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Response Spectrum Concepts Seismic Design of Multistorey Concrete Structures Lecture 3 Response Spectrum & Ductility Course Instructor: Dr. Carlos E. Ventura, P.Eng. Department of Civil Engineering The University of British Columbia [email protected] Short Course for CSCE Calgary 2006 Annual Conference Instructor: Dr. C.E. Ventura Response Spectrum Concepts Seismic Design of Multistorey Concrete Structures No. 2 1 Instructor: Dr. C.E. Ventura SeismicSeismic HazardHazard soil Site conditions can have significant effect on response. Seismic Design of Multistorey Concrete Structures No. 3 Instructor: Dr. C.E. Ventura Linear Response of Structures • Single-degree-of-freedom oscillators W K T Wg 0.0 0.2 0.4 0.6 0.8 Vibration Period T = 2π time, sec K Seismic Design of Multistorey Concrete Structures No. 4 2 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 5 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 6 3 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 7 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 8 4 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 9 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 10 5 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 11 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 12 6 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 13 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 14 7 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 15 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 16 8 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 17 Instructor: Dr. C.E. Ventura Crustal Eq. vs Subduction Eq. 1000 1000 Max_Acceleration_Kobe = 587 cm/s 2 Max_Acceleration_Llayllay = 605 cm/s 2 500 500 0 0 Acceleration (cm/s/s) Acceleration 500 (cm/s/s) Acceleration 500 1000 1000 0 10203040506070 0 10203040506070 Time (s) Time (s) 100 100 Max_Velocity_Llayllay = 73 cm / s Max_Velocity_Kobe = 74 cm / s 50 50 0 0 Velocity (cm/s) 50 Velocity (cm/s) 50 100 100 0 10203040506070 0 10203040506070 Time (s) Time (s) 20 20 Max_Diplacement_Kobe = 20 cm Max_DiplacementLlayllay = 15 cm 10 10 0 0 Displacement (cm) Displacement 10 (cm) Displacement 10 20 20 0 10203040506070 0 10203040506070 Time (s) Time (s) SI_for_Llayllay = 81 SI_for_Kobe = 72 1995 Kobe eq. 1985 Chile eq. Seismic Design of Multistorey Concrete Structures No. 18 9 Instructor: Dr. C.E. Ventura Crustal Eq. vs Subduction Eq. SA spectra Spectral Acceleration (g) 2.5 2 1.5 SA (g) SA 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 T (sec) KOBE LLAYLLAY 5% damping Seismic Design of Multistorey Concrete Structures No. 19 Instructor: Dr. C.E. Ventura Crustal Eq. vs Subduction Eq. SV spectra SD spectra Spectral Velocity (cm/s) Spectral Displacement (cm/s) 300 60 250 50 200 40 150 30 SD (cm) SD SV (cm/s) 100 20 50 10 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0.5 1 1.5 2 2.5 3 3.5 4 T (sec) T (sec) KOBE KOBE LLAYLLAY LLAYLLAY 5% damping Seismic Design of Multistorey Concrete Structures No. 20 10 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 21 Instructor: Dr. C.E. Ventura Design Spectra • Acceleration response spectrum S is shown to the right. a • Displacement response Period, T spectrum can be calculated acceleration response spectrum assuming simple harmonic T motion using expression below: 0 Sd T 2 S = S g d 4π 2 a Period, T displacement response spectrum Seismic Design of Multistorey Concrete Structures No. 22 11 Instructor: Dr. C.E. Ventura Seismic Design of Multistorey Concrete Structures No. 23 Instructor: Dr. C.E. Ventura Effect of Period Change • Rehabilitation design requires an understanding T1 T2 S of how dynamic response a changes when the system is modified. Period, T • Change in period results in acceleration response spectrum change in response S amplitude. d Period, T displacement response spectrum Seismic Design of Multistorey Concrete Structures No. 24 12 Instructor: Dr. C.E. Ventura Effect of Damping Change • Damping dissipates S energy and reduces a response amplitude lower damping Period, T higher damping acceleration response spectrum Sd Period, T displacement response spectrum Seismic Design of Multistorey Concrete Structures No. 25 Instructor: Dr. C.E. Ventura Inelastic Response • Inelastic response reduces stiffness and W increases energy K dissipation. K K • Reduced stiffness e i equates to increased Shear effective period of vibration. • Energy dissipation equates to increased