Guidelines for Seismic Retrofit of Weak-Story Wood-Frame Buildings
Learning Obectives 1. Understand the vulnerabilities and failure modes of weak-story buildings under EQ demands. 2. Recognize the influence of non-structural finishes on the capacity of wood buildings. 3. Learn how to determine the capacity at near collapse. 4. Learn how to determine the optimal retrofit. 5. Understand the use of the Weak Story Tool.
Background and Theory Nuts and Bolts Making it Simple
BAKGROUND & THEORY
4400 Dangerous Multi-unit Buildings: 8% of population
reate Seismic Retrofit Program for Weak-Story Wood-framed Apartment Buildings in Western US
The Scope
Inepensive to onstruct (Work Only In Ground Story) Inepensive to Design (Unsophisticated Engineers) Performs Well (Shelter-In-Place)
Typically: Non-Engineered No Plans Archaic Materials Archaic onstruction Practices
The Problem 1989 Loma Prieta earthquake Image by Raymond B. Seed National Information Service for Earthquake Engineering University of alifornia Berkeley.
San Francisco A Loma Prieta Earthquake 11/17/1989 Beach and Divisadero in the Marina District. U.S.G.S. by Nakata J.K.
Northridge A: Northridge earthquake FEMA News Photo FEMA News Photo
Design for a Population of Buildings not an Individual Building
Pattern Recognition
Pattern Recognition Strong but Brittle Upper Structure Weak and Brittle Lower Structure
Pattern Recognition Limited Damage to Upper Structure Damage oncentrated in Lower Structure
RELATIVE STRENGTH METHOD
The Relative Strength Method Optimize benefits of ground story retrofits Retrofit to add both strength and displacement capacity and reduce torsion Strength limit established by the upper structure reate a damage and deformation absorption level The tough ground story protects the upper stories If too strong no damage absorption forces are transmitted to upper structure
The Relative Strength Method 400 350 300 250 Elevation in. 200 150 Overly strong retrofit (E) Structure 100 50 Optimal-cost retrofit Optimal-performance retrofit 0 0% 1% 2% 3% 4% 5% 6% Drift Ratio
an a Building s apacity be Determined from a Few Parameters?
Local Seismicity 3.5 Mean Median Geomean 3.0 Spectral Acceleration g 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Period sec.
Translational Weakness
Analysis Methodology - Material Forms Sheathing material with D = 1.0 Shear Force Sheathing material with D = 0.0 L = 1.25% L = 4.0% Interstory Drift
Damping and Hysteretic Models 1.5 1 0.5 Hysteresis of idealized high displacement capacity material ductile form Force 0-6 -4-2 0 2 4 6-0.5-1 -1.5 Drift Ratio % 1.5 1 0.5 Force 0-6 -4-2 0 2 4 6 Hysteresis of idealized low displacement capacity material brittle form -0.5-1 -1.5 Drift Ratio %
Torsional Weakness
haracteristic Structural oefficients s V N s 1 1 W Ground-story Strength U min V i N s i W Upper-story Strength i 2 N s W s U Upper to Ground Strength Ratio D F 1 ( 3%) V 1 Strength Degradation T T Torsional Imbalance
reate a ontrolled Eperiment Determine the Influence of Each haracteristic
Analytical Engine: Surrogate Structure oncept Material forms: (2) total Upper-story strength ratios Au: (4) per mat'l form Ductile 0.1 0.2 0.4 0.6 Brittle 0.1 0.2 0.4 0.6 Weak-story ratios Aw: 0.6 to 1.1 by 0.1 (6) per upper-story strength Retrofit strengths: Aw to 1.6 (51) per upper-story strength ratio TOTAL NUMBER OF BUILDINGS: 612 Time-history seed records: (22) Bi-directional records = (44) individual Scaled so that median Sa( T = 0.3 sec ) = 1.0g (35) intensities per seed record varying from 0.1 to 3.5 by 0.1 Recover peak interstory drift ratios for each analysis 1.0 Given drift criteria fit log-normal DF 0.5 0 0 1.0 (Sa = 1g) 3.5 Earthquake Intensity
Simplified Building Model W 50 in. H 100 in. L 111.8 q 1.107 rad 63.4 deg. cos(q) 0.447 Astrut 1 in2 Mg 1 kip (total weight of building)
