This worked example documents the ASME Section VIII Division 1 design of a 24 in OD vertical shell-and-tube heat exchanger with fixed tubesheets (TEMA BEM configuration), shell side at 285 psig and tube side at 150 psig, both at 200 °F. The bundle is 109 SA-179 carbon-steel tubes, 0.75 in OD x 14 BWG (0.083 in wall), 96 in long, on a 1 in triangular pitch, expanded and seal-welded into two 1.500 in SA-516-70 N forged tubesheets. The shell and channel are SA-516-70 N at 0.500 in nominal.
The teaching content is Part UHX-12 for fixed-tubesheet exchangers: seven design load cases (pressure shell only, pressure tube only, both sides, thermal only, and the three pressure+thermal combinations), each producing tubesheet bending, tube axial stress, and shell axial stress. Section 5 example 4 walks the typical-governing case 6 (shell-side pressure plus thermal differential) end to end, including the thermal-expansion compatibility analysis that produces the constrained axial force in the tubes and the corresponding tube tension stress of 11,685 psi against a 13,400 psi allowable. The page mirrors PVEng's heat-exchanger code-design sample with original numbers and a single worked case rather than the full seven-case matrix.
Five sections. Each section is a collapsible block. Open to read the full design basis, summary tables, materials, code clause index, and the worked numerical examples for this configuration.
| Parameter | Shell side | Tube side |
|---|---|---|
| Design pressure | 285 psig | 150 psig |
| Design temperature | 200 °F | 200 °F |
| Design MDMT | -20 °F | -20 °F |
| Corrosion allowance | 0.0625 in | 0.0625 in |
| Service | Non-lethal, gas or liquid cooling | Cooling water or process side |
| Item | Value |
|---|---|
| Code of construction | ASME Section VIII Division 1, 2023 Edition, Part UHX for tubesheets |
| Equipment type | Shell-and-tube heat exchanger, vertical, BEM configuration (fixed tubesheets both ends, removable bonnet head) |
| Joint efficiency, shell | 1.00 (full RT long seam) |
| Joint efficiency, channel | 1.00 (full RT long seam) |
| Radiography | Full RT on Cat. A welds, surface NDE on the tubesheet-to-shell weld and the tubesheet-to-channel-flange weld |
The vessel is analyzed for the loadings listed in UG-22 with the addition of the thermal loads inherent to a fixed-tubesheet exchanger:
SA-516 Grade 70 Normalized shell, channel, and tubesheets; SA-179 carbon-steel tubes. UCS-66 Curve D for the SA-516 N components, Curve B for the SA-179 tubes. Required MDMT at the shell thickness (0.500 in nominal) is approximately -55 °F, and at the tubesheet thickness (1.500 in) is approximately -15 °F. Rated MDMT is -20 °F, set by the 1.500 in tubesheet without UCS-66.1 credit.
Both sides are tested per UG-99(b): shell side at 1.3 × 285 = 371 psig, tube side at 1.3 × 150 = 195 psig. The shell-side and tube-side tests are performed sequentially with the opposite side unpressurized so the tubesheet sees the full design differential pressure during each test. The two tests are then repeated simultaneously at reduced pressures to confirm the UHX-12 simultaneous-pressure load cases.
| Component | Material | t_req (in) | t_avail (in) | MAWP (psig) | Clause |
|---|---|---|---|---|---|
| Shell-side shell | SA-516 Gr 70 N | 0.171 | 0.375 | 625 | UG-27(c)(1) shell-side P |
| Tubes (SA-179, 0.75 in OD x 14 BWG) | SA-179 carbon steel | 0.012 in (internal P) | 0.063 in nominal less mfg tolerance | matches tube-side rating | UG-31 |
| Fixed tubesheets (each) | SA-516 Gr 70 N forged | see UHX-12 Ex. 4 | 1.500 in | per UHX-12 load case | UHX-11, UHX-12 |
| Channel-side shell (top channel) | SA-516 Gr 70 N | 0.090 | 0.375 | 625 | UG-27(c)(1) channel-side P |
| Channel head (2:1 SE) | SA-516 Gr 70 N | 0.090 | 0.388 | 624 | UG-32(d) |
| Girth flange (channel to shell, NPS 24 Cl 300) | SA-105 | standard | standard | 720 | UG-44, B16.5 Gp 1.1 |
The shell governs the shell-side rating at 625 psig and the channel governs the tube-side rating at 625 psig. Vessel ratings: shell side 285 psig (design), tube side 150 psig (design); both well below the component capacities. Tubesheet thickness is set by the UHX-12 simultaneous-pressure-and-thermal case (worked in example 4).
