Machine Nozzle Allowables — API 610, NEMA SM-23, and the Conditional 2× Rule

The situation on site

A 250 °C hot-oil circulation pump, 8″ discharge, 10″ suction. The stress engineer's report is green: every node under the B31.3 allowable, expansion stress 63 % of S_A, sustained 41 % of S_h. The line is signed off, erected, insulated, boxed up.

Four months later the pump is on its third mechanical seal. Vibration is up, the coupling spacer has a hairline crack, and the outboard bearing runs 12 °C hotter than its twin. Nobody has touched the piping since commissioning.

Guess first: the pipe passed its code check by a wide margin. What could the pipe possibly be doing to the pump?

The reveal: at the discharge flange the piping was pulling down with 11.7 kN and twisting it with 7.6 kN·m. For 8″ schedule-40 pipe that is nothing — a few tens of MPa. For the pump it is 2.4 times the API 610 Table 5 vertical allowable of 4.89 kN. The pipe is fine. The pipe was never the thing at risk.

The misconception, stated plainly

"Pipe stress passed, so the pump is fine. Same loads, same steel, same analysis."

Let it stand a moment, because it is reasonable. It is also wrong in the one way that matters: the two checks protect different things from different failures.

The pipe code check asks: will the pipe wall rupture, or crack after N thermal cycles? The limit state is material failure. Allowables are a fraction of yield, and 8″ pipe is a stiff, closed, uniform cylinder — it takes a lot to hurt it.
The machine check asks: will the casing change shape enough to stop the machine working? The limit state is loss of function. A pump casing is a thin, split, machined housing that carries the bearing bores, the seal chamber and the wear rings. Distort it by a few hundredths of a millimetre and the shaft centreline moves, the seal faces go out of square, the wear rings close up and the coupling sees misalignment it was never asked to carry.

Nothing ruptures. The pump simply stops being a pump: seal leak, bearing heat, vibration, rub. That is why machine allowables look absurdly small next to pipe allowables — they are sized to protect a clearance, not a wall thickness.

How small is "absurdly small"?

An 8″ API 610 top nozzle allows F_Y = 4 890 N — about the weight of a 500 kg pallet. The same 8″ sch-40 pipe has a metal area of 5 420 mm², so in pure tension it reaches a 138 MPa B31.3 allowable at roughly 750 kN. The machine allowable is about 0.7 % of the pipe's own capacity — and that comparison flatters the pipe, because bending, not tension, is what the pipe actually shrugs off.

The reason is a stiffness argument, not a strength one. API 610 sets Table 5 so that a pump loaded to the table values suffers a shaft-centreline displacement of no more than about 250 µm (0.010 in) — chosen because that is roughly the point where coupling alignment, seal-face tracking and wear-ring clearance start to be measurably degraded. Every number in the table is reverse-engineered from that single displacement budget, spread across a casing whose stiffness the standard had to assume generically. That is also why the vendor is always allowed to state better numbers for a specific casing: the table is a floor, not a physical law.

API 610 Table 5 — the pump numbers

Table 5 gives, per nozzle size, three allowable forces and three allowable moments in the pump coordinate system (X along the shaft, Y vertical, Z horizontal across the shaft), plus the allowable resultants F_R and M_R. Two features people miss:

The force row is permuted by nozzle orientation. The largest of the three always lines up with the nozzle's own axis: a top nozzle gets the big number on F_Y, a side nozzle on F_Z, an end nozzle on F_X. Moments are not permuted — M_X (about the shaft axis) is always the largest, because that is the direction in which the casing is deepest.
F_R and M_R in the table are the vector resultants of the tabulated components, so you cannot spend your whole force budget on one axis and still claim you are inside F_R.

F_R = √(F_X² + F_Y² + F_Z²)          M_R = √(M_X² + M_Y² + M_Z²)

Representative SI values (8″ nozzle, converted and rounded from the US-customary table):

8" top nozzle:  F_X 3780 N   F_Y 4890 N   F_Z 3110 N   F_R 6920 N
                M_X 3530 N·m M_Y 2580 N·m M_Z 1760 N·m M_R 4710 N·m

Pick your machine, size and orientation and push numbers at it in the nozzle-load checker: ▶ open the interactive: rotating nozzle loads calc — it shows each component against the 1× table, the resultants, and the 2× conditional as a separate gate you have to clear on its own.

The 2× rule — what it actually says

Here is the line that gets quoted in meetings: "API 610 lets you go to twice Table 5."

