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Lecture 10 Urm Out Of Plane Walls Part 2

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Dan Abrams + Magenes Course on Masonry

Dan Abrams + Magenes Course on Masonry


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  • 1. Seismic Design and Assessment of Seismic Design and Assessment of Masonry Structures Masonry Structures Lesson 10a: Response and Analysis of Out-of-Plane URM Walls, Part 2 Notes Prepared by: Daniel P. Abrams Willett Professor of Civil Engineering University of Illinois at Urbana-Champaign October 26, 2004 Masonry Structures, lesson 10a slide 1 Influence of Diaphragm Flexibility on the Out-of-Plane Dynamic Response of Unreinforced Masonry Walls PhD Dissertation by Can C. Simsir September 17, 2004 Department of Civil & Environmental Engineering University of Illinois at Urbana-Champaign Masonry Structures, lesson 10a slide 2
  • 2. Motivation Out-of-plane failure, rather than in-plane failure, of URM walls is considered the main cause of personal injury and loss of life. 1886 Charleston 1994 Northridge 1976 Tangshan 2001 Nisqually Masonry Structures, lesson 10a slide 3 Motivation Central and Eastern US • Attenuation rates are low Consequences • URM buildings are common can be catastrophic • Seismic loads were not considered in design Essential facilities inventory by S. French & R. Olshansky Western US • Earthquakes are frequent • Large numbers of pre-1933 URM buildings remain • Historic URM buildings are preserved Structures, lesson 10a slide 4 Masonry
  • 3. Objectives • Examine stability of URM bearing walls connected to flexible floor diaphragm and subjected to seismic input. • Develop dynamic stability analysis tools to compute response of URM out-of-plane walls. • Establish the factors and their effect on out-of-plane response of URM walls. • Develop recommendations for treating URM wall stability. Masonry Structures, lesson 10a slide 5 Research Scope • Perform shake table tests on URM out-of-plane walls as part of an idealized building. • Develop analytical tools (linear and nonlinear dynamic stability models): • RSA • SDOF • MDOF • 2DOF • Perform parametric studies. • Evaluate seismic guidelines, confirm or develop recommendations. Masonry Structures, lesson 10a slide 6
  • 4. Test Specimen Masonry Structures, lesson 10a slide 7 Connection Details Masonry Structures, lesson 10a slide 8
  • 5. Material Tests Out-of-plane walls: • Unit block compression tests • Mortar (Type O) compression tests • Masonry prism tests • Masonry flexural tension and bond wrench tests In-plane walls: • Mortar (Type S) compression tests • Masonry prism tests • Grout compression tests • Steel reinforcement tension tests Masonry Structures, lesson 10a slide 9 Shake Table Tests Run Record PGA Diaphragm Peak Drift Ratio of Number Name (g) Type the out-of-plane wall 1 0.06 0.05% . . . Nahanni Stiff 12 1.17 0.74% 13 0.39 0.28% . . . Big Bear Stiff 16 1.20 0.96% 17 0.13 0.62% . . . Big Bear Flexible 20 1.08 3.38% 21* 0.13 0.72% Big Bear Flexible 22* 0.37 collapse Masonry Structures, lesson 10a slide 10 * reduced gravity load, increased wall mass
  • 6. Shake table tests + frequency sweep and free vibration tests 1985 Nahanni Ground Acceleration History 1985 Nahanni Response Spectrum 1.2 RUN 1 12 1.4% damping 5 0.8 4 Sd (in) Ground Acceleration (g) 0.4 3 0 2 -0.4 1 -0.8 Spa (g) 0 -1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 4 8 12 16 20 Time (sec) STIFF Period (s) scaled in time 1992 Big Bear Ground Acceleration History 1992 Big Bear Response Spectrum RUN 13 16 17 20 1.4% damping 0.6 5 0.4 4 Ground Acceleration (g) 0.2 3 0 Sd (in) 2 -0.2 1 -0.4 Spa (g) -0.6 0 0 4 8 12 16 20 Masonry Structures, lesson 10a slide0.8 Period (s) 1 11 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (sec) STIFF FLEXIBLE Test Observations • 7th run: – Bedjoint cracking at the base of the out-of-plane wall. • 15th run: – In-plane walls yielded, sustained diagonal shear cracks. • 20th run: 20th run: 2.0 × PGABig Bear= 1.08g – Out-of-plane rocking about the cracked bedjoint at the base – Flexible diaphragm (steel beam) yielded – No mid-height cracks – No collapse – Peak drift ratio=3.4% Masonry Structures, lesson 10a slide 12
