Prestressed Concrete Bridge Design Basic Principles Emphasizing AASHTO LRFD Procedures Praveen Chompreda, Ph. D. EGCE 406 Bridge Design MAHIDOL UNIVERSITY 2010 Part I: Introduction Reinforced vs. Prestressed Concrete Principle of Prestressing Historical Perspective Applications Classifications and Types RC vs. PC vs. PPC Design Codes Stages of Loading 1 2 Reinforced Concrete Reinforced Concrete Cracking moment of an RC beam is much lower than the service moment Recall that in Reinforced Concrete Concrete is strong in compression but weak in tension Steel is strong in tension (as well as compression) Reinforced concrete uses concrete to resist compression and to hold the steel bars in place, and uses steel to resist all of the tension Tensile strength of concrete is neglected (i.e. assumed zero) An RC beam always crack under the service load 3 Source: MacGregor and Wight (2005). 4
Principle of Prestressing Principle of Prestressing Prestressing is a method in which compression force is applied to the reinforced concrete section. The effect of prestressing is to reduce the tensile stress in the section to the point that the tensile stress is below the cracking stress. Thus, the concrete does not crack! It is then possible to treat prestressed concrete as an elastic material The concrete can be visualized to have 2 force systems Internal Prestressing Forces External Forces (from DL, LL, etc ) These 2 force systems must counteract each other Stress in concrete section when the prestressing force is applied at the c.g. of the section (simplest case) 5 6 Principle of Prestressing Historical Perspective Stress in concrete section when the prestressing force is applied eccentrically with respect to the c.g. of the section (typical case) The concept of prestressing was invented centuries ago when metal bands were wound around wooden pieces (staves) to form a barrel. Smaller Compression c.g. e 0 + + = Source: Wikipedia (2006) Cross- Section F/A Fe0y/I MDLy/I MLLy/I Small Compression Prestressing Stress Stress Stress Force from DL from LL Resultant The metal bands were tighten under tensile stress, which creates compression between the staves allowing them to resist internal liquid pressure 7 8
Historical Perspective Historical Perspective The concept of prestressed concrete is also not new. In 1886, a patent was granted for tightening steel tie rods in concrete blocks. This is analogous to modern day segmental constructions. Early attempts t were not very successful due to the low strength th of steel at that time. Since we cannot prestress at high stress level, the prestress losses due to creep and shrinkage of concrete quickly reduce the effectiveness of prestressing. Source: Wikipedia (2006) Eugene Freyssinet (1879-1962) 1962) was the first to propose that we should use very high strength steel which permit high elongation of steel. The high steel elongation would not be entirely offset by the shortening of concrete (prestress loss) due to creep and shrinkage. First prestressed concrete bridge in 1941 in France First prestressed concrete bridge in US: Walnut Lane Bridge in Pennsylvania. Built in 1949. 47 meter span. 9 10 Applications of Prestressed Concrete Classifications and Types Bridges Slabs in buildings Water Tank Concrete Pile Thin Shell Structures Offshore Platform Nuclear Power Plant Repair and Rehabilitations Pretensioning v.s. Posttensioning External vs v.s. Internal Linear v.s. Circular End-Anchored v.s. Non End-Anchored Bonded v.s. Unbonded Tendon Precast v.s. Cast-In-Place v.s. Composite Partial v.s. Full Prestressing Source: Wikipedia (2006) 11 12
