I have a long, slender vessel that is internally pressurized.

Question

I have a long, slender vessel that is internally pressurized. Two sides of the
vessel acts a beams uniformly loaded along their length. From calculation, I
know that the beam beading stress and deflection at mid-length is very high
therefore requiring an attached "fixing rib" or "stay" to limit the stress and
deflection. How can I determine what the vertical load would be at the midpoint
(or several points along the beam length) to size the cross-sectional area of
the rib or stay according?

StructuralEng · Accepted Answer

StructuralEng : Hi
StructuralEng : Im driving right now.
StructuralEng : Can I get back to you shortly? Say 30 minutes to 60 minutes?
Customer:

Sure; how about after 1:00 cst?

StructuralEng : I'm back now
Customer:

Me too.

StructuralEng : Are you an engineer?
Customer:

Yes.

StructuralEng : It sounds like you have a te hnical understanding above a
layperson.
StructuralEng : Ok
Customer:

I'm actually a control valve engineer but work on many projects.

StructuralEng : So the "beams" are being loaded laterally by the internal
pressure.
StructuralEng : what exactly do you need to figure out?
Customer:

The vessel is rectangular and the sides (beams) are also rectangular in
cross-section. It is loaded at 9000 psig and needs reinforcing ribs attached at
one or more intervals to prevent excessive deflection (and stress). I'm trying
to figure out how to calculate that vertical (perpendicular) load on the beam at
the various locations along it's length to determine the rib cross-sectional
area.

Customer:

The ribs would be attached to each side beam spanning through the center of the
vessel.

StructuralEng : Vertical ribs to shorten the span of the sides or horizontal
ribs to act as strong backs for the sides?
Customer:

Vertical ribs that effectively reduce the beam length. The beam is quite thick
and well fixed (wall thickness-wise) at the ends. I ran the calc's for no ribs
initially and actually have a little test data. I don't want to make the
reinforcing rib(s) along the beam length any wide than necessary as it affects
that usefullness of the vessel...it has a viewing slot to see the fluid inside
and wide ribs obstruct the viewing. This is a chamber for a gage glass.

StructuralEng : So these ribs would span from top to bottom of the vessel with
the side "beam" running perpendicular?
Customer:

Yes. The ribs anchor the two side beams together to limit the outward
deflections when pressurized. I could assume various, series of shorter beams
and calculate it backwards but there are many size and length combinations. Is
there some way to relate the calculated deflection at any given point along the
beam to a point load perpendicular to the beam?

StructuralEng : This is a little more complex than a typical question, so would
you mind attachin a sketch for me just to be 100% certain we're on the same
page?
Customer:

Sure; how do I send it to you?

Customer:

Hello? Where do I sent a drawing to?

Customer:

Attachment: 2013-01-18_193450_20130118133215.pdf
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Customer:

In the case of the drawing I just sent, I would want to calculate the
perpendicular "point" load on the beam at the rib centerline (right where
section x-x is shown) to determine the appropriate rib cross-sectional area.

StructuralEng : Sorry. Let me check it out
StructuralEng : It looks like the rob does not attach to the top and bottom of
the vessel. I don't think you can count on it as a beam that way
Customer:

The rib attaches to each side beam...in the center in this case. I goes through
the center of the vessel from inner beam wal-to-inner beam wall and restrains
outward bowing of the part when under internal pressure.

Customer:

So, you know of no calculation that relates deflection to load at the point of
highest deflection for the section under consideration?

StructuralEng : What is to keep the inner and outer wall from bowing out
together?
StructuralEng : it looks like it only attaches to one of the outer walls.
Customer:

The rib that spans between them (the side beams)...it is attached to the inner
wall surface of each side beam. The two "missing" beams (call them top and
bottom) are separate pieces bolted the each side the the chamber. Imagine having
a rectangular piece of barstock and milling a slot down the center. The section
that is not milled away forms the "rib" and holds the two side "beams" together.

Customer:

Attachment: 2013-01-18_195812_20130118135715.pdf
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StructuralEng : Then I would treat the sides as beams with reduced spans. The
reactions from those beams will be the load for ribs.
StructuralEng : the ribs appear to only be loaded axially, not in bending
StructuralEng : Can I ask why you have me a negative rating?
Customer:

Because you have yet to explain how to relate the end (edge) beam reaction
(whether calculated as a moment (in-lbs) or a stress (lbs/sq.in.) to a tensile
load (lbs.) at the center of the rib.

