A reinforced concrete (RC) half-joint bridge consists of a suspended span with a reduced-depth section, i.e. dapped-end beams. An adequate amount and proper arrangement of steel reinforcement must be provided to avoid failure in a brittle manner at the dapped ends. However, this undesirable failure mode might occur in existing structures having insufficient or improper arrangement of reinforcement. Strength assessment methods such as strut-tie models persist as a challenge hindering the accurate evaluation of bearing capacity. This study provides a mechanical model for analysis to ascertain the ultimate strength of the dapped-end beams. Strength derivation is treated as an optimization problem under rigorous formulation of equilibrium equations, which represents a lower-bound solution. The analytically obtained strengths demonstrate excellent agreement with the experimentally obtained results obtained from eight dapped-end beams. Results show that the predictive accuracy is better than that obtained from strut-and-tie idealization. Furthermore, the developed analysis supports quantitative evaluation of the contribution of internal force components to the ultimate strength.