AASHTO- Load and Resistance Factor Design (LRFD) Concrete Structures. The content for this course has been provided by the following PB employees:

Transcription

1 1 AASHTO- Load and Resistance Factor Design (LRFD) Concrete Structures V 1.0 Rev Credits The content for this course has been provided by the following PB employees: Bryce Binney, P.E., S.E. and Teddy Theryo, P.E. If you have any questions about the content of this course please contact Bryce Binney or pbu@pbworld.com.

2 2 Download Information For your convenience and future reference, you may download a PDF version of this course. Click on the ATTACHMENTS link located in the upper right corner of this course window to access the document and save the file to your desktop. Course Navigation

3 3 Reinforcement Throughout the course review questions are provided. These are designed to reinforce what you have learned in this course and help prepare you for the final assessment. The review scores will not count toward your final grade on the assessment. Successful Completion After completing the content within the course you will be asked to take a final test to ensure that you mastered the key training objectives. You will need to make a minimum score of 80% on the final assessment to receive credit for passing the course. Successful completion of the course will earn 0.1 IACET CEU. Please refer to your state s specific continuing education requirements regarding applicability.

4 4 LRFD Design Curriculum This class is the third class in the Structures TRC curriculum for LRFD Design, developed internally at PB. The curriculum focuses on the following ten areas of major change introduced by the LRFD Bridge Design Specifications: Introduction to LRFD Loads and Load Factors Concrete Structures Steel Structures Buried Structures Foundations Decks & Deck Systems Joints and Bearings Abutments, Piers, and Walls Railings Objectives After completing the training program, you will be able to identify: 1. Reasons for the large size difference between the LRFD and Standard Specification concrete sections 2. The components of unified design provisions for concrete members 3. The elements of LRFD shear theories including simplified methods of design, and the Modified Compression Field Theory 4. The concept of strut-and-tie modeling and when it is appropriate 5. Changes to prestressing, including losses and partial prestressing 6. The miscellaneous differences between LRFD and the Standard Specification which may affect everyday design.

5 5 Course Outline Lesson 1: LRFD Concrete Overview Introduction to concrete section Reasons for large size differences Lesson 2: Unified Design Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Strut & Tie Modeling Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items Lesson 1 Lesson 1 LRFD Concrete Overview Narrated by Bryce Binney, P.E., S.E.

6 6 Lesson 1: LRFD Concrete Overview What does the Concrete Section cover? LRFD Standard Specification Section 8: Reinforced Concrete Section 9: Prestressed Concrete Lesson 1: LRFD Concrete Overview Size of Sections LRFD Section 5: 264 Pages 132 Pages Reasons: 1. Commentary (Similar to ACI-318) Commentary Standard Spec. Section 8: 36 Pages Section 9: 26 Pages Total = 62 Pages Code **Still twice as large due to additional content**

7 7 Lesson 1: LRFD Concrete Overview Size of Sections (cont d) Additional Reasons for size differences in sections 2. Combination of reinforced and prestressed concrete 3. Lengthy shear provisions (now include torsion) 4. Strut & Tie modeling 5. New provisions for post-tensioning & anchorage zones 6. Seismic provisions specific to concrete 7. Provisions for specific structure types a. Segmental Construction (AASHTO Guide Specification) b. Precast girders continuous for live load c. Precast spliced girders Lesson 1: LRFD Concrete Overview What s New? Major differences 1. Unified design provision which unite reinforced and prestressed components (flexure & shear) 2. Service design of reinforced concrete is absent (concept of serviceability remains, as well as stress checks for prestressed concrete) 3. Partial prestressing is introduced 4. Shear friction (horizontal shear) 5. No more over-reinforced sections, use smaller φ factor 6. Different equations for prestress losses (for pretensioned concrete) 7. Principle web tension for segmental construction is limited to 3.5 f c 8. Minimum reinforcing (Mcr)

