, lesson 11 slide 2

2. Performance Based Rehabilitation
cost
basic safety objectives
increasing
collapse reliability
life safety
2%
immediate 10%
occupancy
20% probability of
operability 50% exceedance in 50 years
increasing
performance
Masonry Structures, lesson 11 slide 3
Seismic Hazard Maps
NEHRP Provisions and Guidelines
Sa
T
0.2To To 1.0
Masonry Structures, lesson 11 slide 4

3. Scope of Masonry Chapter
Existing, rehabilitated or new masonry lateral-force resisting
elements.
Clay and concrete masonry, hollow clay tile
Unreinforced and reinforced masonry.
In-plane and out-of-plane elements.
See Simplified Rehabilitation or Nonstructural chapters for
parapets, cladding or partition walls.
Masonry Structures, lesson 11 slide 5
Performance of Brick Veneer
brick veneer
Masonry Structures, lesson 11 slide 6

4. Masonry Partition Walls
Masonry Structures, lesson 11 slide 7
Contents Mitigation
ABC Good Morning America
Masonry Structures, lesson 11 slide 8

5. Immediate Occupancy
1.5
Base Shear / Weight
IO
1.0
0.5
0.0 1.00
0.25 0.50 0.75
First Story Drift, %
Masonry Structures, lesson 11 slide 9
Life Safety
1.5
Base Shear / Weight
IO LS
1.0
0.5
0.0 1.00
0.25 0.50 0.75
First Story Drift, %
Masonry Structures, lesson 11 slide 10

6. Collapse Prevention
1.5
Base Shear / Weight
IO LS CP
1.0
0.5
0.0 1.00
0.25 0.50 0.75
First Story Drift, %
Masonry Structures, lesson 11 slide 11
Performance Indices for Masonry
damage control
expected damage wall drift levels*
Immediate minor cracks 0.1%
Occupancy
extensive cracks 0.3%
Life Safety no dislodgment of units
limited safety
Collapse extensive cracks
dislodgment of units 0.4%
Prevention noticeable offsets
* with bed-joint sliding mechanism Masonry Structures, lesson 11 slide 12

7. Enhancement Options
infilled openings
enlarged openings
shotcrete
Masonry Structures, lesson 11 slide 13
Enhancement Options
surface coatings
repointing
braced and stiffened walls
grouted collar joints
reinforced cores
prestressed cores
Masonry Structures, lesson 11 slide 14

8. Behavior of Non-Retrofitted Pier
Masonry Structures, lesson 11 slide 15
Ferrocement Surface Coating
Masonry Structures, lesson 11 slide 16

9. Fiber Reinforced Polymer
Masonry Structures, lesson 11 slide 17
Reinforced Shotcrete
Masonry Structures, lesson 11 slide 18

10. Reinforced Cores
8
6
4
Lateral Load [kips]
2
0
-2
#3 or -4
#5 bar -6 8F
7F
-8
1F
-10
-3 -2 -1 0 1 2 3
Drift %
Masonry Structures, lesson 11 slide 19
Reticulated Reinforcement
Masonry Structures, lesson 11 slide 20

11. Reticulated Reinforcement
Force
Displacement
Masonry Structures, lesson 11 slide 21
Analysis Procedures
Linear Static Procedure
Nonlinear Static Procedure
Linear Dynamic Procedure
Nonlinear Dynamic Procedure
Masonry Structures, lesson 11 slide 22

12. Linear Static Procedure
V=C1C2C3SaW
C1= interpolate between 1.0 and 1.5 for T=0.1 and To
C2= from Table 3-1 for framing type 1
C3= 1.0 for non-bearing wall
Sa = spectral acceleration
W = weight of building
Masonry Structures, lesson 11 slide 23
Linear Static Procedure – FEMA 356
k
QE QCE
Vb
Force
∆i
QCE ∆y
∆y ∆i
Deflection
mκQ CE ≥ Q E
Q CE ∆i
∆y = mi =
k ∆y
io = immediate occupancy
ls = life safety
cp= Masonry Structures, lesson 11 slide 24
collapse prevention

13. Bed-Joint Sliding mκQCE ≥ QE
Deformation-controlled action
Vbjs
Vbjs = v me An
expected strength
Masonry Structures, lesson 11 slide 25
Rocking mκQCE ≥ QE
Deformation-controlled action PCE
Vr
h
L
⎛L⎞
Vr = 0.9αPCE ⎜ ⎟
⎝h⎠
Masonry Structures, lesson 11 slide 26

