Cremona Diagram Software
Cremona diagram for a plane truss The Cremona diagram is a graphical method used in of to determine the forces in members (graphic statics). The method was created by the Italian mathematician. In the Cremona method, first the external forces and reactions are drawn (to ) forming a vertical line in the lower right side of the picture. This is the of all the force and is equal to zero as there is mechanical equilibrium. Since the holds for the external forces on the entire truss construction, it also holds for the internal forces acting on each joint.
English: Placing the forces on a dynamic diagram in order to build the Cremona diagram; a node has the name of the domains that are common to the forces at this node; see also Image:Cremona triangle simple.svg.
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 is the 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 must be considered. Wind will cause pressure on the upwind side of a (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.
Use the sliders to set the two point loads at the center and the right (forces in negative direction, and ). Check 'show member forces' to show the truss member forces. Check 'make members under tension red and under compression green' to show the red and green arrows. Arrows that point outward (green) represent the member response to compression forces, and arrows that point inward (red) represent the member response to tension forces. Compression acts to shorten the member and tension acts to lengthen the member. The black members are zero members; that is, these members are neither in tension nor in compression, so the force is 0 kN. The purpose of zero members is to provide stability and extra support to the structure in the event of another member failing.
When the boxes 'make trusses under tension red and under compression green' and 'show member forces' are checked, move the mouse over a pivot point to show arrows that represent forces (and the values of the forces) in the and directions at that point. This breaks the forces in the diagonal members into their and components. Details The method of joints is used to calculate the forces on each member of the truss.
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