Structural Diaphragm Post-Tensioned Parking · PDF fileStructural Diaphragm Post-Tensioned...

Structural DiaphragmPost-Tensioned Parking Structure

PTI Conference 2010 Fort Worth, TX

Presented by:Rashid Ahmed, SE, PE

Walker Parking Consultants

May 4, 2010

Structural Diaphragm• Today’s presentation will include discussion on the

following topics:o Definitionso Diaphragm Classificationo Diaphragm Analysiso Diaphragm Design Forceso Load Combinations and Amplification Factorso Code and Detailing Requirementso Diaphragm Behavior with Sloped Ramp

Structural Diaphragm

DefinitionsDiaphragm ClassificationDiaphragm AnalysisDiaphragm Design ForcesLoad Combinations and Amplification FactorsCode and Detailing RequirementsDiaphragm Behavior with Sloped Ramp


DefinitionDiaphragms

• A diaphragm is defined in IBC 2006 and IBC 2009, section 1602.1 as, “A horizontal or sloped system acting to transmit forces to the vertical-resisting elements. When the term “diaphragm” is used, it shall include horizontal bracing systems.”

• Floor diaphragm serves as the horizontal element of the lateral load resisting system (LLRS), in which the primary (vertical plane) elements are typically shear walls or moment frames. Floor diaphragms serve both to connect the individual vertical elements to create the LLRS, and in the context of seismic design, transfer the inertial forces that develop in a seismic event.


Definition

Chord

• Chord is diaphragm boundary element perpendicular to the applied load to resist in-plane bending of the diaphragm. The term chord reinforcement refers to the reinforcement at opposing ends of the floor or floor segment.


DefinitionCollector

• Collector elements (also called drag struts or drag elements) collect and transfer diaphragm shear forces to the vertical lateral-force-resisting elements and distribute forces within a diaphragm.

• Collector reinforcement is designed to “collect” the diaphragm forces back to the primary elements of the LLRS (walls or frames).

• Shear reinforcement is designed to resist the in-plane diaphragm shear, analogous to “beam” shear.


Diaphragm Classification

ASCE 7-05, 12.3

• Flexible Diaphragm• Rigid Diaphragm• Semi Rigid Diaphragm



• Flexible Diaphragm (ASCE 7-05, 12.3.1.1)

oUntopped steel decking or wood structural panels when the vertical elements are braced frames, or non-wood shear walls

oUntopped steel decks or wood structural panels in one- and two-family residential buildings of light frame construction


Diaphragm Classification • Calculated Flexible Diaphragm (ASCE 7-05, 12.3.1.3)

o Computed maximum in-plane deflection of the diaphragm is more than twotimes the average story drift of adjoining vertical elements of the seismicforce resisting system. Loads shall be from the equivalent lateral force(ELF) method of section 12.8



• Rigid Diaphragm (ASCE 7-05, 12.3.1.2)oDiaphragms of concrete slabs or concrete filled metal deckoSpan-to-depth ratios of 3 or lessoStructures with no horizontal irregularities

• Semi Rigid Diaphragm (ASCE 7-05, 12.3.1)o If diaphragm cannot be idealized as flexible or rigid, per

ASCE 7-05, section 12.3.1.1, 12.3.1.2, or 12.3.1.3, the structural analysis must model the diaphragm as semi-rigid


Classification of Diaphragm Behavior

(a) Loading (b) Rigid Diaphragm behavior(c) Flexible diaphragm behavior(d) Semi rigid diaphragm behavior


Diaphragm Analysis

• The analysis of a Diaphragm under the influence of horizontal loads is performed assuming that the floor or roof deck behaves as a horizontal continuous beam supported by the vertical lateral load resisting elements.

Structural DiaphragmSeismic Force Distribution

ELF Vertical Distribution

∑=

=

=

n

i

kii

kxx

vx

vxx

hw

hwC

WhereVCF

1

,

Diaphragm Force Distribution

pxDSpi

pxDSpi

pxn

xii

n

xii

px

IwSFIwSF

ww

FF

2.0

4.0

min

max

≥

≤

=

∑

∑

=

=

Fpimin and Fpimax need not to be amplified by Ω0.

Ftop

F4

F3

F2

Fptop

FP4

Fp3

Fp2

0.1

0.1

>

=

=

otherlevel

Top

x

pxx F

F

γ

γ

γ

ASCE 7-05, Eq. 12.10-1

ASCE 7-05, Eq. 12.8-12

ASCE 7-05, Eq. 12.8-11

Scale Factors

Used for the design of verticalelements of LLRS (lateral loadresisting system)

Used for diaphragm design(chords, collectors, diaphragm shear and connections to vertical elements of LLRS)


Diaphragm Analysis

• Flexible Diaphragmo Distribution of horizontal forces to the vertical lateral load

resisting elements is independent of their relative stiffness.o The diaphragm deflection as compared to that of the vertical

lateral load resisting elements will be significantly large.

