Structural analysis — flexibility (force) method: correct applicability Which statement best describes the appropriate use-case for the flexibility (force) method of structural analysis?

Introduction / Context:
The flexibility (force) method and the stiffness (displacement) method are the two classical workhorses in structural analysis. Knowing when the flexibility method is efficient helps engineers choose a suitable solution strategy before building the global system of equations.

Given Data / Assumptions:

• Linear elastic behavior and small deformations.
• Structures may be beams, frames, or trusses.
• Focus is on the number of redundant (independent) forces for indeterminate systems.

Concept / Approach:
The flexibility method treats selected redundants as unknown forces and enforces compatibility of displacements. The number of simultaneous equations equals the degree of static indeterminacy. Therefore, the method is efficient when that degree is small (few redundants), regardless of whether the members are “flexible” in the everyday sense.

Step-by-Step Solution:
Identify the degree of static indeterminacy (number of redundants).Release redundants to form a determinate primary structure.Use unit-load flexibility coefficients to build compatibility equations.Solve for redundants and recover member forces and displacements.

Verification / Alternative check:
For high-indeterminacy systems, the stiffness method is normally preferred because the number of nodal displacement DOFs is often far fewer than redundants, making the global matrix smaller.

Why Other Options Are Wrong:
Determinate structures (a) need no flexibility method. Manual-only (b) is false; computers use both methods. Option (c) misinterprets “flexibility.” Option (e) is overly restrictive; the method applies to many connectivity types.

Common Pitfalls:

• Choosing redundants poorly, leading to cumbersome compatibility equations.
• Confusing flexibility coefficients with stiffness coefficients.

Final Answer:
It is used for indeterminate structures with a relatively low degree of static indeterminacy