Analyzing forces in simple trusses Which set of methods may be used to determine member forces in a statically determinate, simple truss under given loads and supports?

Introduction / Context:
Simple planar trusses are extensively used in roofs and bridges. To compute internal axial forces in members, classical statics offers several complementary techniques. Choosing the right method speeds analysis and improves accuracy.

Given Data / Assumptions:

• Truss is statically determinate and planar.
• Loads are applied at joints; members carry axial forces only.
• Supports provide determinacy (e.g., pin and roller).

Concept / Approach:
The method of joints solves force equilibrium at each joint (sum of forces = 0). The method of sections cuts through the truss to analyze a subset rapidly (sum of forces and moments = 0). Graphical methods (e.g., Cremona diagram) construct force polygons to determine member forces visually, useful for quick checks and conceptual understanding.

Step-by-Step Solution:
Start with global reactions using static equilibrium.Use method of joints for joint-by-joint resolution in small/regular trusses.Apply method of sections to jump directly to critical members (efficient for larger trusses).Use graphical diagrams as a check or for preliminary sizing.

Verification / Alternative check:
All three methods are standard in structural analysis curricula and yield identical results for determinate trusses when applied correctly.

Why Other Options Are Wrong:
Any single-method-only option is incomplete; multiple valid methods exist and are routinely used.

Common Pitfalls:

• Forgetting sign conventions and tension/compression identification.
• Cutting more than three unknowns with method of sections, which breaks determinacy of the single step.

Final Answer:
all the above (graphical method, method of joints, and method of sections)