Civil Engineering Professional Engineer Practice Exam

In determining structural stability, which equation is applied?

1. 2(#joints) = structural members + 2

2. 2(#joints) = structural members + 3

3. 2(#members) = joints + 3

4. 2(#joints) > structural members + 3

The correct answer is: 2(#joints) = structural members + 3

The concept of structural stability in trusses is built upon evaluating the relationships between the number of joints, structural members, and the degree of indeterminacy. The equation 2 times the number of joints equals the number of structural members plus three establishes the necessary condition for a truss to be stable and determinate. This equation essentially derives from the equilibrium conditions governing structures. For a planar truss, each joint can theoretically provide two constraints (allowing for forces in two perpendicular directions, often referred to as horizontal and vertical), and in an ideal scenario, the structure should have enough members to maintain stability while allowing for sufficient support and load transfer. When the equation holds true, it suggests an optimal configuration where the structure can safely distribute loads without excess or shortage of members, thus achieving a stable system. If the number of structural members exceeds this equation, the structure may be indeterminate, leading to potential over-constraining, which can cause issues in structural performance. This foundational relationship is crucial for civil engineers in analyzing the stability of trusses, making the equation vital for assessments during design and construction. Understanding this equation helps engineers ensure that their structures are not only stable but also economical in terms of materials used.