8 8 Lesson 1: LRFD Concrete Overview Section Setup Divided into 14 Articles 5.1 to 5.3: Scope, Definitions, Notations 5.4: Material Properties Tensile Strength, New Creep & Shrinkage Model, Reinforcing Strength 5.5: Limit States Service, Fatigue, Strength (φ factors), Extreme Event 5.6: Design Considerations Strut & Tie, Imposed Deformations 5.7: Flexural and Axial Design (24 pages) 5.8: Shear and Torsion (41 pages) 5.9: Prestressing and Partial Prestressing (24 pages) 5.10: Details of Reinforcement Reinf. Spacing, Shinkage Reinf., Anchorage Zone Provisions, Seismic Provisions (48 pages) 5.11: Development and Splices of Reinforcement 70% of Chapter 5.12: Durability 5.13: Specific Members Diaphragms, Corbels, Beam Ledges, Footings, Piles 5.14: Provisions for Structure Types Spliced Girders, Continuous for live load, Segmental Construction, Slabs (44 pages) Lesson 1: LRFD Concrete Overview Customary Unit Equivalents Standard Specs 1 f c (psi) 3 f c (psi) 6 f c (psi) 7.5 f c (psi) 12 f c (psi) = LRFD Specs f c (ksi) f c (ksi) 0.19 f c (ksi) 0.24 f c (ksi) 0.38 f c (ksi) 2 f c * b w * d f c * b w * d

9 9 Course Outline Lesson 1: LRFD Concrete Overview Introduction to concrete section Reasons for large size differences Lesson 2: Unified Design Approach to Structural Concrete Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Strut & Tie Modeling Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items

10 10 Lesson 2 Lesson 2 Unified Design Approach for Structural Concrete Lesson 2: Unified Design Approach for Structural Concrete Unified Design Approach for Structural Concrete What it does 1. One section will be applicable to reinforced, prestressed, and partially prestressed concrete 2. One flexural and axial force theory 3. One shear theory (Modified Compression Field Theory) Purpose 1. Unify design procedures for all types of concrete 2. Include partially prestressed concrete 3. Eliminate duplication

11 11 Lesson 2: Unified Design Approach for Structural Concrete Most Significant Concepts Members in compression and flexure are treated in a similar manner. Capacity is calculated based upon reinforcement strain which corresponds to an certain φ factor. Cross-sections are defined as compression controlled, tension controlled, or in transition φ (phi) 0.75 Compression Controlled Transition Region Tension Controlled Reinforcing Tensile Strain Lesson 2: Unified Design Approach for Structural Concrete Pure Flexure Example Assumptions: 6 As = 1.22 in 2 f c = 4 ksi f y = 60ksi ρ = 0.75ρ b (under-reinforced) 12 d = 9.5 c = 4.22 Cross-Section Note: 0.75ρ b is a parameter set by the Standard Specification, and is used for comparative purposes

12 12 Lesson 2: Unified Design Approach for Structural Concrete Standard Specification c = (A s *f y ) / (β*0.85*f c*b) = 4.22 (a=3.58, Whitney Stress Block) ε s = (1.82*ε y ) φm n_std Spec = 0.9*(1.22in 2 *60ksi)*( /2) = 42 k-ft 6 ε c = d = 9.5 c ε t /ε y =1.82*ε y ε t = Lesson 2: Unified Design Approach for Structural Concrete LRFD Specification ε c = φ (phi) Compression Controlled Transition Region Tension Controlled ε t = Reinforcing Tensile Strain (ε t ) φm n_lrfd = 0.84*(1.22in 2 *60ksi)*( /2) = 39 k-ft φm n_lrfd = 39 k-ft < φm n_std Spec = 42 k-ft Note: Capacity is function of reinforcement strain, independent of ρ

13 13 Lesson 2: Unified Design Approach for Structural Concrete Prestressed Concrete ε c = φ (phi) Compression Controlled Transition Region Tension Controlled ε t ε serv Prestressing Tensile Strain (ε t ) If ε serv (steel stress at decompression) ~ 0.70f pu /E ps = 189ksi / 28,000ksi = & ε t ~ 0.005, then ε total strain = = = 1.35 ε y Lesson 2: Unified Design Approach for Structural Concrete Compression Members φ (phi) Compression Controlled Transition Region Tension Controlled Reinforcing Tensile Strain (ε t ) ε c = ε c = ε t ε t = small ε t ε t = large

