Time-to-collision is a commonly employed measure for rear-end collision prediction. However, its conventional formulation, which assumes constant speed and heading, is incapable of identifying sideswipe collisions. A two-dimensional extension has been proposed to incorporate lateral interactions with passenger cars, yet it assumes identical, fixed headings and does not accommodate articulated vehicles such as tractor-semitrailers. In this paper, the existing formulation for the car is first refined to incorporate differences in vehicle heading. Subsequently, new two-dimensional time-to-collision measures are proposed for articulated vehicles: and modified . These measures employ constant-speed and constant-acceleration assumptions and are analogous to their one-dimensional counterparts: time-to-collision and modified time-to-collision. The proposed measures are assessed in CARLA using randomly generated cut-in scenarios simulated with a tractor-semitrailer model, incorporating a range of trailer lengths. A short analysis is also conducted to test the measures in a roundabout and tight turn. The analyses demonstrate that the proposed measures substantially improve the detection of sideswipe collisions while maintaining a comparable level of performance to existing measures in detecting rear-end collisions. Across 30 simulated scenarios, they correctly identify 14 of 15 sideswipe collisions, compared with 7 of 15 identified by the existing formulation. Moreover, the mean prediction error for sideswipe collisions is reduced by approximately 20% compared to the existing formulation.