Question

Where is the Neutral Axis located?

Answer 1

Hint: In order to answer this question, first we will discuss the location where the Neutral Axis is located and then we will discuss the Neutral Axis. And then we will also discuss the location of a neutral axis of a beam.

Complete step-by-step solution:
A neutral axis is an axis found in the cross-section of a beam that has no stress or stresses. The neutral axis is normally positioned at the geometric centroid for a regular or homogeneous (symmetric, isotropic, and not curved) beam. The neutral axis will be at a place where the stress is zero if the beam bends. The geometric centroidal axis, however, will not pass through the neutral axis in this case.
There are no longitudinal stresses or strains along the neutral axis in the cross section of a beam (a member resisting bending) or shaft. The neutral axis lies at the geometric centroid if the section is symmetric, isotropic, and not bent before a bend. The fibres on one side of the neutral axis are all in tension, while the fibres on the other are in compression.
A plane on the beam remains plane because it is experiencing homogeneous bending. That is to say:
${\gamma _{xy}} = {\gamma _{zx}} = {\tau _{xy}} = {\tau _{xz}} = 0$
where, $\gamma $ is the shear strain,
$\tau $ is the shear stress.
At the top of the beam, there is a compressive (negative) strain, and at the bottom, there is a tensile (positive) strain. Because the strain in a beam is a continuous function, the Intermediate Value Theorem dictates that there must be some point between the top and bottom with no strain.

Note: If the beam has a square or rectangular cross section, the neutral axis will be in the geometric centre of the cross section, which is also the centre of inertia. In general, though, if you wish to discover the neutral axis of a beam, you must examine its cross section and locate the centre of inertia.