14 14 Lesson 2: Unified Design Approach for Structural Concrete Interaction Diagram Nominal Capacity φ P n (kips) Design Strength Balanced Condition 0.1 A g f c (Std. Spec) LRFD - φ Transition φ M n (kips) Lesson 2: Unified Design Approach for Structural Concrete Ductility Tension Controlled Sections ε c = ε c = Mild Reinforcing ε y 60ksi = Ductility = ε t / ε y Ductility 60ksi = 2.4 ε t = ε serv = ε total Prestressed Reinforcing ε t = Mild Reinforcing Prestressed Steel ε y 270ksi = Ductility = ε t / ε y Ductility 270ksi = 1.4 ε t = does not guarantee same amount of ductility for different steels, but indeed accounts for high strength steels. Also provides same amount of rotation for all steels at nominal strength.

15 15 Lesson 2: Unified Design Approach for Structural Concrete Compression Controlled Sections Compression-Controlled Limit (ε t =0.002) Reinforced ε y = 60ksi/29,000ksi = ~ Prestressed ε y = 243ksi/28,000ksi = ~ = ε c = Defines compression controlled sections as the point of balanced conditions ε t = Lesson 2: Unified Design Approach for Structural Concrete Notes: 1. Flexural components are no longer restricted to 0.75ρ b, rather they are classified as tension controlled or compression controlled with an appropriate resistance factor applied to the capacity. 2. φ (phi) factors can be expressed as a simple formula relating to the c/d ratio. 3. Interaction diagrams for compressive members will use varying phi factors in determining capacity based on the strain in the reinforcing.

16 16 Course Outline Lesson 1: LRFD Concrete Overview Introduction to chapter Reasons for large size differences Lesson 2: Unified Design Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Strut & Tie Modeling Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items

17 17 Lesson 3 Lesson 3 Shear Design & Strut and Tie Modeling Lesson 3 Overview Shear Design: (LRFD - 3 ways to determine capacity) 1. Modified Compression Field Theory 2. Simplified method for shear design (NCHRP 549) 3. Shear design per the AASHTO Guide Specification for Design and Construction of Segmental Concrete Bridges Other Topics 1. Torsion 2. Horizontal Shear (Shear Friction) 3. Strut & Tie modeling (deep beams)

18 18 Method 1 - Modified Compression Field Theory Method 1 - Modified Compression Field Theory θ C T Ritter (1899), also Morsch (1902) defined shear behavior in cracked concrete analogous to truss behavior Both assumed a 45 degree inclination of compression struts From this, Vecchio and Collins have expanded the theory into what it is today

19 19 Method 1 - Modified Compression Field Theory θ d v C T d Applicable to reinforced, prestressed, and partially prestressed conc. Analogous to variable angle truss Concrete resist compression forces as a series of struts (or a field ) Steel resists tension forces as ties (stirrups) Modified to account for friction (aggregate interlock) across the inclined web cracks. Method 1 - Modified Compression Field Theory (cont d) Equilibrium conditions at M = 0 (Collins and Mitchell 1997)

20 20 Method 1 - Modified Compression Field Theory (cont d) Component of V c (Collins and Mitchell 1997) Method 1 - Modified Compression Field Theory (cont d) Equilibrium conditions and material behavior assumptions are made to deduce the angle of crack inclination, θ, and tensile strain in the concrete ε 1. Components of Resistance Unknowns Since the variables of θ & ε 1 are interdependent, the process becomes iterative.

