Structural analysis: Influence lines may be constructed for which types of structures when assessing the effect of moving loads.

Introduction / Context:
Influence lines are indispensable for evaluating the response of structures to moving loads, such as vehicles on bridges or cranes on girders. They depict how a particular response quantity (reaction, shear, moment, or displacement) varies as a unit load traverses the structure.

Given Data / Assumptions:

• The structure may be statically determinate or indeterminate.
• Response quantities of interest include reactions, internal forces, and displacements.
• Linear elastic behavior is assumed for typical influence line use.

Concept / Approach:
Influence lines can be drawn for any linear structure. For statically determinate structures, they are obtained using equilibrium and Muller-Breslau principle in a straightforward manner. For indeterminate structures, influence lines exist as well, but require more advanced methods (e.g., flexibility or stiffness methods) or Muller-Breslau principle with compatibility conditions.

Step-by-Step Solution:
1) Define the response quantity (e.g., shear at a section).2) For determinate structures, cut the structure at the response location and use equilibrium with a unit displacement or rotation released (Muller-Breslau) to sketch the influence line.3) For indeterminate structures, release the corresponding restraint or use structural analysis techniques to compute the response at positions of the unit load; plot those values as the influence line.

Verification / Alternative check:
Check that the area under the influence line multiplied by distributed moving load produces the same effect as summing discrete positions; this validates the influence line curve.

Why Other Options Are Wrong:
Only determinate or only truss options are too restrictive, since influence lines are general."None of these" is incorrect because influence lines are a standard tool across many structure types.

Common Pitfalls:
Assuming influence lines apply only to simple beams; neglecting compatibility effects in indeterminate systems; or confusing influence lines with shear or moment diagrams under fixed loads.

Final Answer:
Structures of any type, whether statically determinate or indeterminate