In structural analysis of determinate structures, if we apply the three static equilibrium equations (ΣH = 0, ΣV = 0, and ΣM = 0), what quantities can be fully determined?

Introduction / Context:
In structural engineering, a statically determinate structure is one in which all unknowns can be found solely from the equations of static equilibrium. Knowing what can be evaluated using ΣH = 0, ΣV = 0, and ΣM = 0 helps decide the analysis path and whether additional compatibility relations are needed.

Given Data / Assumptions:

• The structure considered is statically determinate (no redundancy).
• Material behavior and deformations do not need to be used to close the system of equations.
• Loads are known and applied quasi-statically.

Concept / Approach:
For a determinate structure, the static equations suffice to find: (1) support reactions, (2) internal shear forces, and (3) internal bending moments (and axial forces where relevant). Once reactions are known, section cuts combined with ΣH, ΣV, and ΣM at each cut give internal force diagrams throughout the member.

Step-by-Step Solution:
Use ΣH = 0 and ΣV = 0 to solve for unknown horizontal and vertical support reactions.Use ΣM = 0 about a convenient point to solve for remaining reactions.Make a cut at any section; apply ΣV = 0 and ΣM = 0 to find shear force and bending moment at that section (and ΣH = 0 for axial force).Repeat along the span to build complete internal force diagrams.

Verification / Alternative check:
Determinate beams, trusses, and arches yield unique internal force results independent of stiffness or deflection analysis. This confirms that equilibrium alone is sufficient.

Why Other Options Are Wrong:

• Supporting reactions only: too narrow; internal forces are also obtained.
• Shear forces only / Bending moments only / Internal forces only: each ignores that reactions are also found by the same equations.

Common Pitfalls:

• Confusing determinate with indeterminate systems where compatibility or flexibility/stiffness methods are required in addition to equilibrium.
• Forgetting axial forces when frames have inclined members.

Final Answer:
All of the above.