21 21 Method 1 - Modified Compression Field Theory (cont d) Factors for determining β and θ Three items Longitudinal strain at mid-depth of member (ε x ) Shear stress on concrete (υ u ) Assumed θ (Collins and Mitchell 1997) Method 1 - Modified Compression Field Theory (cont d) Strain at Mid-depth of member

22 22 Method 1 - Modified Compression Field Theory (cont d) Strain at Mid-depth of member Locked-in prestressing (Collins and Mitchell 1997) Strain taken at middepth due to members with transverse reinforcement ability to redistribute shear stress within the section Method 1 - Modified Compression Field Theory (cont d) Shear Stress on Concrete υ u = V u - φv p φ b v d v Assumed Theta (θ) θ assumed

23 23 Method 1 - Modified Compression Field Theory (cont d) Calculated Values: υ u f c & ε x θ assumed iterated in strain equation (ε x ) until matching θ table θ β Method 1 - Modified Compression Field Theory (cont d) Components of Resistance V c = β f c (psi) * b v * d v V s = (A v * f y * d v * cot θ ) / s V n = V c + V s + V p β - term to account for concrete stress along the inclined shear cracked based on the crack width

24 24 Method 1 - Modified Compression Field Theory (cont d) Negative Strain If the value of ε x is negative, use different strain equation This is to account for the increased stiffness of the tension chord due to the member being uncracked. Negative indicates compression Method 1 - Modified Compression Field Theory (cont d) Negative Strain ε x values are found in β and θ tables Note more shallow θ angle, higher β for concrete contribution

25 25 Method 1 - Modified Compression Field Theory (cont d) Sections With LESS Than Minimum Transverse Reinforcing These section do not have ability to redistribute shear stresses within section Absence of 2.0 factor ε x will be taken at level of flexural reinforcing, rather than mid-depth Method 1 - Modified Compression Field Theory (cont d) Sections With LESS Than Minimum Transverse Reinforcing These section also do not have a good ability to distribute crack widths This will cause larger crack widths, thus having a negative impact on V c (aggregate interlock) Crack spacing (s xe ) is based upon longitudinal reinforcing and is a function of: 1. d v or distance between layers of reinforcing 2. aggregate size

26 26 Method 1 - Modified Compression Field Theory (cont d) Sections With LESS Than Minimum Transverse Reinforcing Addition of well distributed longitudinal reinforcing can increase shear capacity (V c ). Poorly Distributed Well Distributed Method 1 - Modified Compression Field Theory (cont d) Sections With LESS Than Minimum Transverse Reinforcing LRFD Provides tables to find β and θ Based upon crack spacing, s xe rather than stress on concrete, υ u Small β Small V c. Note: Could adversely affect footing shear design (deeper footings)

27 27 Method 1 - Modified Compression Field Theory (cont d) Two more important issues Minimum longitudinal reinforcing (equilibrium) Maximum allowable shear stress on a cross section Method 1 - Modified Compression Field Theory (cont d) Minimum Longitudinal Reinforcing Shear can cause significant tension in longitudinal steel. Especially at support locations C T

28 28 Method 1 - Modified Compression Field Theory (cont d) Maximum Allowable Shear Standard Specification: V c ~ 2 f c» 4 f c & V s_max = 8 f c V n_max ~ 10 f c» 12 f c or 0.15*f c LRFD: V n_max = 0.25*f c or 15 f c» 20 f c (much larger) Method 1 - Modified Compression Field Theory (cont d) Maximum Allowable Shear (cont d) The limit of V n_max = 0.25*f c addresses crushing capacity of concrete strut (web crushing) Capacity of concrete (strut) is reduced from full f c Strength of concrete Direction of cracking (parallel to strut or at angle) Tension strains transverse to the strut (from crossing reinforcement) (Collins and Mitchell 1997)

29 29 Course Outline Lesson 1: LRFD Concrete Overview Introduction to concrete section Reasons for large size differences Lesson 2: Unified Design Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory MCFT Subset - Simplified method for non-prestressed sections Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Strut & Tie Modeling Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items

30 30 Method 1a - Simplified Method for Non-Prestressed Sections Method 1a - Simplified Method for Non-Prestressed Sections Special subset of Modified Compression Field Theory This is similar to shear from the Standard Specification Vc = 2 f c (psi) * b * d v Vs = (A v * f y * d v * cot θ) / s (where θ = 45, or cot θ = 1.0) Assumptions 1. No tensile force, nonprestressed sections 2. Section contains minimum shear reinforcing 45 d v C T d v