Classifications and Types Classifications and Types Pretensioning vs. Posttensioning In Pretension, the tendons are tensioned against some abutments before the concrete is place. After the concrete hardened, the tension force is released. The tendon tries to shrink back to the initial length but the concrete resists it through the bond between them, thus, compression force is induced d in concrete. Pretension is usually done with precast members. Pretensioned Prestressed Concrete Casting Factory Concrete Mixer 13 14 Classifications and Types Classifications and Types In Posttension, the tendons are tensioned after the concrete has hardened. Commonly, metal or plastic ducts are placed inside the concrete before casting. After the concrete hardened and had enough strength, the tendon was placed inside the duct, stressed, and anchored against concrete. Grout may be injected into the duct later. This can be done either as precast or cast-in-place. Precast Segmental Girder to be Posttensioned In Place Source: Wikipedia (2006) 15 16
Classifications and Types External vs. Internal Prestressing Prestressing may be done inside or outside Linear vs. Circular Prestressing Prestressing can be done in a straight structure such as beams (linear prestressing) or around a circular structures, such as tank or silo (circular prestressing) Bonded vs. Unbonded Tendon The tendon may be bonded to concrete (pretensioning or posttensioning with grouting) or unbonded (posttensioning without grouting). Bonding helps prevent corrosion of tendon. Unbonding allows readjustment of prestressing force at later times. Classifications and Types End-Anchored vs. Non-End-Anchored tendons In Pretensioning, tendons transfer the prestress through the bond actions along the tendon; therefore, it is non-end-anchored In Posttensioning, tendons are anchored at their ends using mechanical devices to transfer the prestress to concrete; therefore, it is endanchored. (Grouting or not is irrelevant) 17 18 Classifications and Types RC vs. PPC vs. PC Partial vs. Full Prestressing Prestressing tendon may be used in combination with regular reinforcing steel. Thus, it is something between full prestressed concrete (PC) and reinforced concrete (RC). The goal is to allow some tension and cracking under full service load while ensuring sufficient ultimate strength. We sometimes use partially prestressed concrete (PPC) to control camber and deflection, increase ductility, and save costs. 19 20
RC vs. PPC vs. PC RC vs. PPC vs. PC 21 22 Advantages of PC over RC Design Codes for PC Take full advantages of high strength concrete and high strength steel Need less materials Smaller and lighter structure No cracks Use the entire section to resist the load Better corrosion resistance Good for water tanks and nuclear plant Very effective for deflection control Btt Better shear resistance it ACI-318 Building Code (Chapter 18) AASHTO LRFD (Chapter 5) Other related institutions PCI Precast/Prestressed Concrete Institute PTI Post-Tensioning Institute 23 24
Design Principles Stages of Loading In RC, we primarily design the member for either service limit states (Working stress design method), or ultimate limit states (Ultimate strength design). In PC, both service limit states and ultimate limit states must be checked. In service limit states, section must have stresses below the allowable stress limits In ultimate limit states, the moment and shear capacity must be greater than the ultimate (factored) loads. Unlike RC where we primarily consider the capacity of the structure at one stage (i.e. during service), we must consider multiple stages of construction in Prestressed Concrete The stresses in the concrete section must remain below the maximum limit it at all times!!! Source: Wikipedia (2006) 25 26 Stages of Loading Typical stages of loading considered Initial (Immediately Transportation/ Service after Prestress Erection Prestress loss has Transfer) Partial loss of fully occurred Full prestress force May or may not prestress force DL DL+SDL +LL include DL Different support (depending on conditions during construction type) erection from service Part II: Materials and Hardwares for Prestressing Concrete Prestressing Steel Prestressing Hardwares 27 28
