This article shows how bending and torsional moments in three-dimensional frames can be represented via a discontinuous Maxwell–Rankine stress function. The associated Rankine reciprocal contains polygonal faces whose areas represent forces. These faces are orthogonal to the member forces (which may include shear forces) and need not be orthogonal to the beams.
WilliamsCJKMcRobieA. Graphic statics using discontinuous Airy stress functions. Int J Space Struct2016; 31(2–4): 121–134.
2.
VarignonP.Nouvelle mécanique ou statique. Paris: Charles-Antoine JoMBERT, 1725.
3.
MaxwellJC.On reciprocal figures and diagram of forces. Philos Mag1864; 26: 250–261.
4.
MaxwellJC.On reciprocal figures, frames and diagrams of forces. Trans Roy Soc Edinburgh1870; 7: 160–208.
5.
CremonaL.Two treatises on the graphical calculus and reciprocal figures in graphical statics (trans. BeareTH). Oxford: Clarendon Press, 1890.
6.
MitchellTBakerWMcRobieAet al. Mechanisms and states of self-stress of planar trusses using graphic statics, part I. Int J Space Struct2016; 31(2–4): 85–101.
7.
McRobieABakerWMitchellTet al. Mechanisms and states of self-stress of planar trusses using graphic statics, part II. Int J Space Struct2016; 31(2–4): 102–111.
8.
RankineWJM. Principle of the equilibrium of polyhedral frames. Philos Mag J Sci1864; 27: 92.
9.
MalekSMcRobieAShepherdPet al. From a weightless bent wire coat hanger to shell structures via the Beltrami stress tensor. J Int Assoc Shell Spat Struct58(1): 39–50.
McRobieA.The geometry of structural equilibrium. R Soc Open Sci2017; 4: 160759.
12.
RankineWJM. A manual of applied mechanics. London: C. Griffin and Co., 1858.
13.
McRobieA.Maxwell and Rankine reciprocal diagrams via Minkowski sums for 2D and 3D trusses under load. Int J Space Struct2016; 31(2–4): 203–216.
14.
AkbarzadehMVan MeleTBlockP. Equilibrium of spatial structures using 3-D reciprocal diagrams. In: Proceedings of the international association for shell and spatial structures (IASS) symposium, Wroclaw University of Technology, Poland, 23–27 September 2013.
15.
AkbarzadehMVan MeleTBlockP.On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams. Comput Aided Design2015; 63: 118–128.
16.
AkbarzadehMVan MeleTBlockP. 3D graphic statics: geometric construction of global equilibrium. In: Proceedings of the international association for shell and spatial structures (IASS) symposium, Amsterdam, 17–20 August 2015.
17.
MichelettiA.On generalized reciprocal diagrams for self-stressed networks. Int J Space Struct2008; 23(3): 153–166.
