Eads Bridge

Appendix 2

Graphic Solution for Piers and Abutments

In 1929 Carl Gayler, the last surviving member of Eads’ design staff, gave a speech at the Engineers Club in St Louis. In his remarks, Gayler recalled his experience working on the bridge.[1]

Reaction Lines

The drawing that Gayler describes would have been similar to Figure 1, opposite. In the figure, “reaction lines” (pressure lines) describe the path that will be followed by the forces acting on the masonry.

The lines are plotted for the load combinations that Pfeifer identified in his appendix to the 1868 Report of the Engineer in Chief.[3] These are the loads that generate the greatest horizontal thrust (red curve) and loads that cause the strongest moment tending to overturn the masonry (blue curve). The least favorable of the red and blue lines at any elevation within the masonry determines the necessary width of the pier or abutment at that elevation.

Ideally a reaction line will fall within the center third of the thickness of the masonry. This ensures that the entire cross-section is subject to compression. If the line wanders outside of the center third but remains within the boundaries of the masonry, a portion of the pier or abutment on the side farthest from the reaction line will be unloaded. The pier will still be stable but masonry in the unloaded area, relieved of the clamping action of the load, will be susceptible to cracking. A reaction line that passes outside of the masonry indicates that the pier or abutment will fail.

The red reaction line on the pier wanders slightly outside of the center third of the pier’s thickness. The departure is small, less then three feet against a forty-six foot thickness of masonry, but sufficient to lend credibility to Gayler’s story. Pfeifer’s numerical calculations reveal a similar departure, indicated by positive l1 values in his tabulated results.[4]

Construction Load

For the pier only, a third load condition is considered. The black curve represents a special case that occurs during construction when the arch on one side is complete but the one on the other side is not yet closed. The black line passes outside of the middle third but is still safely within the body of the masonry. This violates the “middle third rule” but can be tolerated as a temporary condition during construction.

The black curve was plotted using the same dead-load as the other computations. This is conservative. Because the upper deck and uprights weren’t installed until after the second arch was closed, the weight during construction would have been less, placing the actual reaction line closer to the center of the pier.

Design loads for the Abutment

Pfeifer investigates two critical load conditions for the abutments.[5]

1. Red - Maximum Thrust (Q): The horizontal force exerted by the arch against the abutments varies depending on the load on the arch and the temperature. It is greatest during hot weather when the design live load is applied to the full length of the span.
2. Blue - Maximum Moment (Na): The fixed ends of the arch tend to pry against the masonry as they deflect, imparting a moment that rocks the abutment toward or away from the arch. The critical condition is a load with the greatest tendency to rotate the abutment away from the arch, adding to the displacement already caused by the arch’s thrust. This occurs during hot weather when a live load is applied to the 5/8 of the span farthest away from the abutment while the closest 3/8 is unloaded.

Design Loads for the Pier

The thrust and moment experienced by the pier is the difference between the thrust and moment generated by the arches on each side.

1. Red - Maximum Thrust (QR - QL): The horizontal force against a pier is greatest when the difference between the thrusts of the two arches is the largest. This occurs when the design live load extends all the way across one arch while the other arch is unloaded. Because the arches have similar spans, thermal expansion does not influence the pier. Expansion of one arch is balanced by expansion of the other.
2. Blue - Maximum Moment (NpL - NpR): The strongest overturning moment occurs when the design live load is applied to the most remote 5/8 of one span and the nearest 3/8 of the opposite span while the rest of both spans is unloaded. The moment experienced by the pier is unaffected by temperature.
3. Black - Arch One Side Only: The strongest overturning is experienced during construction when the arch on one side of a pier is complete while the other arch has not yet been closed. Because there is no traffic on the bridge during construction, only dead loads are considered. In this case thermal expansion is important, the strongest overturning occurs during hot weather.

Method

The reaction lines were plotted using the method suggested by Frank E. Kidder in The Architect’s and Builder’s Pocket-Book.[6] This handbook was published in the early 20th century but the technique described was in common use when Eads Bridge was designed. Charles Pfeifer would have used a similar method to make the diagram that Gayler describes.

Forces and moments used to create Figure 1 are from Chapter XXVII of A History of the St Louis Bridge.[7] Data for the final design, tabulated on pages 350, 352 is used in preference to the schematic design values cited in “The Stability of the Foundations” in Woodward.[8]

As-built dimensions for the pier and abutment were obtained from Woodward’s Plate XVIII and from drawing AB058B in Washington University’s Eads Bridge Drawing Collection.[9]

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Footnotes