• Rigid Diaphragm Analysiso Distribute the horizontal forces to the vertical lateral load

resisting elements in proportion to their relative stiffnesso Diaphragm deflection when compared to that of the vertical

lateral load resisting elements will be insignificant.


Diaphragm Analysis

• Semi Rigid Diaphragm Analysiso Complex analysis and such analysis should account for the

relative rigidity of all structural elements.o ASCE 7-05 requires structural analysis to explicitly include the

actual diaphragm stiffness.

Structural Diaphragm Chord Design

• Calculate the moment based on the beam model. For non-flexible diaphragm, the diaphragm loading may not be uniformly distributed load but trapezoidal distributed load, based on relative rigidity of LLRS and accidental torsion (see the figure below).

• Calculate the tension and compression by dividing the moment by the diaphragm depth.

2w1wxf xpx ff γ=

L

LR RR

RL RRLww+=

+

221 Equation (1)

RL and RR are known values

Sum moment about the right support

( ) ( ) LRLLwwLLw L=

−+

321

2 121 Equation (2)

Solve Equations (1) and (2) for w1 and w2

Figure: Rigid diaphragm


Collector Design• Traditional Collector Design – Discrete full-depth collector beams that

receive shear from the diaphragm along their entire length are provided in line with their associated vertical LLRS

• Alternate Collector Design (2008 SEAOC Blue Book, article 05.02.030):Part of the seismic load is resisted by reinforcement directly in line with the shear wall, which transfers the force directly to the end of the shear wall. The balance of seismic force is resisted by reinforcing bars placed along the sides of the wall and uses the slab shear-friction capacity at the wall-to-slab interface to transfer seismic forces to the wall

Perspective View of Wall and Connector Diaphragm Segment Plan

Diaphragm Segment Reinforcement

Perspective View of Wall and Connector


Load Combinations and Amplification Factors

Seismic Design

Category SDC

Basic Seismic

Load Combinations

ASCE 7-05

12.4.2.3

Over-strength

Factor ( Ωo )

ASCE 7-05 12.4.3.2

Redundancy

Factor ρ

ASCE 7-05 12.10.1.1 &

12.3.4

25% Increase in Forces Due

to Irregularities

ASCE 7-05

12.3.3.4

Torsional

Amplification Factor

ASCE 7-05

12.8.4.3

A & B

C

D and higher

(SDC = D and higher) ACI 318-08 Section No.

Structural Diaphragm Reinforcement• Bonded tendons used as reinforcement to resist collector forces or diaphragm shear or flexural

tension shall be proportioned such that the stress due to design earthquake forces does not exceed 60,000 psi.

• Precompression from unbonded tendons shall be permitted to resist diaphragm design forces if a seismic load path is provided.

21.11.7.2

All reinforcement used to resist collector forces, diaphragm shear, or flexural tension shall be developed or spliced for fy in tension.

21.11.7.3

Collector elements with compressive stresses exceeding 0.2f ′cat any section shall have transverse reinforcement satisfying 21.9.6.4(c) over the length of the element. The specified transverse reinforcement is permitted to be discontinued at a section where the calculated compressive stress is less than 0.15f ′c

Where design forces have been amplified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit of 0.2f ′cshall be increased to 0.5f ′c , and the limit of 0.15f ′cshall be increased to 0.4f ′c .

21.11.7.5

Longitudinal reinforcement for collector elements at splices and anchorage zones shall have either:•A minimum center-to-center spacing of three longitudinal bar diameters, but not less than 1-1/2 in., and a minimum concrete clear cover of two and one-half longitudinal bar diameters, but not less than 2 in.; or•Transverse reinforcement as required by 11.4.6.3, except as required in 21.11.7.5.

21.11.7.6


Code Requirements


Code Requirements(SDC = D and higher) ACI 318-08

Section No.

Flexural strengthDiaphragms and portions of diaphragms shall be designed for flexure in accordance with 10.2 and 10.3 except that the nonlinear distribution of strain requirements of 10.2.2 for deep beams need not apply. The effects of openings shall be considered.

21.11.8

Shear strength Vn of structural diaphragms shall not exceed

Vn = Acv(2λ√f ′c + ρt fy)

21.11.9.1

Vn of structural diaphragms shall not exceed 8Acv √f ′c 21.11.9.2

Construction jointsAll construction joints in diaphragms shall conform to 6.4 and contact surfaces shall be roughened as in 11.6.9.

21.11.10

Structural DiaphragmReinforcement Requirements for Chords and Collectors

at Splice and Anchorage Zones Ld per ACI 318

Collector reinforcement Collector reinforcement (typ.)

Per ACI 318-08, 11.4.6.3 for compressive stress < 0.15f’c

Per ACI 318-08, 21.11.7.5 for compressive stress > 0.20f’c

s ≥3db1 ½”2.5db

2”cover ≥

3db1 ½”s ≥

db (typ.)

