Six fundamental methods of supporting beam are shown below:

Which cases fall under the category of statically indeterminate beams?

Explanation:

The beam is a structural member that is subjected to transverse loading to its axis.

Continuous beam:

• It is a statically indeterminate multi-span beam on hinged support.
• The end span may be cantilever, may be freely supported or fixed supported.
• It is a beam having more than 2 supports.

Fixed beam:

• It is a beam with ends restrained from rotation.
• The figure shows a fixed beam subjected to uniformly distributed load throughout.
• It is a statically indeterminate beam on Fixed support.

Overhanging beam:

• It is defined as a beam that has its one or both ends stretching out past its support.
• It can have any number of supports.
• It is a statically determinate multi-span beam on hinged support.

Simply supported beam:

• A simply supported beam is a type of beam that has pinned support at one end and a roller support at the other end.
• It is a statically determinate multi-span beam on hinged support.

Propped cantilever beam:

• The propped cantilever beam is a beam with one end fixed and the other end simply supported.
• It comes under statically indeterminate beams.

Cantilever beam: 

• A beam fixed at one end and free at the other end is known as a cantilever beam.
• It comes under statically determinate beams.

From the above,

Statically determinate beams

1. Cantilever beam
2. Simply supported beam
3. Overhanging beam

Statically indeterminate beams

1. Propped cantilever beam:

2. Fixed beam

3. Continuous beam