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Method of joints for space trusses

The method of joints developed for plane trusses may be extended directly to space trusses by satisfying the complete vector equation

for each joint. We normally begin the analysis at a joint where at least one known force acts and not more than three unknown forces are present. Adjacent joints on which not more than three unknown forces act may then be analyzed in turn.

Method of sections for space trusses :The method of sections discussed in the earlier section may also be applied to space trusses. The two vector equations

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Trusses

There are in all 3 j equations for a space truss with j joints. For the entire truss composed of m members, there are m unknowns plus six unknown support reactions in the general case of a statically determinate space structure. Thus, for any space truss, the equation m +6=3 j will be satisfied if the truss is statically determinate internally. A simple space truss satisfies this relation automatically. Starting with the initial tetrahedron, for which the equation holds, adding three members and one joint at a time extends the structure, thus preserving the equality.