Title: Membrane Analysis
Author(s): A;lex C. Scordelis
Publication: Symposium Paper
Appears on pages(s): 17-40
Keywords: hyperbolic parabolic shells; membrane theory (shells); roofs; reinforced concrete; shells (structural forms); structural analysis; Structural Research
A review of the state of the art for the membrane analysis of hyperbolic parabolic (HP) shells is presented. Membrane solutions using simple statics are given for HP shells having square, rectangular, or parallelogram shapes in plan and subjected only to uniform vertical loading over the horizontal projection of the shell. Statics of shell-edge beam systems are discussed for saddle shells, inverted umbrellas, gable shells, and shells on two supports. Membrane stresses for general loadings on parallelogram-shaped HP shells obtained using a differential equation approach are described. Stress transformation formulas are given that can be used to find principal membrane stresses in the shell and boundary stresses to be transmitted to the edge members. Membrane stresses in HP shells having an arbitrary quadrilateral shape are discussed and procedures for determining them are discussed.