Floor diaphragms, collectors, and podium and backstay effects in tall buildings

April 2008Joe Maffei

RUTHERFORD & CHEKENE

OutlineDesign approach using NLRH analysis

Diaphragm forces and design

Collector design

Podium and backstay effects

Stiffness assumptions

Design approach using nonlinear response-history analysis

Two-stage designDetermine the strengths at hinging locations using the building code requirements

• Code (DBE) level earthquake ÷

R factor

• Minimum base shear

All other actions are designed to remain elastic under MCE level ground motions:

• Wall shear, shear friction, wall flexure outside of intended yield locations, floor and roof diaphragms and collectors and connections, foundation perimeter walls, foundations, etc.

• Check drift limits

Cantilever wall

Plastic hinge location

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Capacity Design: Engineer designs where and how nonlinear response will occur.

Coupled wall

Plastic hinge locations

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Protect against shear failure

Prevent yielding outside of intended hinge location

Prevent sliding shear failure

BASE

13th

ROOF

Buckling- restrained

braces

Floor and roof diaphragm forces and design

Diaphragm design forces (prescriptive)

Story force/weight

Story shear Diaphragm formula (UBC equation 33-1)

Minimum Maximum

Diaphragm design forces

Story force/weight

Minimum diaphragm forces (0.5Ca Iwpx ) can govern for buildings with longer period and/or higher R factor.

Minimum

Story force/weight

Minimum

Collector design forces (prescriptive)Based on Ω0

-magnified earthquake forces. (Ω0

typically equals 2 to 3)

Story force/weight

Collector design forcesFor non-prescriptive approach, use NLRH results for diaphragms and collectors.

Can reinforcement that is provided for slab gravity moments be used for diaphragm or collector forces?

Can use:

excess portion of reinforcement at slab tension surface, plus

equal amount of reinforcement at slab compression surface.

T

C

Collector design

Distribution of forces along a collector line

Diaphragm inertia force (x Ω0

) = 16 kips/ft

Wall reaction = 560 kips

560 kips

Distribution of forces along a collector line

Wall reaction = 560 kips

Assumed uniform diaphragm shear of 7 k/ft

Unnecessarily large

420 kip collector force

140560

Distribution of forces along a collector line

Wall reaction = 560 kips

160 kip collector force

20 k/ft shear transfer

Must check the entire seismic force path through the diaphragm.

160 kip collector force

20 k/ft shear transfer

1. Provide collector for 160 kips 2. Check shear-friction transfer for 20 k/ft 3. Check diaphragm capacity for 20 k/ft

Wall reaction = 560 kips

160 kip collector force

400 kips

4. Provide slab collector bars for 400 kips. 5. Provide bars for diaphragm moment.

400 kip collector force

Strut and tie model

(ACI appendix)

400

400

110

60 160

400

160

100 100290290 34012

0

560 560

155

85

566

400

Podium and backstay effects

BRACKET STIFFNESS ASSUMPTIONS AT BASE

Upper-bound backstay

Lower-bound backstay

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1521 Second Avenue, Seattle

7-story property line walls in one direction

Olivian

Stiffness assumptions

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UCSD Wall Elastic ETABS Model

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

-17.5 -12.5 -7.5 -2.5 2.5 7.5 12.5 17.5

Roof Displacement [in]

Base

Mom

ent [

kip-

ft]Experimental results

EQ4: Non-linear

EQ3: Essentially

linear

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EQ3

-8

-6

-4

-2

0

2

4

6

8

40 45 50 55 60

Time [s]

Roo

f Dis

plac

emen

t [in

]

UCSD TestETABS

Wall: Eeff = 0.2Ec

Slab: Eeff = 0.1Ec

SummaryUse NLRH analysis to directly obtain diaphragm and collector forces.

Define rational collector force paths.

Bracket stiffness assumptions for the backstay effect.

Concrete elements are not as stiff as you think.