14. LSP Acceptability Criteria
mκQCE ≥ QUD = QE
m factors for primary elements
IO LS CP
Bed-joint sliding 1 3 4
Rocking 1.5 heff/L>1 3.0 heff/L>1 4.0heff/L>1
(Multiply m factors by 2 for secondary elements
for Life Safety (LS) and Collapse Prevention (CP))
Masonry Structures, lesson 11 slide 27
Diagonal Tension mκQCE ≥ QE
Force-controlled action
P = f aA
Vdt
L ⎛L⎞ f
for 0.67 < < 1.00 Vdt = f ' dt An ⎜ ⎟ 1 + a
h ⎝h⎠ f ' dt
lower bound value
Masonry Structures, lesson 11 slide 28

15. Toe Crushing mκQCE ≥ QE
Force-controlled action
PCL
Vtc
⎛ L ⎞⎛ fa ⎞
Vtc = αPCL ⎜ ⎟⎜ 1 −
⎜ ⎟
⎟
⎝ h ⎠⎝ 0.7 f ' m ⎠
lower bound value
Masonry Structures, lesson 11 slide 29
Modeling and Acceptability Criteria
Nonlinear Static Procedure
e
d primary walls
force
LS CP
secondary walls
0.75d
LS CP c
0.75e
drift
Masonry Structures, lesson 11 slide 30

16. NSP: Acceptable Drifts
Drifts for Primary Elements
IO LS CP
Bed-Joint Sliding 0.1% 0.3% 0.4%
Rocking 0.1% 0.3 heff/L% 0.4 heff/L%
(Multiply drifts by 2 for secondary elements for LS and CP)
Masonry Structures, lesson 11 slide 31
Example Building
direction of earthquake
• URM clay-unit masonry
• two-wythe brick walls
• constructed prior to 1960
wood roof joists • located in St. Louis
4’-0”
• total roof dead load = 60 kips
• symmetrical structure
8’-0” • soil class B
• case A: no testing, visual exam
URM • case B: testing and inspection
bearing wall
URM
pier
4’-0” Problem: check adequacy of
Problem: check adequacy of
7.63” pier for BSO and suggest
24’-0” 32’-0”
pier for BSO and suggest
rehabilitation scheme if necessary.
rehabilitation scheme if necessary.
4’-0”
Masonry Structures, lesson 11 slide 32

17. Seismic Demand: LSP
Sa S XS Fa SS
Sa = =
BS BS
S FS
Sa = X 1 = v 1
B1 B1
T Fa= Fv= 1 for site class B
0.2To To 1.0
BS = B1 = 1 for 5% damping
Fv S 1 B S S
To = = 1
Fa S S B1 SS
Masonry Structures, lesson 11 slide 33
Seismic Demand: LSP
3 3
T = Ct h 4 = 0.020 ( 12 feet ) 4 = 0.129 seconds
S1 SS To C1 C2 C3 Sa V/W
BSE-1
10% /50 years 0.05g 0.18g 0.278 1.42 1.30 1.00 0.18g 0.332
Life Safety sec.
St. Louis
BSE-2 0.18g 0.58g 0.310 1.43 1.50 1.00 0.58g 1.244
2% /50 years sec.
Collapse Prevention
Masonry Structures, lesson 11 slide 34

18. Lateral Force Distribution
60.0 kips
10.6 kips
2.7 kips
31.8 kips
Weights (kips)
2.7 kips 30.0 + 2(31.8/4) = 45.9
10.6 4’-0”
5.4 8’-0”
total weight per shear wall = 61.9 kips
Masonry Structures, lesson 11 slide 35
Pier Strength: Case A, no tests
PG = 5.29k Vme= 27psi f’me= 900 psi from default values
QCE bed-joint sliding:
Vbjs = v me An = ( 0.027 ksi )( 7.63quot; x 48quot; ) = 9.89 kips
8’-0” rocking:
⎛ L ⎞
Vr = 0.9 α PCE ⎜
⎜h ⎟ = 0.9 ( 1.0 )( 5.29 kips )( 0.5 ) = 2.38 kips
⎟
⎝ eff ⎠
4’-0”
governs
toe crushing:
⎛ L ⎞⎛ fa ⎞ ⎛ 14.4 ⎞
Vtc = αPCL ⎜ ⎟⎜ 1 − ⎟ = ( 1.0 )( 5.29 kips )( 0.5 )⎜ 1 −
⎜ ⎟ = 2.54 kips
⎜h
⎝ eff
⎟⎜
⎠⎝ 0 .7 f ' m ⎟
⎠ ⎝ 0.7 ( 563 ) ⎟
⎠
5290 lbs fme
fa = = 14.4 psi f' m = = 563 psi
7.63quot; ( 48quot; ) 1 .6
Masonry Structures, lesson 11 slide 36

