Eccentric axial loading on a rectangular section: A bar (or column) with direct compressive load and bending is said to be in combined stress. Which of the following sets of statements about bending and axial effects under eccentric compression is correct?

Introduction / Context:
Members under eccentric axial load experience a combination of direct (uniform) stress and bending stress. Understanding how these two components superpose determines whether any region is in compression or tension. This question asks you to identify the correct statements about combined stress behavior.

Given Data / Assumptions:

• Member is prismatic and behaves elastically.
• Plane sections remain plane after bending.
• Axial load is compressive and applied with some eccentricity (causing bending).

Concept / Approach:
Resultant stress at a fiber is the algebraic sum of direct stress and bending stress contributions. If the bending-induced tensile stress is smaller than the direct compressive stress, the entire cross-section remains in compression. If it equals the axial value, stress at one edge becomes zero. If it exceeds the axial compressive stress, a portion goes into tension.

Step-by-Step Solution:
(a) The moment of inertia must be taken about the axis about which bending occurs – correct.(b) If tensile stress from bending is less than axial compressive stress, the net stress everywhere is compressive – correct.(c) If tensile stress equals axial compressive stress, the stress at one extreme edge becomes zero, not compressive – statement is incorrect.(d) If tensile stress from bending is greater than axial compressive stress, part of the section goes into net tension – correct.

Verification / Alternative check:
Use superposition: at an extreme fiber, write
σ_edge = σ_axial ± σ_bendingand compare their magnitudes to see sign changes across the section.

Why Other Options Are Wrong:
Choices listing (c) as correct include a false statement; “All” is therefore wrong.

Common Pitfalls:

• Misinterpreting the sign convention for tensile/compressive stresses.
• Using the wrong centroidal axis for the second moment of area.
• Ignoring section edge where stress is most critical.

Final Answer:
Only (a), (b), and (d) are correct