Analytical Engine: Surrogate-Structure oncept 612 surrogate structures 44 EQs 35 intensities 1 million nonlinear response-history analyses
Analysis Results 2.7 Aw=1.1 2.2 Au = 0.6 Spectral apacity S c 1.7 1.2 Aw=0.6 Aw=0.6 Aw=0.8 Aw=0.8 Aw=0.8 Aw=1.1 Aw=1.1 Aw=1.1 Au = 0.4 Au = 0.2 Au = 0.1 Aw=0.6 Aw=0.8 Aw=0.6 0.7 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Total Ground Floor Strength/Upper Floor Strength
Analysis Results 20th Percentile Intensity Spectral apacity S c20 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 S 0. 48.34 1. A A c 20 0 47 W U Aw = 1.2 Aw = 1.1 Aw = 1 Aw = 0.9 Aw = 0.8 Aw = 0.7 Aw = 0.6 urve fit for Incremental Dynamic Analysis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Upper-Story Strength Ratio A U
Structural apacity S S 0. 48 2.24A 1 0. Q A c1 0.66 0.525 W 5 T s U 0. 60 1.59A 1 0. Q A c0 0.60 0.122 W 5 T s U D = 1.0 D = 0.0
NUTS & BOLTS
Limitations on the Guidelines Up to four stories Strong basement and strong sloped base can be accommodated Wood-framed stud walls and eisting steel moment frames No concrete or masonry walls or steel braced frames 8 12 floor heights for upper structure 8 15 floor heights for ground floor Sloped sites can be accommodated Torsionally regular upper structure No vertical irregularities in upper structure
Ground-story Strength Upper-story Strength Upper to Ground Strength Ratio Toughness Torsional Imbalance haracteristic Structural oefficients s s N i N i i U W V 2 min N s s W V 1 1 T T D V F 1 1 ( 3%) U s W Ground-story Strength Upper-story Strength Upper to Ground Strength Ratio Toughness Torsional Imbalance T T D V F 1 1 ( 3%) Ground-story Strength Upper-story Strength Upper to Ground Strength Ratio Toughness Torsional Imbalance T T U s W D V F 1 1 ( 3%) Ground-story Strength Upper-story Strength Upper to Ground Strength Ratio Toughness Torsional Imbalance T T s s N i N i i U W V 2 min U s W D V F 1 1 ( 3%) Ground-story Strength Upper-story Strength Upper to Ground Strength Ratio Toughness Torsional Imbalance T T T T D V F 1 1 ( 3%) T T U s W D V F 1 1 ( 3%) T T s s N i N i i U W V 2 min U s W D V F 1 1 ( 3%) T T N s s W V 1 1 s s N i N i i U W V 2 min U s W D V F 1 1 ( 3%) T T N s s W V 1 1 s s N i N i i U W V 2 min U s W D V F 1 1 ( 3%) T T
STORY STRENGTH
Structural Use of Non-conforming Materials 3500 3000 Stucco Horizontal wood sheathing Diagonal wood sheathing Brick veneer 2500 Plaster on wood lath Unit Force plf 2000 1500 1000 500 Plywood panel siding Gypsum wall board Plaster on gypsum lath Wood structural panel 8d@6 Wood structural panel 8d@4 Wood structural panel 8d@3 Wood structural panel 8d@2 Wood structural panel 10d@6 Wood structural panel 10d@4 Wood structural panel 10d@3 Wood structural panel 10d@2 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Drift Ratio %
Deflection riteria Brittle Backbone urves L01 L03 L04 L05 L06 L08 Ductile Backbone urves L02 L07 L09 L10 L11 L12 L13 L14 L15 L16 1000 3500 900 800 3000 700 2500 Unit Force plf 600 500 400 Unit Force plf 2000 1500 300 1000 200 100 500 0 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Drift Ratio % Drift Ratio % High Displacement apacity (Hd) Low Displacement apacity (Ld) Ground Upper Ground Upper Name Story Stories Story Stories Onset of Strength Loss Original ondition Onset of Strength Loss Retrofitted 4.0 4.0 1.25 1.25 4.0 4.0 4.0 1.25
Perforated Shearwalls Openings Q perf 2 3 0.92 0.72 0.80 H Floor to eiling A 1 A 2 1 H 1 A i L i L L L 1 2 3 Full-height wall segments Lw A = A + A i 1 2 L = L + L + L i 1 2 3
Story Height Adustment Factor 1.6 Normalized Mean Spectral apacity 1.4 1.2 1 0.8 0.6 0.4 0.2 Linear fit for Story-Height Adustment Factor Q s : Q s = 0.55 + 0.0045 H where H is the mean ground-story height in inches. Perform Model 0 0 50 100 150 200 250 Height of Bottom Story in.