Displacement damping. Seismic Design of Multistorey Concrete Structures No. 26 13 Instructor: Dr. C.E. Ventura Inelastic Response W lower damping Sa K higher damping • Base shear is limited by strength. Period, T acceleration response spectrum • Displacements… T1 T2 – tend to increase due to period shift Sd – tend to decrease due to damping increase – Effects may cancel out (equal Period, T displacement rule) displacement response spectrum Seismic Design of Multistorey Concrete Structures No. 27 Instructor: Dr. C.E. Ventura Ductility Concepts Seismic Design of Multistorey Concrete Structures No. 28 14 Instructor: Dr. C.E. Ventura Ductility SDOF response: V m Ve k K ∆ 1 m ma ∆e ∆ V m Natural Period of Vibration: T = 2π K Seismic Design of Multistorey Concrete Structures No. 29 Instructor: Dr. C.E. Ventura ∆ m V Ve V e = R Vy Vy Force Reduction Factor ∆y ∆e ∆u ∆ ∆ Displacement u = µ Ductility ∆ ∆y Seismic Design of Multistorey Concrete Structures No. 30 15 Instructor: Dr. C.E. Ventura Equal displacement rule V (for structures with T>0.5s) Ve ∆u≈∆e This is not really a rule but simply an observation, however it forms the basis for much of seismic Vy design. If ∆u=∆e then R=µ∆ ∆ ∆y ∆e = ∆u Seismic Design of Multistorey Concrete Structures No. 31 Instructor: Dr. C.E. Ventura V For T<0.5s equal displacement rule does not hold Ve ∆u>∆e Equal energy rule is one often used Vy R=√(2 µ∆-1) but this is not good as the period gets very small and ∆y ∆e ∆u ∆ as the R value increases Seismic Design of Multistorey Concrete Structures No. 32 16 Instructor: Dr. C.E. Ventura Effect of Yielding on Maximum Displacement C1 is the ratio between inelastic and elastic responses (after FEMA 440) Seismic Design of Multistorey Concrete Structures No. 33 Instructor: Dr. C.E. Ventura (after FEMA 440) Seismic Design of Multistorey Concrete Structures No. 34 17 Instructor: Dr. C.E. Ventura Idealized Force-Deformation Relationship (after FEMA 440) Seismic Design of Multistorey Concrete Structures No. 35 Instructor: Dr. C.E. Ventura Strength, Strength Degradation & Stability (after FEMA 440) Seismic Design of Multistorey Concrete Structures No. 36 18 Instructor: Dr. C.E. Ventura Measures of ductility: 1. Displacement ductility – entire structure 2. Rotational ductility – member 3. Curvature ductility – section beam yields-forms ∆y ∆u plastic hinges Elastic Deformation Elastic+Plastic Deformation θp-plastic rotation Seismic Design of Multistorey Concrete Structures No. 37 Instructor: Dr. C.E. Ventura What’s ∆ ? SDOF ∆ majority of mass m Seismic Design of Multistorey Concrete Structures No. 38 19 Instructor: Dr. C.E. Ventura MDOF T<1s, uniform buildings Frame Building Shear Wall Building Linear y~ 0.64 H y ~ 0.77 H y ~ 0.67 H Seismic Design of Multistorey Concrete Structures No. 39 Instructor: Dr. C.E. Ventura θy My My 2L M M L θ = M My y y 3EI My My Ф θu= θy+ θp Seismic Design of Multistorey Concrete Structures No. 40 20 Instructor: Dr. C.E. Ventura Shear Wall ∆u= ∆p + ∆y ∆y Vy θ p µθ =1+ θ y θp What’s θy for shear wall? ∆ F My M 3 2 θy: θy y FL ML ∆ = = 3EI 3EI LL L θ ∆ ML θ = = L 3EI L Beams: θ = M y y M L 3EI M=F*L θ = y y 3EI Seismic Design of Multistorey Concrete Structures No. 41 Instructor: Dr. C.E. Ventura M Curvature ductility My φu φ p µφ = =1+ φ y φ y φy-well defined Фy Фu Ф φu, φp –difficult to estimate Фu=Фy+ Фp θ p φ p ≈ lp lp= length of plastic hinge, not well defined Seismic Design of Multistorey Concrete Structures No. 42 21 Instructor: Dr. C.E. Ventura Concrete sections Fy Wall Fy H θ θy p lp lp/2 W Фp=θp/lp lp = .08H + .022dbfy (m & MPa) for column and beam sections ≈ 0.5W Seismic Design of Multistorey Concrete Structures No. 43 Instructor: Dr. C.E. Ventura Strains In terms of performance strains are the most important parameter, especially in concrete. Unconfined concrete can take strains of 0.004 to 0.005 without failing, while confined concrete can go up to a strain of 0.010 or more µθ and µφ are not good general indicators of damage as the strains are dependent on the size of the member. θp is a better indicator of strains. Seismic Design of Multistorey Concrete Structures No. 44 22 Instructor: Dr. C.E. Ventura εs Strains M M Ф D d' C ε ε = ε +ε c c cy cp c = βD .1 < β < .2 c ' ε = ε . +φ .c d = γD 0.6 < γ < 0.9 c sy d ' p l = αD 0.5 <α <1 θ p φ = p p β β l p εc =εsy. +θ p. c c γ α εc = εsy. ' +θ p. d lp Seismic Design of Multistorey Concrete Structures No.
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