Determinacy in structural engineering refers to the ability of a structure to resist external loads and maintain equilibrium. A determinate structure is one in which all the reactions and internal forces can be determined using the equations of static equilibrium. In other words, the structure has enough supports and constraints to fully determine the internal forces and reactions.

Among the given options, the example of a determinate structure is a beam overhanging on both sides (option D). Here's why:

1. Determinate structure definition
- A determinate structure is one in which all the reactions and internal forces can be determined using the equations of static equilibrium.
- It means that the structure has enough supports and constraints to fully determine the internal forces and reactions.

2. Overview of the options
a) Fixed beam: A fixed beam is a beam that is fully restrained against rotation at both ends. It has supports that prevent any rotation or movement. It is a determinate structure.
b) Continuous beam: A continuous beam is a beam that spans over multiple supports without any joints or interruptions. It is also a determinate structure.
c) Two-hinged arch: A two-hinged arch is a structural element with two hinges at the supports, allowing rotation. It is a determinate structure.
d) Beam overhanging on both sides: A beam overhanging on both sides refers to a beam that extends beyond its supports on both ends. It is an example of an indeterminate structure.

3. Why beam overhanging on both sides is an indeterminate structure
- An indeterminate structure is one in which the reactions and internal forces cannot be determined using the equations of static equilibrium alone.
- In the case of a beam overhanging on both sides, the reactions and internal forces cannot be determined without additional information about the end conditions or the overhanging portions.
- The overhanging portions introduce additional unknowns, making the structure indeterminate.

In conclusion, the correct answer is option D - beam overhanging on both sides. It is an example of an indeterminate structure because the reactions and internal forces cannot be determined using the equations of static equilibrium alone.