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Publication Number: FHWA-HRT-05-056
Date: October 2006

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Chapter 3, Compilation and Evaluation of Results From High-Performance Concrete Bridge Projects, Volume I: Final Report

AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS

The compilation in this section is based on the AASHTO LRFD Bridge Design Specifications, Second Edition, 1998, and the 1999, 2000, and 2001 interim revisions.(7-10) This section only lists articles affected by HPC. For each listed article, the portion affected by HPC is shown in italics, followed by specific comments in regular font. For long articles, only a synopsis, followed by comments, is included. References in the comments to specific sections, articles, or tables refer to the document being reviewed and not the sections, articles, or tables of this report. The end result of the project is stated under the action item. Proposed revisions are included in appendix D. Research problem statements are included in appendix F.

Section 5: CONCRETE STRUCTURES

5.1 SCOPE

The provisions in this section apply to the design of bridge and retaining wall components constructed of normal density or lightweight concrete and reinforced with steel bars and/or prestressing strands or bars. The provisions are based on concrete strengths varying from 2.4 ksi to 10.0 ksi.

The scope should be extended to concrete strengths higher than 70 MPa (10.0 kips/inch2 (ksi)). It should be made clear in the scope that welded wire reinforcement is included in this section. The scope should be expanded to include prestressing wire. Both welded wire reinforcement and prestressing wire have use in HPC.

ACTION: Revisions to include welded wire reinforcement and design for strengths above 70 MPa (10.0 ksi) are proposed.

5.2 DEFINITIONS

A definition of HPC should be included in this article to facilitate the introduction of provisions about HPC.

ACTION: HPC concretes are proposed for the AASHTO LRFD Bridge Construction Specifications.

Normal-Weight Concrete: Concrete having a weight between 0.135 and 0.155 kcf.

The definition should be expanded for unit weights greater than 2.48 Mg/m3 (0.155 kips per cubic foot (kcf)), which can occur with HPC.

ACTION: None. Existing data do not justify a revision.

5.3 Notation

f prime, subscript c =   specified compressive strength of concrete at 28 days, unless another age is specified (ksi) (5.4.2.1).

Since strengths are frequently specified at ages other than 28 days for HSC, rewording of this article should be considered.

ACTION: A revision to delete 28 days is proposed.

5.4 MATERIAL PROPERTIES

5.4.1 General

C5.4.1

Occasionally, it may be appropriate to use materials other than those included in the AASHTO LRFD Bridge Construction Specifications; for example, when concretes are modified to obtain very high strengths through the introduction of special admixtures, such as:

  • Silica fume,
  • Cements other than Portland or blended hydraulic cements,
  • Proprietary high early-strength cements, and
  • Other types of reinforcing materials.

In these cases, the properties of such materials should be established by a specified testing program.

Fly ash, ground granulated blast-furnace slag, and metakaolin should be added to the list of materials.

The different test programs to achieve HPC should be defined.

ACTION: A revision to include slag is proposed.

5.4.2 Normal and Structural Lightweight Concrete

5.4.2.1 Compression Strength

Concrete strengths above 10.0 ksi shall be used only when physical tests are made to establish the relationships between concrete strength and other properties.

The upper limit of 70 MPa (10.0 ksi) needs to be removed to the extent possible to permit the greater use of HSC.

ACTION: A revision to remove the 70-MPa (10.0-ksi) restriction in specific articles is proposed.

The sum of Portland cement and other cementitious materials shall be specified not to exceed 800 pcy.

Although an upper limit may be appropriate for conventional strength concrete, it should be removed for HSC, which frequently contains more than 475 kg/m3 (800 lb/yd3) of cementitious materials. At the same time, excessive use of cementitious materials should be avoided.

ACTION: A revision to increase the maximum cementitious materials content is proposed.

Table C5.4.2.1-1 Concrete Mix Characteristics by Class

This table needs to be extended to incorporate values for HPC.

ACTION: Revisions to add two classes of HPC are proposed.

5.4.2.3 Shrinkage and Creep

5.4.2.3.1 General

In the absence of more accurate data, the shrinkage coefficients may be assumed to be 0.0002 after 28 days and 0.0005 after 1 year of drying.

The final shrinkage strain differs significantly from the 28-day shrinkage strain. However, the final value, 0.0005, may not be appropriate for HPC. The AASHTO Standard Specifications uses a single number, 0.0002, for shrinkage strain. The conditions under which the stated shrinkage strains are applicable need to be defined. The appropriate values for HPC need to be determined.

ACTION: Revisions based on NCHRP project 18-07 are proposed.

5.4.2.3.2 Creep and 5.4.2.3.3 Shrinkage

These articles provide equations for the calculation of creep and shrinkage that are based on the recommendations of ACI Committee 209 as modified by additional published data.

Depending on the constituents used to make HPC, the creep and shrinkage strain can be different from the values given by the equations. The equations need to be modified to include creep and shrinkage of HPC with its different constituent materials.

Depending on the curing conditions for the concrete, the creep and shrinkage strain can vary. High early compressive strength is important for HSC to achieve early release of the pretensioning force. In most cases, this is achieved by applying heat or steam curing. This affects the creep of the concrete and needs to be included in the equation for creep strain. It is anticipated that information about creep will be developed as part of NCHRP project 18-07. This information will need to be incorporated into this article.

ACTION: Revisions based on NCHRP project 18-07 are proposed.

5.4.2.4 Modulus of Elasticity

In the absence of more precise data, the modulus of elasticity, Ec, for concretes with unit weights between 0.090 and 0.155 kcf may be taken as:

Equation 46.  The equation reads E subscript c is equal to 33,000 times w subscript c superscript 1.5, times the square root of f prime subscript c.

(5.4.2.4-1)        [Equation 46]

where

wc = unit weight of concrete (kcf)

f prime, subscript c  = specified strength of concrete (ksi)

Equation 5.4.2.4-1 for the modulus of elasticity may not be appropriate for HSC.(15) The stress-strain behavior of HPC is different than that for conventional strength concrete. There are data that suggest that the Ec for HSC may be influenced by aggregate stiffness.(26) Furthermore, some HSCs have a unit weight greater than 2.48 Mg/m3 (155 lb/ft3). Thus, the equation for Ec in this article needs to be evaluated using recent data.

ACTION: A revision based on NCHRP project 18-07 is proposed.

5.4.2.6 Modulus of Rupture

Unless determined by physical tests, modulus of rupture, fr, in ksi, may be taken as:

  • For normal-weight concrete........................................................... 0.24 the square root of f prime, subscript c
  • For sand-lightweight concrete....................................................... 0.20 the square root of f prime, subscript c
  • For all-lightweight concrete........................................................... 0.17 the square root of f prime, subscript c

The factor in front of the square root of f prime, subscript c should be verified for HPC. A higher coefficient than 0.24 is possible for HSC. However, the coefficient seems to depend on the specific materials in the concrete. Information on the specific materials for a given project may not be available at the design stage. Consequently, the limit needs to be a conservative value.

ACTION: Revisions for normal-weight concrete are proposed. A research problem statement is proposed for other weights of concrete.

5.4.2.7 Tensile Strength
C5.4.2.7

For most regular concretes, the direct tensile strength may be estimated as fr = 0.23the square root of f prime, subscript c.

For HSC, a coefficient greater than 0.23 may be possible.

ACTION: A research problem statement is proposed.

5.4.6 Ducts

5.4.6.2 Size of Ducts

The size of ducts shall not exceed 0.4 times the least gross concrete thickness at the duct.

With HSC precast concrete I-girders, thinner webs are often used to maximize section efficiency. Consideration should be given to allowing larger ducts in the webs of HSC members.

ACTION: A revision to eliminate this provision for precast, pretensioned beams is proposed.

5.5 LIMIT STATES

5.5.3 Fatigue Limit State

5.5.3.1 General

Fatigue need not be investigated for concrete deck slabs in multigirder applications.

With HSC girders and wider girder spacing, it may be necessary to investigate concrete deck slabs for fatigue.

ACTION: None.

The section properties for fatigue investigations shall be based on cracked sections where the sum of stresses, due to unfactored permanent loads and prestress, and 1.5 times the fatigue load is tensile and exceeds 0.095the square root of f prime, subscript c.

