The Cremona diagram is a graphical method used in statics of trusses to determine the forces in members (graphic statics).

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  • The Cremona diagram is a graphical method used in statics of trusses to determine the forces in members (graphic statics). The method was created by the Italian mathematician Luigi Cremona.In the Cremona method, first the external forces and reactions are drawn 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; VA</sup> load at A, force in member 1, member 4 and closing with VA</sup>. 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, force in C going down, force in 2, force in 6 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 must be considered. Wind will cause pressure on the upwind side of a roof (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. (en)
  • Der Cremonaplan dient bei statisch bestimmten Fachwerken der zeichnerischen Bestimmung der Stabkräfte zur Bemessung der Stäbe. Er wurde im 19. Jahrhundert von Antonio Luigi Gaudenzio Giuseppe Cremona entwickelt. Die dem Cremonaplan zugrundeliegenden Methoden sind sehr hilfreich bei der Ausbildung. Im Computerzeitalter erfolgt die Ermittlung der Stabkräfte in der Regel schneller und bequemer ohne die grafische Darstellung des Kraftecks. (de)
  • L'épure de Cremona — du nom de son inventeur, Luigi Cremona, mais on trouve fréquemment les orthographes avec un accent aigu et éventuellement une minuscule initiale (Crémona, crémona) — est une méthode de statique graphique utilisée pour le calcul des efforts dans un treillis . (fr)
  • Cremonas kraftplan är en av den italienske matematikern Luigi Cremona vetenskapligt behandlad metod att bestämma spänningen i de olika stängerna inom ett plant fackverk. Metoden grundar sig därpå, att samtliga krafter i en knutpunkt, yttre belastningar och stångspänningar, håller varandra i jämvikt. Uppritas därför dessa krafter parallellt med sina riktningslinjer i en viss kraftskala, bildar de en sluten polygon, en kraftplan. Metoden fick stor betydelse vid grafisk beräkning av fackverk (broar, takstolar m.m.). (sv)
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  • The Cremona diagram is a graphical method used in statics of trusses to determine the forces in members (graphic statics). (en)
  • Der Cremonaplan dient bei statisch bestimmten Fachwerken der zeichnerischen Bestimmung der Stabkräfte zur Bemessung der Stäbe. Er wurde im 19. (de)
  • L'épure de Cremona — du nom de son inventeur, Luigi Cremona, mais on trouve fréquemment les orthographes avec un accent aigu et éventuellement une minuscule initiale (Crémona, crémona) — est une méthode de statique graphique utilisée pour le calcul des efforts dans un treillis . (fr)
  • Cremonas kraftplan är en av den italienske matematikern Luigi Cremona vetenskapligt behandlad metod att bestämma spänningen i de olika stängerna inom ett plant fackverk. Metoden grundar sig därpå, att samtliga krafter i en knutpunkt, yttre belastningar och stångspänningar, håller varandra i jämvikt. (sv)
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  • Cremona diagram (en)
  • Cremonaplan (de)
  • Épure de Cremona (fr)
  • Cremonas kraftplan (sv)
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