In plastic analysis of beams, identify the correct statements regarding yield moment, plastic moment, plastic neutral axis, and shape factor.

Introduction / Context:
Plastic analysis extends beyond elastic behavior by allowing stress redistribution after yielding. The key milestones are the yield moment (first yielding) and the plastic moment (full plasticity). The shape factor quantifies reserve strength from elastic to plastic states and depends on cross-section shape.

Given Data / Assumptions:

• Material follows an ideal elastic–perfectly plastic model for bending.
• Plane sections remain plane (Bernoulli hypothesis).
• Longitudinal shear permits redistribution as plastic hinges form.

Concept / Approach:
At yield moment, only extreme fibers reach yield stress; stresses elsewhere remain below yield. At plastic moment, compressive and tensile blocks each attain yield stress across their half-areas, and the plastic neutral axis (PNA) lies so the two blocks have equal area. Shape factor = M_p / M_y captures how much higher the full plastic capacity is compared with first yield and is purely geometric (independent of the yield stress value).

Step-by-Step Solution:
Identify yield moment: first reaching of sigma_y at extreme fibers.Identify plastic moment: full-depth yielding with rectangular stress blocks at ±sigma_y.Recognize PNA property: equal tension and compression areas at the plastic state.Define shape factor: M_p / M_y.Since all statements align with theory, select the comprehensive option.

Verification / Alternative check:
For common shapes: rectangle f = 1.5, circle f ≈ 1.7, triangle f ≈ 2.34, confirming geometric dependence of shape factor.

Why Other Options Are Wrong:

• Choosing any single statement omits the full set of correct fundamentals.

Common Pitfalls:
Confusing elastic neutral axis with plastic neutral axis; assuming shape factor depends on material rather than geometry.

Final Answer:
All the above.