This research examines the stability behaviour of long-span, unstiffened, slender I-members. The studies focus on singly-symmetric hybrid I-sections, which are increasingly used in long-span bridges. While it would be greatly advantageous to use fewer transverse stiffeners and cross-frames between members, the reduction in the number of transverse stiffeners decreases the member shear strength and also increases its vulnerability to lateral torsional buckling (LTB). The overall study focuses on the moment-shear interaction behaviour of such mono-symmetric hybrid girders, where the flexure is governed by LTB, rather than compression flange yielding. However, these members are also expected to be highly inelastic. One complexity of understanding the moment-shear behaviour is the estimate of the shear strengths of such members. There are various shear postbuckling theories in literature, with different international codes adapting different theories. The ultimate shear strengths are, however, determined as an algebraic sum of the elastic shear buckling stresses and the postbuckling stresses. Hence, in order to correctly establish the mechanics of shear behaviour, it is vital to understand both elastic shear buckling stresses and the postbuckling mechanics separately. The first part of this work determines the restraints imposed by flanges and transverse stiffeners on the elastic shear buckling stresses of long unstiffened I-girders and establishes girder geometry that achieves a minimum stability equivalent to that of simply-supported web plates subjected to shear. Next, to correctly assess the inelastic strengths of such members, the residual stresses are measured in hybrid mono-symmetric welded I-girders. Residual stresses are well known to affect the inelastic LTB strengths of I-sections, but there is little data on the stress distributions in singly-symmetric or hybrid I-sections or their impact on shear strengths, which is discussed here.