This paper presents a 3-node triangular shell element based on the Reissner-Naghdi shell theory. The proposed shell element, DSPM15, has 5 DOFs per node. The element uses linear functions for translation displacements and incomplete quadratic functions for rotations. Adopting the concept of Bergan's free formulation, the coupling of lower and higher modes in bending is assumed to be zero. The discrete shear projection method defines the mixed transverse shear strains to avoid the phenomenon of shear locking. Standard benchmark problems and comparisons with existing elements are used to evaluate the element's performance. The new shell element is shear-locking free, has no spurious modes, and passes the standard benchmark tests for thick and thin shells with excellent convergence behaviour, reliability, and precision. © 2025