The Art of Designing Ductile Concrete in the Past 50 Years: The Impact of the PCA Book and Mete A. Sozen, Part 2

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1 The Art of Designing Ductile Concrete in the ast 5 Years: The Impact of the CA Book and Mete A. Sozen, art 2 Beth Brueggen, Associate III, Wiss, Janney, Elstner Associates, Inc., Irving, TXrior to joining WJE, Dr. Brueggen worked as a research assistant in the Multi-Axial Subassemblage Testing (MAST) Laboratory at the University of Minnesota. Her work focused on the behavior and seismic detailing of nonrectangular reinforced concrete shear walls under multidirectional lateral loads. ACI WEB SESSIONS ACI Fall 212 Convention October 21 24, Toronto, ON ACI WEB SESSIONS Simplified Modeling of Non-Rectangular RC Structural Walls roud to be part of the Illinois Mafia Beth Brueggen Wiss, Janney, Elstner Associates, Inc. Cathy French University of Minnesota ACI Fall 212 Convention October 21, 212 This research was completed under grant CMS from the National Science Foundation. Outline Introduction Simplified Modeling rocedure Load vs. Deflection Relationship rediction of Damage States alidation Summary & Recommendations Specimen NTW1 4 stories Continuous reinforcement over height Reinforcement concentrated in boundary elements Confinement spacing relaxed from ACI (consistent with ACI ) 1

2 2 stories Lap splices above first floor level Uniformly distributed longitudinal steel in flange Expanded confined region Specimen NTW2 Distributed long. steel: (28) #4 + (12) 3 5 8" Code-required limit of confinement #2 hoops & 2" oc Distributed long. steel: #3@ 12'' oc Concentrated long. steel: (8) #6 + (4) #5 + (4) 32" 1 Applied displacements 12 failure surface Deformations of Interest erformance Level Operational Immediate Occupancy Life Safety Collapse revention Tension Compression Damage State & Needed Repair x/2 Shear Flexure Strain enetration x/2 steel Engineering Limit State Threshold /drift/etc. related to crack size, spalling, crushing, bar buckling or fracture Instructional Materials Complementing FEMA 451 Existing Modeling Tools Simplified Models FEMA 356/ASCE 41 Supplement 1 Hines Bridge ier Model Other Models Waugh & Aaletti OpenSees Wall Model Other finite-element-based approaches Outline Introduction Simplified Modeling rocedure Load vs. Deflection Relationship rediction of Damage States alidation Recommendations 2

3 Desired Capabilities of rocedure Appropriate for general design use More precise than FEMA 356/ASCE 41 Supp. 1 Applicable to any flexural wall geometry (i.e. rectangular or flanged, height, length) Not sensitive to particular detailing (i.e., distributed or concentrated reinforcement, splices, confinement) Applicable to any loading direction, orthogonal or skew Transparent procedure, additional terms can be incorporated F-S-S Integration Model Based on flexural sectional analysis Flexural Component Integrate M- twice Shear Component Calculated from cracked shear stiffness & flexural stiffness Strain enetration Component Calculated from longitudinal s at base Flexural Component of Deformation Section analysis calculates M- relationship Integrate twice over height of specimen to get - for flexural deformations Assumes plane sections remain plane Neglects shear lag in flanged walls Neglects tension shifting Challenges with post-peak behavior Effectiveness of Model Flexural Displacement at 1st story Web Direction measured predicted Flexural Displacement at 4th story Web Direction Displacement (in) -1 measured -15 predicted Displacement (in) Shear Demands and Shear Deformation Deflections Observed Relationship between Shear Deformation and Flexural Damage M vesbwd Kv 1 4n v Uncracked Stiffness 3

4 roposed Method v =C* f or =C* Use cracked shear stiffness & flexural stiffness at yield to define proportional relationship Effectiveness of Model FT v = *61.2 in. C = M K * z v y vesbwd Kv 1 4n y v z = shear span for 45 cracks FC v = *51.3 in. Strain enetration Assume plane sections remain plane Assume behavior in tension and compression similar slip d c slip steel Tension Strain enetration d-c Compression roposed Method Assume constant bond length & gradient 1 slip wallbase* la 2 slip wallbase* l d c 2( d c) a slip steel Tension Strain enetration wall base l a Compression Effectiveness of Model Rotation due to Strain enetration 25 2 using F-S-S model Theta (rad) Damage Negligible Minimum Minimal rediction of Damage Levels Berry, Lehman, & Lowes (28) FEMA 356, ATC 58-2, etc. Moderate Significant erformance Level None Immediate Occupancy Required Repair Local ED Threshold alue Steel tensile Epoxy injection of cracks Steel tensile atching of concrete cover and epoxy injection of cracks Cover concrete compressive NTW1 & NTW2, RW1, RW2, & RW3 s <3.5 y conc. steel s <7 y dist. steel s >3.5 y conc. steel s >7 y dist. steel c > 2f' c /E c or.3 Life Safety Replacement of concrete cover and Core concrete compressive c >4kf' c /E c epoxy injection of cracks Model indicates Collapse revention Replacement of section post-peak loss of capacity 4