It does not. API 610 Annex F says a pump may be considered acceptable above Table 5 only if all of the following hold together. Three gates, not one:

GATE 1  every individual component ≤ 2 × its Table 5 value
GATE 2  at EACH nozzle:   (F_RA / 1.5·F_RT) + (M_RA / 1.5·M_RT) ≤ 2      (a LINEAR sum)
GATE 3  suction + discharge loads RESOLVED AT THE CENTRE of the pump, against
        three separate limits — F_RCA ≤ 1.5(F_RST + F_RDT), |M_YCA| ≤ 2.0(M_YST +
        M_YDT), M_RCA ≤ 1.5(M_RST + M_RDT). Those numbers were themselves derived
        from a ~250 µm shaft-centreline displacement budget

Read Gate 1 again: it is a ceiling, not a permission. Doubling is the most the criterion will ever entertain, and only while Gates 2 and 3 also pass. Gate 2 is the one that actually bites — because it is a resultant check on two terms at once: by the time one component reaches the 2× ceiling of Gate 1 the interaction sum is already at ~1.95, so Gates 1 and 2 run out together and any moment growth alongside the force pushes the sum straight past 2.

Gate 3 is the one that gets forgotten entirely. It is not an interaction check and it is not about the nozzle at all: it is three more resultant limits at the pump centre, and it is about whether the whole machine gets pushed off its baseplate line. That is why Annex F also assumes the baseplate is properly grouted, the foundation is rigid, and the pump is centreline-mounted for hot service. Take away the grout and the gate-3 assumption is void — you can pass every number and still have the pump walk.

Why 1.5 inside, and 2 outside?

Gate 2's form is a classic two-term interaction: force and moment eat the same casing-distortion budget, so neither may be judged alone. The 1.5 in the denominators is a relaxation applied to the table resultants; the ≤ 2 on the right is the interaction ceiling. Net effect: a nozzle carrying only force can reach F_RA = 2 × 1.5 · F_RT = 3.0 × F_RT — but only if the moment is zero, which never happens, and Gate 1 still caps every individual component at 2× its own table value. With force and moment equally loaded each term may reach 1, so each resultant is capped at 1.5× its table value. The algebra is doing the same job as engineering judgement: you may exceed on one axis if you are quiet everywhere else.

Turbines and compressors — a different logic entirely

NEMA SM-23 (mechanical-drive steam turbines, and adopted by API 611) does not tabulate six allowables. It uses a combined index, and it applies at two levels:

Rule 1 — at EACH connection:
    3F + M ≤ 500·D_e          [F in lbf, M in ft·lbf, D_e in inches]
    0.914·F + M ≤ 26.7·D_e    [same rule in F: N, M: N·m, D_e: mm]

    D_e = nominal size for connections ≤ 8"
    D_e = (16 + NPS)/3  for connections > 8"

Rule 2 — all connections (inlet + extraction + exhaust) resolved at the
         exhaust centreline:
    2F_c + M_c ≤ 250·D_c      plus individual component caps
    D_c = diameter of a circle equal in area to the SUM of all connection areas
        = (18 + equivalent NPS)/3 where that equivalent exceeds 9"

Two teaching points hide in there.

The formula is deliberately not dimensionally consistent. 3F + M adds pounds to foot-pounds. It is an empirical index, calibrated in one unit system, not a physical equation — which is exactly why you must use the stated units and cannot "convert the 500". (The SI line above is the honest conversion of the same rule; note the coefficient on F is 0.914, not 3.)

Rule 2 is the killer. The D_e cap means a 12″ connection is scored as if it were (16+12)/3 = 9.33″, and D_c is capped the same way — so a big exhaust does not buy you a proportionally big allowable. Turbine exhausts are large, condensing exhausts are huge, and the allowable stops growing while the pipe keeps getting heavier. That is why a condensing turbine's exhaust nearly always needs a dedicated support and expansion joint scheme, and why the exhaust, not the inlet, is the connection that drives the layout.

API 617 (centrifugal compressors) takes the NEMA numbers and multiplies them by 1.85 — the casings are heavier and stiffer, so the standard grants a flat uplift rather than a new table. It is the same index, same units trap, same Rule-2 combination logic.

Worked example — 8″ discharge, does it survive Annex F?

Applied at the discharge nozzle (top-mounted, 8″), hot case:

F_X = 5200 N   F_Y = 6800 N   F_Z = 2900 N
M_X = 4900 N·m M_Y = 3100 N·m M_Z = 1500 N·m

Against Table 5 (1×): the worst component is F_Y at 6800/4890 = 1.39 (F_X is close behind at 5200/3780 = 1.38). Table 5 fails. Most people stop here and ask for a re-route. Run the gates first.