Concrete Concrete: Compressive Strength Mechanical properties of concrete that are relevant to the prestressed concrete design includes: Compressive Strength (f c ) Modulus of Elasticity y( (E c ) Modulus of Rupture (f r ) AASHTO LRFD For prestressed concrete, f c at 28 days should be 28-70 MPa For reinforced concrete, f c at 28 days should be 16-70 MPa Concrete with f c > 70 MPa can be used only when supported by test data Source: Wikipedia (2006) 29 30 Concrete: Modulus of Elasticity Concrete: Modulus of Rupture Modulus of elasticity can be obtained directly from test or estimated t from compressive strength (AASHTO secion 5.4.2.4) E 043γ (f c = 0.043γ 1.5 c c ) 0.5 MPa γ c in kg/m 3 f c in MPa For normal weight concrete, we can use a simplified equation E c =4800(f c ) 0.5 MPa Indicates the tensile capacity of concrete under bending Tested simply-supported concrete beam under 4-point bending configuration f r = My/I = PL/bd 2 Modulus of rupture can also be estimated from compressive strength (AASHTO section 5.4.2.6) f r = 0.63 (f c ) 0.5 MPa 31 32
Concrete : Summary of Properties Prestressing Tendons Prestressing tendon may be in the form of strands, wires, round bar, or threaded rods Materials 33 Tendons High Strength Steel Fiber-Reinforced Polymer (FRP) Composites (glass or carbon fibers) 34 Prestressing Steel Common shapes of prestressing tendons Most Popular ((7-wire Strand)) Source: Naaman ((2004)) 35 36
Prestressing Strands Prestressing Strands Prestressing strands have two grades Grade 250 (f pu = 250 ksi or 1725 MPa) Grade 270 (f pu = 270 ksi or 1860 MPa) Types of strands Stressed Relieved Strand Low Relaxation Strand (lower prestress loss due to relaxation of strand) Source: AASHTO (2000) 37 38 Prestressing Strands Prestressing Strands Source: AASHTO (2000) Modulus of Elasticity 197000 MPa for Strands 207000 MPa for Bars The modulus of elasticity of strand is lower than that of steel bar because strand is made from twisting of small wires together. 39 40
Hardwares & Prestressing Equipments Pretensioned Beams Pretensioned Members Hold-Down Devices Posttensioned Members Anchorages Stressing Anchorage Dead-End Anchorage Ducts Posttensioning Procedures Source: Wikipedia (2006) 41 42 Pretensioning Hardwares Posttensioned Beams Hold-Down Devices for Pretensioned Beams Posttension Hardwares Stressing Anchorage Dead-End Anchorage Duct/ Grout Tube Source: VSL (2006) 43 44
Posttensioning Hardwares - Anchorages Posttensioning Hardwares - Anchorages Source: VSL (2006) 45 Source: VSL (2006) 46 Posttensioning Hardwares - Anchorages Posttensioning Hardwares - Ducts Source: VSL (2006) Source: VSL (2006) 47 48
Posttensioning Procedures Posttensioning Procedures Grouting is optional (depends on the system used) Source: VSL (2006) 49 Source: VSL (2006) 50 Prestress Losses Part III: Prestress Losses Prestress force at any time is less than that during jacking Sources of Prestress Loss Creep of Anchorage Concrete Set (AS) (CR) Sources of Prestress Losses Lump Sum Estimation i of Prestress Loss Friction (FR) Elastic Shortening (ES) Prestress Loss Shrinkage of Concrete (SH) Prestress Relaxation (RE) 51 52
