10 Analysis of Rigid

The grace and lightness of this rigid frame concrete bridge are impressive.It was built in 1932 for a cattle pass in Rockingham County, N. H. Rigid framestructures of equal beauty and lightness are exceptionally well suited for footbridges. The clear span is 55 feet, and the crown thickness is 11 inches.

The forces of group (1) (characteristic of continuous structures) arethose caused by displacement of foundations and volume changes due to

temperature variations and shrinkage of the concrete. For example, a

drop in temperature will cause a shortening of the deck BC in Fig. 5. Itis evident that a decrease in length from BC to B' C is accompanied bya horizontal reaction, H, which the foundation exerts upon the footing.Shrinkage has an effect similar to that of a temperature drop; the effectof a temperature rise is similar but opposite in direction.

A differential vertical settlement in a frame with two hinged supportsresults in a rotation of the entire frame around a support. The stressesin the frame produced by a small vertical settlement are negligible andwill be disregarded in the following problems. If the supports are considered fixed, a differential vertical settlement creates considerable stressesand should be included in the analysis.

The supports of a rigid frame may be displaced outward by the horizontal thrust due to the dead load and the imposed live load; or inwarddue to the pressure of the backfill and the shortening of the deck. Thecombined dead and live load thrust is predominant for average frame

dimensions, and its predominance increases with growing ratio of spanlength to wall height. Consequently, it is reasonable to assume that thehorizontal displacement is a spreading of the footings and that it increaseswith increasing span length. It is convenient to assume that the spreading is proportional to the span length and to introduce horizontal dis

placement in the analysis as an equivalent coefficient of contraction similar to a shrinkage coefficient. However, some designers assume that the

horizontal displacement is independent of the span length.Moments at the crown section are sensitive to horizontal displace

ments of the footings; and the soil modulus, characterizing the compressi

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