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Lecture 11 Performance Based Evaluation
 

Lecture 11 Performance Based Evaluation

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Dan Abrams + Magenes Course on Masonry

Dan Abrams + Magenes Course on Masonry

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    Lecture 11 Performance Based Evaluation Lecture 11 Performance Based Evaluation Presentation Transcript

    • 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
    • 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
    • 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
    • Masonry Partition Walls Masonry Structures, lesson 11 slide 7 Contents Mitigation ABC Good Morning America Masonry Structures, lesson 11 slide 8
    • 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
    • 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
    • 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
    • Behavior of Non-Retrofitted Pier Masonry Structures, lesson 11 slide 15 Ferrocement Surface Coating Masonry Structures, lesson 11 slide 16
    • Fiber Reinforced Polymer Masonry Structures, lesson 11 slide 17 Reinforced Shotcrete Masonry Structures, lesson 11 slide 18
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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