We investigate the piezoresistive effect of carbon nanotubes (CNTs) within density functional theory (DFT) aiming at application-relevant CNTs. CNTs are excellent candidates for the usage in nano-electromechanical sensors (NEMSs) due to their small band gap at zero strain leading to a finite resistivity at room temperature. The application of strain induces a band gap-opening leading to a tremendous change in the resistivity. DFT with the LDA approximation yields reasonable results for pure carbon systems like CNTs and is applied to calculate the electronic structure of experimentally relevant CNTs. For the transport part, a simple ballistic transport model based on the band gap is used. We compare our DFT results for the band gaps of strained CNTs to results of tight binding (TB) models. By introducing a scaling factor of $\sqrt {2} $, an excellent agreement of the DFT data with TB model, published by Yang and Han [Phys. Rev. Lett. 85, 154 (2000)], is obtained.