  We study how shear moduli of a correlated metal change across superconducting
phase transitions. Using a microscopic theory we explain why for most classes
of superconductors this change is small. The Fe-based and the A15 systems are
notable exceptions where the change is boosted by five orders of magnitude. We
show that this boost is a consequence of enhanced nematic correlation. The
theory explains the unusual temperature dependence of the orthorhombic shear
and the back-bending of the nematic transition line in the superconducting
phase of the Fe-based systems.