19. Pier Strength: Case B
Vte = 150 psi from shove tests f’me = 2000 psi from prism tests
PG = 5.29k
0.75 ( 0.75 x150 psi + 14.4 psi )
QCE v me = = 63.5 psi
1.5
bed-joint sliding:
8’-0”
Vbjs = v me An = ( 0.0635 ksi )( 7.63quot; x 48quot; ) = 23.2 kips
rocking:
4’-0” ⎛ L ⎞
Vr = 0.9 αPCE ⎜
⎜h ⎟ = 0.9( 1.0 )( 5.29kips )( 0.5 ) = 2.38kips
⎟
⎝ eff ⎠
governs
toe crushing:
⎛ L ⎞⎛ fa ⎞ ⎛ 14.4 ⎞
Vtc = αPCL ⎜
⎜h ⎟⎜1 −
⎟⎜ 0.7 f ' ⎟ = ( 1.0 )( 5.29kips )( 0.5 )⎜1 − 0.7 ( 1250 ) ⎟ = 2.60kips
⎟ ⎜ ⎟
⎝ eff ⎠⎝ m ⎠ ⎝ ⎠
Masonry Structures, lesson 11 slide 37
Acceptability Criteria mκQCE ≥ QUD
BSE-1 Q UD = 0 . 332 ( 61 . 9 kips )( 0 . 5 ) = 10 . 3 kips
m = 6 for Life Safety
Case A:
m κ QCE = 6 ( 0 .75 )( 2 .38 kips ) = 10 .7 kips > 10 .3 kips ok
Case B:
mκQCE = 6 ( 1.00 )( 2.38 kips ) = 14.3 kips > 10.3 kips ok
Masonry Structures, lesson 11 slide 38

20. Acceptability Criteria mκQCE ≥ QUD
BSE-2 QUD = 1.244 ( 61.9 kips )( 0.5 ) = 38.5 kips
m = 8 for Collapse Prevention
Case A:
mκQCE = 8( 0.75 )( 2.38 kips ) = 14.3 kips < 38.5 kips NG
Case B:
mκQCE = 8( 1.00 )( 2.38 kips ) = 19.0 kips < 38.5 kips NG
Masonry Structures, lesson 11 slide 39
Rehabilitation Option 1
Enlarge pier width: PG = 5.29k
38.5
L= ( 4.0' ) = 10.8' QCE
14.3
Check:
⎛ L ⎞ 8’-0”
Vr = 0.9αPCE ⎜
⎜h ⎟
⎟ (Eq. 7-4)
⎝ eff ⎠
10.8'
= 0.9( 1.0 )( 5.29kips )( ) 5’-5” 4’-0”
8.0'
new old
= 6.43kips
Case A, Check CP:
mκQCE = 8( 0.75 )( 6.43 kips ) = 38.5 kips ok
Masonry Structures, lesson 11 slide 40

21. Rehabilitation Option 2
Prestress pier:
38.5 Pstress = 8.95k
P= ( 5.29 kips ) = 14.24 kips
14.3 PG = 5.29k
Required prestressing force
= 14.24 - 5.29 = 8.95 kips
⎛ ⎞ 8’-0”
Check: Vr = 0.9αPCE ⎜ L ⎟ (Eq. 7-4)
⎜h ⎟
⎝ eff ⎠
= 0.9( 1.0 )( 14.24kips )( 0.5 ) 4’-0”
= 6.41kips
Case A, Check CP:
mκQCE = 8( 0.75 )( 6.41kips ) = 38.5 kips ok
Masonry Structures, lesson 11 slide 41
Rehabilitation Option 3
2 - No. 4 bars
Reinforce:
Consider as reinforced masonry pier
per Sec. 7.4.4 8’-0”
4’-0”
Masonry Structures, lesson 11 slide 42

