Truss

In medicine, a truss is a kind of surgical appliance, particularly one used for hernia patients. See truss (medicine)

In architecture, a truss is a structure consisting of straight slender members connected at joints.

In the case of a simple truss, we have the following condition for its proper rigidity (the truss will not collapse):

m= 2j-3

where m is the total number of truss members and j is the total number of joints.

Loads must be applied to the joints only, and not to the members themselves. In the analysis of the truss, the weights of bars are either omitted or, if required, they are applied to the joints (a half of the weight to each of the bar joints).

The joints are considered as being 'hinges', consequently the members of the truss are subject only to tension or compression, there are no bending momentss in this simple analysis of the construction.

On the right is a flat truss with 9 joints and (2 x 9 - 3 =) 15 members. External loads are concentrated in the outer joints. Since this is a symmetrical truss with symmetrical vertical loads, it is clear to see that the reactions at A and B are equal, vertical and half the total load.

The internal forces in the members of the truss can be calculated in a variety of ways, one is a graphical method called a 'Cremona diagram', other methods are known as Culmann and Ritter.

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 vectorss 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 A, 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.

The next step would be to determine the cross section of the individual truss members. For members under tension the cross section 'A' can be found using A = F x γ / σ_y where F is the force in the member, γ is a safety factor (usually 1.5) and σ_y is the yield tensile strength of the steel used (usually 240 N/mm²).
The members under compression have to be designed using the methods for buckling, see compressive stress.

After determining the minimum cross section of the members, the last step in the design of a truss would be detailing of the joints, e.g. involving shear of the bolt connections used in the joints, see also shear stress.