The correct answer is: A. Design of simple steel beams.
Steel beam theory is a branch of structural engineering that deals with the design of steel beams. It is based on the assumption that the beam is a linear elastic material, and that the stresses and strains in the beam are proportional to each other. This theory can be used to design simple steel beams, such as those used in buildings and bridges.
Option B is incorrect because steel beams encased in concrete are not considered to be simple steel beams. They are considered to be composite beams, which are made up of two or more materials that work together to resist loads.
Option C is incorrect because doubly reinforced beams are designed to resist both bending and shear loads. Steel beam theory is only used to design beams that are primarily subjected to bending loads.
Option D is incorrect because shear stress is not the only factor that needs to be considered when designing a beam. The beam must also be designed to resist bending, compression, and tension loads.