A fire-exposed closed-cell reinforced-concrete frame consisting of slabs, walls, and columns is analyzed based on (i) Fourier series-based solutions for the heat conduction problem, and (ii) thermo-elastic Timoshenko beam theory [1]. The ingress of heat into the structural elements is quantified from known surface temperature histories. Resulting temperature profiles are converted into thermal eigenstrains. They are subdivided into: their stiffness-weighted cross-sectional averages (= eigenstretches), their stiffness-weighted cross-sectional moments (= eigencurvatures), and the remaining spatially nonlinear eigenstrain distributions (= eigenwarping). Eigenwarping strains are prevented at the cross-sectional scale. This activates self-equilibrated thermal stresses. The eigenstretches and eigencurvatures are constrained at the frame-structural scale. Together with external mechanical loads, they are analyzed using beam theory. The axial normal stresses, quantified from normal forces and bending moments, are superimposed with the self-equilibrated thermal stresses. Total stresses agree well with results obtained by means of the nonlinear FEM [1,2]. Heating of the lateral surfaces of the columns activates tensile stresses in their core regions, which reach the tensile strength of concrete. Significant tensile core cracking starts some 11 minutes after the start of the fire, when the surface temperature of the columns amounts to some 170℃. Thus, tensile cracking is the key material non-linearity of concrete, at least during the first 15 minutes of the fire.