Engineering guide
The EJMA module designs metal bellows of expansion joints to the EJMA Standards (10th Edition, 2015/2016) — the internationally governing code of the Expansion Joint Manufacturers Association for bellows expansion joints. Single-bellows and universal expansion joints with unreinforced, reinforced and toroidal bellows are covered; the user specifies the design pressure and temperature, the bellows geometry with convolution shape and ply build-up, the material properties and the movements to be absorbed.
The EJMA calculation determines the pressure- and deflection-induced stresses in the bellows convolutions (circumferential and meridional stresses from membrane and bending components), evaluates them against the allowable values based on the proof strengths at room and design temperature, checks stability against column squirm and in-plane squirm, and determines the allowable number of load cycles from the stress range. Torsional moments and the movement components from cold pre-setting of the expansion joint can also be taken into account.
Anyone who has to calculate an expansion joint to EJMA — in piping construction, on heat exchangers or in exhaust systems — thus obtains the complete bellows design including spring rates, fatigue verification and stability limits.
Scope
- Design of bellows
Typical workflow
Define configuration and operating data
First the configuration (single-bellows, universal or toroidal expansion joint) and the mode of operation are selected, and the design pressure, test pressure and design temperature are specified.
Assign material properties
For the bellows material, the modulus of elasticity, Poisson's ratio and the 0.2% and 1% proof strengths at room temperature and at design temperature are entered; for work-hardened bellows, the yield strength in the annealed condition per the inspection certificate can be used. From these, the allowable stresses of the individual verifications follow.
Define bellows geometry and movements
Convolution height, convolution pitch, number of plies and wall thickness per ply, as well as tangent collars and reinforcing rings, describe the bellows. The axial, lateral and angular movements to be absorbed — including cold pre-setting where applicable — are converted into an equivalent axial convolution movement.
Verify pressure stresses and stability
The EJMA equations yield the pressure-induced circumferential and meridional stresses of the bellows, tangent collar and reinforcements; in parallel, the limiting pressures against column instability (column squirm) and convolution instability (in-plane squirm) are checked.
Carry out the fatigue verification
From the deflection-induced meridional stresses, the total stress range is formed and converted via the EJMA fatigue curves into an allowable number of load cycles, which is compared with the required number of cycles.
Output spring rates and reactions
Finally, the axial, lateral and angular spring rates as well as the forces and moments acting on the connections — including any torsional moment — are provided for the piping or equipment analysis.
Frequently asked questions
How do single-bellows and universal expansion joints differ in design?
The single-bellows expansion joint absorbs mainly axial movement and limited angular movement. The universal expansion joint consists of two bellows with an intermediate pipe and can therefore absorb large lateral deflections, because these resolve into opposing angular movements of the two bellows. In the EJMA calculation this shows up in the distribution of the equivalent convolution movement and in the stability length of the intermediate pipe, which can reduce the allowable pressure against column instability.
What is squirm and why is it so critical?
Squirm is the pressure-driven instability of the bellows: in column instability the bellows buckles sideways like a column under compression, in in-plane instability individual convolutions tilt out of their plane. Both failure modes occur suddenly and are promoted by long overall lengths, high pressures and pre-deformations. The EJMA limiting pressures against squirm are therefore hard design limits that cannot be compensated by higher material strength.
Why is the calculation carried out with the 1% and 0.2% proof strengths at two temperatures?
The allowable stresses of the individual EJMA verifications refer partly to the installation or test condition at room temperature and partly to the operating condition at design temperature. For austenitic bellows materials, either the 0.2% or the 1% proof strength is used depending on the verification; for work-hardened, non-annealed bellows, the strength condition per the inspection certificate is additionally relevant. Entering these properties separately ensures that each verification is carried out with the correct limit value.
Are EJMA cycle numbers comparable with those to EN 14917 or ASME?
Only to a limited extent. The fatigue curves of the codes are based on different test populations, safety factors and stress definitions. A value for the allowable number of load cycles determined to EJMA must therefore not be equated directly with an EN or ASME value; the contractually agreed code governs.
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