Structural Diaphragm Post-Tensioned Parking Structure

Transcription

1 Post-Tensioned Parking Structure PTI Conference 2010 Fort Worth, TX Presented by: Rashid Ahmed, SE, PE Walker Parking Consultants May 4, 2010

2 Today s presentation will include discussion on the following topics: o Definitions o Diaphragm Classification o Diaphragm Analysis o Diaphragm Design Forces o Load Combinations and Amplification Factors o Code and Detailing Requirements o Diaphragm Behavior with Sloped Ramp

3 Definitions Diaphragm Classification Diaphragm Analysis Diaphragm Design Forces Load Combinations and Amplification Factors Code and Detailing Requirements Diaphragm Behavior with Sloped Ramp

4 Diaphragms Definition A diaphragm is defined in IBC 2006 and IBC 2009, section 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.

5 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.

6 Collector Definition 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.

7 Definitions Diaphragm Classification Diaphragm Analysis Diaphragm Design Forces Load Combinations and Amplification Factors Code and Detailing Requirements Diaphragm Behavior with Sloped Ramp

8 Diaphragm Classification ASCE 7-05, 12.3 Flexible Diaphragm Rigid Diaphragm Semi Rigid Diaphragm

9 Diaphragm Classification Flexible Diaphragm (ASCE 7-05, ) o Untopped steel decking or wood structural panels when the vertical elements are braced frames, or non-wood shear walls o Untopped steel decks or wood structural panels in one- and two-family residential buildings of light frame construction

10 Diaphragm Classification Calculated Flexible Diaphragm (ASCE 7-05, ) o Computed maximum in-plane deflection of the diaphragm is more than two times the average story drift of adjoining vertical elements of the seismic force resisting system. Loads shall be from the equivalent lateral force (ELF) method of section 12.8

11 Diaphragm Classification Rigid Diaphragm (ASCE 7-05, ) o Diaphragms of concrete slabs or concrete filled metal deck o Span-to-depth ratios of 3 or less o Structures with no horizontal irregularities Semi Rigid Diaphragm (ASCE 7-05, ) o If diaphragm cannot be idealized as flexible or rigid, per ASCE 7-05, section , , or , the structural analysis must model the diaphragm as semi-rigid

12 Classification of Diaphragm Behavior (a) Loading (b) Rigid Diaphragm behavior (c) Flexible diaphragm behavior (d) Semi rigid diaphragm behavior

13 Definitions Diaphragm Classification Diaphragm Analysis Diaphragm Design Forces Load Combinations and Amplification Factors Code and Detailing Requirements Diaphragm Behavior with Sloped Ramp

14 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.

15 Seismic Force Distribution ELF Vertical Distribution F C x vx = C Where, = vx n V i= 1 w h x k x w h i k i Diaphragm Force Distribution F F F px = pi max pi min n i= x n i= x F i w i 0.4S 0.2S w px DS DS Scale Factors Fpx γ x = F γ γ Top = 1.0 otherlevel x > 1.0 Iw Iw ASCE 7-05, Eq ASCE 7-05, Eq px px ASCE 7-05, Eq F pimin and F pimax need not to be amplified by Ω 0. F top F ptop F 4 F 3 F 2 F P4 F p3 F p2 Used for the design of vertical elements of LLRS (lateral load resisting system) Used for diaphragm design (chords, collectors, diaphragm shear and connections to vertical elements of LLRS)

16 Diaphragm Analysis Flexible Diaphragm o 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 Analysis o Distribute the horizontal forces to the vertical lateral load resisting elements in proportion to their relative stiffness o Diaphragm deflection when compared to that of the vertical lateral load resisting elements will be insignificant.

17 Diaphragm Analysis Semi Rigid Diaphragm Analysis o 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.

18 Definitions Diaphragm Classification Diaphragm Analysis Diaphragm Design Forces Load Combinations and Amplification Factors Code and Detailing Requirements Diaphragm Behavior with Sloped Ramp

19 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. L w1 + w2 L = R L + R R 2 R L and R R are known values Equation (1) Sum moment about the right support L 1 L ( w1 L) + ( w2 w1 ) L = RLL Equation (2) RL RR Solve Equations (1) and (2) for w 1 and w 2 w 1 w 2 f x f px = γf x Figure: Rigid diaphragm

20 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 ): 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 Perspective View of Wall and Connector Diaphragm Segment Plan Diaphragm Segment Reinforcement

21 Definitions Diaphragm Classification Diaphragm Analysis Diaphragm Design Forces Load Combinations and Amplification Factors Code and Detailing Requirements Diaphragm Behavior with Sloped Ramp

22 Load Combinations and Amplification Factors Seismic Design Category SDC Basic Seismic Load Combinations ASCE Over-strength Factor ( Ω o ) ASCE Redundancy Factor ρ ASCE & % Increase in Forces Due to Irregularities ASCE Torsional Amplification Factor ASCE A & B C D and higher

23 Definitions Diaphragm Classification Diaphragm Analysis Diaphragm Design Forces Load Combinations and Amplification Factors Code and Detailing Requirements Diaphragm Behavior with Sloped Ramp

