Definition of pure bending in a beam A beam section is said to be under “pure bending” when it experiences which combination of internal actions?

Introduction / Context:Pure bending is a key idealization used to derive the flexure formula and to understand stress distributions in beams without the complicating influence of shear.

Given Data / Assumptions:

• Straight prismatic beam in the elastic range.
• Plane sections remain plane (Bernoulli–Euler hypothesis).
• No torsion; loads cause bending about a principal axis.

Concept / Approach:Pure bending occurs in a beam segment where the internal shear force is zero while the bending moment is constant (nonzero). This situation arises in the region between equal and opposite couples or within the constant-moment portion of some loading cases.

Step-by-Step Solution:Shear–moment relation: dM/dx = V.If V = 0 → dM/dx = 0 → M = constant.With V = 0, the cross-section experiences only bending; the flexure formula σ = M y / I applies cleanly without shear stress complications.

Verification / Alternative check:Example: a beam segment loaded only by two end couples produces a region of constant moment and zero shear—classic pure bending.

Why Other Options Are Wrong:Option (a) includes a nonzero shear, which contradicts dM/dx = V = 0. Option (b) with zero M is not bending. Option (d) is trivial and not representative of bending behavior. Option (e) is general bending, not pure.

Common Pitfalls:Assuming “no shear” means no transverse stresses at all—note that in reality, Saint-Venant effects near loads exist; pure bending is an interior idealization.

Final Answer:Constant bending moment and zero shear force