## Section 6: Pretensioned Concrete I Beams and I Girders

Anchor: #i1350803### Materials

Use Class H concrete with a minimum = 4.0 ksi and_{} = 5.0 ksi and a maximum = 6.0 ksi and = 8.5 ksi.

Design beams with 0.5-in. low-relaxation strands. Use 0.6-in. low-relaxation strands as necessary.

Use prestressing strand with a specified tensile strength, *f _{pu}* of
270 ksi.

### Geometric Constraints

The minimum numbers of I-beams or I-girders in any roadway width is four.

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.

Anchor: #i1352561### 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
_{}< 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, however, this design assumption must be noted on the plans. - Live load distribution factors must conform to 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, treat the exterior beam as if it were an interior beam to determine 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 of comparable length.
- Do not use the special analysis based on conventional approximation for loads on piles per Article C4.6.2.2.2d, unless the effectiveness of diaphragms on the lateral distribution of truck loads is investigated.
- For interior and exterior girders, do not take the live
load distribution factor, for moment or shear, as less than ,
Where,

*m*= multiple presence factor per Article 3.6.1.1.2- = number of lanes
- = number of beams or girders

- When prestressed concrete deck panels or stay-in-place metal forms are allowed, design the beam using the basic slab thickness.

### 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 for I beams and IGND for I girders.
- Use hold-down points shown on the IBD standard drawing for I beams and IGD for I girders.
- Strand stress after seating of chucks is not greater than
0.75
*f*for low-relaxation strands._{pu} - Initial tension in the amount of 0.24 (ksi) is allowed for all standard TxDOT I-beam and I-girder sections.
- Initial compression in the amount of 0.65 (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 () is typically based on compressive stresses, which must
not exceed the following limits:
- 0.60 for stresses due to total load plus effective prestress.
- 0.45 for stresses due to effective prestress plus permanent (dead) loads.
- 0.40 for stresses due to Fatigue I live loads plus one-half of the sum of stresses due to prestress and permanent (dead) loads.

- Tension in the amount of 0.24 is allowed for checking concrete stresses during deck and diaphragm placement.
- Use an effective strand stress after release of , with defined in AASHTO LRFD Specifications 2004.
- 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 procedure for determining shear
resistance as allowed by Article 5.8.3.4.3. Use the General Procedure
as provided by Article 5.8.3.4.2. Do not use provisions of Appendix
B of the
*AASHTO LRFD Bridge Design Specifications*. - Calculate required stirrup spacing for #4 Grade 60 bars according to the Article 5.8. Change stirrup spacing as shown on IBD standard drawing for I beams and IGD for I girders only if analysis indicates the inadequacy of the standard design.
- Replace Equation 5.8.4.2-1 with the following:
Where is the first moment of the area of the slab with respect to the neutral axis of the composite section.

Take

*b*, width of the interface, equal to the beam top flange width. Do not reduce_{vi}*b*to account for prestressed concrete panel bedding strips._{vi} - Determine interface shear transfer in accordance with
Article 5.8.4. Take Cohesion and Friction Factors as provided in
Article 5.8.4.3 as follows:
*c*= 0.28 ksi- = 1.0
- = 0.3
- = 1.8 ksi

- Replace Equation 5.4.2.3.2-2 with the following:
= 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 = 5,000 ksi for beams with < 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 and I girders reinforced as shown on the IBD and IGD standard drawings are adequate for the 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 *2012,
6th Ed., Article 5.9.5 Loss of Prestress with the following
changes.

- Replace AASHTO LRFD (2012)
Eq. 5.9.5.1-1 with the following:
- Replace AASHTO LRFD (2012) 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)

- In the AASHTO LRFD (2012) Eq. 5.9.5.2.3a-1,
replace
*E*with_{ct}*E*where_{ci}*E*= modulus of elasticity of concrete at transfer (ksi)._{ci} - Add the following to AASHTO LRFD (2012)
Article 5.9.5.2.3a:
"For pretensioned components of usual design,

*f*may be calculated on the basis of a prestressing steel stress assumed to be 0.65_{cgp}*f*for stress-relieved strand and high-strength bars and 0.70_{pu}*f*for low relaxation strand._{pu}For components of unusual design, more accurate methods supported by research or experience should be used."

- Disregard all commentary in AASHTO LRFD (2012) Article C5.9.5.2.3a until Equation C5.9.5.2.3a-1.
- Disregard AASHTO LRFD (2012) Article 5.9.5.3.
- Replace AASHTO LRFD (2012) 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.

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

*f*_{pu}_{}, 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)- = initial stress in the tendon at the end of stressing (ksi)
- = 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.