Large-End Cone-to-Cylinder Junction for
$30\degree \lt \alpha \le 60 \degree$
Section VIII, Division 1

Inquiry

Where radiography of a circumferential joint is not required, may a cone without a knuckle at the large end of the cone-to-cylinder junction having a half-apex angle α greater than 30 deg be used in the construction of a vessel complying with the Section VIII, Division 1 rules without the special analysis specified in 1-5(g)?

Reply

It is the opinion of the Committee that when radiography of a circumferential joint is not required, a cone without a knuckle at the large end of a cone-tocylinder junction having a half-apex angle α greater than 30 deg may be used for Section VIII, Division 1 construction without the special analysis specified in 1-5(g), provided:

1. Equations (1) and (2) and Figures 1 and 2 given below shall be used for calculating the localized stress at the discontinuity.
   $$ \sigma _{\theta} = \frac {PR} t \biggl( 1 - Y \sqrt {\frac R t} \biggr) $$

   (1)
   $$\sigma _{x} = \frac {PR} t \biggl( 0.5 + X \sqrt {\frac R t} \biggr) $$

   (2)
   where

   $\sigma _{\theta}$

   =

   membrane hoop stress plus average discontinuity hoop stress, psi

   $\sigma _{x}$

   =

   membrane longitudinal stress plus discontinuity longitudinal stress due to bending, psi

   $P$

   =

   internal pressure, psi

   $R$

   =

   inside radius of the cylinder at large end of cone, in.

   $t$

   =

   cylinder thickness, in.

   $X, Y$

   =

   factors taken from Figure 1 or 2 (or tabular values taken from Table 1 or 2)
   Show solver for eqns 1 and 2

   Solver for Eqns 1 and 2

   Close

   Input

   Example Clear

   Read the values of $X$ and $Y$ from Figure 1, below, for an angle of {{tba.data.i.angle.value}} {{tba.data.i.angle.units}} and an / value of {{tba.data.i.R.value/tba.data.i.t.value}}.

   Results : Warning - the input has changed! Rerun the calculation contain errors or warnings

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   = {{tba.data.o.sigma_theta.units}}

   = {{tba.data.o.sigma_x.units}}
2. The half-apex angle $\alpha$ is not greater than 60 deg.
3. The axial forces come solely from internal pressure acting on the closed ends. When other loads (such as wind loads, dead loads, etc.) are involved, the design shall be in accordance with U-2(g).
4. $\sigma _{\theta}$ shall not be greater than 1.5$S$ and $\sigma _{x}$ shall not be greater than 3$S$ where $S$ is the maximum allowable stress value, in psi, obtained from the applicable table of stress values in Section II, Part D.
5. After the required thickness for the shell has been determined by UG-27(c), and that for the cone by UG-32 (g), the stress limits of (d) above must be checked with eqs. (a)(1) and (a)(2) using the calculated required thicknesses. If the limits of (d) are not met, the shell and cone thicknesses near the junction must be increased so that the limits of (d) are met. When additional thickness is required, the section of increased thickness shall extend a minimum distance from the junction as shown in Figure 3.
6. The angle joint between the cone and cylinder shall be designed equivalent to a double butt-welded joint and there shall be no weak zones around the joint.
7. This Case number shall be shown on the Manufacturer's Data Report.