Terminology and Notation

LRFD refers to Load and Resistance Factor Design, a design methodology that makes use of load factors and resistance factors based on the known variability of applied loads and material properties. Bracketed <references> reference relevant sections of the AASHTO LRFD Bridge Design Specifications.

Limit states

TxDOT recommends the following limit states for design of bridge system components <Article 3.4.1>:

Load Factors

TxDOT recommends the following permanent loads <Article 3.5>: The engineer may reduce the maximum load factor for wearing surfaces and utilities <DW in Table 3.4.1-2> to 1.25.

In areas of the state where de-icing agents are frequently used during winter storms, it is recommended that additional corrosion protection measures be incorporated into the bridge design and details.

District-specific requirements are available for review.

Phased Construction Recommendations

Do not use abutment, bent, or trestle standard detail sheets for phased structures.

Geometric Constraints

In most cases, the phase line in an abutment or interior bent will be offset from the phase line for the slab. The phase line should not be under a beam or within a bearing seat.  Extend the abutment or interior bent past the slab phase line in order to provide support for the beam or girder. Preferably, the phase line should be a minimum of 4 inches from the bearing seat or edge of beam, whichever is greater. At a minimum, the abutment or interior bent phase line will need to be at the edge of the bearing seat or beam.

When phasing an abutment or an interior bent, consider providing enough space between the existing structure and the new construction to accommodate splicing of the reinforcement and formwork. Consider how the next phase of construction will be impacted by the placement of phase lines and reinforcement that extends beyond the phase line. Piles and drilled shaft for the next phase may lie within the length necessary for splicing. Avoid having splices that overlap pile or drilled shaft locations in order to facilitate construction.

If unable to provide enough room to splice the reinforcement through traditional overlapping, use welded splices or mechanical couplers.  Extend reinforcement that will be spliced by welds or mechanical couplers beyond the end of the cap by at least 1-foot.

As alternative to splicing or welding the reinforcement, a full depth joint may be used at the phase line. For abutments, if a full depth joint is used, limit the space between abutments to 1-inch. Use bituminous fiber to fill the gap between the phases. Use a PVC waterstop across the space along the full height of the cap and backwall.

For bent caps, the full depth open joint at the phase line should be at least 1-foot wide to allow for forming of the adjacent phases. Individual bent caps would support each phase. If the lower roadway/finished grade allows, use at least two columns per phase.

When selecting column or drilled shaft/pile spacing, try to keep the distance from face of column or drilled shaft/pile to the phase line between 0.5 and 4 feet.  Overhangs greater than 4 feet can result in high negative moments and permanent deflection of the overhang under loading.  The construction of additional phases will not remove this deflection.

Phased construction of abutments or bents may require that columns or drilled shafts be spaced at irregular intervals.

Offset old bent lines and new bents by at least 5 feet, if possible, to keep from fouling foundations on the existing structure.

Structural Analysis

When designing bents and abutments to be continuous after phasing, consider all stages of construction (including temporary loads) and the final configuration.  Select flexural and shear reinforcement so that loading in all phases can be supported.

Design bents and abutments that have full depth joints at the phase line as individual components.

Software

Use CAP18 with a modified input file adjusted for LRFD (see design examples). Use this spreadsheet for shear design.

• Engineering Software

Geometric Constraints

Supporting an approach slab on wing walls is strongly discouraged. Compaction of backfill is difficult and loss of backfill material can occur. Without the bearing on the backfill, the approach slab is supported on only three sides (at the two wing walls and the abutment backwall), and the standard approach slab is not reinforced for this situation nor are the wing walls designed to carry the load. The approach slab should be supported by the abutment wall and approach backfill only, and appropriate backfill material is essential. TxDOT supports the placement of a cement-stabilized sand (CSS) wedge in the zone behind the abutment. CSS solves the problem of difficult compaction behind the abutment, and it resists the moisture gain and loss of material common under approach slabs.

Design Criteria

A construction joint is recommended in abutment caps longer than 90 ft. The joint should clear the bearing seat areas.

Geometric Constraints

Cap width should be 3 in. wider than the supporting columns to allow column reinforcing to extend into the cap without bending.

