Discussion
Static indeterminacy for pin-jointed 2D frame is given by:
(Where, m is the number of members, r is the number of reactions and j is the number of joints)
Answer: D
For a pin-jointed plane frame, static indeterminacy = (m + r) - 2j.
Each member of a pin-jointed truss carries one unknown, its axial force, and each support reaction is one unknown, giving m + r unknowns. At every joint the forces must satisfy two equilibrium equations (ΣFx = 0 and ΣFy = 0), giving 2j equations. The excess of unknowns over equations is (m + r) - 2j; zero means a statically determinate truss.
(m + r) - 3j is the form for space trusses, with three equations per joint. (3m + r) - 3j applies to rigid-jointed plane frames, where each member has three unknowns, and (6m + r) - 6j to rigid space frames.
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