Some Contributions to the Theory of the Stiffened Suspension Bridge

Citation

Morelli, Dino Anthony (1946) Some Contributions to the Theory of the Stiffened Suspension Bridge. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZAVX-HG34. https://resolver.caltech.edu/CaltechETD:etd-05142003-112733

Abstract

Part I of this thesis contains a review of the basic theory of the cable and stiffening girder combination according to the method of Dr. Rode which takes into account the inevitable longitudinal displacements of the suspender connections, when the cable is deflected from its normal configuration.

Numerical calculations have been carried out to establish the order of magnitude of approximations in the ordinary deflection theory as developed in this country by F. E. Turneare from the work of J. Melan. Besides the essential omission which is evident in the comparison of the fundamental differential equation of Rode's theory with that of the ordinary deflection theory, the most significant error is the neglect of the effect of inclination of the suspenders on cable deflection. It would appear that an error of three percent can arise from this source which although unimportant from the structural engineer's point of view, is important as a limit on accuracy required of any theory which neglects it.

Rode's differential equation is not integrable and an approximation has been developed which is tractable by the methods of Part II and yet does not sacrifice entirely the improved representation of structural action given by Rode's theory.

Part II utilizes trigonometric series for the development of a simple method of determination of the deflections and girder bending moments in a span. As applied to the ordinary deflection theory there result formulae of extreme simplicity which bring into sharp perspective the related functions of cable and stiffening girder. From these formulae a pictorial representation of bridge stiffness in terms of certain basic parameters has been developed.

The theory and method of computation have then been extended to take into account the effect of a prestress introduced by arbitrary adjustment of suspender lengths which may be necessary in the rehabilitation of old structures or reduction of peak bending stresses in new designs.

The approximation to Rode's theory developed in Part I is then solved in terms of the methods developed for the simple theory and formulae result which are but slightly more complicated than the elegant formulae of the previous work. The practicability of application has been tested by examples.

Finally, in order to dispel certain erroneous conceptions of the efficacy of the stiffening girder in controlling the bending moments, (and consequently, the deflections) in a span, the method has been extended to permit the investigation of the influence of variation in flexural rigidity of the girder. This leads to formulae, not overly lengthy, which show in proper relation the influence of the various harmonic components of the flexural rigidity of the girder.

The methods of this thesis are simple in conception and application while still retaining a proper physical basis, and are capable of extension beyond the bounds of current methods without loss of algebraical and arithmetical tractability.

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