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20 studies were conducted using the computer program ABAQUS reinforced concrete design that was 33 ft 10 in. (10.31 m) wide and a special 7-degree-of-freedom beam-column element that and 4 ft 10 in. (1.47 m) deep and had a radius of curvature of can account for warping. These studies, which were designed 282 ft (86 m). A 1/29 scale aluminum model was studied to investigate warping-related stresses in these bridges, found for spans of 60 in. (1,500 mm), 45 in. (1,140 mm), and 30 in. that in all cases the effect of warping stress was insignificant. (760 mm), with or without a midspan radial diaphragm. The The 1997 AASHTO curved girder specifications limits the quantities measured were (1) Boundary reactions; (2) strains span-to-radius ratio for designing the bridges as straight. at a radial section close to midspan; and (3) deflections at These ratios were found to be conservative by a factor of selected points. The data were reduced by computer, and dis- 2 or more when it comes to the need to consider warping. tribution graphs of tangential plate forces, radial-bending (Given that concrete box-girders will have thicker webs and moments, and deflections were plotted by Calcomp plotter. soffits, they are even less vulnerable to warping, and it is likely Based on the model data, some general observations are made that the effects of warping can be ignored in almost all of these regarding the behavior of curved box-girder bridges. bridges.) Fam, A. R. M. and Turkstra C. J. (1976) "Model Study of Horizontally Curved Box-Girder," Journal of the Structural Laboratory Experiments Division, Vol. 102, No. 5, pp. 10971108. Most, although not all, laboratory experiments related to curved concrete box-girder bridges have been conducted on This paper describes an experimental study of a single- small-scale Plexiglas or metal models of these bridges. A large- span horizontally curved Plexiglas box-girder beam with di- scale test of a concrete structure was performed at the Univer- aphragms and flange overhangs. Static loads were applied at sity of California at Berkeley during the 1970s. In general, these midspan to cause a complex pattern of membrane and bend- tests have shown that refined analytical techniques predict ing stresses with the effects of diaphragms clearly evident. structural behavior quite well. The following paragraphs discuss Experimental results in typical cases are shown graphically published papers and reports on these tests in greater detail. and compared with the results of a special-purpose finite element program developed especially for curved box analysis. Aneja, I. K., and Roll, F. (1971) "A Model Analysis of Curved This program used the softened truss model theory applied Box-Beam Highway Bridge," Journal of the Structural to a prestressed concrete multiple-cell box. In this theory, the Division, Vol. 97, No. 12, pp. 28612878. concrete torsional problem is solved by combining equilib- rium and compatibility conditions and constitutive laws of Fabrication, preparation, and instrumentation of a Plexiglas materials. Until now, the theory has been applied only to the model of a horizontally curved box-beam highway bridge case of pure torsion with a single-cell section. An algorithm is are described. The model was extensively instrumented with presented to deal with the torsional problem for reinforced rosette strain gages at three cross sections. Experimental data for concrete and prestressed concrete box-girder bridge super- three lane-loading conditions were obtained. An approximate structures with multiple-cell sections. Results are compared theoretical analysis of the model was obtained by using the finite with previous theoretical and experimental work for single-cell element method, which showed that finite element models with cases. Good agreement was obtained between experimental curved shell elements provide better predictions than those with and analytical results. straight plate elements. A typical comparison between the experimental and theoretical stress distribution across the mid- Heins, C. P., Bonakdarpour, B. P., and Bell, L. C. (1972) span gage section for one of the loading conditions is shown "Multicell Curved Girder Model Studies," Journal of the graphically. The comparison shows a good agreement between Structural Division, Vol. 98, No. 4, pp. 831843. the shapes but not the magnitudes of the stress plots obtained experimentally and theoretically. Experimental data at the three The behavior of a single two-span, three-cell Plexiglas gage sections for each load condition is also given. model is predicted by the Slope Deflection Fourier Series Technique. This analytical technique had previously been Aslam, M., and Godden, W. G. (1975) "Model Studies of applied to only open cross-sectional, I-type bridge systems. Multicell Curved Box-Girder Bridges," Journal of the Engi- The model was tested under various static concentrated neering Mechanics Division, Vol. 101, No. 3, pp. 207222. loads. The resulting experimental deflection, rotation, and strain data for some loadings are reported. Effects of single A model study on the static response of curved box-girder and multicell torsional properties are examined. Results bridges is presented, and a close agreement is found between the indicate that single-cell properties can be applied in the analy- test and analytical results. The prototype bridge was a four-cell sis, and warping effects may be neglected.