The yrast and yrare lines are obtained for 40 Ca using a statistical method by assuming the nucleons to move in a triaxially deformed Nilsson harmonic oscillator potential. The backbending and yrast traps are observed in the case of 40 Ca at certain spins. A shift in the first yrast minima towards higher angular momentum states with an increase in entropy is observed. A second backbending is found to occur at spin M ϭ17ប for all entropies. The excitation energy, the nuclear level density, the single-particle level density parameter, and the spin cutoff parameter are determined as functions of temperature and angular momentum by minimizing the free energy. The Strutinsky method is used to study the variation of the shell correction with angular momentum for equilibrium shapes. The Fermi energies obtained as a function of angular momentum are used for calculating this shell correction. The nucleus is found to be spherical up to M ϭ6ប and becomes oblate with a further increase in angular momentum. The shell correction is found to increase with the deformation having a minimum value for the spherical shape.