Seismic Design Recommendations for PT Slab-Column Connections

Seismic Design Recommendations for PT Slab-Column Connections Thomas Kang, Ph.D., P.E. Assistant sta t Professor, Univ. of Oklahoma a Punching during Northridge EQ. (1994; Four Seasons Bldg., Sherman Oaks, CA) Localized damage in PT flat plate systems after shake table tests (Kang and Wallace, 2006) (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 1 of 35

PT Background and Efforts Education, Research, and Services PhD / Post-doc. UCLA, Currently teaching at OU PT Research Shake table tests & modeling of PT flat plate systems (Ph.D.) Cyclic tests of Isolated PT conn. (Post-doc.) Development of PT conn. design models (Post-doc. / Now with OU) Professional Services in PT Area Ed. Subcomm.: ACI 352.1R-XX (Seismic design of PT conn.) Ed. Subcomm.: ACI 369.R-XX (Modeling of PT conn. ASCE 41) Ed. Subcomm.: Practical design guide for PT bldg. (PTI BD) Recently joined ACI-ASCE ASCE 423 Comm. to serve. 2 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 2 of 35

PT Flat Plate Systems Very popular in North America, except for NYC As intermediate moment frames (w/ non-special B-C Cframes or bearing walls) As non-participating frames w/ core walls ATC 63: allows 30% lat. resistance by perimeter flat plates Longer span-to to-thickness thickness ratio Better seismic performance Easier to construct, and costly efficient (materials, time) Careful design consideration Short- and long-term cracking control Earthquake-resistant resistant design for PT connections 7 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 7 of 35

Non-participating frames Flexural design for gravity loads Punching shear design / lateral drift capacity check Moment transfer in flexure Intermediate t PT slab-column l connections Earthquake-resistant shear reinf. details 8 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 8 of 35

Tendon Layouts Gravity Analysis Banded in one dir., distributed in the other dir. If same loading & geometry, same A ps and ecc. for both layouts Flexure design for gravity loads 3D FE analysis (commercial software) commonly used As available Deals with irregular plans and secondary moments Hand cal. possible at least should re-check by hand 9 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 9 of 35

Hand Cal. / Check for Flexure Using design P, Pe, and service M grav & M sec Service M grav & M sec from FE software or per PTI manual Working stress check: at early age, just after PT σ = Pi Pe i + A c S M grav + S M sec Working stress check: at service loads σ = P A e c Pe e S + M grav + S M sec 10 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 10 of 35

Strength Check At ultimate Strength check: at ultimate (using design M grav & M sec ) M n d = Aps f ps p M u _ grav+ sec where f ps = a a + As f y d 2 2 f c fse + 10,000 + 300ρ Recent research (Kang and Wallace, 2008; PTI journal) revealed that f ps Eq. is conservative for PT slabs. f ps ps can be used at any location/section of PT members. Experimentally verified (shake table tests Kang and Wallace, 2008; PTI journal) p 11 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 11 of 35

) Strength Check At ultimate (Kang and Wallace, 2008; PTI journal) tendon stress (ksi Change in 35 30 25 20 15 10 5 0-5 + drift ratio: W direction (see Fig. 1) + change in tendon stress: Increase in tensile stress After Run 4 Δ = 22 ksi At peak lateral load LC3 (Run 4) 4.1 ksi (28.3 MPa) -5-4 -3-2 -1 0 1 2 3 4 5 Δ = 8-10 ksi @ 2% drift Mean Drift Ratio (%) 200 150 100 50 Δ = 12-15 ksi @ 3% drift 0 ress (MPa a) Ch hange in tendon st 12 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 12 of 35

Strength Check At ultimate (Kang and Wallace, 2008; PTI journal) tendon st tress (ksi) Change in 35 30 25 20 15 10 5 0 LC4 (Run 5) At peak lateral load Δ = 22 ksi 200 150 100 50 0 Ch hange in tendon str ress (MPa a) -5-5 -4-3 -2-1 0 1 2 3 4 5 Δ= 7-10 ksi @ 2% drift Mean Drift Ratio (%) Δ = 12-14 ksi @ 3% drift 13 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 13 of 35

Flexural design for gravity loads Punching shear design / lateral drift capacity check Moment transfer in flexure Intermediate PT slab-column connections Earthquake-resistant shear reinf. details 14 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 14 of 35