The tensile stress limit in the last paragraph should be investigated for its applicability with HPC.

ACTION: None.

5.5.4 Strength Limit State

5.5.4.2 Resistance to Factors

5.5.4.2.1 Conventional Construction

Resistance factor phishall be taken as:

  • For flexure and tension of reinforced concrete...................................... 0.90

  • For flexure and tension of prestressed concrete.................................... 1.00

  • For shear and torsion:
    normal-weight concrete.............................................................. 0.90
    lightweight concrete................................................................... 0.70


  • For axial compression with spirals or ties, except as specified in Article 5.10.11.4.1b for Seismic Zones 3 and 4 at the extreme event limit state........................................................... 0.75

  • For bearing on concrete......................................................................... 0.70

  • For compression in strut-and-tie models................................................ 0.70

  • For compression in anchorage zones:
    normal-weight concrete.............................................................. 0.80
    lightweight concrete................................................................... 0.65

  • For tension in steel anchorage zones...................................................... 1.00

  • For resistance during pile driving.......................................................... 1.00

These resistance factors have been developed for conventional concrete. HPC tends to be very sensitive to water contents and constitutive materials. The chance of understrength concrete may increase, especially at very high compressive strength levels. On the other hand, HPC is produced with stricter quality control and a lower coefficient of variation than conventional concrete. Also, HSC has less lateral expansion than conventional strength concrete, so the effect of confinement is less. This affects column behavior. Therefore, there is a need to verify the suitability of the given resistance factors for HPC, especially HSC.

ACTION: Revisions to include strength design for pretensioned concrete members at release are proposed. A research problem statement is proposed to address resistance factors.

5.6 DESIGN CONSIDERATIONS

5.6.3 Strut-and-Tie Model

5.6.3.3 Proportioning of Compressive Struts

5.6.3.3.3 Limiting Compressive Stress in Strut

The limiting compressive stress, fcu , shall be taken as:               

Equation 47.  The equation reads f subscript cu is equal to f prime subscript c divided by .8 plus 170 times epsilon subscript 1 less than or equal to .85 times f prime subscript c.

(5.6.3.3.3-1)        [Equation 47]

for which

Equation 48.  The equation reads epsilon subscript 1 is equal to epsilon subscript s plus open parentheses epsilon subscript s plus .002 close parentheses, cotangent of alpha subscript s squared.

(5.6.3.3.3-2)      [Equation 48]

where

alphas = the smallest angle between the compressive strut and adjoining tension ties (deg.)

epsilons = the tensile strain in the concrete in the direction of the tension tie (inches/inch)

f prime, subscript c  = specified compressive strength (ksi)

The appropriateness of the limiting compressive stress should be verified for HSC.

ACTION: A research problem statement is proposed.

5.6.3.5 Proportioning of Node Regions

Unless confining reinforcement is provided and its effect is supported by analysis or experimentation, the concrete compressive stress in the node regions of the strut shall not exceed:

  • For node regions bounded by compressive struts and bearing areas:   0.85 phif prime, subscript c
  • For node regions anchoring a one-direction tension tie:   0.75 phif prime, subscript c
  • For node regions anchoring tension ties in more than one direction:   0.65 phif prime, subscript c

The appropriateness of the maximum values of the concrete compressive stress in the node regions should be verified for HSC.

ACTION: A research problem statement is proposed.

5.6.3.6 Crack Control Reinforcement

Structures and components or regions thereof, except for slabs and footings, which have been designed in accordance with the provisions of Article 5.6.3, shall contain an orthogonal grid of reinforcing bars near each face. The spacing of the bars in these grids shall not exceed 12.0 inches.

The ratio of reinforcement area to gross concrete area shall not be less than 0.003 in each direction.

Since HSC has a higher tensile strength than conventional strength concretes, the minimum reinforcement ratio needs to increase as the concrete compressive strength increases. A revision to this article should be considered.

ACTION: A research problem statement is proposed.

5.7 DESIGN FOR FLEXURAL AND AXIAL FORCE EFFECTS

5.7.1 Assumptions for Service and Fatigue Limit States

The following assumptions may be used in the design of reinforced, prestressed, and partially prestressed concrete components:

  • The modular ratio is not less than 6.0.

An effective modular ratio of 2n is applicable to permanent loads and prestress.

The modular ratio of concrete is a function of modulus of elasticity of concrete, which is a function of the concrete compressive strength. HSC will frequently result in a modular ratio that is less than 6.0. Therefore, the validity of limiting the modular ratio, n, to 6.0 needs to be evaluated.

Traditional methods of prestressed concrete design do not use an effective modular ratio of 2n for permanent loads and prestress. The validity of this article needs to be verified for HSC.

ACTION: A revision to use the actual value of n is proposed.

5.7.2 Assumptions for Strength and Extreme Event Limit States

5.7.2.1 General

Factored resistance of concrete components shall be based on the conditions of equilibrium and strain compatibility, the resistance factors as specified in Article 5.5.4.2, and the following assumptions:

  • If the concrete is confined, a maximum usable strain exceeding 0.003 may be utilized if verified.
  • The concrete compressive stress-strain distribution is assumed to be rectangular, parabolic, or any other shape that results in a prediction of strength in substantial agreement with the test results.

This article defines the assumption for calculating flexural resistance of concrete members. An assessment should be made to determine if the maximum useable strain of 0.003 is applicable for HSC and if it is appropriate to assume any shape for the compressive stress-strain distribution.

ACTION: None. Further research is the objective of NCHRP project 12-64.

5.7.2.2 Rectangular Stress Distribution

The natural relationship between concrete stress and strain may be considered satisfied by an equivalent rectangular concrete compressive stress block of 0.85 f prime, subscript c over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = beta1c from the extreme compression fiber. The distance c shall be measured perpendicular to the neutral axis. The factor beta1 shall be taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi, beta1 shall be reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that beta1 shall not be taken less than 0.65.

The stress-strain curve for HSC is more linear than for conventional strength concrete. However, the stress block factors are generally considered to be still valid for members where flexure predominates. For members where axial compression predominates, the concrete stress of 0.85 f prime, subscript c may need to be reduced as concrete strength increases.(27) In the Canadian Standard for Design of Concrete Structures, the 0.85 factor is replaced by (0.85 – 0.0015 f prime, subscript c) ³ 0.067, in which f prime, subscript c is in megapascals.(28) A review is needed to determine if the rectangular stress block and factors are valid with HSC.

ACTION: None. Further research is the objective of NCHRP project 12-64.

5.7.3 Flexural Members

5.7.3.1 Stress in Prestressing Steel at Nominal Flexural Resistance

5.7.3.1.1 Components With Bonded Tendons

For rectangular or flanged sections subjected to flexure about one axis where the approximate stress distribution specified in Article 5.7.2.2 is used and for which fpe is not less than 0.5 fpu, the average stress in prestressing steel, fps, may be taken as:                  

      fps = fpu     Equation 49.  The equation reads f subscript ps is equal to f subscript pu times open parentheses 1 minus k times c divided by d subscript p close parentheses.

(5.7.3.1.1-1)             [Equation 49]

for which                          

     k = 2   Equation 50.  The equation reads kappa equals 2 times open parentheses 1.04 minus f subscript py divided by f subscript pu close parentheses.

(5.7.3.1.1-2)             [Equation 50]

for T-section behavior              

     c =    Equation 51.  The equation reads c equals A subscript ps times f subscript pu plus A subscript s times f subscript y minus A prime, subscript s times f prime, subscript y minus .85 times beta subscript 1 times f prime, subscript c times open parentheses b minus b subscript w close parentheses, times h subscript f all divided by .85 times f prime subscript c times beta subscript 1 times b subscript w plus kappa times A subscript ps times f subscript pu divided by d subscript p.

(5.7.3.1.1-3)  [Equation 51]

for rectangular section behavior

   Equation 52.  The equation reads c equals A subscript ps times f subscript pu plus A subscript s times f subscript y minus A prime, subscript s times f prime, subscript y

(5.7.3.1.1-4)  [Equation 52]

The equations in this article are based on the assumption of a rectangular stress block as defined in article 5.7.2.2. If a different stress distribution is required for HSC, these equations may need to be revised or their application restricted to lower concrete strengths.

