What is the moment-free theory? What are the limitations of its applicability?

Thread Content

Theory can prove that within a thin shell, the ratio of bending stress to tensile (compressive) stress is on the order of δ/R. Therefore, the effect of bending stress is minimal; even if it is ignored, the engineering requirements can still be met. The stress analysis method that ignores the effect of bending moments and considers only tensile (compressive) stresses is commonly referred to as the moment-free theory of thin shells or the membrane theory; the stresses obtained in this way are known as membrane stresses. Conversely, the method of performing stress analysis on thin shells without ignoring the effect of bending moments is called the moment theory. Thin-shell theory applies to rotating thin shells, and its use requires that the following conditions be met simultaneously: ① The shell’s surface must be continuous, with no sudden changes in curvature or thickness; ② External loads must also be continuous, with no external torques or concentrated loads; ③ The shell’s boundaries must be free, with no supports or constraints. If even one of the above conditions is not met, the internal torque in the corresponding part of the shell will have a significant effect and cannot be ignored; in such cases, stress analysis should be carried out using the torque theory.