Drift-induced Punching of PT Conn. Pimanmas et al. (2004) Static, cyclic PT interior i Drift ratio at punching = 2% V ug φv c / φ = 0.5 Loading direction Kang and Wallace (2005; 2006; 2008) Dynamic, PT systems with shear reinforcement Drift ratio at punching = 4.5% V / φ = 0.33 ug V c 15 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 15 of 35

Drift-induced Punching of PT Conn. Loading Direction Han et al. (2006a) Static, cyclic PT interior i conn. Drift ratio at punching = 4% V / φ = 0.4 ug V c Han et al. (2006b) Static, cyclic PT exterior conn. Drift ratio at punching = 3.3% V / φ = 0.35 ug V c 16 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 16 of 35

Drift-induced Punching Stress-induced punching Shear Demand (V V u ) Drift-induced punching due to potential shear-strength degradation Shear Capac city (V n ) 0 1 2 3 4 5 Ductility (μ) 17 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 17 of 35

Connection Punching Shear Design First, punching design only for gravity loads without shear reinf. per ACI 318-08, Ch. 11 Deform. compatibility check (lateral drift capacity check) per ACI 318-08, S21.13.6 RC If design story drift ratio of the system > drift limit, min. shear reinf. should be provided per 21.13.6. V / φ ug V c 18 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 18 of 35

PT Connection Drift Limit Drift ratio at pu unching 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Lateral drift limit for RC Connections Best-fit line for Lateral drift limit for PT Connections RC interior RC without shear reinf. (Kang and Wallace, 2006) connections PT without t shear reinforcement without shear reinforcement Specimens with slab span -to-thickness ratio of 17 g Best-fit line for all PT connections without shear reinforcement 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Gravity shear ratio, (V u /φv c ) ACI 352.1R-XX (Kang et al., 2008; PTI journal) V / φ ug V c 19 PT RC (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 19 of 35

Design Story Drift Ratio Design story drift ratio of PT flat plate systems = that of SFRS (Special walls / SMRF) δ = 0. 7 u RΔ s, where R is for SFRS Should use UBC-97 to get δ u, according to ACI 318-08 S21.1; δ u = design drift expected for DBE Conservatively,, can use IBC-06 to get (Δ a /h x ) related to MCE ACI 318: Life-safety under DBE For collapse prevention under MCE Str. Integrity bars 20 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 20 of 35

ACI 318-08, S21.13.6(a) ALTERNATIVELY, Limit Analysis Max possible unb. moment, M unb = M n,slab + M + n,slab f ps M n,slab ; Plug M unb into Vu b d unb c Use φ = 0.60 (instead of 0.75) per S9.3.4 to account for shear strength degradation @ δ u v n o γ vm + J c 21 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 21 of 35

Shear Strength of PT Conn. ACI 318-08: PT Interior PT Exterior Conn. 09 0.9 0.8 (Kang et al., 2008; PTI journal) 2 ) (MPa 1/2 c / (f' c )1/2 v c 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Eq. (11-36) of ACI 318-05 Gravity loading tests (connections, frames) Eq. (11-33) Interior connections under lateral loads of ACI 318-05 Exterior conn. with banded PT under lateral loads Exterior conn. with distributed PT under lateral loads 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 f pc / (f' c ) 1/2 (MPa 1/2 ) 22 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 22 of 35

Shear Strength of PT Conn. ACI 352.1R-XX: PT Interior = PT Exterior Conn. V c = β pλ fc psi + 0.3 f pc bod + Vp, where β p 3.5 Kang et al. (2008); PTI Journal Higher (v( c + v s ) for PT conn. with any shear reinf. (incl. headed studs) than that for RC conn. V n = V V f c + s 8λ c psi b o d where V c 3 λ fc psi b o d 23 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 23 of 35

Flexural design for gravity loads Punching shear design / lateral drift capacity check Moment transfer in flexure Intermediate t PT slab-column l connections Earthquake-resistant shear reinf. details 24 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 24 of 35

γ M f unb in Effective Transfer Width No adjustment in γ f permitted by ACI 318 for PT conn. For banded layout, always OK For distributed layout, may not be OK with 1 or 2 tendons and bonded reinf. Based on the test data (Han et al., 2006a; 2006b), had NO problems for PT i.e., Effec. transfer width seems larger than c 2 + 3h (RC), possibly due to improved 3D integrity it by PT. 25 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 25 of 35