The LRFD method relates beta1 to the concrete area in compression rather than the neutral axis depth. The results are consistent only if the compression zone has a uniform width, as in a rectangular section. Significant differences may arise for sections with non-rectangular geometry. This can be seen from equation 5.7.3.1.1-3.

Also, equation 5.7.3.1.1-1 of the LRFD provides prestressing steel stress at ultimate as a function of c. This requires iteration, since c is a function of fps. Combining equation 5.7.3.1.1-1 and equation 5.7.3.1.1-3, and by carrying on further mathematical manipulation, the equations can be written as follows:             

   Equation 53.  The equation reads beta subscript 1 times open parentheses .85 times f prime, subscript c close parentheses, times open bracket b subscript w times c plus open parentheses b minus b subscript w close parentheses, times h subscript f close bracket, is equal to A subscript ps times f subscript ps plus A subscript s times f subscript y minus A prime, subscript s times f subscript y.

[Equation 53]

or

beta1 (0.85 f prime, subscript c) (total compression area bounded by neutral axis) = (total tensile force in reinforcement)

These equations may considerably overestimate the neutral axis depth, c, and need to be evaluated for use with HSC.

ACTION: None. Further research is the objective of NCHRP project 12-64.

5.7.3.2 Flexural Resistance

5.7.3.2.2 Flanged Sections

For flanged sections subjected to flexure about one axis and for biaxial flexure with axial load as specified in Article 5.7.4.5, where the approximate stress distribution specified in Article 5.7.2.2 is used and the tendons are bonded, and where the compression flange depth is less than c, as determined in accordance with Equation 5.7.3.1.1-3, the nominal flexural resistance may be taken as:

   Equation 54.  The equation reads M subscript n is equal to A subscript ps time f subscript ps times open parentheses d subscript p minus a divided by 2 close parentheses, plus A subscript s times f subscript y open parentheses d subscript s minus a divided by 2 close parentheses, minus A prime subscript s times f prime subscript y times open parentheses d prime subscript s minus a divided by 2 close parentheses, plus .85 times f prime subscript c times open parentheses b minus b subscript w close parentheses, beta subscript 1 times h subscript f times open parentheses a divided 2 all minus h subscript f divided by 2 close parentheses.

(5.7.3.2.2-1)    [Equation 54]

LRFD specifies a T-section behavior if c > hf. This is inconsistent with the traditional definition in the ACI 318 Building Code and the AASHTO Standard Specifications where a section is considered a T-section if a > hf . The impact of this article needs to be evaluated for use with HSC.

ACTION: None. Further research is the objective of NCHRP project 12-64.

5.7.3.3 Limits for Reinforcement

5.7.3.3.1 Maximum Reinforcement

The maximum amount of prestressed and nonprestressed reinforcement shall be such that:               

   Equation 55.  The equation reads c divided by d subscript e less than or equal to .42.

(5.7.3.3.1-1)             [Equation 55]

for which                   

   Equation 56.  The equation reads d subscript e equals A subscript ps times f subscript ps times d subscript p plus A subscript s  times f subscript y times d subscript s that sum divided by A subscript ps times f subscript ps plus A subscript s times f subscript y.

(5.7.3.3.1-2)              [Equation 56]

The appropriateness of these equations for use with HSC needs to be evaluated.

ACTION: None. Further research is the objective of NCHRP project 12-64.

5.7.3.3.2 Minimum Reinforcement

Unless otherwise specified, at any section of a flexural component, the amount of prestressed and nonprestressed tensile reinforcement shall be adequate to develop a factored flexural resistance, Mr , at least equal to the lesser of:

  • 1.2 times the cracking strength determined on the basis of elastic stress distribution and the modulus of rupture, fr , of the concrete as specified in Article 5.4.2.6, or
  • 1.33 times the factored moment required by the applicable strength load combinations specified in table 3.4.1-1.

The provisions of Article 5.10.8 shall apply.

The purpose of this article is to ensure that the section does not go to the ultimate strength state as soon as it cracks. HSC is known to have proportionately higher tensile strength than conventional strength concrete. This means that the actual value of cracking strength is higher that that calculated using 0.24 the square root of f prime, subscript cfor the modulus of rupture. Therefore, any factor of safety provided by this article would be lost. Revision to the equation for the modulus of rupture and/or the 1.2 factor may be needed. With high-strength, post-tensioned concrete I‑girder bridges, the requirement of 1.2 times the cracking moment may result in excessive minimum reinforcement. The cracking moment is relatively large in this application because of the large total prestressing force. It is conceivable that 1.2 times the cracking moment may be very close to or even higher than the required factored load moment Mu. Thus, the section may not even crack under factored load. The problem is further complicated by the fact that in some applications, the section is reinforced to its maximum limit. Thus, 1.33 times the factored moment would make the section significantly over-reinforced. Consequently, the extra reinforcement required to satisfy the minimum reinforcement limit would be largely ineffective. A revision is needed to address this situation.

ACTION: Revisions to article 5.4.2.6 are proposed.

5.7.3.6 Deformations

5.7.3.6.2 Deflection and Camber

Unless a more exact determination is made, the long-time deflection may be taken as the instantaneous deflection multiplied by the following factor:

  • If the instantaneous deflection is based on Ig:   4.0
  • If the instantaneous deflection is based on Ie:   3.0−1.2(As’/As) > 1.6

HSC usually has lower creep than conventional strength concrete, so long-term deflection multipliers may be less. Long-term deflection factors were developed for conventional strength concrete and need to be verified for use with HSC.

An approach similar to that of ACI 318 could be adopted.(18) However, the ACI factors may also need to be modified for use with HSC.

ACTION: A research problem statement is proposed.

5.7.4 Compression Members

5.7.4.2 Limits for Reinforcement

The maximum area of prestressed and nonprestressed longitudinal reinforcement for noncomposite compression components shall be such that:                         

Equation 57.  The equation reads A subscript s divided by A subscript g that sum plus A subscript ps times f subscript pu that sum divided by A subscript g times f subscript y less than or equal to .08.   

(5.7.4.2-1)              [Equation 57]

and                   

Equation 58.  The equation reads A subscript ps times f subscript pe all divided by A subscript g times f prime, subscript c less than or equal to .3.   

  (5.7.4.2-2)              [Equation 58]

The minimum area of prestressed and nonprestressed longitudinal reinforcement for noncomposite compression components shall be such that:                    

Equation 59.  The equation reads A subscript s times f subscript y all divided by A subscript g times f prime, subscript c plus A subscript ps times f subscript pu all divided by A subscript g times f prime, subscript c greater than or equal to .135.   

  (5.7.4.2-3)              [Equation 59]

This article provides maximum and minimum reinforcement limits for compression members. These equations are different than those that appear in the AASHTO Standard Specifications. The limits given by these equations should be evaluated for use with HSC.

ACTION: None. Further research is the objective of NCHRP project 12-64.

5.7.4.4 Factored Axial Resistance

The factored axial resistance of reinforced concrete compressive components, symmetrical about both principal axes, shall be taken as:

Equation 60. The equation reads P subscript r equals phi times P subscript n.   

    (5.7.4.4-1)       [Equation 60]

for which

  • For members with spiral reinforcement:

Equation 61. The equation reads P subscript n equals .85 times open bracket .85 times f prime, subscript c times open parentheses A subscript g minus A subscript st close parentheses, plus f subscript y times A subscript st close bracket.   

    (5.7.4.4-2)    [Equation 61]
  •   For members with tie reinforcement:                       

Equation 62. The equation reads P subscript n equals .80 times open bracket .85 times f prime, subscript c times open parentheses A subscript g minus A subscript st close parentheses, plus f subscript y times A subscript st close bracket.   

    (5.7.4.4-3)     [Equation 62]

HSC has less lateral expansion than conventional strength concrete, so the confinement effect is less. This affects column behavior. The constants used in equations 5.7.4.4-2 and 5.7.4.4-3 need to be evaluated for use with HSC.

ACTION: None. Further research is the objective of NCHRP project 12-64.

