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+ Pressure Vessel Design Calculations and Safety · Mechanical Engineering Made Simple

• 0:00
  Welcome back design junkies to mechanical Engineering made
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  Simle. Today we are undertaking a deep
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  dive into, well, the retty, dense world of pressure vessel
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  design. We're going to try and
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  synthesize these complex standards, the geometry, the
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  loading procedure. It's a heavy lift for sure.
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  Our mission today is to really get past the textbook stuff.
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  We're unpacking the critical calculations, you know, the ones
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  that govern how these massive containers are actually
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  engineered for safety. And for compliance, we're
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  talking standards like ASME. Exactly from shell thickness
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  right down to how you bolt them to the ground.
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  OK, let's unpack it. Let's start with the absolute
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  fundamentals, the structure itself.
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  When you picture pressure vessel, you're usually thinking
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  of a thin walled cylinder with end closures.
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  We call those heads. And those heads can be different
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  shapes, right? Ellipsoidal.
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  Spherical. Precisely ellipsoidal, spherical
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  or tors spherical. But the physics it all comes
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  back to thin walled cylinder theory, and that immediately
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  introduces the two main stresses you have to deal with.
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  Right circumferential, which is also called hoop stress and then
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  the longitudinal stress running the length of.
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  It, and this is foundational. When you run the numbers PD over
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  2, T for hoop and PD over 4T for longitudinal, you see it
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  immediately. That classic 2 to one ratio.
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  That ratio is everything. The circumferential stress is
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  literally double the longitudinal stress, which means
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  the vessel is fundamentally weaker around its girth.
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  So that hoop strength is almost always what drives your design.
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  It's the controlling parameter. Almost always it has huge
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  implications for how you build it, especially the welds.
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  The quality of that long longitudinal Weld is absolutely
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  critical because it's holding back twice the force.
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  OK, that makes sense. The weakest link.
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  Let's stick with geometry for a second though.
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  Those 2.1 ellipsoidal heads are super common, but they're not
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  simple, are they? Not at all.
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  This is where simple formulas meet a real world complexity.
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  Under pressure, the cylinder part wants to expand outwards,
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  but the ellipsoidal head actually tries to contract,
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  especially right near that junction where it meets the
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  shell. So you have two parts literally
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  fighting each other at the Weld seam.
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  Essentially, yes. And that creates these very high
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  localized bending stresses. If you actually map the hoop
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  stress in the head, you see it flip from tensile pulling out to
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  compressive pushing in, right? And that compressive stress
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  introduces a really nasty failure mode, local buckling.
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  And that's why just knowing PD over 2T is not the end of the
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  story. Not even close.
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  OK, let's move from the shape to the numbers that get stamped on
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  the nameplate. We hear MAWPMAP design pressure.
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  They sound similar. What's the functional
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  difference? The one you really need to
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  remember is MAWP Maximum Allowable Working Pressure.
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  And that's the limit for the vessel when it's.
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  What when it's in it's hot and corroded condition?
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  It's the safety limit that's calculated after you've already
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  subtracted the corrosion allowance from the thickness.
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  It's the true operating ceiling. Got it.
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  So it already factors in future damage.
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  Exactly. The relief valves have to be set
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  to that number now. MAP or maximum allowable press
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  pressure is a bit different. That's the limit for the vessel
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  when it's new and cold uncorroded.
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  So why do we even need that one? Isn't MAWP the only one that
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  matters for safety? You need MAP mostly for testing.
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  The hydrostatic test pressure when the vessel is first built
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  is based on MAP. You test it at a higher pressure
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  to prove its initial strength. And design pressure.
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  That's just the number you use for your calculations.
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  It's the worst case combo of pressure and temperature you
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  expect in normal operation. It's what drives drives the
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  initial math. Okay, you mentioned temperature,
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  that brings out the MDMT, the minimum design metal
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  temperature. MDMT is crucial.
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  A lot of steels get brittle at low temperatures.
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  If your vessel is going to operate in a cold climate or
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  with a process that gets cold, you have to make sure the
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  material doesn't just shatter on impact.
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  So what's the fix? A different material.
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  That's one option, but it creates this iterative decision
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  tree for the designer. You can use a more expensive
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  tougher alloy, or you could just make the shell thicker.
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  Or you can just decide to do expensive impact testing to
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  prove the cheaper material works.
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  It's an economic trade off. It's almost always an economic
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  trade off. Which leads us perfectly into
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  optimizing the whole vessel, the link to diameter ratio, the LD.
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  How do you find the cheapest shape for a given volume?
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  Well, theoretically the most efficient shape is a sphere.
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  Maximum volume, minimum surface area.
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  But you almost never see giant spherical process vessels.
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  Why not? They're a nightmare to build,
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  forming thick plates into perfect spheres, welding them.
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  It's just incredibly expensive. Cylinders are much, much easier
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  to roll and fabricate. So for a cylinder, what's the
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  sweet spot? The most economical LD.
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  It's generally somewhere between 1:00 and 10:00.
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  For a simple atmospheric tank. It's actually one, but for your
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  average pressure vessel, you're usually looking at a ratio
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  between 3:00 and 5:00. And what pushes you toward 5
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  instead of 3? Things like higher pressure or a
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  larger corrosion allowance, but practically a vessel in that 3
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  to 5 range is also easier to transport and support against
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  things like wind, which is a whole other problem Let's.
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  Get into that external forces first.
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  Let's clarify 2 failure modes, buckling versus collapse.
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  They sound similar. They're very different.
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  Buckling is a local instability. Think of squeezing an aluminum
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  can until one spot suddenly wrinkles or dimples.
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  That's buckling. The force that causes it is
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  always less than the materials actual compressive strength.
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  It's a failure of geometry, not just material.
