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Section 5: Prestressed Concrete I Beams and I Girders

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Materials

Use Class H concrete with a minimum ƒ'ci = 4.0 ksi and ƒ'c = 5.0 ksi.

Design beams for 0.5-in. low-relaxation strands. You may use 0.6-in. low-relaxation strands for Type VI beams or other beams as necessary but should check its availability with fabricators.

Use prestressing strand with a specified tensile strength, ƒpu, of 270 ksi.

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Geometric Constraints

Intermediate diaphragms are not required for structural performance. Do not use intermediate diaphragms unless required for erection stability of beam sizes stretched beyond their normal span limits.

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Structural Analysis

Beam designs must meet the following requirements:

  • Distribute the weight of one railing to no more than three beams, applied to the composite cross section.
  • Use section properties given on the standard drawings.
  • Composite section properties may be calculated assuming the beam and slab to have the same modulus of elasticity (for beams with ƒ'c < 8.5 ksi). Do not include haunch concrete placed on top of the beam when determining section properties. Section properties based on final beam and slab modulus of elasticity may also be used.
  • Live load distribution factors must conform to AASHTO LRFD Bridge Design Specifications, Article 4.6.2.2.2 for flexural moment and Article 4.6.2.2.3 for shear, except as noted below:
    • For exterior beam design with a slab cantilever length equal to or less than one-half of the adjacent interior beam spacing, use the live load distribution factor for the interior beam. The slab cantilever length is defined as the distance from the center line of the exterior beam to the edge of the slab.
    • For exterior beam design with a slab cantilever length exceeding one-half of the adjacent interior beam spacing, use the lever rule with the multiple presence factor of 1.0 for single lane to determine the live load distribution. The live load used to design the exterior beam must never be less than the live load used to design an interior beam.
    • Do not use the special analysis based on conventional approximation for loads on piles per AASHTO LRFD Bridge Design Specifications, Article C4.6.2.2.2d, unless the effectiveness of diaphragms on the lateral distribution of truck loads is investigated.
  • When precast concrete deck panels or stay-in-place metal forms are allowed, design the beam using the basic slab thickness.
  • When calculating the cracking moment of a member in accordance with Article 5.7.3.3.2, take the modulus of rupture ƒr, as 0.24, for all normal weight concrete.
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Design Criteria

Standard beam designs must meet the following requirements:

  • Strands should be added and depressed in the order shown on the IBND standard drawing, available at http://www.dot.state.tx.us/insdtdot/orgchart/ cmd/cserve/standard/bridge-e.htm.
  • Use hold-down points shown on the IBD standard drawing, available at http://www.dot.state.tx.us/insdtdot/orgchart/cmd/cserve/standard/bridge-e.htm.
  • Strand stress after seating of chucks is not greater than 0.75ƒpu for low-relaxation strands.
  • Initial tension in the amount of 0.24 (ksi) is allowed. Based on TxDOT experience, additional bonded reinforcement is not required.
  • Initial compression in the amount of 0.6ƒ'ci (ksi) is allowed.
  • Final stress at the bottom of beam ends need not be checked except when straight debonded strands are used or when the effect of the transfer length of the prestressing strand is considered in the analysis.
  • Final tension in the amount of 0.19 (ksi) is allowed.
  • The required final concrete strength (ƒ'c) is typically based on compressive stresses, which must not exceed the following limits:
    • 0.60 ƒ'c for stresses due to total load plus prestress.
    • 0.45 ƒ'c for stresses due to effective prestress plus permanent (dead) loads.
    • 0.40 ƒ'c for stresses due to live loads plus one-half of the sum of stresses due to prestress and permanent (dead) loads.
  • Use an effective strand stress after release of .
  • Take for low-relaxation strands.
  • The end position of depressed strands should be as low as possible so that the position of the strands does not control the release strength. Release strength will occasionally be controlled by end conditions when the depressed strands have been raised to their highest possible position.
  • Do not use the simplified shear design procedure as allowed by AASHTO LRFD 5.8.3.4.3. Use the General Procedure as provided by AASHTO LRFD 5.8.3.4.2.
  • Calculate required stirrup spacing for #4 Grade 60 bars according to the AASHTO LRFD Bridge Design Specifications, Article 5.8. Change stirrup spacing as shown on IBD standard drawing, available at http://www.dot.state.tx.us/insdtdot/ orgchart/cmd/cserve/standard/bridge-e.htm, only if analysis indicates the inadequacy of the standard design.
  • Replace AASHTO LRFD equation 5.8.4.2-1 with the following:

  • Take bvi, width of the interface, equal to the beam top flange width. Do not reduce bvi to account for precast panel bedding strips.

  • Determine interface shear transfer in accordance with AASHTO LRFD 5.8.4. Take Cohesion and Friction Factors as provided in AASHTO LRFD Article 5.8.4.3 as follows:
    • c = 0.28 ksi
    • m = 1.0
    • K1 = 0.3
    • K2 = 1.8 ksi
  • Replace AASHTO LRFD equation 5.4.2.3.2-2 with the following:

    ks = 1.45 - 0.13 (V/S) > 0.0

    Compute deflections due to slab weight and composite dead loads assuming the beam and slab to have the same modulus of elasticity. Assume Ec = 5,000,000 psi for beams with ƒ'c < 8.5 ksi. Predicted slab deflections should be shown on the plans although field experience indicates actual deflections are generally less than predicted. Use the deflection due to slab weight only times 0.8 for calculating haunch depth.
  • TxDOT standard I beams reinforced as shown on the IBD standard drawing are adequate for the AASHTO LRFD Bridge Design Specifications requirements of Article 5.10.10.
  • A calculated positive (upward) camber is required after application of all permanent (dead) loads.