31 31 Method 2 - Simplified for Prestressed and Non-Prestressed Method 2 - Simplified for Prestressed and Non-Prestressed (NCHRP 549) Similar to ACI 318 & AASHTO Std. Spec. for P/S Structures V ci (flexural shear resistance) V cw (web shear resistance) 1.9 f c (psi) vs. 3.5 f c (psi) (OLD) V s (shear resistance) (modified θ angle if web shear controls) Smaller limit to account for non & partially prestressed components

32 32 Method 2 - Simplified for Prestressed and Non-Prestressed V s (shear resistance) (modified θ angle if web shear controls) θ d cotθ (V cw ) d (V ci ) Method 3 - AASHTO Segmental Specification

33 33 Method 3 - AASHTO Segmental Specification Serves to simplify V c equation V c (concrete resistance) - Uses a K factor based upon how much pre-compression is in the section. V c = 2.0 * K * f c * b v * d v < 4.0 f c * b v * d v V s (shear resistance) Uses a 45 degree crack inclination angle to eliminate the need to check equilibrium of reinforcement (Modified Compression Field Theory) V s = (A v * f y * d v ) / s Method 3 - AASHTO Segmental Specification (cont d) V c = 2 * K * f c * b v * d v If the extreme fiber of the section exceeds 6 f c, K will be limited to 1.0 By limiting K = 1.0 for flexural cracked sections, it intrinsically accounts for flexural shear cracking (V ci ).

34 34 Lesson 3 Shear Theory History LRFD 1 st Edition (1994) & 2 nd Edition (1998): MCFT is only shear theory LRFD 3 rd Edition (2004): AASHTO Segmental Specification for Shear Resistance for Segmental Bridges is incorporated into the code LRFD 4 th Edition (2007): Simplified methods for prestressed and non-prestressed sections subject to shear is incorporated. This was a result of NCHRP Report 549, which was conducted to produce a direct method of determining shear resistance. Simplified method is similar to determining shear resistance for prestressed members using the Standard Specification From this, it can be noted the MCFT is the only new theory contained in the LRFD Specification Course Outline Lesson 1: LRFD Concrete Overview Introduction to concrete section Reasons for large size differences Lesson 2: Unified Design Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Strut & Tie Modeling Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items

35 35 Torsion Torsion Torsion provisions are included in LRFD Provisions are adapted using similar truss analogies as that for shear using the Modified Compression Field Theory Applicable to both prestressed and reinforced concrete Also can be applied to both hollow and solid crosssections

36 36 When to Consider Torsion? Torsion shall be considered when the moment due to torsion is greater than 25% that required to create cracking When to Consider Torsion? For Modified Compression Field Theory, calculation of longitudinal strain (ε x ) and shear stress on concrete (υ u ) are altered to include combination of shear and torsion. θ is iterated similar to MCFT shear process Minimum Longitudinal Reinforcing Accounts for combination of flexure, shear, and torsion

37 37 Horizontal Shear and Shear Friction Old Equations (Standard Specification): Shear Friction Horizontal Shear Drawbacks: Shear friction limited to 800psi on cross-section Horizontal shear limited to 350psi on cross-section regardless of amount of reinforcing. Horizontal shear requires large amount of reinforcing for wide flange beams. Horizontal Shear and Shear Friction (cont d) LRFD combines Std. Specification Articles on Shear Friction and Horizontal Shear. New Equation: Concrete Cohesion Steel Contribution Precompression Benefit

38 38 Horizontal Shear and Shear Friction (cont d) Benefits: Accounts for concrete cohesion Takes advantage of precompression benefits Shear friction has higher limits of max nominal shear stress (up to 1800psi from old limit of 800psi) Uses a more rational approach for horiz. shear, considering quantity of steel crossing the plane, rather than blindly using 350psi. Horiz. shear will require less steel for wide flange beams, since A v > 50psi*A c can be waived if φv ni > 1.33V ui / φ

39 39 Course Outline Lesson 1: LRFD Concrete Overview Introduction to concrete section Reasons for large size differences Lesson 2: Unified Design Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Strut & Tie Modeling Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items Strut & Tie Modeling

