Indeterminate Prestressed Structures

Transcription

1 Indeterminate Prestressed Strutures Introdution Use of ontinuous sstems results in redution of moments and stresses at midspans. Shallower members are used Stiffer than simpl supported members of equal span and omparable loading Lower defletions ompared to simpl supported members 1

2 Shallower members Lighter strutures with lighter foundations Redution of material and onstrution ost Strutural stabilit and resistane to lateral loads improved Span to depth ratio also improved Flat plates ratio 40 to 45 Box girders ratio 25 to 30 Continuit eliminates anhorages at intermediate supports Further redution in material and labor ost 2

3 Use of Continuous Prestress Flat plates for floors and roofs Continuit in one or both diretions Prestressing in one or both diretions Long span prestressed bridges Cantilever box girder bridges Cable staed bridges with prestressed deks Disadvantages of Continuit Higher fritional losses (More bends and longer tendons) Presene of shear and moment at supports (redution in the moment strength of the setion) Exessive lateral fores and moments at supporting olumns (Due to elasti shortening) 3

4 Effets of higher seondar stresses due to shrinkage, reep, temperature variations and settlement of supports Seondar moment due to indued reations at supporting olumns aused b prestressing fores Possible reversal of moments from alternate loading of spans. Moments at interior supports require additional reinforement Elasti Analsis of Prestress Continuit Support Displaement Method Primar moments from prestressing fore M 1 = P e 1 Seondar moments from indued fore or reations at internal supports M 2 Seondar moment shifts the loation of C-Line Deviation of C-Line from.g.s. line = M 2 / P e 4

5 The tendon profile also hanges due to the presene of the seondar moment. New loation of tendon gs is based on M 3 = M 1 +M 2 Limit eentriit = 3 = M 3 / P e Note that is negative when the C-Line is above the neutral axis as in the ase of the intermediate support setion Moments Due to Post-Tensioning in Continuous Beams (ont d) M 2 = M PS M 1 = M PS Pe Seondar reations at supports due to prestressing seondar moments, M 2 Seondar moments var linearl between supports 5

6 6 Conrete Fiber Stresses Due to Prestress Onl t e e top I P A P = ' σ b e e bot I P A P + = ' σ Note that the eentriit is different ompared to the eentriit used for determinate strutures Conrete Fiber Stresses Due to Prestress and Self-Weight t sw t e e top I M I P A P + = ' σ b sw b e e bot I M I P A P + + = ' σ

7 Soures of Loss: Prestress Losses P/T ONLY Anhorage set (seating), A Frition (urvature and wobble), F Elasti shortening, ES Instantaneous Shrinkage of onrete, SR Creep of onrete, CR Relaxation of Steel, R1, R2 Time- Dependent POST-TENSIONED CONCRETE BRIDGES CONSTRUCTION METHOD CONTROLS THE DESIGN 7

8 CONSTRUCTION METHODS ALL SPANS - CIP OR PRECAST SPAN-BY-SPAN - CIP - PRECAST BALANCED CANTILEVER - CIP - PRECAST ALL SPANS IN UNIT (CIP ON FALSEWORK) 8

9 SPAN-BY-SPAN CONSTRUCTION BALANCED CANTILEVER CONSTRUCTION 9

10 Transverse Post-Tensioning Wh use transverse PT? More Durabilit Thinner Deks Where it is applied? Dek Slabs Bent Caps End Diaphragms Single-Cell Box Girder with Dek PT Transverse Post-Tensioning Modeling 3-D FEM model, or 2-D frame model (using Puher or Homberg harts) Live load ases PT equivalent loads Analsis Input Dead Loads Live load ases PT equivalent loads Output M max (-) in antilever M max (+-) along dek M max (+-) in webs and soffit 10

11 (ourtes of ASBI) (ourtes of ASBI) 11

12 12

13 13

14 Conflits 14

15 TIGHTLY CIP CURVED BOX GIRDERS LOGAN AIRPORT INTERCHANGE-BOSTON PRECAST SEGMENTAL CURVED BOX GIRDERS BOSTON 15

16 POST-TENSIONED CONCRETE COLUMNS Wh use post-tensioned onrete olumns? Speed of Constrution Durabilit More Eonomial Temporar or Staged Constrution 16

17 POST-TENSIONED CONCRETE COLUMNS TYPES: Prismati Non-Prismati ( slight flares) V-Shaped Piers C or Cantilever Bents Setions: Hollow Box Setion H- Setion Ellipse Others POST-TENSIONED CONCRETE COLUMNS ANALYSIS AND DESIGN: Allowable Stresses P-M Interation Diagrams (inluding Prestress) Flexural and Shear Strength Transverse Reinforement Requirements Seismi Design (Dutilit?) Vessel Impat P- Analsis 17

18 Preast Hollow Box Pier C or Cantilever Bent (Courtse of ASBI) 18