Membrane Solution of Domical Surfaces

As the solution of a 3D elasticity problem is tough, shell theory may be viewed as a 3D subset of elasticity valid for certain classes of structures. For this subset we shall develop appropriate kinematics, constitutive and equilibrium relations. 

Now consider an element at the dome in the middle surface of the shell of revolution as shown in Fig. 4.11 where R is the radius of curvature of the parallel circle and a is the radius of curvature of the meridian. 

The membrane stress, stress resultants and the load components can be designed as Px, Py, Pz The coordinate axes, as in Section 4.2.2, are 

X = along tangent to parallel circle y = along tangent to meridian z = normal to the shell surface 

Equations of equilibrium of the element of a shell of revolution. As shown in Figs. 4.11, 4.12 and 4.13, the equations are given below. Equations of forces in the X direction. 

---

Membrane Solution of Domical Surfaces To find the meridional thrust... 

---