5.7.4.6 Spirals and Ties

Where the area of spiral and tie reinforcement is not controlled by:

  • Seismic requirements,
  • Shear or torsion as specified in Article 5.8, or
  • Minimum requirements as specified in Article 5.10.6,

the ratio of spiral reinforcement to total volume of concrete core, measured out-to-out of spirals, shall not be less than: 

Equation 63. The equation reads rho subscript s equals .45 times open parentheses A subscript g divided by A subscript c minus 1 close parentheses, times f prime subscript c divided by f subscript yh.   

    (5.7.4.6-1)              [Equation 63]

Spirals are less effective for confinement in HSC. Another formula is reported by ACI Committee 363 and should be considered.(15) In addition, the ratio of reinforcement required by equation 5.7.4.6-1 may be too high to be practical with HSC. The concept for providing spiral reinforcement to strengthen the core to offset the loss of strength when the concrete shell is lost may not be appropriate for HSC.

ACTION: A research problem statement is proposed.

5.7.5 Bearing

In the absence of confinement reinforcement in the concrete supporting the bearing device, the factored bearing resistance shall be taken as:

Equation 64. The equation reads P subscript r equals phi times P subscript n.   

[Equation 64]

for which

Equation 65. The equation reads P subscript n equals .85 times f prime subscript c times A subscript 1 times m.   

[Equation 65]

The coefficient of 0.85 needs to be verified for HSC.

ACTION: A research problem statement is proposed.

5.8 SHEAR AND TORSION

5.8.2 General Requirements

5.8.2.2 Modifications for Lightweight Concrete

Where lightweight aggregate concretes are used, the following modifications shall apply in determining resistance to torsion and shear:

  • Where the average splitting tensile strength of lightweight concrete, fct , is specified, the term the square root of f prime, subscript c in the expressions given in Articles 5.8.2 and 5.8.3 shall be replaced by:

Equation 66. The equation reads 4.7 times f subscript ct less than or equal to the square root of f prime subscript c.   

[Equation 66]
  • Where fct, is specified, the term 0.75 the square root of f prime, subscript c for all-lightweight concrete, and 0.85 the square root of f prime, subscript c for sand-lightweight concrete shall be substituted for the square root of f prime, subscript c in the expressions given in Articles 5.8.2 and 5.8.3.

Linear interpolation may be employed when partial sand replacement is used.

The coefficients in front of the square root of f prime, subscript c need to be verified for both all-lightweight concrete and sand-lightweight HPC.

ACTION: A research problem statement is proposed.

5.8.2.5 Minimum Transverse Reinforcement

Where transverse reinforcement is required, as specified in Article 5.8.2.4, the area of steel shall not be less than:      

Equation 67. The equation reads A subscript v equals .0316 times the square root of f prime subscript c times b subscript v times s that sum divided by f subscript y.   

(5.8.2.5-1)              [Equation 67]

Equation 5.8.2.5-1 is similar to that developed for ACI 318 to allow for an increase in the minimum amount of shear reinforcement as concrete strength increases.(18) However, the coefficient in the ACI equation is 0.24. The appropriate coefficient for use with HSC needs to be determined.

ACTION: None. Further research is being conducted under NCHRP project 12-56.

5.8.2.8 Design and Detailing Requirements

The design yield strength of nonprestressed transverse reinforcement shall not exceed 60.0 ksi.

The use of a design yield strength higher than 60.0 kips/inch2 should be considered for both HSC and conventional concretes.

ACTION: Revisions to allow higher design yield strengths are proposed.

5.8.3. Sectional Design Model

5.8.3.3 Nominal Shear Resistance

The nominal shear resistance, Vn , shall be determined as the lesser of:                        

Equation 68. The equation reads V subscript n is equal to V subscript c plus V subscript s plus V subscript p.   

(5.8.3.3-1)              [Equation 68]

   

Equation 69. The equation reads V subscript n is equal to .25 times f prime subscript c times b subscript v times d subscript v plus V subscript p.   

(5.8.3.3-2)              [Equation 69]

for which  

Equation 70.  The equation reads V subscript c is equal to .0316 times beta times the square root of f prime subscript c times b subscript v times d subscript v.   

(5.8.3.3-3)              [Equation 70]

  

Equation 71.  The equation reads V subscript s is equal to A subscript v times f subscript y times d subscript v times open parentheses cotangent theta plus cotangent alpha close parentheses, times the sine of alpha that sum all divided by s.   

(5.8.3.3-4)              [Equation 71]

This article provides a maximum limit on the nominal shear Vn. In equation 5.8.3.3-2, the presence of f prime, subscript c allows much higher shear forces than the equivalent limits in the AASHTO Standard Specifications, which are stated in terms of limiting Vs. The nominal shear resistance of a member increases with an increase in concrete strength. The factor 0.25 needs to be verified for HSC.

At higher compressive strengths, HSC is more brittle and the shear cracks are smoother. As a result, there is less friction along the shear cracks. Since this friction carries some of the shear load, shear provided by the concrete may be less. Consequently, the constants 0.0316 and betaused in equation 5.8.3.3-3 need to be investigated.

ACTION: None. Further research is being conducted under NCHRP project 12-56.

5.8.3.4 Determination of betaand theta

5.8.3.4.2 General Procedure

This article provides a procedure for determining beta and theta using equations, tables, and figures. The equations, tables, and figures were developed considering f prime, subscript c no higher than 10 ksi. These tables and curves need to be revisited to be sure that they are applicable to HSC.

ACTION: None. Further research is being conducted under NCHRP project 12-56.

5.8.4 Interface Shear Transfer–Shear Friction

5.8.4.1 General

Interface shear transfer shall be considered across a given plane at:

  • An existing or potential crack,
  • An interface between dissimilar materials, or
  • An interface between two concretes cast at different times.

The nominal shear resistance of the interface plane shall be taken as:

Equation 72.  The equation reads V subscript n is equal to c times A subscript cv plus mu times open bracket A subscript vf times f subscript y plus P subscript c close parentheses.   

(5.8.4.1-1)              [Equation 72]

The nominal shear resistance used in the design shall not exceed:

Equations 73.  The equation reads V subscript n less than or equal to .2 times f prime subscript c times A subscript cv.   

(5.8.4.1-2)              [Equation 73]

or        

Equations 74.  The equation reads V subscript n less than or equal to .8 times A subscript cv.   

(5.8.4.1-3)              [Equation 74]

Reinforcement for interface shear between concretes of slab and beams or girders may consist of single bars, multiple-leg stirrups, or the vertical legs of welded wire fabric. The cross-sectional area, Avf , of the reinforcement per unit length of the beam or girder should not be less than either that required by Equation 1 or:        

Equations 75.  The equation reads A subscript vf greater than or equal to .05 times b subscript v that sum divided by f subscript y.   

(5.8.4.1-4)              [Equation 75] (5.8.4.1-3)

Equation 5.8.4.1-3 imposes a limit of 28 MPa (4000 psi) on the compressive strength of concrete that can be used in design. This limit needs to be evaluated based on recent test data.

Equation 5.8.4.1-4 should be changed so that the minimum reinforcement is a function of the concrete compressive strength.

ACTION: A research problem statement is proposed.

5.8.4.2 Cohesion and Friction

The following values shall be taken for cohesion factor, c, and friction factor, mu:

  • For concrete placed monolithically:                 

Equation 76. The equation reads c equals .15 KSI.   

[Equation 76]

 

Equation 77. The equation reads mu equals 1.4 times lambda.   

[Equation 77]
  • For concrete placed against clean, hardened concrete with surface intentionally roughened to an amplitude of 0.25 inch:

Equation 78. The equation reads c equals .1 KSI.   

[Equation 78]

 

Equation 79. The equation reads mu equals 1 times lambda.   

[Equation 79]
  • For concrete placed against hardened concrete clean and free of laitance, but not intentionally roughened:

Equation 80. The equation reads c equals .075 KSI.   

[Equation 80]

 

Equation 81. The equation reads mu equals .6 times lambda.   

[Equation 81]
  • For concrete anchored to as-rolled structural steel by headed studs or by reinforcing bars where all steel in contact with concrete is clean and free of paint:                               

Equation 82. The equation reads c equals .025 KSI.   

[Equation 82]

                                               

Equation 83. The equation reads mu equals .7 times lambda.   

