The Cremona diagram, also known as the Cremona- Maxwell method, is a graphical method used in

statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...

truss A truss is an assembly of ''members'' such as beams, connected by ''nodes'', that creates a rigid structure. In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assembl ...

es to determine the forces in members (

graphic statics In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. Actively used in the architecture of the 19th century, the methods of graphic statics were largel ...

). The method was developed by the Italian mathematician

Luigi Cremona Antonio Luigi Gaudenzio Giuseppe Cremona (7 December 1830 – 10 June 1903) was an Italian mathematician. His life was devoted to the study of geometry and reforming advanced mathematical teaching in Italy. He worked on algebraic curves and alge ...

. However, recognizable Cremona diagrams appeared as early as 1725, in

Pierre Varignon Pierre Varignon (1654 – 23 December 1722) was a French mathematician. He was educated at the Jesuit College and the University of Caen, where he received his M.A. in 1682. He took Holy Orders the following year. Varignon gained his first ex ...

's posthumously published work, ''Nouvelle Méchanique ou Statique''.. See also . In the Cremona method, first the external forces and reactions are drawn (to scale) forming a vertical line in the lower right side of the picture. This is the sum of all the force vectors and is equal to zero as there is mechanical equilibrium. Since the equilibrium holds for the external forces on the entire truss construction, it also holds for the internal forces acting on each joint. For a joint to be ''at rest'' the sum of the forces on a joint must also be equal to zero. Starting at joint ''Aorda'', the internal forces can be found by drawing lines in the Cremona diagram representing the forces in the members 1 and 4, going clockwise; ''V_A'' (going up) load at ''A'' (going down), force in member 1 (going down/left), member 4 (going up/right) and closing with ''V_A''. As the force in member 1 is towards the joint, the member is under compression, the force in member 4 is away from the joint so the member 4 is under tension. The length of the lines for members 1 and 4 in the diagram, multiplied with the chosen scale factor is the magnitude of the force in members 1 and 4. Now, in the same way the forces in members 2 and 6 can be found for joint ''C''; force in member 1 (going up/right), force in ''C'' going down, force in 2 (going down/left), force in 6 (going up/left) and closing with the force in member 1. The same steps can be taken for joints ''D'', ''H'' and ''E'' resulting in the complete Cremona diagram where the internal forces in all members are known. In a next phase the forces caused by

wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few hou ...

must be considered. Wind will cause pressure on the upwind side of a

roof A roof ( : roofs or rooves) is the top covering of a building, including all materials and constructions necessary to support it on the walls of the building or on uprights, providing protection against rain, snow, sunlight, extremes of temper ...

(and truss) and suction on the downwind side. This will translate to asymmetrical loads but the Cremona method is the same. Wind force may introduce larger forces in the individual truss members than the static vertical loads.

References

Mechanics Structural system Diagrams {{classicalmechanics-stub