Prestress Losses Sources of Prestress Loss Elastic Shortening : Caused by concrete shortening when the prestressing force is applied. The tendon attached to it also shorten, causing a stress loss Prestress Losses Sources of Prestress Loss (cont.) Friction : Friction in the duct of posttensioning system causes stress at the far end to be less than that at the jacking end. Thus, the average stress over the entire tendon is less than the jacking stress Source: VSL (2006) Anchorage Set : The wedge in the anchorage may set in slightly to lock the tendon, causing a loss of stress 53 54 Prestress Losses Prestress Losses Sources of Prestress Loss (cont.) Shrinkage : Concrete shrinks over time due to the loss of water, leading to stress loss on attached tendons Creep : Concrete shortens over time under compressive stress, leading to stress loss on attached tendons Sources of Prestress Loss (cont.) Steel Relaxation : Steel loss its stress with time due to constant elongation, the larger the stress, the larger the loss. 55 56
Time Line of Prestress Loss Posttensioning FR Pretensioning (against abutment) Jacking AS ES Initial SH CR RE Effective f pj f pi f pe (AS RE) SH CR RE Jacking ES Release Initial Effective (cutting f strands) f pi f pe pj Prestress Loss By Types Pretensioned Posttensioned Instantaneous Elastic Shortening Friction Anchorage Set Elastic Shortening Time-Dependent Shrinkage (Concrete) Shrinkage (Concrete) Creep (Concrete) Creep (Concrete) Relaxation (Steel) Relaxation (Steel) Instantaneous Losses Time-Dependent Losses 57 58 Prestress Loss - Pretensioned Prestress Loss - Posttensioned 59 60
Lump Sum Prestress Loss Pretress losses can be very complicate to estimate since it depends on so many factors In typical constructions, a lump sum estimation of prestress loss may be accurate enough. This may be expressed in terms of: Total stress loss (in unit of stress) Percentage of initial prestress Some common methods Naaman ACI-ASCE TY T.Y. Lin Lump Sum Prestress Loss A. E. Naaman Method not including FR, AS Start with 240 MPa for Pretensioned Normal Weight Concrete with Low Relaxation Strand Add 35 MPa for Stress-Relieved Strand or for Lightweight Concrete Deduct 35 MPa for Posttension Types of Prestress Pretensioned Posttensioned Types of Concrete Normal Weight Concrete Lightweight Concrete Normal Weight Concrete Lightweight Concrete Prestress Loss (fpi-fpe) (MPa) Stress-Relieved Strand 275 310 240 275 Low Relaxation Strand 240 275 205 240 61 62 Lump Sum Prestress Loss Lump Sum Prestress Loss ACI-ASCE Committee Method (Zia et al. 1979) This is the Maximum Loss that you may assume Types of Prestress Types of Concrete Maximum Prestress Loss (fpi-fpe) (MPa) Stress-Relieved Strand 345 380 Low Relaxation Strand 276 311 Pretensioned Normal Weight Concrete 345 276 Lightweight Concrete T.Y. Lin & N. H. Burns Method Sources of Loss Percentage of Loss (%) Pretensioned Posttensioned Elastic Shortening (ES) 4 1 Creep of Concrete (CR) 6 5 Shrinkage of Concrete (SR) 7 6 Steel Relaxation (R2) 8 8 Total 25 20 Source: Lin and Burns (1981) Note: Pretension has larger losses because prestressing is usually done when concrete is about 1-2 days old; while posttensioning is done at much later time when concrete is stronger. 63 64
Lump Sum Prestress Loss AASHTO LRFD (for CR, SR, R2) (5.9.5.3) (5953) Lump Sum Prestress Loss AASHTO LRFD (Cont.) Partial Prestressing Ratio (PPR) is calculated as: PPR Apsfpy A f A f ps py s y PPR = 1.0 for Prestressed Concrete PPR = 0.0 for Reinforced Concrete Elastic Shortening Loss ( f pes ) is calculated as: f E E F Fe M e 2 ps ps i i 0 G 0 pes fcgp, F i G Eci Eci Ac I I Stress of concrete at the c.g. of tendon due to prestressing force and dead load Source: AASHTO (2000) 65 66 Part IV: Allowable Stress Design Basics Stress Inequality Equation Allowable Stress in Concrete Allowable Stress in Prestressing Steel Feasible Domain Method Envelope and Tendon Profile Sign Convention Concrete Section Properties Overview of Design Procedures 67 68
