Dear Waseem
Your concern is valid but the lower limit given in FEMA example doesn't make sense to me as in a general the usage of time period in seismic analysis is not more than the evaluation of ground acceleration that will be imparted in structure in accordance with specific structural characteristics.
Similarly if the specific structural characteristics of a building reveals a time period lesser than generalized approximate time period , then it doesn't make sense to skip the accurate time period and to use approximate one when code itself defines approximate time period as a basis to start analysis for actual T.
More interesting is to note that indicated FEMA example is based on 2009 NEHRP seismic provisions , whereas in a separate document issued by NEHRP afterwards (named expanded seismic commentary to ACE-10) it is recommended to use "Tcomp" if "Tcomp < Ta".
Moreover, i didn't find any lower bound on time period in UBC97 and even in ASCE 7 which is based on same ELF procedure as given in FEMA example.
Therefore, it seems that indicated provisions in FEMA example are overlooked that they have fixed later and usage of Tcomputed if "Tcomputed < Tapproximate" seems valid.