  • 7. Test Results Displacement Response History of Out-of-Plane Wall During Run 20 Mid-height displacements 80 top of wall mid-height of wall are in phase with the 60 40 displacements at the top. Displacement (mm) 20 0 -20 Comparison of Displacements During the 20th Run -40 40 -60 Displacement (mm) at Mid-height 30 -80 2 7 12 17 22 20 Time (s) of the Wall 10 0 -10 -20 Mid-height displacements are -30 ~½ of the displacements at -40 -80 -60 -40 -20 0 20 40 60 80 the top: Rigid-body rocking Displacement (mm) at the Top of the Wall Masonry Structures, lesson 10a slide 13 Test Observations 22nd run: 0.67 × PGABig Bear= 0.37g Gravity load on walls reduced by 46% Masonry Structures, lesson 10a slide 14
  • 8. Test Observations Masonry Structures, lesson 10a slide 15 Test Results Masonry Structures, lesson 10a slide 16
  • 9. Test Results • Peak accelerations were similar at the top and mid-height of the out-of-plane walls, and up to 4.5 times the peak base accelerations. • Diaphragm flexibility significantly increased (up to 5 times) the out-of-plane displacement response, but not the acceleration response. • Diaphragm flexibility significantly increased displacement (~7 times) and acceleration (~2 times) amplifications of diaphragm mid-span w.r.t. in-plane wall tops. Masonry Structures, lesson 10a slide 17 Models for Dynamic Stability Analysis 1. Response Spectrum Analysis (RSA) Linear elastic response spectra were computed from recorded table acceleration histories. 5 4.5 4 Pseudo Spectral Acceleration (g) 3.5 3 2.5 2.36 g 2 1.5 Floor diaphragm period was the 1 0.5 dominant period of vibration 0.41 s 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (SDOF assumption). Period (s) Masonry Structures, lesson 10a slide 18
  • 10. 1. Response Spectrum Analysis (RSA) 4 Computed Sd Good correlation verified Measured (West Wall Top) 3.5 3 that the response of the 2.5 out-of-plane walls was Displacement (in) associated with the change 2 in the period of vibration 1.5 1 0.5 of the flexible diaphragm. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Dynamic Test Run Discrepancy between computed and measured results may be attributed to the use of: • smaller than true viscous damping ratios. • elastic response spectra as opposed to inelastic spectra. Masonry Structures, lesson 10a slide 19 2. Single-degree-of-freedom (SDOF) Model 2k w k d kT = 2k w + k d kT Wall is assumed strong and rigid as it freely h rotates about its base. u g (t ) && Masonry Structures, lesson 10a slide 20
  • 11. 2. Single-degree-of-freedom (SDOF) Model Generalized SDOF response: ⎛ 2 ⎞ ⎛ md g mw g ⎞ ⎜ m d + m w ⎟ u (t ) + (c ) u (t ) + ⎜ k T − && & − ⎟ u (t ) = −(m d + m w ) u g (t ) && ⎝ 3 ⎠ ⎝ h h ⎠ Bilinear model was based on measured values of mass, damping, and stiffness. Masonry Structures, lesson 10a slide 21 2. Single-degree-of-freedom (SDOF) Model 4 Computed (SDOF) Computed (modified SDOF) 3.5 Computed Sd (RSA) SDOF model was more Measured (out-of-plane wall top) 3 accurate than the RSA 2.5 and the modified SDOF Displacement (in) 2 models. 1.5 1 Modified SDOF (similar to 0.5 RSA): kT was calculated 0 based on measured T. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Dynamic Test Run Displacement and acceleration responses were computed with reasonable accuracy using the nonlinear SDOF system subjected to the measured table excitations. Masonry Structures, lesson 10a slide 22