Basics: Sign Convention Basics: Section Properties In this class, the following convention is used: Tensile Stress in concrete is negative (-) Compressive Stress in concrete is positive i (+) Positive Moment: Concrete Cross- Sectiona Area: Ac yt (abs) e (-) c.g. of Prestressing Tendon Area: Aps I K K t K b Positive i Shear: h (abs) e (+) kt (-) kb (+) Center of Gravity of Concrete Section (c.g.c) Z t Z b yb (abs) In some books, the sign convention for stress may be opposite so you need to reverse the signs in some formula!!!!!!!!! c.g. of Prestressing Tendon Area: Aps 69 70 Basics: Section Properties Basics: Section Properties Moment of Inertia, I Moment of Inertia for typical sections I A 2 y da Rectangular section about c.g. I xx = 1/12 bh 3 I x x = I xx + Ad 2 y t and y b are distance from the c.g. of section to top and bottom fibers, respectively Sectional modulus, Z (or S) Z t = I/y t Z b = I/y b 71 72
Basics: Section Properties Basics: Section Properties 73 74 Basics: Section Properties Basics: Section Properties Kern of the section, k, is the distance from c.g. where compression force will not cause any tension in the section Consider Top Fiber Consider Bottom Fiber (Get Bottom Kern, k b ) (Get Top Kern, k t ) F Fe0y t 0 F Fe0y b 0 Ac I Ac I I e I 0 kb e k Ay c t Ay 0 t c b Note: Top kern has negative value Source: Nawy (2000) 75 76
Basics: Depths General Design Procedures Definitions of depths used Check Check shear cracking load Check Ultimate moment strength Check allowable stresses at various stages Select Girder type and number/ location of strands 77 78 General Design Procedures General Design Procedures 79 80
Stress in Concrete at Various Stages Allowable Stress Stress in concrete at various stages Stress inequality equation Allowable stresses Sections 81 Source: Nawy (2000) 82 Stress in Concrete at Various Stages Stress Inequality Equations We can write four equations based on the stress at the top and bottom of section at initial and service stages No. Case Stress Inequality Equation 83 I Initial-Top F i Fe i o Mmin Fi eo Mmin σt 1 σ Ac Zt Zt Ac kb Zt II Initial-Bottom III Service-Top! IV Service-Bottom σ σ σ F Fe M F e M σci F Fe o Mmax Fi eo Mmax 1 σ Ac Z t Z t Ac kb Zt i i o min i o min b 1 A c Z b Z b A c k t Z b t b F Fe o Mmax F eo Mmax 1 σ Ac Zb Zb Ac kt Zb 84 ti cs ts
Allowable Stress in Concrete Allowable Stress in Concrete AASHTO LRFD (5.9.4) provides allowable stress in concrete as functions of compressive strength at that time Allowable compressive stress in concrete is used to control creep, which causes prestress loss over time Consider the following limit states: Immediately after Prestress Transfer (Before Losses) Compression Tension Service (After All Losses) Compression Tension Allowable tensile stress in concrete is used to prevent cracking, which reduces the usable section (remember that once the concrete cracks, it can no longer support tensile stress, even at levels smaller than tensile strength) 85 86 Allowable Stress in Concrete Allowable Stress in Concrete Immediately after Prestress Transfer (Before Losses) Using compressive strength at transfer, f ci Allowable compressive stress = 0.60 f ci Allowable tensile stress At service (After All Losses) Compressive Stress Source: AASHTO (2000) Source: AASHTO (2000) 87 88
Allowable Stress in Concrete At service (After All Losses) Tensile Stress Allowable Stress in Concrete - Summary Stage Where Load Limit Note Initial Tension at Top F i +M Girder -0.58 f ci With bonded reinf -0.25 f ci Without bonded > -1.38 MPa reinf. Source: AASHTO (2000) Service Compression at Bottom Compression at Top F i +M Girder 0.60 f ci F+M Sustained 0.45f c * 0.5(F+M Sustained )+M LL+IM 0.40f c * F+M Sustained +M LL+IM 0.60Ø w f c * Tension F+M Sustained +0.8M LL+IM -0.50 f c Normal/ Moderate at Bottom (Service III Limit State) exposure -0.25 f c Corrosive exposure 0 Unbonded dtendon 89 * Need to check all of these conditions (cannot select only one) 90 Allowable Stress in Prestressing Steel Allowable Stress in Prestressing Steel Both ACI and AASHTO code specify the allowable stress in the prestressing steel at jacking and after transfer Prevents accidental rupture during jacking Control long-term relaxation AASHTO LRFD (5.9.3) 91 Source: AASHTO (2000) 92