40 40 Strut & Tie Modeling New section in code (Article 5.6.3) Used to determine internal force effects at regions near supports and locations of concentrated loads Used in disturbed regions or those where plane section do not remain plane What is a strut and tie model? A design tool used to determine the flow of forces through a member Uses equilibrium conditions at strength limits Relies on concrete providing compression struts and reinforcing providing tension ties to resist internal forces Compression struts and tension ties meet at nodal locations Strut & Tie Modeling When to use? Diaphragms, Prestressing Anchorages, Deep beams Span-to-Depth < 2*d

41 41 Strut & Tie Modeling (Load Paths) Elastic analysis load paths can be helpful (MacGregor, 1997) Significant stress redistribution can occur after cracking Remains a good tool to guide reinforcement placement and quantity required Vertical Bursting 0.6H 0.4H 1.75 P P 11.5 T P 3 P 26.5 End of Beam Elevation

42 42 Prestressing Forces 0.5H 0.5H Force T P 11.5 Force 1 Force 1 3 Force 2 P Force Force 2 End of Beam Elevation Elastic Stress Distribution St. Venant s principle suggests localized disturbances reduce approximately one member depth from the point of disturbance Prestressing - Force Whirl T T Prestress T 2 nd Stage P/T -T Prestress Stage 1 & P/S Steps to Determine 1. Find Reactions 2. Compute internal stresses 3. Replace stresses with resultant forces 4. Draw a truss of struts and ties to represent load paths 5. Check Stresses in truss members and at nodal regions

43 43 Size of Struts Function of: Loading area Tie anchorage area 2 nd Stage P/T Anchored Area Stage 1 & P/S Loaded Area Strength of Struts Similar to that of MCFT, strength of strut is a function of the strain perpendicular to thrust 2 nd Stage P/T (Collins and Mitchell 1997) Full f c Partial f c Stage 1 & P/S f cu = limiting compression stress α s = smallest angel between strut and adjoining ties ε s = tensile strain in concrete in direction of tension tie

44 44 Compressive Stress of Nodal Regions Function of amount of confinement of region C C 2 nd Stage P/T T C C C T C CCC = 0.85 * φ * f c CCT = 0.75 * φ * f c CTT = 0.65 * φ * f c φ = 0.70 (compression struts) T Strut & Tie Modeling Strength of Struts & Ties Strength of Struts φp n = φ * f cu * A cs Strength of Nodal Regions CCC = 0.85 * f * f c ; CCT = 0.75 * f * f c ; CTT = 0.65 * f * f c Strength of Tension Ties φp n = φ * f y * A st

45 45 Strut & Tie Modeling Crack Control Reinforcement Structures designed using strut and tie models are required to contain an orthogonal grid of reinforcing at each face to control cracking. Spacing not to exceed 12inches Ratio of reinforcing to gross area shall be in each direction

46 46 Course Outline Lesson 1: LRFD Concrete Overview Introduction to concrete section Reasons for large size differences Lesson 2: Unified Design Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Strut & Tie Modeling Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items Lesson 4 Lesson 4 Prestressing

47 47 Lesson 4 Prestressing Partial Prestressing LRFD Article allows the use of partial prestressing What is Partial Prestressing? A flexural member in which prestressing is applied to satisfy serviceability constraints, but allows limited crack widths in the section under full loading Most commonly designed so the structure remains uncracked under permanent loads, but has limited cracking when live load is present. Lesson 4 Prestressing Partial Prestressing Pros: Reduces required amount of prestressing Reduces reserve strength capacity normally provided by fully prestressed components Excessive dead load camber is mitigated Cons: Due to cracking, serviceability checks become more tedious than that for reinforced bending members due to presence of axial force (prestressing) Normally requires addition of mild reinforcing Reduced stiffness for deflection Reduced φ factor based on amount of prestressing to mild reinf.

