Internal force components at the end of a planar frame member In planar (2D) frame analysis, how many transverse shear force components can act at either end of a member (considering the standard internal force set at a member end)?

Introduction / Context:
In two-dimensional frame and beam theory, the internal forces transmitted across a member end section are resolved into a standard set. Understanding how many independent components exist helps when writing equilibrium equations, assembling global stiffness matrices, and interpreting analysis outputs.

Given Data / Assumptions:

• Planar (2D) behavior only; out-of-plane actions are excluded.
• Standard internal force set at a member end: axial force (N), shear force (V), and bending moment (M).
• Member and joints are idealized as line elements with no warping/torsion DOF in 2D.

Concept / Approach:

At the cut end of a 2D frame member, there are three independent internal actions: one axial force along the member axis (N), one transverse shear force perpendicular to the axis (V), and one bending moment about the out-of-plane axis (M). Therefore, the number of transverse shear force components at either end is exactly one.

Step-by-Step Solution:

Verification / Alternative check:

In 3D frames, two orthogonal shear components exist at a cut section. Restricting to 2D reduces these to a single transverse shear degree of freedom per end, aligning with classical beam theory and standard finite element formulations (2D frame element with 3 DOF per node: u, v, θ).

Why Other Options Are Wrong:

• Two/three/four: Not applicable in 2D; only one shear component exists.
• Zero: Incorrect; shear is a fundamental internal action even in pure bending segments adjacent to loads/reactions.

Common Pitfalls:

• Mixing 2D and 3D internal action sets (which would include two shear components and a torsional moment).
• Confusing shear flow distribution with the single resultant transverse shear component.

Final Answer:

one.