[PSUBS-MAILIST] head strength

[Sean T. Stevenson via Personal_Submersibles]

It's not quite that simple. When you have a wall thickness which is quite thin with respect to the mean diameter of the shell (small t/D ratio), we can analyze it using a "thin wall assumption".  What this means is that you have the hoop stress and axial stress in the case of a cylinder, or biaxial hoop stress in the case of a sphere, but may safely ignore the radial stress and assume that the hoop stresses are uniformly distributed throughout the cross-sectional area of the shell. As the t/D ratio becomes larger, this is no longer a valid assumption, and you have to account for the shear stress in the radial direction through the wall, owing to the difference in applied stress on the outside versus the inside, which is not a linear distribution.  This will change the magnitude and direction of the greatest principal stress. Additionally, the t/D ratio, in conjunction with the material properties, will determine whether the shell will fail first by buckling or by yield.  The
critical pressure calculation is different for each, so working depth is not a continuous function of shell thickness, but rather has a step change where this transition occurs.

If you refer to the 2016 ABS Rules, have a look at Section 6/23.11. Here, shape limits are given for hemispherical heads which place the outer bounds on acceptable t/D ratios. Within that window, the equations shown in 6/23.3 determine the critical yield pressure (P_ys) and the critical buckling pressure (P_es). Depending on the ratio between the two (indicating which failure mode is dominant), there are two different equations for the sphere limit pressure, and then that value multiplied by the usage factor gives you the maximum allowable working pressure.

Once you're into the region where strength failures and not buckling dominate, then the upper "limit" would be where t = 0.16 D, where t is shell thickness and D is the mean diameter of the shell.  The other limitation is of course the strength of your selected material.

The software I wrote that is on the PSubs site handles all of this automatically for spherical shells (and will soon for cylindrical shells as well).

Sean



On April 22, 2016 11:38:28 AM MDT, hank pronk via Personal_Submersibles <personal_submersibles at psubs.org> wrote:
>Hi Sean,I have been studying the head maximum pressure chart on Psubs
>and found that the pressure rating increases the same amount
>proportionately with thickness.Is there a limit to this?  Thank youHank
>
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