48 48 Lesson 4 Prestressing Partial Prestressing Serviceability Checks Crack Width Spacing of steel, involves steel stress calculation Steel stress used in crack width calculation is that produced after decompression Concrete Compression Stress Identical to those for fully prestressed components Deflection Must use a cracked section analysis (for areas where cracking occurs) Fatigue of Steel May or may not need to be considered - existence of tension in concrete at 1.5*fatigue loading Cracked section only need be considered for stress over 3 f c under 1.5*fatigue loading Lesson 4 Prestressing Partial Prestressing Cracked Section Analysis How to conduct cracked section analysis? Similar to reinforced concrete, but must determine the magnitude of forces to create decompression in the section P total_service = P decompress + P cracked M total_service = M decompress + M cracked Where P cracked &M cracked are forces placed on cracked section

49 49 Lesson 4 Prestressing Partial Prestressing Cracked Section Analysis, cont. Steps to Determine Stresses and Strains 1. Calculate σ and ε at transfer 2. Changes in σ and ε due to creep, shrinkage, relaxation 3. Changes in σ and ε due to decompression (opposite of 1 + 2) 4. Changes in σ and ε in the cracked stage (M cracked = M total_service M decompress ) & (P cracked = P total_service P decompress ) Calculate compression block depth (third order equation) 5. Sum strains in reinforcing Note: Curvature of section will be the summation of Steps 1 to 4 Prestress Losses

50 50 Lesson 4 Prestressing Total Prestress Losses Equations (Pretensioned) (Post-tensioned) Long-Term Losses Friction Losses Anchorage Seating Elastic Shortening Lesson 4 Prestressing Long-Term Prestress Losses Equations LRFD Prestents Three (3) Methods of f plt : 1. Lump Sum (without composite topping) 2. Approximate Method 3. Refined Estimate

51 51 Lesson 4 Prestressing Long-Term Prestress Losses Method 1 Used for members without composite toppings Double T, Solid Slabs, Voided Slabs, etc Lesson 4 Prestressing Long-Term Prestress Losses Method 2 Approximate Method Simplified method used for members with composite toppings Uses similar simplified equations to Standard Specification Yields conservative results Strand Relaxation Creep Losses Shrinkage Losses

52 52 Lesson 4 Prestressing Long-Term Prestress Losses Method 3 Refined Estimate Refined method of loss calculation Gain due to deck shrinkage Uses a two step method Losses occurring on beam alone prior to deck placement Losses occurring on combined section Non-Composite Composite Lesson 4 Prestressing Long-Term Prestress Losses Method 3 Cont d Refined method uses time dependent creep and shrinkage coefficients LRFD Creep & Shrinkage Model CEB-FIP Model Code (segmental construction) ACI 209

53 53 Course Outline Lesson 1: LRFD Concrete Overview Introduction to concrete section Reasons for large size differences Lesson 2: Unified Design Unified Design Lesson 3: Shear Design & Strut and Tie Modeling Modified Compression Field Theory Simplified method for shear design Shear design per the Segmental Specification Torsion and Shear Friction Shear Theories (including Strut & Tie) Lesson 4: Prestressing Partial Prestressing Prestress losses Lesson 5: Miscellaneous Items

54 54 Lesson 5 Lesson 5 Miscellaneous Items Non-Linear Temp. Gradient Minimum Flexural Reinforcing Minimum Shear Reinforcing Span-to-Depth Ratios Crack Width ( z factor) Lesson 5 Miscellaneous Items Non-Linear Temperature Gradient ~40 Mostly applicable to prestressed concrete superstructures (Chapter 3 Loads) Vertical gradient due to solar radiation Reversible for night conditions when rapid cooling of bridge can occur (Factor = -0.3) Applied only to Service Limit States Used with a 0.5 factor when accompanied by live load Used with a 1.0 factor when live load is not present

55 55 Lesson 5 Miscellaneous Items Non-Linear Temperature Gradient (cont d) Since gradient is non-linear, stresses cannot self-equilibrate This will cause stress in the crosssection regardless if determinate or nondeterminate For most structures will cause in the range of 3 f c» 5 f c tension in the top or bottom of section Some agencies ignore this loading if history has shown no distress in particular bridge types Lesson 5 Miscellaneous Items Non-Linear Temperature Gradient (cont d) Current LRFD temperature gradients are a simplification from that recommended in the AASHTO Guide Spec: Thermal Effects in Concrete Bridge Superstructures Positive Gradient (Thermal Spec) Negative Gradient (Thermal Spec) Simplified Gradient (LRFD Spec)

