Reinforced concrete slab bridges are assessed for a combination of loads that include self-weight, superimposed loads, and distributed and concentrated live loads. The shear capacity of reinforced concrete slabs subjected to a combination of loads is thus an important topic for the assessment of existing bridges. Currently, a plastic model exists for the assessment of reinforced concrete solid slabs subjected to a concentrated load: The Extended Strip Model, based on the Strip Model for concentric punching shear. To apply this model to slabs subjected to a combination of loads, the model needs to be adapted based on theoretical principles. The results are then compared with the results from experiments on half-scale slab bridges subjected to a combination of a concentrated load close to the support and a line load. The result of this comparison is that the proposed method is suitable to find a safe estimate of the maximum concentrated load on the slab. The implication of this development is that an improved tool is available to estimate the maximum load of a truck that can be placed on a reinforced concrete bridge, thus improving the current assessment.