Thermo‐Elastic Formulae for the Analysis of Beams: Stress Distributions within a Structure due to Temperature Gradients and their Influence on Strength and Stiffness

THE kinetic heating associated with supersonic flight produces temperature gradients within the aircraft structure. These in their turn are responsible for so‐called ‘thermal stresses’ in the components. The calculation of these effects falls into two stages. The first stage consists in the application of the theory of heat transfer to obtain the history of the temperature distribution in the structure. The second stage uses this data to obtain distributions of stress within the structure, resulting from these imposed temperature gradients and proceeds to assess their influence on strength and stiffness. The present paper is concerned entirely with this second stage of the problem and derives basic formulae for the analysis of beam‐like structures and components. The results can be applied to wings, fuselages, etc., on the one hand, and to linear reinforcing members like stringers and longerons on the other, in the same way as the usual theories of bending and torsion are applied in the isothermal case.