56 56 Lesson 5 Miscellaneous Items Minimum Flexural Reinforcing φm n > 1.2*M cr or 4/3 * M u f r = 12 f c (7.5 f c ) (accounts for variable tensile rupture strength) Will produce higher cracking moments Can significantly impact members designed for small allowable tensile stresses. (segmental construction: allowable tensile stress = zero) Lesson 5 Miscellaneous Items Minimum Column Reinforcing Standard Specification = 1% * A g_col LRFD = Due to most columns dominated by flexural behavior 1.35% ** Assumed 60ksi Reinforcing Yield Stress

57 57 Lesson 5 Miscellaneous Items Minimum Amount of Shear Reinforcing Standard Specification: A v_min = (50psi * b * s) / f y LRFD: A v_min = ( f c * b * s) / f y Test data has shown that beams with small reinforcement ratios can yield unconservative capacities Therefore minimum shear reinforcement has increased for higher strength concretes Note: 10,000psi = 100psi ; twice that of Standard Specification Lesson 5 Miscellaneous Items Span-to-Depth Ratios for Concrete LRFD gives guidelines for both prestressed and reinforced concrete Found in deflection articles contained in Chapter 2 L/22 L/25

58 58 Lesson 5 Miscellaneous Items Control of Cracking by Distribution of Reinforcement Standard Specification z factor equation is modified In sections where cracking can occur, spacing of reinforcing is limited New equation uses three parameters: 1. Spacing of reinforcement 2. Concrete cover 3. Steel stress γ e = exposure factor d c = distance from extreme tension fiber to centroid reinf. f ss = tensile stress in steel at service h = overall depth of component Objectives You should now be able to identify the following: 1. Reasons for the large size difference between the LRFD and Standard Specification concrete sections 2. The components of unified design provisions for concrete members 3. The elements of LRFD shear theories including simplified methods of design, and the Modified Compression Field Theory 4. The concept of strut-and-tie modeling and when it is appropriate 5. Changes to prestressing, including losses and partial prestressing. 6. The miscellaneous differences between LRFD and the Standard Specification which may affect everyday design.

59 59 References The following references were used in the preparation of this course. AASHTO, Standard Specifications for Highway Bridges, 17th Edition, American Association of State Highway and Transportation Officials, Washington D.C., AASHTO, LRFD Bridge Design Specifications, 4th Edition, American Association of State Highway and Transportation Officials, Washington D.C., Collins, M.P., and Mitchell, D. (1980), Shear and Torsion Design of Prestressed and Non- Prestressed Concrete Beams, Journal of the Prestressed Concrete Institute, V. 25, No. 5, Sept.-Oct., pp Collins, M.P., and Mitchell, D., Prestressed Concrete Structures, Response Publications, Canada, Ghali, A., Favre, R., and Elbadry, M., Concrete Structures, 3rd Edition, E & FN Spon, London, MacGregor, James G., Reinforced Concrete, Prentice Hall, New Jersey, Vecchio, F.J., and Collins, M.P., The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear, ACI Structural Journal, V. 83, No. 2, Mar.-Apr. 1986, pp Final Assessment Instructions You are now ready to begin the final assessment. The assessment consists of 10 multiple choice questions. You will need to achieve a minimum score of 80% to receive credit for passing the course. If you score below 80%, please go back and review the content of this course, and then retake the assessment to achieve a passing score. When ready, click the Right arrow below to advance to the assessment.

60 60 Conclusion Thank you for completing this course. If you received a passing score on the assessment, simply close this window to exit the course. Your score will be recorded on your transcript. If you did not achieve a passing score, please review the content of this course and then retake the assessment to achieve a passing score. If you have any questions or problems with the functionality of this course, please us at pbu@pbworld.com and specify the name of the course and the issue you are experiencing so that we may assist you.