[Equation 83]

The following values shall be taken for lambda:

  • For normal-weight concrete....................................................... 1.00
  • For sand-lightweight concrete.................................................... 0.85
  • For all other lightweight concrete.............................................. 0.75

Tests have indicated that a smoother crack plane occurs with HSC.(15) Consequently, the values of c,mu, andlambda need to be evaluated for HSC.

ACTION: A research problem statement is proposed.

5.9 PRESTRESSING AND PARTIAL PRESTRESSING

5.9.4 Stress Limits for Concrete

5.9.4.1 For Temporary Stresses Before Losses—Fully Prestressed Components

5.9.4.1.1 Compression Stresses

The compressive stress limit for pretensioned and post-tensioned concrete components, including segmentally constructed bridges, shall be 0.60 f prime, subscript c (ksi).

In article 9.15.2.1 of the AASHTO Standard Specifications, the compressive stress limit for concrete at release for post-tensioned members is 0.55 f prime, subscript c, compared to 0.60 f prime, subscript cin this article. The use of 0.55f prime, subscript c or 0.60f prime, subscript c for HSC should be assessed.

ACTION: Revisions to include strength design for pretensioned concrete members at release are proposed.


5.9.4.1.2 Tension Stresses

The limits in table 1 shall apply for tensile stresses.

Table 5.9.4.1.2-1. Temporary tensile stress limits in prestressed concrete before losses, fully prestressed components.

Bridge Type Location Stress Limit

Other Than Segmentally Constructed Bridges

  • In precompressed tensile zone without bonded reinforcement.
N/A
  • In areas other than the precompressed tensile zone and without bonded auxiliary reinforcement.
0.0948 Square root of f prime, subscript ci less than or equal to0.2 (ksi)
  • In areas with bonded reinforcement sufficient to resist 120% of the tension force in the cracked concrete computed on the basis of an uncracked section.
0.22 Square root of f prime, subscript ci (ksi)
  • For handling stresses in prestressed piles.
0.158 Square root of f prime, subscript ci (ksi)

Segmentally Constructed Bridges

Longitudinal Stresses Through Joints in Precompressed Tensile Zone
  • Type A joints with minimum bonded auxiliary reinforcement through the joints, which is sufficient to carry the calculated tensile force at a stress of 0.5 f ,with internal tendons or external tendons.
0.0948 Square root of f prime, subscript ci maximum tension (ksi)
  • Type A joints without the minimum bonded auxiliary reinforcement through the joints.
No tension
  • Type B joints with external tendons.

0.100 ksi minimum compression

Transverse Stresses Through Joints
  • For any type of joint.

(ksi)

Stresses in Other Areas
  • For areas without bonded, nonprestressed reinforcement.
No tension
  • Bonded reinforcement sufficient to carry the calculated tensile force in the concrete computed on the assumption of an uncracked section at a stress of 0.5 fsy.

0.19 the square root of f prime, subscript c(ksi)

HSC is known to have a proportionally higher tensile strength than conventional concrete. It may be possible to have higher stress limits in table 5.9.4.1.2-1.

ACTION: A research problem statement is proposed.

5.9.4.2 For Stresses at Service Limit State After Losses-Fully Stressed Components

5.9.4.2.2 Tension Stresses

For service load combinations that involve traffic loading, tension stresses in members with bonded or unbonded prestressing tendons should be investigated using Load Combination Service III specified in table 3.4.1-1. The limits in table 1 shall apply.

Table 5.9.4.2.2-1. Tensile stress limits in prestressed concrete at service limit state after losses, fully prestressed components.

Bridge Type Location Stress Limit

Other Than Segmentally Constructed Bridges

Tension in the Precompressed Tensile Zone Bridges, Assuming Uncracked Sections
  • For components with bonded prestressing tendons or reinforcement that are subjected to not worse than moderate corrosion conditions.
0.19 the square root of f prime, subscript c (ksi)
  • For components with bonded prestressing tendons or reinforcement that are subjected to severe corrosion conditions.
0.0948 the square root of f prime, subscript c(ksi)

For components with unbonded prestressing tendons.

No tension

Segmentally Constructed Bridges

Longitudinal Stresses Through Joints in the Precompressed Tensile Zone
Type A joints with minimum bonded auxiliary reinforcement through the joints sufficient to carry the calculated longitudinal tensile force at a stress of 0.5 f , internal tendons.  
Type A joint without the minimum bonded auxiliary reinforcement through joints. No tension

Type B joints, external tendons.

0.100 ksi minimum compression

Transverse Stresses Through Joints
  • Tension in the transverse direction in precompressed tensile zone.

0.0948 the square root of f prime, subscript c(ksi)

Stresses in Other Areas
For areas without bonded reinforcement. No tension

Bonded reinforcement sufficient to carry the calculated tensile force in the concrete computed on the assumption of an uncracked section at a stress of 0.5 fsy.

0.19 the square root of f prime, subscript c (ksi)

HSC is known to have a proportionally higher tensile strength than conventional concrete. It may be possible to have higher stress limits in table 5.9.4.2.2-1.

ACTION: A research problem statement is proposed.

5.9.5 Loss of Prestress

5.9.5.3 Approximate Lump Sum Estimate of Time-Dependent Losses

An approximate lump sum estimate of time-dependent prestress losses resulting from creep and shrinkage of concrete and relaxation of steel in prestressed and partially prestressed members may be taken as specified in table 1 for:

  • Post-tensioned, nonsegmental members with spans up to 160 ft and stressed at a concrete age of 10 to 30 days, and

Pretensioned members stressed after attaining a compressive strength f prime, subscript c= 3.5 ksi, provided that

  • Members are made from normal-weight concrete,
  • The concrete is either steam or moist cured,
  • Prestressing is by bars or strands with normal and low relaxation properties, and
  • Average exposure conditions and temperatures characterize the site.

Table 5.9.5.3-1. Time-dependent losses in ksi.

Type of Beam Section Level For Wires and Strands Withfpu = 235, 250, or 270 ksi For Bars With fpu = 145 or 160 ksi

Rectangular Beams, Solid Slab

Upper Bound Average

29.0 + 4.0 PPR
26.0 + 4.0 PPR

19.0 + 6.0 PPR

Box Girder

Upper Bound Average

21.0 + 4.0 PPR
19.0 + 4.0 PPR

15.0

I-Girder

Average

33.0 PPR This graphical element, which occurs in four places, reads open bracket 1.0 minus the product of 0.15 times the quotient of f prime subscript c minus 6.0 divided by 6.0, close bracket, plus 6.0 times P P R. PPR

19.0 + 6.0 PPR

Single-T, Double-T, Hollow Core, and Voided Slab

Upper Bound

Average

39.0 PPR This graphical element, which occurs in four places, reads open bracket 1.0 minus the product of 0.15 times the quotient of f prime subscript c minus 6.0 divided by 6.0, close bracket, plus 6.0 times P P R. PPR

33.0 PPR This graphical element, which occurs in four places, reads open bracket 1.0 minus the product of 0.15 times the quotient of f prime subscript c minus 6.0 divided by 6.0, close bracket, plus 6.0 times P P R. PPR

31.0 PPR This graphical element, which occurs in four places, reads open bracket 1.0 minus the product of 0.15 times the quotient of f prime subscript c minus 6.0 divided by 6.0, close bracket, plus 6.0 times P P R. PPR

The equations in this article are based on parametric studies for a limited range of ultimate creep and shrinkage coefficients. Generally, HSC has lower creep and similar shrinkage values relative to conventional strength concrete. In table 5.9.5.3-1, the equations do not reflect the higher prestress levels used with HSC. The lump-sum equations may need to be evaluated for use with HSC.

NCHRP project 18-07 has the objective of developing design guidelines for estimating prestress losses in pretensioned HSC bridge girders. Results of the NCHRP project need to be incorporated into this article.

ACTION: Revisions to articles 5.9.5.1, 5.9.5.2, and 5.9.5.3 based on NCHRP project 18-07 are proposed.

5.9.5.4 Refined Estimates of Time-Dependent Losses

5.9.5.4.1 General

More accurate values of creep-, shrinkage-, and relaxation-related losses than those specified in Article 5.9.5.3 may be determined in accordance with the provisions of either Article 5.4.2.3 or this article for prestressed members with:

  • Spans not greater than 250 ft,
  • Normal density concrete, and
  • Strength in excess of 3.50 ksi at the time of prestress.

