Structural fire assessment is organized around the heated member, an organization that is exact only for statically determinate elements. This numerical study examines the demand that a localized fire beneath the deck transfers to the unheated parts of a continuous prestressed concrete box-girder bridge of 35 + 50 + 35 m. Two-dimensional heat transfer with temperature-dependent properties is reduced to an equivalent axial thermal strain, a thermal curvature and a degraded flexural stiffness imposed on the girder. The framework is verified against grid and time-step refinement, closed-form solutions and a second, independent implementation; it has not been validated against experiments. For a 20 m hydrocarbon fire at midspan, the hogging moment at the never-heated intermediate support rises by 48.8 % after 240 min, and restrained thermal curvature supplies 75 % or 96 % of that increase, depending on the order in which the two mechanisms are introduced. The support, 7 % more utilized than midspan at ambient temperature, becomes 6.4 times as utilized, and a check confined to the fire-exposed member reports 60 to 67 % of the system demand for the five fire positions compared. The ratio of the two checks factorizes exactly into the relative increase of the support moment, the ambient utilization balance of the competing sections and the resistance retention of the heated one. The first factor is positive in every variant examined; the other two depend on the design, and cracked supports or a draped continuity tendon can bring the ratio to unity or below. Utilization ratios compare an elastic demand with an ultimate resistance and do not predict collapse.