Unusual patterns in the time dependent behavior of the pore pressure in poroelastic solids (the Mandel-Cryer effect) were predicted and then observed over 25 years ago. Recently we formulated the problem of poroelastic beams dominated by axial diffusion, and results were found for several cases. It was observed that response peculiarities similar to those previously observed in massive structures are possible also for this case. We now show that not only are such unexpected results possible also for the deflection and slope, but that the time dependent patterns of all these variables may even be more complicated than in the case of the Mandel-Cryer effect. These interesting behavior patterns are qualitatively unobtainable with structures whose time dependent behavior results from modeling material behavior as viscoelastic. In this paper we present various behaviors of unusual nature exhibited by poroelastic beams and columns with axial diffusion.