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Thomas Kang, Ph.D., P.E.(CA)Assistant Professor
University of Oklahoma
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 1 of 29
Introduction
Non-participating PT frames and lateral systems
Deformation compatibility checks for PT slabs
PT slab-column moment frames or dual systems
Summary
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 2 of 29
OKC Airport Parking Lot(Oklahoma City, OK)
One-way beams
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 3 of 29
Ulsan Park Polis(Ulsan, Korea)
T
Two-way slabs
Courtesy: K. Chung
Designed by: Dongyang
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 4 of 29
Introduction
Non-participating PT frames and lateral systems
Deformation compatibility checks for PT slabs
PT slab-column moment frames or dual systems
Summary
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 5 of 29
PT frames: not to resist lateral loads in high seismic regions
Lateral systems (SMRF or walls) designed for all lateral load resistance and stiffness
Deformation compatibility should be met for PT connections & frames
Kang and Wallace (2005)
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 6 of 29
Four seasons bldg., CA
Punching during Northridge EQ
Kang & Wallace (2006)
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 7 of 29
Ties @ 18” spacing (1971 San Fernando EQ) Spiral @ 3” pitch (1971 San Fernando EQ)
ΔDesign story drift ratio
NISEENISEE
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 8 of 29
RC drift limit(ACI 318‐08,S21.13.6)
PT drift limit(ACI 352R,Approved)
Minimum shear reinforcementis required per S21.13.6.
Shear reinforcementis not required.
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 9 of 29
Lateral stiffness (linear model)◦ Shell-type “plate” element (ETABS)◦ ACI 318-08, S8.8 and 10.10
Members Ultimate state
Beams 0.35EcIg
Columns 0.70EcIg
WallsUncracked 0.70EcIg
Cracked 0.35EcIg
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 10 of 29
Lateral stiffness (linear model) Δ = (δei+1 – δei)Cd / IE
as per ASCE 7-05(S12.8.6 & Fig. 12.8-2)
Based on past design experienceand verification by checking wall stresses (Shin et al, 2009)
Members Ultimate state
Beams 0.35EcIg
Columns 0.70EcIg
WallsUncracked 0.70EcIg
Cracked 0.35EcIg
Upper 7/8 ~ 5/6 of total height
Lower 1/8 ~ 1/6 of total height
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 11 of 29
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 12 of 29
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 13 of 29
Introduction
Non-participating PT frames and lateral systems
Deformation compatibility checks for PT slabs
PT slab-column moment frames or dual systems
Summary
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 14 of 29
◦ 1. Obtain Mu,unb at Δ from nonlinear analysis (S21.13.6(a))Also, use φ = 0.6 in φVn as per ACI 318-08, S9.3.4(b).
◦ 2. Drift capacity check (S21.13.6(b))φ = 0.75 in φVc
◦ 3. Limit analysis (PTI Building Design Committee)Get probable Mu,unb based on slab probable moment capacities
PT
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 15 of 29
Gravity loads Lateral loads
Interior Exterior Interior
M–u_RM+
u_L
Mu,unb ≈ 0
M–u_R
Mu,unb = M–u_R
M–pr_RM+
pr_L
probable Mu,unb
= M+pr_L + M–
pr_R
≈ 1.25(M+pr_L + M–
pr_R)
Vu,direct = Design direct (gravity) shear
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 16 of 29
Vo
=vu,direct bg
dcu,unb=v Mvγ
u,ecc Jc
probable Mu,unb = Mpr_L + Mpr_R
Direct shear and unbalanced moment transfer◦ Direct shear transfer (Vg)
◦ Eccentric shear transfer (γv Mu,unb)
◦ The 3rd option is to maximize Mu,unb
and use φ = 0.75 (per S9.3.4(a)).
M–pr_RM+
pr_L
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 17 of 29
ACI 318-08, S21.13.6 ◦ If deformation compatibility is not satisfied, or without
checking it, minimum shear reinforcement is required.
◦ As per ACI 352R(Avfy)/(sbo) ≥ 3.5√f’cs ≤ d/2First line at s/2
from the columnExtend at least 3h(note: 4h for RC)and so forth..
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 18 of 29
Introduction
Non-participating PT frames and lateral systems
Deformation compatibility checks for PT slabs
PT slab-column moment frames or dual systems
Summary
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 19 of 29
Dual systems of RC walls and slab-column framesor MWFRS (main wind-force-resisting systems)
Designed by: Rosenwasser/Grossman (not PT)
• Use dual systems: if slab-column frames take more than 25% of design seismic forces (0.25E)
• If not likely, design walls to resist 1.0E!
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 20 of 29
A linear lateral model should be built to obtain designforce and moment demands.
Reduced stiffnesses are used as per S8.8 and S10.10.4.1 of ACI 318 (at ultimate limit state).◦ Columns: 70% of EIg◦ PT slabs: ~50% of tributary slabs (vs. ~25% for RC slabs)
Factored gravity moments, lateral load moments, and secondary moments are compared with φMn.
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 21 of 29
2‐D equivalentframe
modeling
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 22 of 29
RC walls: Shell-type “plate” element0.35EIg (lower stories - cracked)0.7EIg (upper stories)
Link-beams, columns: Frame element0.35EIg (link beams - cracked)0.7EIg (columns - cracked)
PT slabs: Frame element0.5EIg (cracked - based on
research; Kang & Wallace, 2005)
Within frame elements: Membrane element with trivialstiffness (just to distribute tributary gravity loads to vertical elements)
Shin et al. (2009)
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 23 of 29
Based on various calibrations,
◦ Core wall dual systems: efficient in lateral resist.
◦ esp. for irregular shapes
◦ Adjust wall thickness (t) (as height up, t down)
◦ Stiffness modeling is appropriate…
Shin, Kang & Grossman (2009)
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 24 of 29
Should be determined separately.
Msec = Balanced loading induced moment – Mp
where Mp is the primary moment = P x eP is the effective post-tensioning forcee is the eccentricity; “positive” above c.g.c.
Then check Mu,grav + Mu,lat + Msec ≤ φMn per S18.10.3
PP
ωbal_1
ωbal_2
ωbal_3
Balanced loads
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 25 of 29
(PERFORM‐3D) modeled by Kang
If nonlinear PBEE analysis methods are used, dual system is allowed (SEAONC, 2007; LATBSDC, 2008)
Fiber wall elements (RC & CIP-PT), equivalent frame models (PT slabs), and lumped-plasticity at slab-beam ends, etc. [working using PERFORM-3D in collaboration with Tipping▪Mar and Arup-Los Angeles]
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 26 of 29
Introduction
Non-participating PT frames and lateral systems
Deformation compatibility checks for PT slabs
PT slab-column moment frames or dual systems
Summary
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 27 of 29
Non-participating PT slab-column frames ◦ Only deformation compatibility should be checked.◦ Design story drift of lateral systems is used.
Lateral-force-resisting PT slab-column frames◦ Linear lateral model should be built for design demands.◦ Reduced stiffness (considering cracking at ultimate states)◦ Mu,grav + Mu,lat + Msec ≤ φMn per S18.10.3 ◦ Msec is determined separately, or may be neglected if you
think it’s minor [and you know you’re neglecting].
2009 PTI Technical Conference Lateral Analysis and Design of PT Slab-Column Frames Thomas Kang, Ph.D., P.E.(CA)
© Copyright Post-Tensioning Institute all rights reserved. Page 28 of 29