Validity of Yieldline Theory for Polyhedral Shells

The methods of limit analysis have had little application to shell analysis. In attempting to develop Yieldline Theory for shells, the question of the importance of shell deformation must be considered since it complicates the analysis considerably. A sufficient condition for a stationary collapse load factor for shells with membrane forces is derived. A completely regular reinforced concrete shell composed of flat polyhedral faces is analyzed for collapse load. Under uniform external pressure, the simplification of ignoring shell deformation results in an error of up to 15% for a cubical shell, while under uniform internal pressure, the correct collapse load is obtained. Examination of parts of rectilinear shells suggests that for these, the neglect of shell deformation may be justified.