Determinacy of a compound truss from two simple trusses Two individually simple and rigid trusses have m1 and m2 members, respectively. If they are connected to form a compound truss, choose the condition on total members m for the overall frame to be rigid and statically determinate.

Introduction / Context:Compound trusses are built by connecting two or more simple rigid trusses. To remain statically determinate and rigid, a specific number of linking bars must be added so that the combined frame has exactly the necessary constraints without redundancy.

Given Data / Assumptions:

• Each component truss is simple and individually rigid.
• The connection is made using straight bar members.
• Planar truss assumptions (pin-jointed, axial-force members).

Concept / Approach:To properly constrain the relative motion between two rigid trusses in a plane, three independent constraints are needed (two translations and one rotation). Therefore, three appropriately placed bars are required to make the compound system rigid and statically determinate.

Step-by-Step Solution:

Verification / Alternative check:If fewer than three bars are used, the assembly will have mechanisms; if more than three, it becomes statically indeterminate due to redundant constraints.

Why Other Options Are Wrong:

• m = m1 + m2, +1, +2: Insufficient constraints leave mechanisms.
• None of these: Incorrect because +3 is the established condition.

Common Pitfalls:Using three bars that are concurrent or parallel so that constraints are not independent; bars must be placed to remove all three relative motions.

Final Answer:m = m1 + m2 + 3