22. Damage to Out-of-Plane Walls
1886 Earthquake
Charleston, South Carolina
1994 Northridge Earthquake,
Hollywood
Masonry Structures, lesson 11 slide 43
Out-of-Plane Walls
k P
Flexural cracking limits IO
Dynamic stability for LS and CP
dynamic stability ok if h/t < table values
Wall types SX1 < 0.24g 0.24g < SX1<0.37g 0.37g<SX1<0.5g
1-story bldgs 20 16 13
multistory bldgs
1st story 20 18 15
top story 14 14 9
all other walls 20 16 13
Masonry Structures, lesson 11 slide 44

23. Masonry Infills
URM Infill, Tangshan, PRC URM Infill, Campania, Italy
Masonry Structures, lesson 11 slide 45
Masonry Infills
300
Infill Shear Stress, psi
Infill Shear Stress, psi
200
100
0
-100
Static Cyclic Tests of URM infills -200
University of Illinois
-300
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Lateral Drift, %
Lateral Drift, %
Masonry Structures, lesson 11 slide 46

24. Infill Damage Patterns
crack pattern, large-scale static test
crack pattern, half-scale dynamic test
Masonry Structures, lesson 11 slide 47
Frame-Infill Systems
Masonry Structures, lesson 11 slide 48

25. In-Plane Masonry Infills
at inf E me
Stiffness k=
rinf
rinf
a = 0.175 ( λ1 hcol ) −0.4 rinf
H
1
⎡ E t sin 2 θ ⎤ 4
a λ1 = ⎢ me inf ⎥
⎣ 4 E fe Icol hinf ⎦
Masonry Structures, lesson 11 slide 49
In-Plane Masonry Infills
Strength
QCE = Vine = Ani fvie
mκQCE ≥ QE
Masonry Structures, lesson 11 slide 50

26. m Factors for Masonry Infills
Table 7-6
m
Example: 8.0
Life Safety 6.0
7.0
4.0
5.2
3.5
6.0
3.0 4.5
V fre
β =
L inf V ine
0.3
h inf 0.7 0.5
1.3 1.0
2.0
page 7-20 Masonry Structures, lesson 11 slide 51
Out-of-Plane Infill Strength
Pressure, psf
Center Deflection / Height %
Masonry Structures, lesson 11 slide 52

27. Out-of-Plane Infills
Table 7-8: maximum h/t ratios for
which no analysis is necessary
low moderate high
seismicity seismicity seismicity
IO 14 13 8
LS 15 14 9
CP 16 15 10
Masonry Structures, lesson 11 slide 53
Out-of-Plane Infills
If arching action is prevalent:
⎛h ⎞
0.002 ⎜ inf
⎜t ⎟
⎟
∆ inf ⎝ inf ⎠ ∆inf
=
hinf ⎛h ⎞
2
hinf
1 + 1 − 0.002 ⎜ inf
⎜t ⎟
⎟
⎝ inf ⎠
< 2% for IO and 3% for CP
Masonry Structures, lesson 11 slide 54

28. Out-of-Plane Infills
If arching action is prevalent:
0.75 f ' m λ 2
QCL = q in = x144
⎛ hinf ⎞
⎜
⎜t ⎟ ⎟
⎝ inf ⎠
< load per Sec. 2.11.7
Masonry Structures, lesson 11 slide 55
Undesirable Interventions
Maintain deformation controlled mechanisms
– do not change rocking to shear mechanism with
coatings, overlays, shotcrete or reinforcement
– do not change bed-joint sliding to diagonal
tension with brittle coatings or overlays
Alter force controlled mechanisms
– enlarge openings to promote rocking
– lighten gravity loads to piers to avoid toe
compression
Masonry Structures, lesson 11 slide 56

29. Concluding Remarks
• Systematic rehabilitation of
masonry buildings.
• Guidelines are first
performance-based provisions
for masonry structures.
• Judgement of engineer is
essential for proper
application of Guidelines.
Masonry Structures, lesson 11 slide 57
Famous Last Words
Infrequent events will not
happen tomorrow….
1886 Charleston, South Carolina 2001 Gujarat
Masonry Structures, lesson 11 slide 58