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Mechanical principles of static engineering systems
Published in Alan Darbyshire, Charles Gibson, Mechanical Engineering, 2023
Alan Darbyshire, Charles Gibson
At a point of contraflexure, where the bending moment is zero, the deflected shape of a beam changes from sagging to hogging or vice versa. The location of these points is of importance to structural engineers since it is here that welded, bolted or riveted joints can be made which will be free of bending stress.
Timber Arch Bridges with V-shaped Hangers
Published in Structural Engineering International, 2019
Roberto Crocetti, Jorge M. Branco, Jorge F. Barros
The critical buckling length of the system with V-shaped hangers is approximately one half the buckling length of the traditional system with vertical hangers. This results in a buckling load which is approximately four times greater in the system with V-shaped hangers as compared to the system with the arrangement that makes use of vertical hangers. Structurally speaking, the fact that the arch with V-shaped hangers is superior to the arch with vertical hangers could be predicted by looking at either the first vertical vibrational mode or the first buckling mode. In both cases, the modes related to the arch with V-shaped hangers, show a higher number of points of contraflexure than the corresponding arch with vertical hangers. The higher the number of points of contraflexure, the larger the strain energy needed to bend the structure—which in other words means: (a) stiffer structure and (b) greater buckling load. The vertical stiffness of the two systems above also show large discrepancies. For example, for a concentrated load applied in the deck, at the attachment of the hanger closest to the support, the vertical stiffness of the system with V-shaped hangers is approximately 4.5 times greater than the stiffness of the system with vertical hangers. Regarding stiffness, vibrational and buckling properties, it is evident that the system with V-shaped hangers is significantly more efficient than the one with vertical hangers, thus allowing for slender geometries. Structural slenderness is not only advantageous in terms of material economy; it is indeed often pleasant from the aesthetical point of view. There are also some shortcomings in arches with V-shaped hangers, such as the slightly more complicated attachment devices, the introduction of axial forces in the deck, and the fact that compression forces may occur in some hangers for some particular asymmetric loading. However, the design compression forces in the hangers are generally small, especially when a heavy bridge deck is adopted.