For typical beam loading cases, which of the following statements are correct about the shapes of shear force (SF) and bending moment (BM) diagrams?

Introduction / Context:
Recognizing the qualitative shapes of shear force (SF) and bending moment (BM) diagrams is a core skill in structural analysis. It speeds up checking, helps catch modeling errors, and guides efficient design decisions.

Given Data / Assumptions:

• Beam theory with small deflections and linear elasticity.
• Distributed loads expressed per unit length.
• Sign conventions are consistent along the beam.

Concept / Approach:
The governing relationships are: dV/dx = −w(x) and dM/dx = V(x), where w(x) is the load intensity. Integrating these relations establishes how the curve shapes evolve with the load pattern.

Step-by-Step Solution:
Uniformly distributed load w = constant: dV/dx = −w ⇒ V is linear; integrating again gives M as a quadratic function, i.e., a parabola.Linearly varying load w = kx: dV/dx = −kx ⇒ V is quadratic ⇒ M is cubic upon integration, i.e., a cubic parabola.Point loads produce jumps in V and linear segments in M, consistent with the derivative relations.

Verification / Alternative check:
Dimensional and boundary checks (zero moments at simple supports for simply supported beams) align with the predicted polynomial orders. Numerical examples reproduce these curve shapes exactly.

Why Other Options Are Wrong:

• Each individual statement (a)–(d) is correct; hence the combined correct choice is 'All of the above'.

Common Pitfalls:

• Mistaking the order of the BM curve, especially under triangular loading where M becomes cubic.
• Forgetting that jumps in V correspond to point loads and that M remains continuous at those points.

Final Answer:
All of the above.