Metallic Expansion Joints - Thorburn Flex Inc

THORBURN
FLEXIBLE PIPING SPECIALIST
HOW TO INTERPRET THORBURN'S
BELLOWS DESIGN ANALYSIS DOCUMENTATION
All custom bellows designs should be documented to prove that the design has been analyzed to the proper code, the design
is safe and mechanically stable, the cycle life is in accordance with the specification requirements and the important stress
values have been satisfied. Thorburn bellows design analysis shows all the critical information in a summary format. This
paper is offered to help a customer interpret the information that is shown on Thorburn's bellows design analysis so the
information is more meaningful.
THORBURN REF: ABI-001-06/19/95 ITEM: 01 THORBURN EQUIPMENT INC.
CUSTOMER REF: LTD-401
SHEET __/__ OF __/__
JUNE 19, 1995 REV 08-06-92
PREPARED BY: LUCIAN BODOCAN
APPROVED BY:KEN McCORMICK
The bellows' effective area is the area of the
bellows that creates pressure thrust when
acted upon by the operating pressure. The
system anchors and/or the hardware on the
expansion joint must be designed to
withstand pressure thrust at the operating
and test conditions.
Torsional spring rate is offered for those pipe
stress analysts who are inputting bellows
characteristics into a pipe stress program.
Bellows are not generally designed for
torsional movements. But, the torsional
stiffness value can affect the output of a pipe
stress analysis that includes a Thorburn
expansion joint.
THORBURN SINGLE BELLOWS DESIGN ANALYSIS
THIS EXPANSION JOINT DESIGN ANALYSIS WAS CALCULATED WITH THE DESIGN
EQUATIONS STATED IN THE STANDARDS OF THE EXPANSION JOINT MANUFACTURER'S
ASSOCIATION INC., SIXTH EDITION.
CODE REQUIREMENT: ANSI B31.3
DESIGN PRESSURE:
256 PSI
DESIGN TEMPERATURE:
266 DEG. F
BELLOWS MATERIAL:
A240-T304
ALLOWABLE STRESS:
17,000 PSI
MODULUS OF ELASTICITY:
27,304,000 PSI
WELD JOINT EFFICIENCY 0.85
DESIGN MOVEMENT CONDITIONS
COND AXIAL LATERAL ANGULAR S5 S6 CYCLES TYP
A. 0.25 0.13 0.10 0.20 1.00 2.00 2515 179315 4780
INSIDE DIAMETER:
OUTSIDE DIAMETER:
NUMBER OF CONVOLUTIONS:
MATERIAL THICKNESS:
NUMBER OF PLIES:
FREE LENGTH OVER CONVOLUTIONS:
7.250 IN
8.500 IN
14 CONS
0.024 IN
2 PLIES
8.75 IN
S2 (CIRCONFERENTIAL MEMBRANE STRESS DUE TO PRESSURE): 9,206 PSI
S3 (MERIDIONAL MEMBRANE STRESS DUE TO PRESSURE): 1,598 PSI
S4 (MERIDIONAL BENDING STRESS DUE TO PRESSURE): 25,051 PSI
S5 (MERIDIONAL MEMBRANE STRESS DUE TO DEFLECTION): SEE TABLE ABOVE
S6 (MERIDIONAL BENDING STRESS DUE TO DEFLECTION): SEE TABLE ABOVE
S t (STRESS RANGE FOR PRIMARY DESIGN CONDITION): 200,485 PSI
DESIGN CYCLE LIFE FOR PRIMARY DESIGN CONDITIONS: 3,000 CYCLES
RATED CYCLE LIFE FOR PRIMARY DESIGN CONDITION:
4,780 CYCLES
MAXIMUM DESIGN PRESSURE BASED ON SQUIRM:
AXIAL SPRING RATE:
LATERAL SPRING RATE:
ANGULAR SPRING RATE:
TORSIONAL SPRING RATE:
BELLOWS EFFECTIVE AREA:
361 PSI
1,220 LBS/IN
1,500 LBS/IN
167 IN LBS/DEG
74,457 IN LBS/DEG
49.30 SQ/IN
The proposed design has this calculated cycle
life at the specified conditions.
There are two types of squirm or instability
that can occur for internally pressurized
bellows. One is called column squirm (similar
to buckling of a column) and the other is called
in-plane squirm (localized plastic deformation).
Thorburn calculated the maximum
design pressures based on the most
conservative of the two methods. The value
stated on the design analysis is the predicted
squirm pressure with a safety factor of 2.25.
Thorburn's spring rate calculations are based
on the elastic spring rate criteria from EJMA.
This is the actual temperature that was used for the
bellows design. For certain special applications such as
refractory lined expansion joints, the bellows is designed
for a lower temperature than the media.
This is the allowable stress for the bellows material at
the bellows design temperature.
This is the modulus of elasticity of the bellows material at
the design temperature which is used to calculate spring
rate and column squirm pressure. The room temperature
modulus of elasticity is used to calculate the deflection
stresses (S5 & S6).
The weld joint efficiency is 1.0 if the bellows' longitudinal
weld is 100% radiographically examined in accordance
with the specified code.
The design movements create the deflection stresses that
determine cycle life. One complete cycle is based upon
moving the bellows from the neutral length to position 1,
back through the neutral length to position 2 and then
back to the neutral length.
Material thickness is generally stated as the standard
sheet gauge thickness.
S2 (hoop stress) is an important membrane stress that
runs circumferentially around the bellows. The value must
be lower than the allowable stress for the bellows' material
multiplied by the bellows' longitudinal weld joint efficiency.
S4 (pressure bending) is an important bending stress
that is located in the side wall of the convolution running
in the longitudinal direction. It is the stress that makes a
"U" shaped convolution balloon out into an omega shape.
The value of (S3 + S4) must be lower than the allowable
stress of the bellows’ material multiplied by material
strength factor which is equal to 3.0 for bellows in the as
formed condition (with cold work) and 1.5 bellows in the
annealed condition (without cold work).
S6 (deflection bending) is the primary bending stress
influencing fatigue life. This stress runs in the longitudinal
direction and is most severe in the side wall of the
convolution near the crest of root. There is no upper limit
on this stress. It is calculated based on elastic theory,
and the value of S6 is generally far in excess of the yield
strength of the bellows material. That means that a typical
expansion joint bellows undergoes plastic strain during
each stroke.
This is the specified cycle life expectancy value as per
EJMA, ANSI B31.3 Appendix X, ASME Section VIII or
ASME Section III Equations.
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