For lightweight concrete, loss of prestress shall be based on the representative properties of the concrete to be used.

Equations are then provided for calculation of individual components of prestress losses.

Results of NCHRP project 18-07 will need to be incorporated into this article.

ACTION: Revisions based on NCHRP project 18-07 are proposed.

5.10 DETAILS OF REINFORCEMENT

5.10.11 Provisions for Seismic Design

5.10.11.4 Seismic Zones 3 and 4

5.10.11.4.1d Transverse Reinforcement for Confinement at Plastic Hinges

The cores of columns and pile bents shall be confined by transverse reinforcement in the expected plastic hinge regions. The transverse reinforcement for confinement shall have a yield strength not more than that of the longitudinal reinforcement, and the spacing shall be taken as specified in Article 5.10.11.4.1e.

For a circular column, the volumetric ratio of spiral reinforcement, rhos, shall not be less than either that required in Article 5.7.4.6 or:

Equation 84. The equation reads rho subscript s is equal to .12 times f prime subscript c divided by f subscript y.   

(5.10.11.4.1d-1)              [Equation 84]

For a rectangular column, the total gross sectional area, Ash, of rectangular hoop reinforcement shall not be less than either:

Equation 85. The equation reads A subscript sh equals .3 times sh subscript c all times f prime, subscript c divided by f subscript y times open bracket A subscript g divided by A subscript s that quotient minus 1 close bracket.   

(5.10.11.4.1d-2)              [Equation 85]

or

Equation 86.  The equation reads A subscript sh equals .12 times sh subscript c all times f prime, subscript c divided by f subscript y.   

(5.10.11.4.1d-3)              [Equation 86]

The volumetric ratio of spiral reinforcement and the total gross sectional area of rectangular hoop reinforcement required by equations 5.10.11.4.1d-1 and 5.10.11.4.1d-2, respectively, may be too high to be practical with HSC. The concept of providing reinforcement to strengthen the core to offset the loss of strength when the concrete shell is lost may not be appropriate for HSC.

ACTION: A research problem statement is proposed.

5.10.11.4.2 Requirements for Wall-Type Piers

The factored shear resistance, Vr, in the pier shall be taken as the lesser of:

Equation 87.  The equation reads V subscript r equals .253 times the square root of f prime subscript c times b times d.   

(5.10.11.4.2-1)       [Equation 87]

and                        

Equation 88.  The equation reads V subscript r equals phi times V subscript n.   

(5.10.11.4.2-2)         [Equation 88]

for which                       

Equation 89.  The equation reads V subscript n equals open bracket .063 times the square root of f prime subscript c plus rho subscript h times f subscript y close bracket, times b times d.   

(5.10.11.4.2-3)         [Equation 89]

Equations 5.10.11.4.2-1 and 5.10.11.4.2-3 should be evaluated for use with HSC.

ACTION: A research problem statement is proposed.

5.10.11.4.3 Column Connections

The nominal shear resistance, provided by the concrete in the joint of a frame or bent in the direction under consideration, shall not exceed:

  • For normal-weight aggregate concrete:                                         

Equation 90.  The equation reads V subscript n less than or equal to .038 times b times d times the square root of f prime subscript c.   

(5.10.11.4.3-1)              [Equation 90]
  • For lightweight aggregate concrete:                                          

Equation 91.  The equation reads V subscript n less than or equal to .285 times b times d times the square root of f prime subscript c.   

(5.10.11.4.3-2)              [Equation 91]

Equations 5.10.11.4.3-1 and 5.10.11.4.3-2 should be evaluated for use with HSC.

ACTION: A research problem statement is proposed.

5.11 DEVELOPMENT AND SPLICES OF REINFORCEMENT

5.11.2 Development of Reinforcement

5.11.2.1 Deformed Bars and Deformed Wire in Tension

5.11.2.1.1 Tension Development Length

The tension development length, ld, shall not be less than the product of the basic tension development length, ldb, specified herein and the modification factor or factors specified in Articles 5.11.2.1.2 and 5.11.2.1.3. The tension development length shall not be less than 12.0 inches, except for lap splices specified in Article 5.11.5.3.1 and development of shear reinforcement as specified in Article 5.11.2.6

The basic tension development length, ldb, in inches, shall be taken as:

  • For No. 11 bar and smaller...............................................................This graphical element reads the product of 1.25 times A subscript b times f subscript y divided by the square root of f prime subscript c.
    but not less than ................................................................................ 0.4 db fy

  • For No. 14 bars.................................................................................This graphical element reads the product of 2.70 times f subscript y divided by the square root of f prime subscript c.
  • For No. 18 bars ................................................................................       This graphical element reads the product of 3.5 times f subscript y divided by the square root of f prime subscript c.    

  • For deformed wire ............................................................................This graphical element reads the product of 0.95 times d subscript b times f subscript y divided by the square root of f prime subscript c.

This article contains provisions for the development length of reinforcement based on the provisions of ACI 318-89. These were extensively modified in the ACI 318-95 provisions, with a view toward formulating a more user-friendly format while maintaining the same general agreement with research results and with professional judgment. Limited tests have indicated that the development lengths calculated using the above provisions are applicable to HSC.(29) However, the tests resulted in a more sudden failure than occurs with conventional strength concrete. Consideration should be given to adopting similar provisions as ACI 318-95 after the development lengths have been verified for HSC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.2.1.2 Modification Factors That Increase ld

The basic development length, ldb, shall be multiplied by the following factor or factors, as applicable:

  • For top horizontal or nearly horizontal reinforcement, so placed that more than 12.0 inches of fresh concrete is cast below the reinforcement......................................................................... 1.4
  • For bars with a cover of db or less, or with a clear spacing of 2db or less........ 2.0
  • For lightweight aggregate concrete, where fct (ksi) is specified....This equation reads the product of 0.22 times the square root of f prime subscript c divided by f subscript c t greater than or equal to 1.0.
  • For all-lightweight concrete, where fct is not specified...................................... 1.3
  • For sand-lightweight concrete, where fct is not specified.................................. 1.2

Linear interpolation may be used between all-lightweight and sand-lightweight provisions when partial sand replacement is used.

  • For epoxy-coated bars with a cover less than 3db or with clear spacing between bars less than 6db..........................1.5
  • For epoxy-coated bars not covered above........................................................ 1.2

The product obtained when combining the factor for top reinforcement with the applicable factor for epoxy-coated bars need not be taken to be greater than 1.7.

5.11.2.1.3 Modification Factors That Decrease ld

The basic development length, ldb, modified by the factors as specified in Article 5.11.2.1.2, may be multiplied by the following factors, where:

  • Reinforcement being developed in the length under consideration is spaced laterally not less than 6.0 inches center to center, with not less than 3.0 inches clear cover measured in the direction of the spacing....................... 0.8
  • Anchorage or development for the full yield strength of reinforcement is not required, or where reinforcement in flexural members is in excess of that required by analysis .......................................................................................................This graphical element reads open parenthesis A subscript s required divided by A subscript s provided, close parenthesis.
  • Reinforcement is enclosed within a spiral composed of bars not less than 0.25 inch in diameter and spaced at not more than a 4.0-inch pitch........................................................................ 0.75

The above factors need to be verified for HPC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.2.2 DEFORMED BARS IN COMPRESSION

5.11.2.2.1 Compressive Development Length

The development length, ld, for deformed bars in compression shall not be less than either the product of the basic development length specified herein and the applicable modification factors specified in Article 5.11.2.2.2 or 8 inches.

The basic development length, ldb, for deformed bars in compression shall not be less than:

Equation 92.  The equation reads l subscript db is equal to .63 times d subscript b times f subscript y that product divided by the square root of f prime subscript c.   

(5.11.2.2.1-1)              [Equation 92]

or

Equation 93.  The equation reads l subscript db is equal to .3 times d subscript b times f subscript y.   