5 Outline Introduction Simplified Modeling rocedure Load vs. Deflection Relationship rediction of Damage States alidation Summary & Recommendations Model alidation Comparison to NTW1 & NTW2 Comparison to results of 6 tests reported in literature Comparison to FEMA 356/ASCE 41 Supplement 1 & Hines models All validation based on reported as-built material properties In general Moment capacity predicted within 5% in all cases Displacement capacity typ. underpredicted 5 to 4% Sections Used for alidation Sections Used for alidation Johnson (2 walls) h/l=2.7 Sittipunt & Wood h/l=3. Hines (2 piers) h/l=2.6 Wallace h/l=3. Comparison to FEMA 356/ASCE 41 Supp. 1 NTW1 WD - whole structure C IO IO LS C F-S-S FEMA356 Load (k.) NTW2 WD - Whole Structure C IO IO Displacement (in.) LS C F-S-S FEMA 356 Evaluation of roposed Model NTW1 Flange Direction Load capacity within 3% Underestimates drift capacity NTW1 FD First Story NTW1 FD - Whole Structure

6 Outline Introduction Simplified Modeling rocedure Load vs. Deflection Relationship rediction of Damage States alidation Summary & Recommendations Summary of Model Takes advantage of relative ease of modeling flexure Applicable to more generalized cases than existing simplified tools More accurate than existing simplified tools rovides framework for predicting damage levels alidated using results of tests with aspect ratios of 2.5 to 3. Does not track damage due to prior load history ossible Modifications to F-S-S Integration Model Questions? Calibration of threshold s for damage prediction using larger data set Incorporate shear lag effects Add artificial plastic hinge length to represent tension shifting Improve prediction of post-peak behavior Refine shear crack angle prediction Refine penetration model vs. Curvature otential Implications of Neglecting Tension Shifting Confined region degrading Bars buckling 6

7 ariation in Crack Angle General relationships can be established for crack angle; reliable prediction is difficult ure Shear Shear + Axial Compression Shear + Axial Tension Lap Splices Outside lastic Hinge Region Splices in 2nd story did not slip during testing Rectangular wall with lap splices at base 45 <45 >45 Lap Splices Outside lastic Hinge Region Splices in 2nd story did not slip during testing Lap splices did interrupt yielding Neglecting splice increases flexibility ~1-2% OR Use a 2 nd model with double steel for lap region y Effectiveness of Flexural Model with Lap Splices Load (k.) NTW2 WD - Whole Structure Displacement (in.) -including splice -neglecting splice Evaluation of roposed Model NTW2 Web Direction Load capacity within.5% Underestimates drift capacity Evaluation of roposed Model NTW2 Flange Direction Load capacity within 3% Underestimates drift capacity NTW2 WD - First Story 25 NTW2 WD - Whole Structure 25 NTW2 FD - First Story 1 NTW2 FD - Whole Structure Load (k.) Load (k.) Displacement (in.) Displacement (in.)

8 Hines Bridge ier Model Modeling of bridge piers based on sectional analysis Limited to cantilevers loaded at tip Results only at tip Assumes relationship between flexure and shear/ penetration Includes tension shifting term Comparison to Hines Model NTW1 WD - whole structure F-S-S Hines -15 Key Contributions erformance Based Engineering Developed simplified pushover model appropriate for routine design use Model separates contributions of flexure, shear, and penetration Established thresholds linking significant damage levels to local s Shear and Flexure Interaction revious researchers have reported a linear relationship between deformation components at tip of specimen Displacement due to Shear (in.) Observed relationship between measured deformations at top of 4th story attributed to flexure and shear at ramp peaks, specimen NTW Displacement due to Flexure (in.) Comparision of Bar Slip Models bar stress at loaded end (ksi) Zhao & Sritharan 27 2 Lowes & Altoontash 23 1 F-S-S integration model Bar slip due to penetration (in.) Evaluation of roposed Model NTW1 Web Direction Load capacity within 2% Overestimates drift capacity (exceptional case) NTW1 WD - first story NTW1 WD - whole structure

9 FEMA 356 model Modeling of flexure-controlled walls based on elastic flexural stiffness, yield moment, prescribed inelastic drift capacity Thought to be very conservative Load y Immediate Occupancy Life Safety Collapse revention Estimating slip Bar slip is found by integrating over anchorage length Simplified procedure Assume bond length constant regardless of applied bar stress Assume gradient constant over anchorage length More detailed model (i.e., Simplified model Lowes & Altoontash) < y > y < y > y.1 4%y s s s l a s l a.15 y/h Drift=/h Shear and Flexure Interaction erformance-based Design rofile of shear deformation similar to profile of rotation over height =C*or v =C* f Height (in.) Comparison of Curvature and Shear Strain Distributions at eak 52, 15% nominal yield displacement, 3 Shear Strain 25 Curvature*35 in Statistically-based expectation of seismic events Model of Structure erformance expectation for each design option Multiple design options Cost analysis over entire building life Shear Strain (in/in) or Curvature (1/in)*35 in. Recommendation to building owner 9