StructuralEng : I'm not sure what you mean with that statement.
StructuralEng : The reaction of the side beam at the rib is what it is. It's
simpe statics.
StructuralEng : Tensile stress in the rib or tensile stress in the side beam?
Customer:

Tensile stress (tensile pull) at the rib center.

StructuralEng : The moment in the side beam has no impact on that.
StructuralEng : the only thing that affects the tension in the rib is the
horizontal reaction of the side beam.
StructuralEng : As I said, look at the side beams two span continuous instead of
a simple beam.
StructuralEng : thesimple the reaction at the center support (rib) is the
tensile force that needs to be resisted by the rib.
StructuralEng : If you could rate my answer, I would appreciate it. I'll be
happy to answer additional questions on the topic.
Customer:

The calculated "reaction" force is measured in what units? I don't see
(understand) how to get to a tensile load in lbs. from the calc.

StructuralEng : It's in pounds.
StructuralEng : If you know how to get the bending stresses, but not the
reaction?
StructuralEng : 0.625*length of side beam *pressure*height
StructuralEng : thst is the reaction (in pounds), which is the tensile force
Customer:

where is the .625 coming from? Referring to the drawing...if the side beam (1
slot length) = 3.45", the height = 1.228 and the pressure is 9000psig, then...?

StructuralEng : 0.625 is the factor for the interior reaction of a two span beam
with equal spans
StructuralEng : 24,000 pounds
StructuralEng : thatspound stats a tiny vessel. 3" and 1.5".
StructuralEng : Thats a tiny vessel
Customer:

from what source can I document that "factor" from? So your saying (referring to
the drawing)...

Customer:

opps...still typing

Customer:

.625*3.45*1.228*9000=23,831 pounds? That is the tensile load on the center rib
in the drawing? Seems like that only "solves" for 1/2 the load.

StructuralEng : The 0.625 factor is in any structural analysis text, mechanics
text, AISC steel manual. It's all over.
StructuralEng : Use the length of the vessel with the o.625
StructuralEng : It looks like it's 8.5" long. I was using your numbers
Customer:

0.625*3.45*1.228*9000=23,831 lbs. Are you saying that that is the tensile load
on the rib? Seems like that considers only 1/2 the applied load.

StructuralEng : goingnumbers going back to the sketch, I get 142,000 pounds
StructuralEng : Using the numbers on the sketch, I get 142,000 pounds
StructuralEng : I was using your numbers without looking back at the sketch
Customer:

No way...The maximum applied pressure load across the entire beam area (7.66"
long X 1.228" wide) at 9000psig is only 84,658 lbs.

StructuralEng : The sketch shows 8.4" long and 3.0" tall
StructuralEng : 8.5*3*9000*0.635=141,750
StructuralEng : 0.625, not 0.635
Customer:

Trust me, the pressure boundry/beam size is 7.66 lg. X 1.228 wide...X 9000 X
.625 = 52,911 lbs. You're saying that that is the tensile pull on the center
rib???

StructuralEng : Correct.
StructuralEng : With the approximate methods we're using. Only a finite element
analysis will give you exact loads
Customer:

I understand...wish I had that available. So, your saying use the .625 factor
for a design such as in the drawing that I sent....what is the factor for 3 and
4 equal lengths...do you have that readily available? That would solve probably
all of the cases I'm looking at.

StructuralEng : The more spans you have the closer it gets to 0.5, but I
typically use 0.635 to be a little conservative
StructuralEng : 0.625
StructuralEng : If you could rate my answer I would appreciate ot
Customer:

So you're saying that this "factor" never falls below .5? even if I had 20 equal
sections?

StructuralEng : Correct
StructuralEng : well, let me clarify
StructuralEng : that factor is multiplied by the two adjacent spans. It just so
happens that this case (a two span condition) has the two adjacent spans as the
entire length
Customer:

For these vessels, the number of spans, whether 2, 3, 4, or 99 would always be
the same lengths with equally spaced and sized ribs.

Customer:

This is some real "seat of the pants" engineering...I expected a more direct
solution...than what amounts to trial and error.

StructuralEng : It's not trial and error.
Customer:

Okay...spent nearly 3-1/2 hours on this.

StructuralEng : its pretty straightforward.

I have a long, slender vessel that is internally pressurized.

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