Meridian shells

Head radiat distance to meridian Shell radius... 

During compression testing of the layered structure, the high tensile stress, which is perpendicular to the direction of loading, leads - as before - to the formation of meridian cracks. According to Fig. 7.22, the shell first deforms around the contact point. Then, a crack (1) is released and reaches the surface that separates the stiff nucleus (2) from the shell (3). The force-displacement curve of Fig. 7.23 shows that, after the formation of a meridian crack in the shell (Point Bi), deformation and then... 

X = along tangent to parallel circle y = along tangent to meridian 2 = normal to the shell surface... 

The differential Eq. (4.8) and the common Eq. (4.6) are sufficient to determine meridian force A <, and the hoop force Ng for an axisymmetrically loaded shell of revolution. 

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. 

When referring to Fig. 6.4a, the middle surface of a shell is taken as a surface of revolution. This is generated by the rotation of a plane curve about an axis in its plane. This generating curve is called a meridian. An arbitrary point on the middle surface of the shell is specified by the particular meridian on which it is found and by giving the value of a second coordinate that varies along the meridian and is constant on a circle around the shell s axis. Because these circles are parallel to one another, tiiey are called die paralled circles. ... 

In a true elliptical head the radii of curvature vary between adjacent points along a meridian. To simplify the calculations and fabrication, the ASME Code established the following various approximations. A 2 1 elliptical head can be assumed to consist of a spherically dished head with a radius of 90% and a knuckle radius of 17% of the shell diameter to which they are attached, as shown in Fig. 9.3. The smallest knuckle radius allowed for a hanged and dished head is 6% of the shell diameter and a spherical radius of 100% of the shell diameter. 

Equation 6.38 is similar to Eq. 5.21 for cylindrical shells except that in Eq. 6.38 the quantity jS is a function of r2 that is variable along the meridian. This requires numerical integration of all moment, force, deflection, and slope expressions at angles less than = 90°. 

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