24 Code Requirements (SDC = D and higher) ACI 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 All reinforcement used to resist collector forces, diaphragm shear, or flexural tension shall be developed or spliced for f y in tension. Collector elements with compressive stresses exceeding 0.2f c at any section shall have transverse reinforcement satisfying (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 c shall be increased to 0.5f c, and the limit of 0.15f c shall be increased to 0.4f c. 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 , except as required in

25 Code Requirements (SDC = D and higher) ACI Section No. Flexural strength Diaphragms 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 for deep beams need not apply. The effects of openings shall be considered Shear strength V n of structural diaphragms shall not exceed V n = A cv (2λ f c + ρ t f y ) V n of structural diaphragms shall not exceed 8A cv f c Construction joints All construction joints in diaphragms shall conform to 6.4 and contact surfaces shall be roughened as in

26 Reinforcement Requirements for Chords and Collectors at Splice and Anchorage Zones L d per ACI 318 Splice per ACI 318 Shear reinforcing Collector reinforcement Shear reinforcing (typ.) Chord reinforcement B B Collector reinforcement (typ.) A 2.5d cover { b 2 s { 3d b 1 ½ A d b (typ.) Per ACI , for compressive stress < 0.15f c Per ACI , for compressive stress > 0.20f c s { 3d b 1 ½ Section A-A Chord Reinforcement Other reinforcement not shown for clarity Section B-B

27 Definitions Diaphragm Classification Diaphragm Analysis Diaphragm Design Forces Load Combinations and Amplification Factors Code and Detailing Requirements Diaphragm Behavior with Sloped Ramp

28 Computer Simulation of 3-Bay Parking Structure Lateral force 1.26 kips/joint Shear Walls in y-direction Shear Walls in x-direction Ramp Structure size 292 long x 180 wide X-direction: 2 end 38 and 6 interior 36 Y-direction: 3 60 Load calculation Assume 20 psf wind load, 10-6 story height Therefore, Windward pressure at each tier = 20 psf x 10.5 ft = 210 plf Floor mesh: 6 x 6 Convert the line load to point load at each joint, 210 plf x 6 = 1.26 kips/joint Two-story parking structure, with four exterior shear walls in y-direction and two walls in x-direction (along the ramp).

29 3-Bay Parking Structure (cont.)- with Ramp Modeled Y-direction deformation: in A Y-direction deformation: in B 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 : 1 3.For seismic load, the lateral deformation is based on inertial load of each bays considering the ramp cavity.

30 3-Bay Parking Structure (cont.)- without Ramp Modeled A Y-direction deformation: in. > in (with ramp modeled) Y-direction deformation: in. < in (with ramp modeled) B 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

31 Computer Simulation of 4-Bay Parking Structure Shear Walls in x-direction Lateral force 1.26 kips/joint (subjected to the same load as the 3-bay structure) Ramp Shear Walls in y-direction Structure size 292 long x 240 wide X-direction: 2 end 38 and 6 interior 36 Y-direction: 4 60 Two-story parking structure, with four exterior shear walls in y-direction and two walls in x-direction (along the ramp).

32 4-Bay Parking Structure (cont.) Intersecting ramps Y-direction deformation: in. Y-direction deformation: in. Y-direction deformation: in. Y-direction deformation: in., 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

33 Design Recommendation for Parking Structure with Sloped Ramp Wind Load Wind Pressure (Windward) Chord reinforcement based on maximum T value Section A C T C T D A Shear Wall Ramp Section B D B Section C C T C T D C Wind Pressure (Leeward) Chord Reinforcement: Section A T A = C A = M u (due to windward pressure) / Depth of Section A only T A = C A = M u / (0.95D A ) Section C T C = C C = M u (due to leeward pressure) / Depth of Section C only T C = C C = M u / (0.95D C ) Use maximum value of T A, T B & T C, and provide chord reinforcement based on maximum T in all the bays.

34 Design Recommendation for Parking Structure with Sloped Ramp Seismic Load F px Chord reinforcement based on maximum T value Section A C T C T D A Shear Wall Ramp Section B D B Section C C T C T D C Chord Reinforcement: 1.Calculate M u based on F px at the floor 2.Divide M u by the contribution of Mass A, B and C. If Mass A, B and C are equal, then divide M u by 3 (i.e., M ua = M ub = M uc = M u /3). 3.Determine chord reinforcement required for each floor section. T A = C A = M ua / Depth of Section A = M ua / (0.95D A ) T B = C B = M ub / Depth of Section B = M ub / (0.95D B ) T C = C C = M uc / Depth of Section C = M uc / (0.95D C ) Use maximum value of T A, T B & T C and provide chord reinforcement based on maximum T in all the bays.

35 Summary Today s presentation covered discussion on the following topics: o Definitions o Diaphragm Classification o Diaphragm Analysis o Diaphragm Design Forces o Load Combinations and Amplification Factors o Code and Detailing Requirements o Diaphragm Behavior with Sloped Ramp

36 Questions and Comments? Thanks