Non-participating frames Flexural design for gravity loads Punching shear design / lateral drift capacity check Moment transfer in flexure Intermediate PT slab-column connections Earthquake-resistant shear reinf. details 26 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 26 of 35

Lateral Analysis You may need to use different software Effective slab width method (ASCE 41, Chapter 6) αl 2 l 2 αβl 2 Dynamic tests (Kang and Wallace, 2005); α =070 0.70, β =2/3 l 1 2c + 1 1 3 l2 β = 1/2 Constant Interior bay (uni-axial shaking) ASCE 41 (2007);α α = or Design aid tables (Allen & Darvall, 1977) (vs. β = 1/3 for RC) 27 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 27 of 35

Linear Lateral Analysis 1.2DL + 1.6LL (no EQ) & 1.2DL + 0.5LL 1.0E per IBC-06 Col. per ACI 318-08, S10.10.4.1 07E 0.7E c I g Effec. slab width (αβ αβe c I slab lb slab lb ) based on ASCE 41 Also, ACI 318-08, S8.8, S10.10.4.1, R13.5.1.2, R21.2.2, R21.1.2 28 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 28 of 35

Flexure, Punching Shear Design Moment and shear demands due to design forces u v unb u + 0. 6 Design conn. such that i) & ii) per ACI 352.1R-XX v n V b d o γ M J c c V φv V u /φv c can be greater than 0.6, IF design drift ratio (δ u ) should not exceed the drift limit (S21.3.6.8). c 29 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 29 of 35

Flexural design for gravity loads Punching shear design / lateral drift capacity check Moment transfer in flexure Intermediate PT slab-column connections Earthquake-resistant shear reinf. details 30 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 30 of 35

EQ-Resistant Design of Shear Reinf. ACI 352.1R-XX (Kang et al., PTI Journal ) >3h = < = 2d < = 2 d < = s /2 should be located < = 0.75d between 0.5 dand 0.85d away from the column face 31 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 31 of 35

ACI 352.1R-XX Verified from static tests (Pilakoutas and Li, 2003) & seismic tests of RC conn. (Kang and Wallace, in-press) Shearbands l load [kn] Latera 60 40 20 0-20 Drift ratio [%] -8-6 -4-2 0 2 4 6 8 (a) C0 Conversion: 1 kn = 0.2248 kips Primary (CP) Secondary (LS) Drift ratio [%] -8-6 -4-2 0 2 4 6 8 (b) PS2.5 Primary (CP) Secondary (LS) 15 10 5 0-5 load [kips] Lateral -40-60 Secondary (LS) Primary (CP) a b Secondary Primary Experimental data FEMA 356 modeling curves (LS) (CP) c -10-15 -8-6 -4-2 0 2 4 6 8 Drift ratio [%] -8-6 -4-2 0 2 4 6 8 Drift ratio [%] Test specimen with thin plate stirrups (spacing = 2.5") 32 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 32 of 35

Str. Integrity (Collapse Prevention) New ACI 318-08, S18.12.6 & 18.12.7 Two tendons in both dir. or 2 tendons in one dir. + min. bottom reinforcing bars in two dir. A bit conservative ACI 352.1R-XX A sm = 0.5ωul1l 2 φ f y in each dir. 33 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 33 of 35

Non-participating S-C Frames Summary Deform. compatibility check (lateral drift check) or limit analysis Intermediate S-C Frames 2D linear lateral analysis Effec. slab width method Contact Information tkang@ou.edu http://www.cees.ou.edu edu PTI Journal (Kang and Wallace, 2008) PTI Journal (Kang et al., 2008) or after the session... 34 (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 34 of 35

train [μs] Micro St 1600 1200 800 RC 400 0-400 -800 red, line blue, dot -1200 RC-Run4-FL1NW (Top Bar Strains) C -1600 L 10 12 14 16 18 20 22 24 26 28 30 Time [sec] Questions? Thank you!! PT RC 35 PT (C) COPYRIGHT POST-TENSIONING INSTITUTE, ALL RIGHTS RESERVED Page 35 of 35