Structural Analysis

• Apply dead load reactions due to slab and beam weight as point loads at centerline of beam. Distribute the weight of one railing to no more than three beams, applied to the composite cross section. Distribute dead loads due to sidewalks, medians, and overlay evenly to all beams.
• Model the total live load reaction as two wheel loads, distributing the remainder of the live load over a 10-ft. design lane width. Carefully consider lane boundaries to produce the maximum force effect at various critical locations:
  
  Where:
  W = The uniform load portion of the live load (kip/ft.).
  LL_Rxn = Live load reaction/lane or (LL_Truck * 1.33) + LL_Lane (kip).
  P = The load on one rear wheel of the HL-93 truck increased 33% for dynamic load allowance (kip). Typically, P = 16k * 1.33.
  The following figure shows the recommended live load model:
  

Software

Use CAP18 with modified input file adjusted for LRFD (see design examples). Use this spreadsheet for shear design.

• Use a construction joint in multicolumn bents when the distance between outside columns exceeds 80 ft. Locate the joint close to a dead-load inflection point but not under a bearing seat buildup.
• Typically the minimum number of bars is four top and bottom, and the maximum number in a layer is limited by a 2 1/2-in. clear-spacing requirement to facilitate concrete placement and vibration. A second layer may be placed 4 in. on center from the outside layer. A third layer should be used only in very deep caps. A horizontal tie bar tied to the vertical stirrup legs should support second and third layers. In heavily reinforced caps, bundling bars in two-bar bundles may be used to maintain necessary clear spacing. Layered and bundling bars should comply with <Articles 5.10.3.1.3 (layered) or 5.10.3.1.5 (bundled)>.
• For most caps more than four top bars can be cut off in compression zones between columns. To simplify design, usually extend bars past an inflection point rather than adhering to the requirements in <Article 5.11.2.2>. For bottom reinforcement, limit the number of bars across a column and into a cantilever to three or four to avoid congestion with vertical column steel when possible. Additional bars should end at the column face. These top and bottom bar cut-off criteria apply to conventional caps with moderate amounts of reinforcement. For large caps with heavy reinforcement, follow the provisions in <Articles 5.11.1.2.2. and 5.11.1.2.3>.
• Bars longer than 60 ft. require laps. Try to locate these laps in compression or very low tension zones. Base lap lengths on tension lap requirements (see the Bridge Detailing Manual). Consider staggering or alternating laps in adjacent bars to minimize congestion. Mechanical couplers or welded splices may be specified for staged construction.
• Many cantilevers are too short to allow full development length for the #11 Grade 60 top reinforcement. However, the reaction from the outside beam provides a clamping effect and a bar extension of 15 in. beyond the center of the beam will develop the bar. The standard distance from centerline beam to end of cap is 1 ft.-9 in., which is a minimum for new designs.
• For most conventional caps, use #5 stirrups with a 4-in. minimum and 12-in. maximum spacing. Double stirrups may be required close to column faces. For large heavily reinforced caps, use #6 stirrups.
• Pay attention to the bearing seat build-up for prestressed beam spans. Extreme grades and skews can produce conflicts between the bearing seat or bent cap and the beams or bearings if the seats are not shown properly on the bent details. The Bridge Detailing Manual shows typical bearing seat configurations. Bearing seat build-ups taller than 3 in. require reinforcement, which should be shown on the detail.

Geometric Constraints

Stem width should be at least 3 in. wider than column width to allow column reinforcing to be extended into the cap without bending. Use a stem height to the nearest whole inch. Ledge depth depends on the punching shear capacity required. Determine ledge width from the development of the ledge tie bars as shown in this figure.

Design Criteria

• Design for primary moment and shear is similar to that for rectangular caps. When considering moment, b is the bottom width for negative bending and top width for positive bending. When considering shear, b is the stem width.
• Because the caps are usually deeper than 3 feet, provide beam side reinforcing according to this figure. This reinforcing steel should meet the requirements of <Equation 5.7.3.4-4>.
• Because the bearings are relatively far from the center of the cap, consider torsion in single-column bents.
• Ledge reinforcing is determined by shear friction and flexure as indicated in <Article 5.13.2.5>.
• Size web reinforcing for hanger loads, vertical shear, and vertical shear/torsion when applicable. Hanger load stresses, which usually control, are not added to shear and torsion stresses.

• For a skewed bent, place hanger and ledge reinforcing perpendicular to the centerline of the bent. Detail the skewed ends of the bent with a section of skewed stirrups and ledge reinforcing. Extend caps at least 2 ft. past centerline of the exterior beam to prevent excessive hanger and ledge reinforcing requirements and to provide adequate punching shear capacity. For skewed bridges or phased designs, consider punching shear capacity for the exterior beams: a cap extension of 2 ft. may not be adequate.
• Model the total live load reaction as two wheel loads, distributing the remainder of the live load over a 10-ft. design lane width. Carefully consider lane boundaries to produce the maximum force effect at various critical locations.
  
