Report

VIRGINIA CONCRETE CONFERENCE March 3-4, 2011 Presented by: Teddy Theryo, P.E. Parsons Brinckerhoff SEGMENTAL BRIDGE GROUP 1. 2. 3. 4. 5. Introduction Understanding of Creep & Shrinkage Code Development of Creep & Shrinkage Impact of Creep & Shrinkage on Post-Tensioned Bridges Conclusions Definitions Creep is time dependent deformations of concrete under permanent loads (self weight), PT forces and permanent displacement Shrinkage is shortening of concrete due to drying and is independent of applied loads Factors Affecting Creep Concrete mix proportion Cement properties Curing conditions Size and shape of members Environment Age at loading Stress level Factors Affecting Shrinkage Concrete mix proportion Cement properties Aggregate properties Curing conditions Size and shape of members Environment In structural concrete creep and shrinkage strains are coexist and occur together. The rate of both creep and shrinkage decrease with time. Theoretically the creep and shrinkage are considered diminished at 10,000 days (27 years) after construction. For practical purposes the ending time of 4,000 days (11 years) is also commonly used in creep and shrinkage calculations . Mathematically the non linear shape of creep and shrinkage has been assumed as hyperbolic, exponential or logarithmic. Strain Strain Creep strain Instantaneous strain Time Time TYPICAL CREEP – TIMECURVE TYPICAL SHRINKAGE – TIMECURVE Strain Drying creep Basic creep Total creep Shrinkage Nominal elastic strain t0 Time (t – t0) Strain - 10 -6 1500 1000 Instantaneous recovery Creep recovery Residual deformation 500 Strain on application of load 0 50 100 150 Time since application of load - days 200 1. 2. 3. 4. 5. Introduction Understanding of Creep & Shrinkage Code Development of Creep & Shrinkage Impact of Creep & Shrinkage on Post-Tensioned Bridges Conclusions Relationship between creep and elastic deformations cr = where: = el E28 cr = creep strain el = elastic strain = stress E28 = elastic modules of concrete at age 28 days = creep factor 3.72 3.5 2.0 2.22 2.00 1.5 1.70 1.44 0 3 Days 3 4 56 0.90 14 21 28 42 56 0.96 7 0.5 1.00 1.0 0.88 2.57 0.91 2.5 0.94 3.03 1.07 3.0 1.20 TOTAL ELASTIC AND CREEP STRAIN 4.0 9 1 1.5 2 Months DURATION OF LOADING Years 3 5 t Mcr(t) = (1 – e - (t)) (MII – MI) MFinal(t) = MII + (MI – MII) e- (t) where: (t) = creep factor at time t e = Base of Napierian logarithms = 2.7182 MI = Movement due to permanent loads before change of statical system MII = Movement due to the same loads applied on changed statical system (build on false-work) q Fixed Fixed 2 qL MI = 8 MI ½L ½L Free Cantilever Statical System 2 MII qL MII = 12 2 qL 24 Changed Statical System (Midspan Continuous) MFinal (t) Mcr (t) MI MII Cantilever Beam el (t 0 ) cr (t el (t 0 ) Simple Beam P P Pef Pef cr (t ) ) Post-Tensioned Beam P P PT Tendon el (t0) P P (t ) el (t0) el Pef Pef 1. 2. 3. 4. 5. Introduction Understanding of Creep & Shrinkage Code Development of Creep & Shrinkage Impact of Creep & Shrinkage on Post-Tensioned Bridges Conclusions CEB-FIP 1970 Model Code CEB-FIP 1978 Model Code CEB-FIP 1990 Model Code FIB 2010 Draft Model Code ACI-209 BP3 1. 2. 3. 4. 5. Introduction Understanding of Creep & Shrinkage Code Development of Creep & Shrinkage Impact of Creep & Shrinkage on Post-Tensioned Bridges Conclusions There are two major impacts of creep and shrinkage on structural concrete Deformations (simply supported and indeterminate structures) Redistribution of stresses / forces on indeterminate structure, including support reactions Bearing & Expansion Joint Bearing In-span Hinge CL CL Mid-span Hinge In-span Hinge Expansion Joint Bearing Old Generation of Midspan Hinge (not recommended) In-Span Hinge Mid-Span Hinge Deformation (cm) 2.5 S 5.0 7.5 5.1% Span Length: 79m (260 feet) 1.8% C L EXP. JT. NO. 3 Deck Profile based on As-Built Dwgs STA. 65+74 C L PIER 9 STA. 68+16.59 0.46’ C L PIER 8 STA. 67+16.50 0.82’ 0.36’ Reference Line Existing Deck Profile BEGIN S.E. TRANSITION STA. 68+18 C L EXP. JT. NO. 3 Deck Profile based on As-Built Dwgs STA. 67+16.50 0.84’ 0.49’ C L PIER 9 STA. 68+16.59 0.35’ C L PIER 8 STA. 65+74 Reference Line Existing Deck Profile Midspan expansion joint Active hinge member Typical internal diaphragm Hydraulic jack Active Hinge (proposed by Jean M. Muller) C L Mid-Span Fixed Sliding Expansion Joint Teflon Surface (typ) Elastomeric Bearing Steel Strong Back Mid-span Hinge with Strong Back L L o @ TF creep L Point of rotation V 3’-6” creep 12’-0” Abutment Back Wall 8’-6” 0.079 Degree creep = 0.079 x 3.5 x 12 = 3.31” Assuming 50% of the creep had been corrected camber during segment casting. L available gap at 60Fo in 2010 Abutment 1 = 3-3/4” - 0.5 (3.31) = 2.09” vs 1.75” Elastomeric Bearing Abutment 29 = 3-3/8” - 0.5 (3.31) = 1.75” vs 1” End Span Girder Rotation at Abutment 1 (Varina-Enon Bridge Case Study) Vertical Displacement (in) 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -0.05 0 200 400 600 800 Distance Along the Bridge (ft) Camber Diagram of Unit 1 at T = Abutment Span 1 Expansion Joint at Abutment X CL Expansion Joint Top Plate Bottom Pot Ideal/preferred position at T= >X CL Top Plate creep at T = Incorrect position at T= CL Bottom Pot X min. CL Top Plate e= CL Bottom Pot creep at T = Correct bearing & joint expansion preset at construction Over Extended of Bearing Top Plate Top Abutment Elevation Roadway Axis Girder Axis GOOD BAD A BAD STRATEGY Support Axis A SECTION A-A GOOD STRATEGY Torsional Creep Deformation in Horizontally Curved Bridge Introduction Understanding of Creep & Shrinkage Code Development of Creep & Shrinkage Impact of Creep & Shrinkage on Post-Tensioned Bridges Conclusions In order to avoid the negative impacts of long-term creep and shrinkage: 1. Good understanding of creep and shrinkage behaviors 2. Accurate estimation of creep and shrinkage on structural concrete design 3. Proper counter measures of long-term creep and shrinkage effects 4. Implement simple structural details