The Cremona diagram, also known as the Cremona-

Maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of N ...

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 acting on a physical system that does not experience an acceleration, but rather is in mechanical equilibrium, equilibrium with its environment ...

truss A truss is an assembly of ''members'' such as Beam (structure), 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 ...

es to determine the forces in members ( graphic statics). 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 alg ...

. 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 Society of Jesus, Jesuit College and the University of Caen, where he received his Magister Artium, M.A. in 1682. He took Holy Orders the following ...

'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

vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

s and is equal to zero as there is

mechanical equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is ze ...

. 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 Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...

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

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

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(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