(5.11.2.2.1-2)              [Equation 93]

5.11.2.2.2 Modification Factors

The basic development length, ldb, may be multiplied by applicable factors, where:

  • Anchorage or development for the full yield strength of reinforcement is not required, or where reinforcement is provided in excess of that required by analysis..............This graphical element reads open parenthesis A subscript s required divided by A subscript s provided, close parenthesis.
  • Reinforcement is enclosed within a spiral composed of a bar not less than 0.25 inch in diameter and spaced at not more than a 4.0-inch pitch.................................................................... 0.75

The above factors need to be verified for HPC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.2.3 BUNDLED BARS

The development length of individual bars within a bundle, in tension, or compression shall be that for the individual bar, increased by 20 percent for a three-bar bundle and by 33 percent for a four-bar bundle.

For determining the factors specified in Articles 5.11.2.1.2 and 5.11.2.1.3, a unit of bundled bars shall be treated as a single bar of a diameter determined from the equivalent total area.

The above factors need to be verified for HPC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.2.4 STANDARD HOOKS IN TENSION

5.11.2.4.1 Basic Hook Development Length

The development length, ldh, in inches, for deformed bars in tension terminating in a standard hook specified in Article 5.10.2.1 shall not be less than:

  • The product of the basic development length, lhb, as specified in Equation 1, and the applicable modification factor or factors, as specified in Article 5.11.2.4.2;
  • 8.0 bar diameters; or
  • 6.0 inches.

Basic development length, lhb, for a hooked bar with yield strength, fy, not exceeding 60.0 ksi shall be taken as:

Equation 94.  The equation reads l subscript hb is equal to 38 times d subscript b that product divided by the square root of f prime subscript c.   

(5.11.2.4.1-1)              [Equation 94]

The above factors need to be verified for HPC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.2.4.2 Modification Factors

Basic hook development length, lhb, shall be multiplied by the following factor or factors, as applicable, where:

  • Reinforcement has a yield strength exceeding 60.0 ksi.................................This graphical element reads f subscript y divided by 60.0.
  • Side cover for No. 11 bar and smaller, normal to plane of hook, is not less than 2.5 inches, and for 90o hook, cover on bar extension beyond hook is not less than 2.0 inches....................... 0.7
  • Hooks for No. 11 bar and smaller, enclosed vertically or horizontally within ties or stirrup ties that are spaced along the full development length, ldh, at a spacing not exceeding 3db. 0.8
  • Anchorage or development of the full yield strength of reinforcement is not required, or where reinforcement is provided in excess of that required by analysis......................................This graphical element reads open parenthesis A subscript s required divided by A subscript s provided, close parenthesis.
  • Lightweight aggregate concrete is used.......................................................... 0.75
  • Epoxy-coated reinforcement is used.................................................................. 1.2

All provisions of article 5.11.2.4 need to be verified for HPC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.2.5 WELDED WIRE FABRIC

5.11.2.5.1 Deformed Wire Fabric

For applications other than shear reinforcement, the development length, lhd, in inches, of welded deformed wire fabric, measured from the point of critical section to the end of wire, shall not be less than either:

  • The product of the basic development length and the applicable modification factor or factors, as specified in Article 5.11.2.2.2, or
  • 8.0 inches, except for lap splices, as specified in Article 5.11.6.1.

5.11.2.5.2 Plain Wire Fabric

The yield strength of welded plain wire fabric shall be considered developed by embedment of two cross wires with the closer cross wire not less than 2.0 inches from the point of critical section. Otherwise, the development length, ld, measured from the point of critical section to outermost cross wire shall be taken as:

Equation 95.  The equation reads l subscript d equals 8.5 times the sum of A subscript w times f subscript y divided by s subscript w times the square root of f prime subscript c.   

(5.11.2.5.2-1)              [Equation 95]

The development length shall be modified for reinforcement in excess of that required by analysis as specified in Article 5.11.2.4.2, and by the factor for lightweight concrete specified in Article 5.11.2.1.2, where applicable. However, ld shall not be taken to be less than 6.0 inches, except for lap splices, as specified in Article 5.11.6.2.

All provisions of article 5.11.2.5 need to be verified for HPC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.4 Development of Prestressing Strand

5.11.4.1 GENERAL

For the purposes of this article, the transfer length may be taken as 60 strand diameters and the development length shall be taken as specified in Article 5.11.4.2.

5.11.4.2 BONDED STRAND

Pretensioning strand shall be bonded beyond the critical section for development length, in inches, taken as:

Equation 96. The equation reads l subscript d greater than or equal to open parentheses f subscript ps minus the sum of 2 divided by the 3 times f subscript pe close parentheses, times d subscript b.   

(5.11.4.2-1)              [Equation 96]

This article contains general requirements for the transfer and development lengths of prestressing strand. It is defined in the article that the transfer length for pretensioned prestressing strand may be taken as 60 strand diameters. This value is increased from the 50 diameters used in the AASHTO Standard Specifications,article 9.20.2.4. A lower transfer length is possible for HPC. These provisions should be evaluated for HSC. Researchers at FHWA have suggested new equations for transfer and development lengths of bonded prestressing strand.(30) Those equations should be reviewed for their appropriateness with HSC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.11.5 Splices of Bar Reinforcement

5.11.5.3 SPLICES OF REINFORCEMENT IN TENSION

5.11.5.3.1 Lap Splices in Tension

The length of lap for tension lap splices shall not be less than either 12.0 inches or the following for Class A, B, or C splices:

Class A splice..................................................................................................... 1.0 ld
Class B splice..................................................................................................... 1.3 ld
Class C splice.................................................................................................... 1.7 ld

The tension development length, ld, for the specified yield strength shall be taken in accordance with Article 5.11.2.

The class of lap splice required for deformed bars and deformed wire in tension shall be as specified in table 1.

Table 5.11.5.3.1-1. Classes of tension lap splices.

Ratio of
This graphical element reads open parenthesis A subscript s required divided by A subscript s provided, close parenthesis.
Percent of As Spliced With Required Lap Length
50 75 100
greater than or equal to 2
A
A
B

< 2

B

C

C

All provisions of article 5.11.5 need to be verified for HPC.

ACTION: None. Further work is the objective of NCHRP project 12-60.

5.12 DURABILITY

5.12.2 Alkali-Silica Reactive Aggregates

The contract documents shall prohibit the use of aggregates from sources that are known to be excessively alkali-silica reactive.

If aggregate of limited reactivity is used, the contract documents shall require the use of either low-alkali-type cements or a blend of regular cement and pozzolanic materials, provided that their use has been proven to produce concrete of satisfactory durability with the proposed aggregate.

For HPC, testing should be conducted or field experience should be used to determine if a given source of aggregate can be safely used with specific cementitious materials.

ACTION: Revisions referencing AASHTO M 6 and M 80 are proposed.

5.12.3 Concrete Cover

Cover for unprotected prestressing and reinforcing steel shall not be less than that specified
in table 1 and modified for the W/C ratio, unless otherwise specified either herein or in Article 5.12.4.

Concrete cover and placing tolerances shall be shown in the contract documents.

Cover for pretensioned prestressing strand, anchorage hardware, and mechanical connections for reinforcing bars or post-tensioned prestressing strands shall be the same as for reinforcing steel.

Cover for metal ducts for post-tensioned tendons shall not be less than:

  • That specified for main reinforcing steel,
  • One-half the diameter of the duct, or
  • That specified in table 1.

For decks exposed to tire studs or chain wear, additional cover shall be used to compensate for the expected loss in depth due to abrasion, as specified in Article 2.5.2.4.

Modification factors for the W/C ratio shall be the following:

  • For W/C less than or equal to 0.40......................................................................................... 0.8
  • For W/C greater than or equal to 0.50......................................................................................... 1.2

Minimum cover to main bars, including bars protected by epoxy coating, shall be 1.0 inch.

Cover to ties and stirrups may be 0.5 inch less than the values specified in table 1 for main bars, but shall not be less than 1.0 inch.

This article provides minimum cover requirements for a range of exposure conditions. HPC is less permeable than conventional concrete, and a longer service life is expected.

The second bullet after the fourth paragraph that says “One-half the diameter of the duct” should be revised to allow the use of wider ducts in 152-mm- (6-inch-) thick webs.

In this article, modification factors for w/c ratios of 0.40 and 0.50 are given. A gradual transition would be more logical. Furthermore, there are ways to reduce the permeability without lowering the w/c ratio.

ACTION: None.

