Truss
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In medicine, a truss is a kind of surgical appliance, particularly one used for hernia patients. See truss (medicine)
In architecture and structural engineering, a truss is a structure consisting of straight slender members connected at joints.
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Statics of trusses
In the case of a simple truss, we have the following condition for its proper stability (the truss will not collapse):
- m = 2 · j - 3
where m is the total number of truss members and j is the total number of joints.
This analysis assumes that loads are applied to joints only, not to the members themselves. In the analysis of the truss, the estimated 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). As the joints are considered as being 'hinges' in the analysis the members of the truss are subject only to tension or compression, there are no bending moments in the members of this simple truss.
Analysis of trusses
Forces in members
On the right is a simple, statically determinate 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 including the graphical methods:
- Cremona diagram
- Culmann diagram (devised by Carl Culmann)
- or the analytical Ritter method.
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 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; VA</sup> (going up) load at A (going down), force in member 1 (going down/left), member 4 (going up/right) 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 (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 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.
Design of members
The next step would be to determine the cross section of the individual truss members.
For members under tension the cross-sectional area A can be found using A = F × γ / σy, where F is the force in the member, γ is a safety factor (typically 1.5 but depending on building codes) and σy is the yield tensile strength of the steel used (typically 240 MPa).
The members under compression also have to be designed to be safe against buckling.
Design of joints
After determining the minimum cross section of the members, the last step in the design of a truss would be detailing of the bolted joints, e.g. involving shear of the bolt connections used in the joints, see also shear stress.
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