Stability of trusses by graphic statics.

This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell-Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the 'product forces' that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses

curved footbridges supported by a shell obtained through thrust network analysis

After Maillart's concrete curved arch bridges were built before the Second World War, in the second half of the past century and this century, many curved bridges have been built with both steel and concrete. Conversely, since the construction of Musmeci's shell supported bridge in Potenza, few shell bridges have been constructed. This paper explains how to design a curved footbridge supported by an anticlastic shell by shaping the shell via a thrust network analysis (TNA). By taking advantage of the peculiar properties of anticlastic membranes, the unconventional method of shaping a shell by a TNA is illustrated. The shell top edge that supports the deck has an assigned layout, which is provided by the road curved layout. The form of the bottom edge is obtained by the form-finding procedure as a thrust line, by applying the thrust network analysis (TNA) in a non-standard manner, shaping the shell by applying the boundary conditions and allowing relaxation. The influence of the boundary conditions on the bridge shape obtained as an envelope of thrust lines is investigated. A finite element analysis was performed. The results indicate that the obtained shell form is effective in transferring deck loads to foundations via compressive stresses and taking advantage of concrete mechanical properties. Keywords: Shell footbridges, Cantilevered deck, Anticlastic shell, Thrust network analysis (TNA), Concret

Curved footbridges supported by a shell obtained through thrust network analysis

After Maillart's concrete curved arch bridges were built before the Second World War, in the second half of the past century and this century, many curved bridges have been built with both steel and concrete. Conversely, since the construction of Musmeci's shell supported bridge in Potenza, few shell bridges have been constructed. This paper explains how to design a curved footbridge supported by an anticlastic shell by shaping the shell via a thrust network analysis (TNA). By taking advantage of the peculiar properties of anticlastic membranes, the unconventional method of shaping a shell by a TNA is illustrated. The shell top edge that supports the deck has an assigned layout, which is provided by the road curved layout. The form of the bottom edge is obtained by the form-finding procedure as a thrust line, by applying the thrust network analysis (TNA) in a non-standard manner, shaping the shell by applying the boundary conditions and allowing relaxation. The influence of the boundary conditions on the bridge shape obtained as an envelope of thrust lines is investigated. A finite element analysis was performed. The results indicate that the obtained shell form is effective in transferring deck loads to foundations via compressive stresses and taking advantage of concrete mechanical properties