Thomas Kang, Ph.D., P.E.(CA) Assistant Professor ... Convention... · Lateral stiffness (linear model) Shell-type “plate” element (ETABS) ACI 318-08, S8.8 and 10.10. Members

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



OKC Airport Parking Lot(Oklahoma City, OK)

One-way beams



Ulsan Park Polis(Ulsan, Korea)

T

Two-way slabs

Courtesy: K. Chung

Designed by: Dongyang



Introduction




Summary



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)



Four seasons bldg., CA

Punching during Northridge EQ

Kang & Wallace (2006)



Ties @ 18” spacing (1971 San Fernando EQ) Spiral @ 3” pitch (1971 San Fernando EQ)

ΔDesign story drift ratio

NISEENISEE



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.



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



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







Introduction




Summary



◦ 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



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



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



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..



Introduction




Summary



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!



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.



2‐D equivalentframe

modeling



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)



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)



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



(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]



Introduction




Summary



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].



Kang and Wallace (2005)Kang et al. (2006)

Punching during shake table tests

Punching during static tests



Documents

Thomas Kang, Ph.D., P.E.(CA) Assistant Professor ... Convention... · Lateral stiffness (linear model) Shell-type “plate” element (ETABS) ACI 318-08, S8.8 and 10.10. Members