Good question! I'll try to answer.

In my opinion, the TBT range of applicability depends not only on the slenderness ratio but also on the heterogenity of the beam cross section. When you consider a multilayered composite or a sandwich beam, the value of slenderness ratio that allows the use of the TBT is usually higher than that of a isotropic single layer beam. Due to the influence of the beam cross section heterogenity, it is hard to find a threshold value for the slenderness ratio that defines a beam as a Timoshenko one. 

Furthermore, according to me, the slenderness ratio criterion is equivalent to that based on the higher frequencies, since it is a matter of transverse shear strain effect.

I take the liberty to suggest you a paper (http://www.sciencedirect.com/science/article/pii/S0263822313003425) wherein the First-Order Shear Deformation Theory for plate is widely discussed and limit of applicability for bending, free vibration and buckling problems highlighted.

I hope I have been of use to you.

Timoshenko beam: when shear deformations are non negligible

one application: link beam in coupled shear walls

https://www.researchgate.net/post/Whats_the_basic_difference_between_Euler-Bernoulli_and_Timoshenko_beam_theory

The Euler-Bernoulli beam theory neglects shear deformations by assuming that plane sections remain plane and perpendicular to the neutral axis during bending, but during testings it was found that cross section become curved. Instead of modelling this curved shape of the cross-section, the Timoshenko beam theory retains the assumption that the cross-section remains plane during bending. However, the assumption that it must remain perpendicular to the neutral axis is relaxed. Hence Timoshanko model takes into account shear deformation and rotational inertia effects.

This additional capability of Timoshanko beam over Euler-Bernoulli beam makes it better suitable for describing the behaviour of short beams, sandwich composite beams and beams subject to high-frequency excitation (when the wavelength approaches the thickness of the beam) - Reference (Wiki).

So in my opinion Timoshanko beam theory will predict the behavior of a beam always better than Euler-Bernoulli beam. But the difference between the results of the two theories will be prominent in the above mentioned cases only, because in these cases only the contribution of shear deformation will be a significant portion of the total deformation.

Hope that makes some sense.

Regards

I would second the opinion that Timoshenko's beam theory is always applicable, it is just that it will not be significantly better in many usual cases where beams are used and the Euler-Bernoulli will provide very similar results if shear is negligible.

To generalize a little bit, one does not have to use the assumptions that Naveen Bhatt mentioned to formulate either E-B model or Timoshenko model. These are just two common beam models. You can always use a Timoshenko model or E-B model to analyze a beam. Timoshenko model will be more accurate because it has six fundamental kinematic variables and six strains while the E-B beam only has four fundamental kinematics variables and four strains. Generally speaking Timoshenko model predicts better than E-B model particularly for not so slender beams or transverse shear deformation is significant. If these models are constructed without using assumptions, they can reproduce 3D FEA results as long as the structure is slender. See the many examples we have in Analysis of Slender Structures Using Mechanics of Structure Genome and Open Source Codes https://cdmhub.org/resources/1099. The codes developed in that thesis can be launched freely in the cloud at https://cdmhub.org/resources/scstandard.  

https://cdmhub.org/resources/scstandard

Euler Beam theory provides deflections caused by bending action only. Timoshenko Beam Theory also adds shear deformation in obtaining a beam's transverse displacements. Shear deflections are comparatively small for long thin beams and so the results show little difference in such cases. When beams are short and thick and the material shear modulus is low, the differences become noticeable as the shear deflections become more important.