The refined theory of transversely isotropic beam is analyzed. Based on the transversely isotropic thermoporoelastic theory, a refined theory for bending beam is derived using the general solution and the Lur'e method without ad hoc assumptions. First, the expressions for all of the displacements and stress components of a transversely isotropic thermoporoelastic beam were obtained in terms of four functions with one independent variable. Second, using homogeneous boundary condition, the refined equation and the decomposed form of the thermoporoelastic beam were obtained. Finally, the approximate equations and solutions for the beam under general anti-symmetric loadings were derived from the refined theory.

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