Wall Height Adustment Factor D h H wall H H Tallest wall in ground story Wall 1 Wall 2 2 H 1200 1000 Adusted load-deflection curve 1 2 Unit Force plf 800 600 400 200 Shorter walls Taller walls Dh < 1.0 Dh = 1.0 Dh > 1.0) H Tallest wall in ground story Wall 1 Drift ratio = / H 1 Wall 2 Drift ratio = / H 2 2 H 2 Unit load-deflection curve adusted for height of Wall 2 0 0 1 2 3 4 5 6 7 8 Assembly unit load-deflection curve Unit load-deflection curve adusted for height of Wall 1 Drift Ratio % 2 1 2 1 Unadusted assembly unit load-deflection curve 1 2 Actual Drift Ratio = / H Normalized Drift Ratio
Pushover urve to Find Peak Strength shear force f1y f 2y 1y drift ratio 1y 1y 1y f 3y f 4y Wall: 1 2 3 4 f ( ) v ( ) L w w w Q perf Q ot Translational strength of the Ground Story V 1y Ground Story translational load-deflection curve in the y-direction F 1y 1y Drift ratio at which translational strength occurs
SIMPLIFIED OVERTURNING ADJUSTMENT
Overturning Reduction Factor 300 250 Story Shear kips 200 150 100 50 Ground story fied 0 Ground story with uplift 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 300 Interstory Drift Ratio 250 Story Shear kips 200 150 100 50 Second story fied Second story with uplift 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% Interstory Drift Ratio 300 250 Story Shear kips 200 150 100 50 Third story fied Overturning Reduction Factor Q ot for Upper Structure Perpendicular to Parallel to Level Framing Framing Unknown or mied Third story with uplift 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% Interstory Drift Ratio 300 250 Two or more stories above 0.95 0.85 0.85 One story above 0.85 0.8 0.8 Story Shear kips 200 150 100 Top story 0.75 0.8 0.75 Fourth story fied 50 Fourth story with uplift 0 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% Interstory Drift Ratio
STRENGTH DEGRADATION RATIO
Strength Degradation Ratio 1200 1000 Peak Strength V Load-Deflection urve Strength at 3% Drift V 3% 800 Unit Force plf 600 400 Strength Degradation Ratio D = V 3% /V 200 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Drift Ratio %
TORSIONAL IMBALANE
Weak-Story Wood-Frame Buildings
Torsion Demand Wall: 1 2 3 4 Ground Story torsion demand = V 1ye + V 1ey V1y enter of strength at Ground Story OS 1 e V1 y e yv1 e y V1 V1 enter of strength at Story 2 (above) OS 2 V1y e OS2 OS1 e e y OS 2 y OS1 y
Torsion apacity Wall: 1 2 3 4 d 1 d 2 d3 d Ay d 4 Twist Level 2 by the twist angle A f A at d Ay B D Dy Ay d d By d1 enter of strength at Ground Story Torsional moment that causes a twist of for the Ground Story t ( ) 1 E f 1y at d 1 f 2y at d 2 f 3y at d 3 f 4y at d 4 d y d f B at d By d f at d y Ey f D at d Dy f E at d Ey Torsion Backbone urve t( ) T ma N walls w y w y d w y f w ) d w f w y w1 H1 H1 t ( ) d d d 1 d 2 Torsional strength of the Ground Story Torsional moment that causes a twist of for the Ground Story t ( ) 1 T 1 d 3 1 d 4 Ground Story torsional load-deflection curve t 1 Maimum twist angle to consider for the Ground Story