Gate 1 (2× ceiling):

F_X 5200/7560 = 0.69   F_Y 6800/9780 = 0.70   F_Z 2900/6220 = 0.47
M_X 4900/7060 = 0.69   M_Y 3100/5160 = 0.60   M_Z 1500/3520 = 0.43     all < 1  ✓

Gate 2 (interaction at the nozzle):

F_RA = √(5200² + 6800² + 2900²) = 9038 N        1.5 × F_RT = 1.5 × 6920 = 10 380 N
M_RA = √(4900² + 3100² + 1500²) = 5989 N·m      1.5 × M_RT = 1.5 × 4710 =  7065 N·m

9038/10380 + 5989/7065 = 0.871 + 0.848 = 1.72  ≤ 2   ✓

Verdict: the nozzle passes Annex F at 1.39× the worst table component — provided Gate 3 also passes at the pump centre, the baseplate is grouted, and the vendor confirms it. Notice how little headroom is left: push F_Y to 9 000 N and the interaction sum climbs to 1.89; to 9 500 N and it is 1.93; and at 9 780 N (sum 1.95) you simultaneously hit the Gate 1 ceiling of 2 × 4 890. The "2×" that sounded generous is nearly spent.

Fixing it — and the fix that makes it worse

Watch what the load is actually doing to the machine in ▶ open the interactive: rotating nozzle loads 3d: turn on the arrows, then exaggerate the casing distortion and watch the shaft centreline and the coupling go out of line — that is the whole failure mechanism in one picture. Then switch the spring support in and watch it relax.

The instinct is to stiffen everything — add rigid rests, weld in more steel near the nozzle. For weight that helps. For thermal it is the exact wrong move:

Weight load is force-driven: the pipe weighs what it weighs, and a support carries it. Adding a support near the nozzle removes real load. Do this.
Thermal load is displacement-driven: the pipe is going to grow Δ regardless, and the force it delivers is k·Δ. Stiffen the system and you raise k with Δ unchanged — the nozzle load goes up. This is the single most common own-goal in machine piping.

What actually works, roughly in order of preference:

Add flexibility — a loop, an offset, one more elbow between the anchor and the machine. Cheap in steel, powerful in k.
Move the anchor — put a proper anchor between the machine and the expansion source, so the growth is discharged into the anchor and the pump only sees the short flexible leg. Relocating one anchor often does more than any amount of local strengthening.
Spring supports — a variable or constant-effort spring at the first support off the nozzle carries dead weight in both cold and hot positions without fighting the vertical growth. A rigid rest there does the opposite: it lifts off cold or loads up hot.
Take the valve weight off the nozzle — a strainer full of product, a hung valve and its actuator are dead weight that lands straight on the flange. Support them independently.
Cold spring / cold pull — legitimate, but it buys you hot-case relief at the price of a worse cold case, needs site discipline to install, and codes only credit it partially.
Expansion joint — last resort. It does not remove force, it moves it: pressure thrust has to be tied or anchored, and an untied bellows near a pump is a new failure mode, not a fix.

Common pitfalls

Quoting "2× is allowed" without Gates 2 and 3 — the interaction check is what governs.
Checking only the hot case. Cold, upset, steam-out and settlement cases all land on the nozzle, and the cold case is often the worse one after cold spring.
Using Table 5 for a pump the table does not cover (vertical in-line, cast-iron casing, API 685 sealless, non-API pumps) — get vendor allowables.
Forgetting the flange itself: passing Annex F says nothing about whether the gasket leaks. A high moment can unload one side of a raised-face joint on hot hydrocarbon.
Assuming the baseplate is grouted. Annex F assumes it. Check it.
Applying the NEMA index in mixed units, or converting the 500 constant. Use one unit form whole.
Treating the turbine exhaust like any other nozzle — D_e and D_c are both capped; the allowable stops growing long before the pipe does.
Stiffening the pipe to "protect" the pump from a thermal load.

Outcome

Pipe-code and machine-nozzle checks have different limit states: rupture/fatigue of a wall versus distortion of a casing. Passing one says nothing about the other.
API 610 Table 5 is sized from a ~250 µm shaft-displacement budget; forces are permuted by nozzle orientation, moments are not, and F_R/M_R are resultants of the tabulated components.
The 2× rule is conditional and triple-gated: components ≤ 2× and the 1.5/≤2 interaction at each nozzle and the translated check at the pump centre, on a grouted baseplate.
NEMA SM-23 uses the empirical index 3F + M ≤ 500·D_e per connection plus a combined 2F_c + M_c ≤ 250·D_c at the exhaust; API 617 = 1.85 × NEMA. D_e and D_c are capped for large sizes — that cap is why exhausts govern layouts.
Fix by adding flexibility, relocating the anchor and spring-supporting the first hanger. Do not stiffen a displacement-driven load.
Tools: ▶ open the interactive: rotating nozzle loads calc (three machine standards, live utilisation and gates) and ▶ open the interactive: rotating nozzle loads 3d (distortion → misalignment → spring relief).

Open items

Add API 610 Table 5 rows for 18″–24″ and the vertically-suspended (VS) criteria from Annex F.
Worked Gate-3 translation to the pump centre with a real baseplate geometry.
Compare a vendor's stated allowables for one specific BB2 casing against Table 5, to show how much the generic table under-sells a stiff casing.

Know why, not just what.

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