Allowable Stress in Prestressing Steel Allowable Stress in Prestressing Steel ACI-318 (2008) 93 94 Allowable Stress Design Allowable Stress Design There are many factors affecting the stress in a prestressed girder Prestressing Force (F i or F) Location of prestress tendon (e 0 ) Section Property (A, Z t or Z b, k t or k b ) External moment, which depends on The Section used (dead load) Girder Spacing (larger spacing larger moment) Slab Thickness (larger spacing thicker slab) Stages of construction Composite/ Noncomposite behavior How to Start the Design? For bridges, we generally has a preferred section type for a given range of span length and we can select a girder spacing to be within a reasonable range 95 96
Sections Sections AASHTO Type I-VI Sections AASHTO Type I-VI Sections (continued) ft m 50 15 75 23 100 30 150 46 97 98 Bridge Girder Sections Bridge Girder Sections Source: Nawy (2000) Source: Nawy (2000) 99 100
Feasible Domain Feasible Domain & Envelope For a given section, we need to find the combination of prestressing force (F i or F, which depends on the number of strands), and the location of strands (in terms of e 0 ) to satisfy these equations Possible methods: Trying to select some number of strands and locations (Trial & Error) Using Feasible Domain Method Graphical Method 101 102 Feasible Domain - Equations We can rewrite the stress inequality equations and add one more equation to them Feasible Domain Graphical Interpretation No. Case Stress Inequality Equation I Initial-Top 1 e0 kb Mmin σtizt II III IV V Initial-Bottom Service-Top Service-Bottom Practical Limit F i 1 e0 k Mmin σ Z F i t ci b 1 b cs t e k M σ Z 0 max! F 1 e k M σ Z 0 F max t ts b e e y d y cm 0 0 b c,min b 7.5 mp 103 104
Envelope Feasible domain tells you the possible location and prestressing force at a given section to satisfy the stress inequality equation We usually use feasible domain to determine the location and prestressing force at the most critical section (e.g. midspan of simply-supported beams) After we get the prestressing force at the critical section, we need to find the location for the tendon at other points to satisfy stress inequalities We use the prestressing envelope to determine the location of tendon along the length of the beam (tendon profile) Envelope - Equations We use the same equations as those in the feasible domain, except that we ve already known the F or F i and want to find e 0 at different points along the beam I II No. Case Stress Inequality Equation III IV V Initial-Top Initial-Bottom Service-Top Service-Bottom Practical Limit 1 e0 kb Mmin σtizt F i 1 e0 k Mmin σ Z F i 0 t ci b 1 σ e k M σ Z 0 b max cs t F 1 e k 0 t M σ max tszb F e e y d y cm 0 0 y b c,min y b 7.5 mp! 105 106 Envelope - Equations Envelope & Tendon Profile We then have 5 main equations I & II provide the lower bound of e 0 (use minimum of the two) III and IV provide the upper bound of e 0 (use maximum of the two) IIIa uses F+M Sustained IIIb uses 0.5(F+M Sustained )+M LL+IM IIIc uses F+M Sustained +M LL+IM IV uses F+M Sustained +0.8M LL+IM V is a practical limit of the e 0 (it is also the absolute lower bound) 107 108
Envelope & Tendon Profile Envelope & Tendon Profile Notes The tendon profile of pretensioned members are either straight or consisting of straight segments The tendon profile of posttensioned member may be one straight tendon or smooth curve, but no sharp corners 109 110 Envelope & Tendon Profile Alternative to draping the strands at ends, we can put plastic sleeves around some strands at supports to prevent the bond transfer so the prestress force will be less at that section Source: Nawy (2000) 111