We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a liquid crystal with T-shaped molecules. We find that the ratio, K33/K11 ≃1 in the entire nematic range except very close to the nematic to Sm-A (SN) transition. Both K33 and K11 show pretransitional divergence as the SN transition is approached from higher temperature. The ratio, K33/K11 suggests that the length (L) to effective width (D) ratio (i.e., L/D ) is significantly smaller due to the presence of long and flexible lateral group, compared to that of rigid rodlike molecules. It is argued that apart from the extra contribution to the elasticity the long and flexible lateral group also has a significant contribution to the suppression of the splay fluctuations in the onset of smectic short-range fluctuation. The structure of the Sm-A phase is investigated by using small angle x-ray diffraction, and a possible arrangement of the molecules in the Sm-A layer is proposed.