  • 12. 3. Multi-degree-of-freedom (MDOF) Model MDOF model computes out-of-plane wall response and considers bedjoint cracks developing along the wall under combined bending moments and axial forces. Location (or eccentricity) of the two fibers was determined by considering the stiffness and strength of the whole cross- section of the wall under combined bending moments and axial forces. Masonry Structures, lesson 10a slide 23 3. Multi-degree-of-freedom (MDOF) Model F (kips) kw and kd: Fd/2=16.0 STIFF Bilinear springs with inelastic unloading. kd/2=15.1 k/in ∆ (in) Blocks: -16.0 Linear elastic beam-column elements that F (kips) ignore shear deformations and are rigid at Fd/2=3.54 0.694 k/in FLEXIBLE the interface with the mortar bedjoint. kd/2=1.83 k/in ∆ (in) Fiber element: -3.54 Mortar and block-mortar interface lumped into one element (simplified Stress, f (psi) micro-modeling). fc=704 Bilinear tensile behavior (per the ½fc Fictitious Crack Model) with inelastic Unloading 1.25E-3 2.5E-4 Strain unloading and no stiffness degradation. 1.7 0.01 1.0 ft=17 Masonry Structures, lesson 10a slide 24
  • 13. 3. Multi-Degree-of-Freedom (MDOF) Model MDOF model response compared very well with the measured out-of-plane wall response. Static pushover analyses of the out-of-plane wall with the MDOF model were used in the development of the 2DOF model. Simulations with the MDOF model were also used in the parametric studies. Masonry Structures, lesson 10a slide 25 4. Two-degree-of-freedom (2DOF) Model Two rigid wall segments are connected by bilinear rotational springs. Wd k3 q1 and q2 are the two DOF. h/6 h/3 Ww/3 h/6 q2 Model considers a known k2 failure mechanism. h/3 Hinge location is based on 2h/3 2Ww/3 experimental and analytical results. h/3 q1 k1 Masonry Structures, lesson 10a slide 26
  • 14. 4. Two-degree-of-freedom (2DOF) Model k1 and k2 are determined from 0.12 post-cracked static moment- 0.1 from MDOF model rotation relationships of the two 0.08 Force (kips) semi-rigid wall segments. 0.06 0.04 Wd F 0.02 M Ww /3 0 h/3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Displacement (in) Mmax F F 3 M max = Ww t (1 + 3Ψ ) W d +W w/3 2 2h/3 3t ⎡1 + 3Ψ ⎤ 2W w/3 q 2 max = h ⎢1 + 6Ψ ⎥ ⎣ ⎦ q 2 3 qmax/9 qmax M max = Wwt (1 + Ψ ) t 3 2 F 3t Ψ=Wd/Ww q max = Masonry Structures, 1lesson 10a slide 27 W d+W w 2h 4. Two-Degree-of-Freedom (2DOF) Model Run 22 Measured response was simulated well, especially during the post-cracked stage. Compared to MDOF model, 2DOF: • is a less complicated nonlinear dynamic model with fewer DOF. • has a shorter computing time. 2DOF model successfully integrates URM wall behavior with flexible diaphragm with the semi-rigid-body dynamics while considering the failure mechanism. Masonry Structures, lesson 10a slide 28
  • 15. Parametric Studies 720 simulations were performed with the MDOF model. Out-of-plane wall in the simulations was composed of full-scale normal-weight masonry units. Parameters: h/t Unit n P/A e/t L/b aV Ground motion weight (stories) (psi) records 10.5 Concrete 1 10 0 2.0 No Nahanni (intra-plate) 15.7 hollow 2 20 0.25 2.5 Yes Big Bear (SD) 21.0 block or 3 30 0.50 3.0 Valparaiso (LD) 26.2 clay solid 4 40 Loma Prieta (FD) 31.5 brick 5 50 Determined not to have Not considered a significant effect on in the ABK tests Masonry Structures, lesson 10a slide 29 URM wall stability 1980s h/t ratios αug(t) ABK In ABK tests: Joint Venture • e/t, aV were not considered. Basis for • Diaphragm flexibility was not ug(t) h/t values in considered by a nonlinear element. FEMA 356 The allowable h/t ratios in FEMA 310 (1998) Regions of Moderate Regions of High Seismicity Seismicity Sx1 > 0.3g or Sxs > 0.75g 0.1g < Sx1< 0.3g or with crosswalls without crosswalls 0.25g < Sxs< 0.75g Walls of one story buildings 16 16 13 First story walls of 18 16 15 multistory buildings Walls in top story of 14 14 9 multistory buildings All other walls 16 16 13 Parapet walls 2.5 1.5 1.5 • Given h/t ratios are somewhat conservative. • Presence of cross walls may not necessarily increase stability of walls. • Other parameters are influential too. Masonry Structures, lesson 10a slide 30 • SDOF, MDOF, 2DOF are introduced for stability check.