When calculating prestress losses, use AASHTO LRFD Bridge Design Specifications 2004, 3rd. Ed., Article 5.9.5 Loss of Prestress. In the absence of AASHTO LRFD Bridge Design Specifications 2004, use AASHTO LRFD Bridge Design Specifications 2007, 4th Ed., Article 5.9.5 Loss of Prestress with the following changes.

  • Replace AASHTO LRFD (2007) Eq. 5.9.5.1-1 with the following:
  • Replace AASHTO LRFD (2007) Eq. 5.9.5.1-2 with the following:

    Where,

    • = total loss (ksi)

    • = loss due to friction (ksi)

    • = loss due to anchorage set (ksi)

    • = loss due to elastic shortening (ksi)

    • = loss due to shrinkage (ksi)

    • = loss due to creep of concrete (ksi)

    • = loss due to relaxation of steel after transfer (ksi)
  • Add the following to AASHTO LRFD (2007) Article 5.9.5.1:

    "In pretensioned members, where the approximate lump sum estimate of losses specified in Article 5.9.5.3 is used, the part of the loss due to relaxation occuring before transfer, , should be deducted from the total relaxation.

    For post-tensioned members, consideration should be given to a loss of tendon force, as indicated by pressure readings, within the stressing equipment."

  • In the AASHTO LRFD (2007) Eq. 5.9.5.2.3a-1, Replace Ect with Eci where Eci = modulus of elasticity of concrete at transfer (ksi).
  • Add the following to AASHTO LRFD (2007) Article 5.9.5.2.3a:

    "For pretensioned components of usual design, may be calculated on the basis of a prestressing steel stress assumed to be 0.65 for stress-relieved strand and high-strength bars and 0.70 for low relaxation strand.

    For components of unusual design, more accurate methods supported by research or experience should be used."

  • Disregard all commentary in AASHTO LRFD (2007) Article C5.9.5.2.3a until Equation C5.9.5.2.3a-1.
  • Disregard AASHTO LRFD (2007) Equation 5.9.5.3-1.

    For low relaxation strands, the values for I-beams and I-girders in AASHTO LRFD Table 5.9.5.3-1 may be reduced by 6.0 ksi.

  • Add the following to AASHTO LRFD (2007) Table 5.9.5.3-1:

    Type of Beam Section

    Level

    For Wires and Strands with = 235,

    250 or 270 ksi

    For Bars with =

    145 or 160ksi

    I-Girder

    Average



  • Replace AASHTO LRFD (2007) Article 5.9.5.4 with the following:

    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 this article for prestressed members with:

    • Spans not greater than 250 ft.,
    • Normal weight 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.

    For segmental construction, for all considerations other than preliminary design, prestress losses shall be determined as specified in Article 5.9.5, including consideration of the time-dependent construction method and schedule shown in the contract documents.

    5.9.5.4.2 Shrinkage

    Loss of prestress, in ksi, due to shrinkage may be taken as:

    • For pretensioned members:

      (5.9.5.4.2-1)

    • For post-tensioned members:

      (5.9.5.4.2-2)

      Where,

      H = the average annual ambient relative humidity (percent) 5.9.5.4.3 Creep

      Prestress loss due to creep may be taken as:

      (5.9.5.4.3-1)

      Where,

      = concrete stress at center of gravity of prestressing steel at transfer (ksi)

      = change in concrete stress at center of gravity of prestressing steel due to permanent loads, with the exception of the load acting at the time the prestressing force is applied. Values of should be calculated at the same section or at sections for which is calculated (ksi).

    5.9.5.4.4 Relaxation

    5.9.5.4.4a General

    The total relaxation at any time after transfer shall be taken as the sum of the losses specified in Articles 5.9.5.4.4b and 5.9.5.4.4c.

    5.9.5.4.4b At Transfer

    In pretensioned members, the relaxation loss in prestressing steel, initially stressed in excess of 0.50 , may be taken as:

    • For stress-relieved strand:(5.9.5.4.4b-1)
    • For low-relaxation strand:(5.9.5.4.4b-2)

      Where,

      t = time estimated in days from stressing to transfer (day)

      ƒpj = initial stress in the tendon at the end of stressing (ksi)

      ƒpy = specified yield strength of prestressing steel (ksi)

      5.9.5.4.4c After Transfer

      Losses due to relaxation of prestressing steel may be taken as:

    • For pretensioning with stress-relieved strands:

      (5.9.5.4.4c-1)

    • For post-tensioning with stress-relieved strands:

      (5.9.5.4.4c-2)

      Where,

      =the friction loss below the level of 0.70 at the point under consideration, computed according to Article 5.9.5.2.2 (ksi)

      =loss due to elastic shortening (ksi)

      = loss due to shrinkage (ksi)

      = loss due to creep of concrete (ksi)

    • For prestressing steels with low relaxation properties conforming to AASHTO M 203 (ASTM A416 or E328):

      Use 30 percent of given by Eq. 1 or 2.

    • For post-tensioning with 145 to 160 ksi bars:

      Loss due to relaxation should be based on approved test data. If test data is not available, the loss may be assumed to be 3.0 ksi.

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