What is the difference between the Mindlin–Reissner theory and Timoshenko beam theory?

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Wenbin Yu

Mindlin-Reissner theory is a plate/shell theory for structures having one dimension much smaller than the two other dimensions. It is a refinement from Kirchhoff-Love plate/shell theory with introducing two additional transverse shear measures. Timoshenko theory is a beam theory for structures having one dimension much larger than the two other dimensions. It is a refinment from Euler-Bernoulli beam theory with introducing two additional transverse shear measures.

Chaidul Chaudhuri

I am interested to know the governing equation for Timoshenko beam resting on soil !!