  • 16. Story Drift Levels Tests: Except for cracking at the base, walls were undamaged at 3.4% drift. Parametric studies: Walls were stable at 3.8% drift. Slight damage observed would correspond to an IO performance level, when such large story drifts would imply LS or CP demand levels. Masonry Structures, lesson 10a slide 31 Floor Anchorage • Proper anchorage of URM wall to floor diaphragm should be the first step in retrofitting the wall to mitigate out-of-plane failure. • Diaphragm-wall connections with pockets in the wall for diaphragm joist seating are encouraged to minimize e/t of axial compressive force on the wall. • Force demands on walls with stiffer flexible diaphragms will be greater than on those with more flexible diaphragms; a distinction not made in the current seismic guidelines. FEMA 356 coefficient χ for calculation of out-of-plane wall forces Structural Performance Level Flexible Diaphragms Other Diaphragms Collapse Prevention 0.9 0.3 Life Safety 1.2 0.4 Immediate Occupancy 1.8 0.6 Masonry Structures, lesson 10a slide 32
  • 17. Conclusions • Unlike shear walls, nonlinear response of a URM out-of-plane wall is governed by rocking, not by f’m. Geometry and boundary conditions of the wall are important rather than type and strength of masonry. • Nonlinear rocking provides a reserve of capacity over that calculated using conventional methods. • Proper anchorage of wall to diaphragm is the first step in retrofitting a URM out-of-plane wall to prevent sliding or pullout. • A moderate increase in axial compressive stress in a URM building is beneficial to the stability of out-of-plane walls. Masonry Structures, lesson 10a slide 33 Conclusions • Eccentricity of floor diaphragm should be kept at a minimum for dynamic stability of out-of-plane walls. Pockets may be introduced in the wall to minimize eccentricity of diaphragm joist seating. • Flexible diaphragms reduce in-plane forces on shear walls at the cost of driving out-of-plane displacement response higher. • Out-of-plane walls with flexible diaphragms can have large displacement demands but they remain stable if proper anchorage is provided. Stiffer diaphragms induce larger force demands on the walls, which are then likely to lose their stability. • A diaphragm stiffened for seismic rehabilitation can induce instability in a previously stable out-of-plane wall; dynamic stability of the wall should be re-evaluated. Masonry Structures, lesson 10a slide 34
  • 18. Conclusions • Allowable h/t ratios can be increased from 16 or 20 to as much as 31 for low intensity ground accelerations. Influence of other parameters on wall stability needs to be addressed in the guidelines. • The effect of vertical accelerations can be significant on stability of URM walls under large axial stresses. • General trends discussed so far remain the same for different earthquakes: A wall with a smaller h/t ratio, larger concentric axial stress and larger diaphragm aspect ratio is more likely to maintain its stability for a given ground motion. • Results of the parametric studies as well as the analytical models that were developed can be used as tools for dynamic stability analysis of URM out-of-plane walls. Masonry Structures, lesson 10a slide 35