A plane frame is considered statically determinate when which of the following equations holds?

In the context of structural analysis, a plane frame is deemed statically determinate when it can be solved using only equilibrium equations, without the need for additional methods such as deformation or compatibility. The fundamental equation that characterizes this condition is derived from the relationship between members, reactions, joints, and constraints in the structure.

The correct equation, which is applied here, expresses the relationship as 3m + r = 3j + c.

Here’s the breakdown of the terms in the equation:

• m represents the number of members in the frame.
• r denotes the number of external reactions.
• j is the number of joints.
• c accounts for the number of internal constraints or redundant connections provided by the frame.

In this equation, 3m corresponds to the total number of internal force equations available to analyze members (three equations per member in a planar structure: two for equilibrium of forces and one for moment equilibrium). The right side of the equation, which is 3j + c, accounts for the relationships involving joints (with three equilibrium equations per joint for planar structures) and considers internal constraints that may reduce the degrees of freedom within the system.

When the equation holds true, it indicates