Other reinforcement not shown for clarity

Section A-A – Chord Reinforcement Section B-B

Splice per ACI 318

A

A

B BChord reinforcement

Shear reinforcing(typ.)

Shear reinforcing

Structural DiaphragmComputer Simulation of 3-Bay Parking Structure

Two-story parking structure, with four exterior shear walls in y-direction and two walls in x-direction (along the ramp).

Shear Wallsin y-direction

Shear Wallsin x-direction

Ramp

Lateral force1.26 kips/joint

Structure size292’ long x 180’ wideX-direction: 2 end bays @ 38’ and6 interior bays @ 36’Y-direction: 3 bays @ 60’Load calculationAssume 20 psf wind load,10’-6” story heightTherefore, Windward pressure at each tier= 20 psf x 10.5 ft = 210 plfFloor mesh: 6’ x 6’ Convert the line load to point load at each joint,210 plf x 6’ = 1.26 kips/joint

Structural Diaphragm3-Bay Parking Structure (cont.)- with Ramp Modeled

Observations:1.When there is a ramp in the middle bay, the lateral load is resisted primarily by the floor portion directly hit by the applied load, such as wind load. The floor on the other side of the opening is lightly engaged. 2.Deformation Ratio: ∆A : ∆B = 4 : 13.For seismic load, the lateral deformation is based on inertial load of each bays considering the ramp cavity.

Y-direction deformation:≈ - 0.0185 in

Y-direction deformation:≈ - 0.0047 in

A

B

Structural Diaphragm3-Bay Parking Structure (cont.)- without Ramp Modeled

Observations:1.No matter whether the ramp is modeled or not, the lateral load is resisted primarily by the floor portion directly hit by the applied load, such as wind load. The floor on the other side of the opening is lightly engaged. 2.The ramp helps reduce the deformation difference of the two floor portions, although the effect is not significant. 3.Deformation Ratio: ∆A : ∆B = 5 : 1

Y-direction deformation:≈ - 0.0201 in. > - 0.0185 in (with ramp modeled)

Y-direction deformation:≈ - 0.0039 in. < - 0.0047 in

(with ramp modeled)

A

B

Structural DiaphragmComputer Simulation of 4-Bay Parking Structure

Two-story parking structure, with four exterior shear walls in y-direction and two walls in x-direction (along the ramp).

Shear Wallsin y-direction

Shear Wallsin x-direction

Ramp

Lateral force1.26 kips/joint(subjected to thesame load as the 3-bay structure)

Structure size292’ long x 240’ wideX-direction: 2 end bays @ 38’ and6 interior bays @ 36’Y-direction: 4 bays @ 60’

Structural Diaphragm4-Bay Parking Structure (cont.)

Observations:1.When there are intersecting ramps between the flat floor portions (as shown), the lateral load is resisted primarily by the floor directly hit by the applied load, such as wind load. The floor on the other side of the opening is lightly engaged. 2. Deformation Ratio: ∆A : ∆B = 3 : 1

Y-direction deformation:≈ - 0.0153 in.

Y-direction deformation:≈ - 0.0048 in. ,



Intersecting ramps

Structural DiaphragmDesign Recommendation for Parking Structure with Sloped Ramp

Wind Load Wind Pressure (Windward)

Wind Pressure (Leeward)

Shear Wall

Section A

Section B

Section C

Ramp

DA

DC

DB

T T

Chord reinforcementbased on maximumT value

Chord Reinforcement:Section ATA = CA = Mu (due to windward pressure) / Depth of Section A onlyTA = CA = Mu / (0.95DA)

Section CTC = CC = Mu (due to leeward pressure) / Depth of Section C onlyTC = CC = Mu / (0.95DC)

Use maximum value of TA , TB & TC , and provide chord reinforcement based on maximum T in all the bays.

C C

T T

C C

Structural DiaphragmDesign Recommendation for Parking Structure with Sloped Ramp

Seismic Load Fpx

Shear Wall Ramp

DA

DC

DB

T T

Chord reinforcementbased on maximumT value

Chord Reinforcement:1.Calculate Mu based on Fpx at the floor2.Divide Mu by the contribution of Mass A, B and C. If Mass A, B and C are equal, then divide Mu by 3 (i.e., MuA = MuB = MuC = Mu/3). 3.Determine chord reinforcement required for each floor section.

TA = CA = MuA / Depth of Section A = MuA / (0.95DA)TB = CB = MuB / Depth of Section B = MuB / (0.95DB)TC = CC = MuC / Depth of Section C = MuC / (0.95DC)

Use maximum value of TA , TB & TC and provide chord reinforcement based on maximum T in all the bays.

C C

T T

C C

Section A

Section B

Section C


Summary• Today’s presentation covered discussion on the

following topics:o Definitionso Diaphragm Classificationo Diaphragm Analysiso Diaphragm Design Forceso Load Combinations and Amplification Factorso Code and Detailing Requirementso Diaphragm Behavior with Sloped Ramp

Questions and Comments?

Thanks

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