Accounting for Torsion 1.2 apacity Reduction Factor 1.0 0.8 0.6 0.4 Ductile Aw = 0.60AB Ductile Aw = 0.60R Ductile Aw = 0.80AB Ductile Aw = 0.80R Brittle Aw = 0.60AB T T Direction of drift assessment 0.2 Brittle Aw = 0.60R Brittle Aw = 0.80AB Brittle Aw = 0.80R 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Torsion oefficient T
ALULATE SPETRAL APAITY
Spectral apacity Sc S 0. 48 2.24A 1 0. Q A c1 0.66 0.525 W 5 T s U D = 1.0 S 0. 60 1.59A 1 0. Q A c0 0.60 0.122 W 5 T s U D = 0.0 Modifier for POE = 0.2 3 D S c0 3 S c DSc 1 1 for intermediate values Mean spectral capacity S m S S c MS if true no retrofit required Onset of Strength Loss drift criteria OSL 20% Probability of Eceedance POE
ALULATE OPTIMAL RETROFIT
Range of Retrofit Strength For buildings with strong upper structures (V rma > V re ) upper limit lower limit 0.11AU 1. VU V r ma 22 V re S MS X X 1 2 3 D 1 3 D Y2 1 Y 1 3 D 3 D s 1 X 5 T 0.48 0 AU Q 1 0. 1 1. 48X 0 0.6 0 AU Qs 0. T 1 0. 96Y0 Y 5 X X 2 0. 35X 0 Y Y2 0. 07Y0 For buildings with weak upper structures (V rma < V re ) Estimate of the minimum ground-story strength that gets POE below 0.2 use 90% 110% of upper limit 0.11AU 1. VU V r ma 22 If the upper structure is etremely weak such that the Guidelines are not applicable use alternative methodology 2 S cr S 3 MS this corresponds to a 50% POE at the ME
Range of Retrofit Strength Acceptable Retrofit Range Spectral apacity S c S c = S MS Au = 0.4 Aw = 0.6 Minimum Strength V r min (Adequate Performance) Maimum Strength V r ma (Best Performance) V re S MS X X 1 2 3 D 1 3 D Y2 1 Y 1 3 D 3 D Strength of Retrofitted Ground-Story 0.11AU 1. VU V r ma 22
Range of Retrofit Strength Spectral apacity S c S MS S c Acceptable Retrofit Range 2/3 S MS Au = 0.1 Aw = 0.6 Minimum Strength V r min = 0.9V r ma Estimated Minimum Strength V re Maimum Strength V r ma Strength of Retrofitted Ground-Story 0.11AU 1. VU V r ma 22
Retrofit
Regularizing Diaphragms This frame must support lateral loads from both diaphragms D and D L antilevered Diaphragm hord capacity must be checked if L > 10 feet. D D D y W W y D D Direction of motion considered : y > 2 : 1 Aspect ratios : y < 2 : 1 : y < 2 : 1 antilevers y : < 2 : 1 y : < 2 : 1 W D This wall must support lateral loads from both diaphragms D and D N > 0.25y Openings Depending on the width this portion may be considered a separate sub-diaphragm D W E S North-South Analysis > 0.25 Re-entrant corners
Retrofit Placement to Minimize Torsion L Added retrofit strength - e r e V V 1 Vr V1 Force resultant of strengths of retrofit elements in the y-direction Place to eliminate torsion limited by building dimension e V 1 y e V L OS2 V1 y Eisting enter of strength at Ground Story OS 1 V1y Vry V1y Retrofit element enter of strength at Story 2 (above) OS 2 Retrofit element Range of acceptable eccentricity - enter of strength at Ground Story after retrofit OS r V 1 y e min e e e V Vr y e e 0. 05L ma min OS 2 e
MAKING IT SIMPLE
WST IDA Data Base Graphic Utility