5.13 SPECIFIC MEMBERS

5.13.2 Diaphragms, Deep Beams, Brackets, Corbels, and Beam Ledges

5.13.2.4 BRACKETS AND CORBELS

5.13.2.4.2 Alternative to Strut-and-Tie Model

  • For normal-weight concrete, nominal shear resistance, Vn, shall be taken as the lesser of:

Equation 95.  The equation reads l subscript d equals 8.5 times the sum of A subscript w times f subscript y divided by s subscript w times the square root of f prime subscript c.   

(5.13.2.4.2-1)     [Equation 97]

and

Equation 98.  The equation reads V subscript n is equal to .8 times b subscript w times d subscript e.   

(5.13.2.4.2-2)    [Equation 98]
  • For all-lightweight or sand-lightweight concretes, nominal shear resistance, Vn, in kips, shall be taken as the lesser of:

Equation 99.  The equation reads V subscript n is equal to open parentheses .2 minus the product of .07 times a subscript v divided by d close parentheses, times f prime subscript c times b subscript w times d subscript e.   

(5.13.2.4.2-3)   [Equation 99]

or

Equation 100.  The equation reads V subscript n is equal to open parentheses .8 minus the product of .28 times a subscript v divided by d subscript e close parentheses, times b subscript w times d.   

(5.13.2.4.2-4)    [Equation 100]

Equations 5.13.2.4.2-1 and 5.13.2.4.2-2 impose a limit of 28 MPa (4.0 ksi) on the compressive strength of concrete that can be used in design. The limits of equation 5.13.2.4.2-2 and 0.2 fc need to be evaluated for HSC.

ACTION: A research problem statement is proposed.

5.13.2.5 BEAM LEDGES

5.13.2.5.4 Design for Punching Shear

Nominal punching shear resistance, Vn, in kips, shall be taken as:

  • At interior pads:                 

Equation 101.  The equation reads V subscript n is equal to .125 times the square root of f prime subscript c times open parentheses W plus 2 times L plus 2 times d subscript e close parentheses, times d subscript e.   

(5.13.2.5.4-1)               [Equation 101]
  • At exterior pads:                     

Equation 102.  The equation reads V subscript n is equal to .125 times the square root of f prime subscript c times open parentheses W plus L plus d subscript e close parentheses, times d subscript e.   

(5.13.2.5.4-2)               [Equation 102]

The equations in this article should be verified for use with HSC.

ACTION: A research problem statement is proposed.

5.13.2.5.5 Design of Hangar Reinforcement

Using the notation in Figure 2, the nominal shear resistance of the ledges of inverted T-beams shall be the lesser of that specified by Equation 2 and Equation 3.

  • At interior pads:

Equation 103.  The equation reads V subscript n is equal to open parenthesis .063 times the square root of f prime subscript c times b subscript f times d subscript f close parentheses, plus A subscript hr times f subscript y divided by s times open parentheses W plus 2 times d subscript f close parentheses.   

(5.13.2.5.5-3)       [Equation 103]

Equation 5.13.2.5.5-3 should be verified for use with HSC.

ACTION: A research problem statement is proposed.

5.13.3 Footings

5.13.3.6 SHEAR IN SLABS AND FOOTINGS

5.13.3.6.3 Two-Way Action

For two-way action for sections without transverse reinforcement, the nominal shear resistance, Vn, in kips, of the concrete shall be taken as:     

Equation 104.  The equation reads V subscript n is equal to open parenthesis .063 plus .126 divided by beta subscript c close parentheses, times the square root of f prime subscript c times b subscript o times d subscript v less than or equal to .126 times the square root of f prime subscript c times b subscript o times d subscript v.   

(5.13.3.6.3-1)       [Equation 104]

For two-way action for sections with transverse reinforcement, the nominal shear resistance,
Vn, in kips, shall be taken as:  
                    

Equation 105.  The equation reads V subscript n is equal to V subscript c plus V subscript s less than or equal to .192 times the square root of f prime subscript c times b subscript o times d subscript v.   

  (5.13.3.6.3-2)         [Equation 105]

for which

                         

Equation 106.  The equation reads V subscript c is equal to .1264 times the square root of f prime subscript c times b subscript o times d subscript v.   

  (5.13.3.6.3-3)          [Equation 106]

and               

Equation 107. The equation reads V subscript s is equal to A subscript v times f subscript y times d subscript v that sum divided by s.   

  (5.13.3.6.3-4)          [Equation 107]

The equations in this article should be verified for use with HSC.

ACTION: A research problem statement is proposed.

5.13.4 Concrete Piles

5.13.4.4 PRECAST PRESTRESSED PILES

5.13.4.4.1 Pile Dimensions

The wall thickness of cylinder piles shall not be less than 5.0 inches.

A wall thickness of less than 127 mm (5.0 inches) should be allowed when HPC is used.

ACTION: A revision to eliminate the minimum wall thickness is proposed.

5.14 PROVISIONS FOR STRUCTURE TYPES

5.14.1 Beams and Girders

5.14.1.2 PRECAST BEAMS

5.14.1.2.5 Concrete Strength

For slow-curing concretes, the 90-day compressive strength may be used for all stress combinations that occur after 90 days.

For normal-weight concrete, the 90-day strength of slow-curing concretes may be estimated at 115 percent of their 28-day strength.

This article is very relevant to HSC. It should be revised to clarify the meaning of slow-curing concrete and allow the use of 56-day strengths. The factor of 115 percent should be evaluated based on data from the FHWA HPC showcase bridges.

ACTION: A research problem statement is proposed.

5.14.2 Segmental Construction

5.14.2.3 DESIGN

15.4.2.3.3 Construction Load Combinations at the Service Limit State

Tensile stresses in concrete due to construction loads shall not exceed the values specified in table 1; except for structures with Type A joints and less than 60 percent of their tendon capacity provided by internal tendons, the tensile stresses shall not exceed 0.095 the square root of f prime, subscript c. For structures with Type B joints, no tensile stresses shall be permitted.

HSC has a relatively higher tensile strength than conventional strength concrete. The tensile stress limit in this article and in table 5.14.2.3.3-1 should be evaluated for HSC.

ACTION: A research problem statement is proposed.

5.14.2.4 TYPES OF SEGMENTAL BRIDGES

5.14.2.4.7 Precast Segmental Beam Bridges

5.14.2.4.7b Segment Reinforcement

Segments of segmental beam bridges shall preferably be pretensioned for dead load and all construction loadings to limit the tensile stress in the concrete to 0.0948 the square root of f prime, subscript c.

The tensile stress limit should be evaluated for use with HSC.

ACTION: A research problem statement is proposed.

5.14.5 Additional Provisions for Culverts

5.14.5.3 DESIGN FOR SHEAR IN SLABS OF BOX CULVERTS          

Equation 108.  The equation reads V subscript c is equal to open parentheses .0676 times the square root of f prime subscript c plus the product of 4.6 times A subscript s divided by b times d subscript e times V subscript u times d subscript e divided by M subscript u close parentheses, times b times d subscript e.   

  (5.14.5.3-1)               [Equation 108]

but Vc shall not exceed 0.126 the square root of f prime, subscript cbde.

Although HSC may not be used in slabs for box culverts, the limits for Vc in this article should be evaluated for use with HSC.

ACTION: A research problem statement is proposed.

Section 9: Decks and Deck Systems

This section contains provisions for the analysis and design of bridge decks and deck systems
of concrete, metal, and wood, or combinations thereof, subject to gravity loads. No provisions affected by HPC were identified in the section.

ACTION: None.

AASHTO LRFD BRIDGE CONSTRUCTION SPECIFICATIONS

Section 8 of the AASHTO LRFD Bridge Construction Specifications deals with concrete structures. The technical provisions are essentially the same as those in the AASHTO Standard Specifications for Highway Bridges, Division II, Section 8, Concrete Structures, except for the use of metric units in the LRFD version. Consequently, a separate review of the LRFD specifications was not undertaken. Proposed revisions to the AASHTO LRFD Specifications, similar to those proposed for division II, section 8 of the AASHTO Standard Specifications, are included in appendix D. The proposed revisions are based on AASHTO LRFD Bridge Construction Specifications, First Edition, 1998, and the 1999, 2000, and 2001 interim revisions.(11-14)

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FHWA-HRT-05-056

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