In-plane thermoelastic behaviour and buckling of pin-ended and fixed circular arches

This paper presents a systematic treatment of the in-plane thermoelastic analysis of pin-ended and fixed circular arches that are subjected to a uniform temperature field. A virtual work method is used to develop the differential equations of equilibrium. It is found that the membrane stresses and strains in arches that are subjected to a uniform temperature field form a special state for which compressive stresses are associated with tensile strains. It is also found that the thermal effects of the uniform temperature field on shallow arches are significant. The strains and stresses produced by the uniform temperature field in shallow arches are much higher that those in deep arches. Under a uniform temperature field, the central radial deflection of shallow arches may exceed the deflection limit for serviceability and the stresses in shallow arches may reach the yield stress of the material. The in-plane thermoelastic bifurcation buckling of arches under a uniform temperature field is also investigated using classical buckling theory. It is found that, in practice, thermoelastic bifurcation buckling is possible only for very shallow arches. For most arches, the critical temperature for in-plane thermoelastic bifurcation buckling is quite high, so the central radial deflection of the arches may exceed the deflection limit for serviceability and the stresses in the arches may reach the yield stress of the material before the critical temperature for the thermoelastic buckling is reached.