The following revisions have been made to “A” Dimension Calculations. These revisions replace the BDM article 5.7.1C as follows:

The distance from the top of the slab to the top of the girder at centerline bearing is represented by the “A” Dimension. It is calculated in accordance with the guidance of Appendix B. This ensures that adequate allowance will be made for excess camber, superelevation, vertical and horizontal curvatures. Ideally the section at centerline of span will have the final geometry shown in Figure 5.7.1-1. Where temporary prestress strands at top of girder are used to control the girder stresses due to shipping and handling, the “A” dimension must be adjusted accordingly.

The note in left margin of the Layout Sheet should read: “A” Dimen. = X” (not for design).

Appendix 5-B1 shall be replaced in it’s entirety with the following:

Appendix 5-B1: “A” Dimension for Precast Girder Bridges

Introduction

The basic concept in determining the required “A” dimension is to provide a haunch over the girder such that the top of the girder is less than the fillet depth (typically Ύ”) below the bottom of the slab at the center of the span. This provides that the actual girder camber could exceed the calculated value by 1Ύ” before the top of the girder would interfere with the bottom mat of slab reinforcement.

It is desirable to have points of horizontal and vertical curvature and super elevation transitions off the bridge structure as this greatly simplifies the geometric requirements on the girder haunch. However, as new bridges are squeezed into the existing infrastructure it is becoming more common to have geometric transitions on the bridge structure.

Each geometric effect is considered independently of the others. The total geometric effect is the algebraic sum of each individual effect.

Fillet Effect

Excessive Camber Effect

Profile Effect

When all of the girders in a span are parallel and the span is contained entirely within the limits of a vertical and/or horizontal curve, the profile effect is simply the sum of the Vertical Curve Effect and the Horizontal Curve Effect.

The horizontal curve effect is, assuming a constant super elevation rate along the length of the span,

The vertical curve effect is

• change in the super elevation rate
  grade break

  point of horizontal curvature

  point of vertical curvature

  flared girders

The exact value of the profile effect may be determined by solving a complex optimization problem. However it is much easier and sufficiently accurate to use a numerical approach.

The figure below, while highly exaggerated, illustrates that the profile effect is the distance the girder must be placed below the profile grade so that the girder, ignoring all other geometric effects, just touches the lowest profile point between the bearings.

In the case of a crown curve the haunch depth may reduced. In the case of a sag curve the haunch must be thickened at the ends of the girder.

To compute the profile effect:

1.    Create a chord line parallel to the top of the girder (ignoring camber) connecting the centerlines of bearing. The equation of this line is
            
            where


2.   At 10th points along the span, compute the elevation of the roadway surface



Girder Orintation Effect

The girder orientation effect accounts for the difference in slope between the roadway surface and the top of the girder. Girders such as I-beams are oriented with their Y axis plumb. Other girders such as U-beam, box beam, and slabs are oriented with their Y axis normal to the roadway surface. The orientation of the girder with respect to the roadway surface, and changes in the roadway surface along the length of the girder (super elevation transitions) define the Girder Orientation Effect.

If the super elevation rate is constant over the entire length of the span and the Y-axis of the girder is plumb, the girder orientation effect simplifies to the Top Width Effect,





If there is a change in super elevation rate and/or the Y-axis of the girder is not plumb, then once again a more complex computation is required.









"A" Dimension

The “A” dimension is the sum of all these effects

If a Drain Type 5 crosses the girder, “A” shall not be less than 9 inches


Limitations

These computations are for a single girder line. The required haunch should be determined for each girder line in the structure. Use the greatest “A” dimension.

These computations are also limited to a single span. A different haunch may be needed for each span or each pier. For example, if there is a long span adjacent to a short span, the long span may have considerably more camber and will require a larger haunch. There is no need to have the shorter spans carry all the extra concrete needed to match the longer span haunch requirements. With the WF series girders, the volume of concrete in the haunches can add up quickly. The shorter span could have a different haunch at each end as illustrated below.




Stirrup Length and Precast Deck Leveling Bolt Considerations

For bridges on crown vertical curves, the haunch depth can become excessive to the point where the girder and diaphragm stirrups are too short to bend into the proper position. Similarly the length of leveling bolts in precast deck panels may need adjustment.

Stirrup lengths are described as a function of “A” on the standard girder sheets. For example, the G1 and G2 bars of a WF74G girder are 6’-5”+ “A” in length. For this reason, the stirrups are always long enough at the ends of the girders. Problems occur when the haunch depth increases along the length of the girder to accommodate crown vertical curves and super elevation transitions.

If the haunch depth along the girder exceeds “A” by more than 2 inches, an adjustment must be made. The haunch depth at any section can be compute




"A" Dimension Worksheet - Simple Alignment




Example

Slab: Thickness = 7.5”, Fillet = 0.75”
WF74G Girder: Wtop = 49”
Span Length = 144.4 ft
Crown Slope = 0.04ft/ft
Camber: D = 7.55”, C = 2.57”
Horizontal Curve Radius = 9500ft through centerline of bridge



Background:

The revised "A" dimension proposal is more suitable for the BDM and PGSuper Program. This method is completely general and should handle every prestressed girder including trapezoidal tub-girder bridge configuration. The simple method we have always used is incorporated into the text.

If you have any questions regarding these issues, please contact Rick Brice at 705-7174 or Bijan Khaleghi at 705-7181.

cc:   Mohammad Sheikhizadeh, Bridge Construction - 47354

       F. Posner, Bridge and Structures – 47340