Compound member under preload – Rod inside a tube tightened by rigid washers\nA slender rod is enclosed centrally within a tube, and the assembly is pre-tightened by rigid washers (nutting). If a net external compressive load is applied to the assembly, what stress state most appropriately describes the members?

Introduction / Context:
Preloaded compound members (a central rod within a surrounding tube) are classic examples of load sharing through differential stiffness and initial stresses. Understanding the initial state and its evolution under external loading is important for bolts, tie-rods, and composite columns.

Given Data / Assumptions:

• Rod and tube are concentric and connected by rigid end washers/nuts.
• Preload is applied by tightening (nutting) without external load.
• Linear elastic behavior; compatible deformations at the ends.

Concept / Approach:
During tightening (no external force), the rod is placed in compression while the tube is stretched in tension; the rigid washers enforce equal end displacements. When an external compressive load is later applied to the assembly, it first reduces the tube’s tensile stress; only after a threshold might the tube go into compression, depending on load magnitude.

Step-by-Step Reasoning:
Initial state (preload only): rod in compression, tube in tension.Apply external compression: total tube stress = tension from preload minus portion of external load; rod compression increases.Unless the external load exceeds the preload in the tube, the tube remains in tension while the rod remains in compression.

Verification / Alternative check:
Force–displacement compatibility analysis for two springs in parallel with initial strains reproduces the same conclusion.

Why Other Options Are Wrong:
Options (a), (b), (c) ignore preload directions; both in compression occurs only beyond a specific external load; “stress-free” is impossible after tightening.

Common Pitfalls:
Neglecting the effect of preload; assuming immediate compression in both members under any external compressive load.

Final Answer:
Tube is under tension and rod is under compression