  Where:
  W = The uniform load portion of the live load (kip/ft.).
  LL_Rxn = Live load reaction/lane or (LL_Truck * 1.33) + LL_Lane (kip).
  P = The load on one rear wheel of the HL-93 truck increased 33% for dynamic load allowance (kip). Typically, P = 16k * 1.33.
  The following figure shows the recommended live load model:
  

Software

Use CAP18 for analysis of primary moment and shear (see design example). Use this spreadsheet for shear design.

Structural Analysis (for typical bridges only)

• Round columns are preferred for multicolumn bents with rectangular caps and are used for most structures. See this figure for available column size, typical reinforcement, and recommended height limits.
• Square or rectangular columns are occasionally used for aesthetic enhancement of a structure.
• The designer should consider predicted scour when determining column heights.
• Moments can be magnified to account for slenderness (P-delta) effects by using <Article 5.7.4.3> or other analytical methods. However, results are highly conservative.
• Analyze slender columns by taking effective length factors as 1.0 transversely and 1.5 longitudinally or by investigating secondary effects and biaxial bending using the PIER program or other computational methods.
• For multi-tier bents with square or round columns separated by tie beams, analyze as a frame, and magnify transverse and longitudinal moments separately.
• Column size may change within the bent height, producing a multi-tiered bent. Consider multi-columns bent tiers with web walls to be braced in the transverse direction. Column capacity in the longitudinal direction is not affected by the web wall.
• Round columns within recommended height limits and with column spacing between 10 ft. and 18 ft. may use the following diameters without analysis for axial load and bending: slab spans - 24 in., pan form spans - 24 in., Types A and B and C prestressed beam spans - 30 in., and Type IV prestressed beam spans - 36 in.
• Refer to this figure for guidance for reinforcement in square columns.
• Refer to this figure for desirable column-to-tie-beam connection details.
• Design and model single-tier bent columns as individual columns with bottom conditions fixed against rotation and deflection in the transverse direction but free to rotate and deflect in the longitudinal direction. Top-of-column conditions should be considered free to translate but not rotate in the transverse direction.
• When determining fixity conditions for loads other than temperature and shrinkage, assume that columns on single drilled shafts are fixed at three shaft diameters but not more than 10 ft. below the top of the shaft, and that columns on footings with multiple drilled shafts or piling in both transverse and longitudinal directions are considered fixed at the top of the footing.
• Refine designs by limiting longitudinal deflections to the maximum movement allowed due to joint closure.

Use FRAME11, BMCOL51, PIER, or equivalent applications.

Structural Analysis (for typical bridges only):

• For columns taller than 100 ft., consider wind loads more appropriate for the location and height. See "Wind Forces on Structures," J. M. Briggs, Transactions, American Society of Civil Engineers, Paper No. 3269, Volume 126, Part 2, Final Report, 1961.
• Longitudinal and transverse moments must be magnified separately for P-delta effects using the method in <Article 4> or with a second order analysis computer program such as BMCOL51.
• Effective length factor may be taken as 2.0 in both directions unless restraints provided by the superstructure sufficiently limit secondary moments.
• Refine designs by limiting longitudinal deflections to the maximum movement allowed due to joint closure. This value can be determined by taking the total number of joints along the entire bridge length minus 1 plus the thermal contraction along half the unit of the critical bent for joint closure.

Design Criteria

For column design, use Strength I, Strength III, and Strength V limit states. Column design must meet the requirements of <Article 5.7.4>.

Software

Use BMCOL51 or equivalent applications.

For additional information on LRFD bridge design as implemented by TxDOT, consult the following resources:

• LRFD Bridge Design Manual
• Design Software Programs
• LRFD Frequently Asked Questions

Inverted Tee Reinforced Concrete Caps

• Design Example (Not working templates. PDF files presented in MathCAD format)

Rectangular Reinforced Concrete Caps

• Design Example (Not working templates. PDF files presented in MathCAD format)

Column for Single Column Bent

• Design Example (Not working templates. PDF files presented in MathCAD format)

Two Shaft Footing

• Design Example Using Strut-and-Tie Method (Not working templates. PDF files presented in MathCAD format)

Spreadsheets

• Shear Design

Foundation Loads

• Abutment Pile Loads Calculation