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  Perfectly put. Collapse, on the other hand, is
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  a general failure of the entire cross section.
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  The whole thing just flattens, usually due to external pressure
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  or a vacuum. And to prevent that, we see
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  stiffening rings on the outside of some vessels.
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  Right. Those rings are another economic
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  choice. You could just make the shell
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  super thick to resist buckling, but that's a lot of steel.
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  Or you could use a very thin shell with tons of rings, but
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  that's a lot of welding labor. So you find a balance you.
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  Find a balance. For vessels up to about 8 feet
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  in diameter, you'll often see rings spaced at about two times
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  the diameter. For bigger ones, it's closer to
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  1 diameter. OK.
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  Now for the really big external forces, wind and earthquakes.
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  These are lateral forces basically trying to tip the
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  vessel over, and the codes for calculating them are incredibly
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  specific. For winds, you have to start by
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  classifying the structure. Is it category I like a barn
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  with a low hazard to human life? Or is it category 5, an
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  essential facility like a hospital?
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  And a hospital would need a much higher safety factor.
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  A much higher factor then you look at the exposure category,
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  is it in open terrain or right on the coast where winds are
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  stronger? All these coefficients feed into
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  the final design, wind pressure. It's.
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  Very site specific and for seismic.
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  For seismic, the key calculation is the base shear V.
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  It's a function of the vessel's operating weight and a seismic
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  factor for that specific geographic zone.
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  And there's a little gift from the ASME code here, isn't there
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  for these kinds of loads? There is the code allows a 1/3
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  increase in the materials allowable stress for wind or
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  seismic loads. Why is that?
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  Because they're short duration transient loads, the material
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  can handle a brief spike in stress without permanent damage,
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  so the code lets you take it advantage of that.
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  It saves a lot of material and cost.
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  A great example of balancing safety and economics.
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  OK, let's talk about how these things actually meet the ground
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  supports. You've got a few main types.
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  Skirts, legs, saddles for horizontal vessels, lugs.
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  For a tall vertical vessel, the skirt is pretty standard.
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  What determines how thick that skirt needs to be?
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  It's a combination of things. The load during erection is a
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  big one, also the anchor chair design, any openings you have to
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  cut in the skirt and of course the total weight plus the
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  overturning moment from wind or seismic.
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  And for horizontal vessels on saddles, the design method is
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  old. It is.
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  Zic's analysis from 1951 is still the cornerstone.
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  It's based on the assumption that the saddles are rigid,
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  which isn't perfectly true, but the model has proven to be
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  incredibly reliable for decades. And the rule of thumb for
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  placing them. You generally locate them near
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  the heads within about 1/4 of the vessels diameter from the
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  end. You're taking advantage of the
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  stiffening effect from the curved head.
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  OK, what about transportations? This is where things can go
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  really wrong. Absolutely.
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  If a vessel is over 50,000 lbs or has an LD ratio over 5, you
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  need specialized lifting analysis.
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  You have to analyze 2 completely different load cases just for
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  tilting it upright. What are those?
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  When it's horizontal on the ground, the load is shared
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  between the top lifting lugs and a tailing lug at the base.
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  But as you lift, you pass a point where the entire crushing
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  weight of the vessel is hanging only from those top lugs.
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  They better be designed for that.
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  If they're not, the lift ends very badly.
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  And for shipping it on a truck, I've heard there are strict
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  rules about the number of supports.
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  Yes, you use only two shipping saddles, period.
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  Why only two? Wouldn't 3 be more stable?
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  You'd think so, but it actually creates what we call a
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  statically indeterminate structure.
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  You have no idea how the load is being shared between the three
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  points. A small bump in the road could
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  put the entire weight on the middle saddle and buckle the
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  shell. So 2 points keeps it simple and
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  predictable. Exactly, and you only lash it
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  down over the saddles, never on the shell itself.
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  OK, finally, let's touch on the regulatory world that enforces
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  all of this. In the US, it's all about ASME
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  certification. The ASME stamp is the proof of
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  compliance. The manufacturer issues a data
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  report and the vessel gets a physical stamp, S for a power
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  boiler key, P for a pressure piping, and so on.
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  And in Europe, there's the PED, the Pressure Equipment
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  Directive. How does that work?
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  The. PED classifieds equipment based
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  on risk. It looks at the product of the
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  maximum pressure PS and the volume V.
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  The higher that PS times V number, the higher the risk.
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  And risk also depends on what's inside it, right?
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  Group 1 fluids are the dangerous ones, flammable, explosive,
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  toxic. Group 2 is everything else, like
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  steam or air. Those two factors, the PS times
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  V and the fluid group, put the vessel into a category from I to
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  IV, which determines how much inspection and quality control
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  is required. This has been wow.
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  It's clear that designing one of these is a massive effort.
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  So many iterative calculations and rigid codes.
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  What's really fascinating to me is a tension you see now between
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  the old school and new school methods designed by formula or
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  DBF using those classic equations we talked about.
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  And designed by analysis or DBA. Exactly.
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  DBA uses finite element analysis and powerful software.
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  It's essential for unusual shapes or when you have to
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  combine complex loads like wind and seismic in a way the old
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  formulas just can't handle. It lets you push the boundaries
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  while still proving safety. So what does this all mean for
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  you, the learner? It means every high pressure
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  cylinder, every head, every single Weld you see out there Is
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  the result of this intense, calculated, regulated balance.
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  It's an engineer walking a tightrope between absolute
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  regulatory compliance on one side and the constant economic
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  pressure to use less material on the other.
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  That safety margin you rely on is the direct result of hundreds
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  of these small decisions, all aimed at predicting and
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  preventing failure before it can ever happen.
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  That's it for today. Design junkies.
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• 11:23
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