All components meet UG-16(b).
| Test | Component | Test pressure | Result |
|---|---|---|---|
| Shell-side hydrotest, tube side at 0 psig | Shell wall (hoop), tubesheet (membrane) | 371 psig | PASS |
| Tube-side hydrotest, shell side at 0 psig | Tubes, channel, tubesheet (membrane) | 195 psig | PASS |
| Simultaneous-pressure verification (both sides) | Tubesheet, tube joints | 185 / 95 psig (reduced) | PASS |
| Component | Specification | S at 200 °F (psi) | UCS-66 Curve | Form |
|---|---|---|---|---|
| Shell | SA-516 Grade 70, normalized | 20,000 | D | 24 in OD x 0.500 in plate x 96 in tan-tan |
| Tubes (109 ea on 1 in triangular pitch) | SA-179 carbon steel, seamless | 13,400 | B | 3/4 in OD x 14 BWG (0.083 in wall) x 96 in long, expanded and seal-welded at both tubesheets |
| Fixed tubesheets (2 ea) | SA-516 Grade 70 N forged | 20,000 | D | 1.500 in thick, 24 in OD, drilled for 109 tube holes on 1 in triangular pitch |
| Channel (top, bonnet) | SA-516 Grade 70 N | 20,000 | D | 24 in OD x 0.500 in plate x 24 in tall |
| Channel head (2:1 SE) | SA-516 Grade 70 N | 20,000 | D | 2:1 ellipsoidal, one-piece formed, 0.500 in nominal |
| Channel flange (girth) and tubesheet flange | SA-105 | 17,500 | B | NPS 24 Cl 300 RFWN-equivalent custom forging, paired with tubesheet acting as the mating flange face |
| Tube-side nozzles | SA-106 Gr B + SA-105 Cl 300 | 17,100 / 17,500 | B | NPS 6 inlet, NPS 6 outlet (both on the top channel) |
| Shell-side nozzles | SA-106 Gr B + SA-105 Cl 300 | 17,100 / 17,500 | B | NPS 4 inlet (lower shell side), NPS 4 outlet (upper shell side) |
| Bolting | SA-193 Gr B7 studs, SA-194 Gr 2H nuts | 25,000 | n/a | standard B16.5 stud-and-nut sets |
BEM configuration per the TEMA letter designation: B = bonnet inlet head, E = single-pass shell, M = fixed-tubesheet rear head (the bonnet at the bottom is also a removable cover, but the fixed-tubesheet construction means the bundle is not removable from the shell; both tubesheets are welded to the shell). For ASME UHX, the rear-end M designation governs the tubesheet analysis: UHX-12 for fixed-tubesheet exchangers.
Tubes are expanded into the tubesheet hole using mechanical expansion (rolling) followed by a seal-weld per UW-20. The tube-to-tubesheet joint is qualified to UW-20 (strength weld or strength weld plus expansion). For a 14 BWG tube under 150 psig, the joint shear strength comfortably exceeds the pressure end load.
Cat. A welds (shell long seam, channel long seam, channel-head circumferential) fully radiographed per UW-11(a)(1). The tubesheet-to-shell welds (two, one at each tubesheet) are full-penetration with surface NDE per UW-50. The tubesheet drilling pattern and the tube-to-tubesheet joints receive pre-service visual examination per UHX-18.
| Item | Value |
|---|---|
| Shell OD | 24.000 in |
| Shell wall, nominal | 0.500 in |
| Shell tube length | 96 in (8 ft) |
| Tube count | 109 (1 in triangular pitch, square-cut layout) |
| Tube OD x wall | 0.750 in x 0.083 in (14 BWG) |
| Tube ID (corroded) | 0.521 in |
| Tubesheet thickness (each) | 1.500 in |
| Channel OD x height | 24 in x 24 in |
| Channel head depth (2:1 SE) | 5.6 in |
| Internal volume, shell side | ~28,500 in³ (123 US gal) |
| Internal volume, tube side | ~5,500 in³ (24 US gal) |
| Heat-transfer area | ~171 ft² (based on tube OD) |
| Empty weight, new | ~3,800 lb |
| Test weight (water in both sides) | ~5,000 lb |
Every clause applied. Part UHX (fixed-tubesheet rules) is the central content.
| Clause | Use |
|---|---|
| UHX-1 through UHX-10 | General requirements for heat exchanger tubesheets (scope, definitions, materials) |
| UHX-11 | Loadings for fixed-tubesheet exchangers, defines the seven design load cases |
| UHX-12 | Rules for fixed-tubesheet exchangers, equations for tubesheet thickness, tube stress, shell stress under each of the seven load cases |
| UHX-13 | Tubesheet calc for floating-head exchangers (not used in this BEM configuration) |
| UHX-14 | Tubesheet calc for U-tube exchangers (not used here) |
| UHX-18 | Examination of tube-to-tubesheet joints |
| Case | Description |
|---|---|
| 1 | Tube-side pressure only, shell-side at 0 psig |
| 2 | Shell-side pressure only, tube-side at 0 psig |
| 3 | Both sides pressurized to design |
| 4 | Thermal differential only, no pressure |
| 5 | Tube-side pressure plus thermal differential |
| 6 | Shell-side pressure plus thermal differential |
| 7 | Both sides pressurized plus thermal differential |
Cases 5 and 7 typically govern tube tension and tubesheet bending; case 2 typically governs shell hoop and tubesheet membrane; case 6 typically governs tube compression buckling. The full matrix is computed in a commercial program; the worked example below shows case 6 (the typical-governing case for shell-and-tube heat exchangers in cooling service).
| Clause | Component | Use |
|---|---|---|
| UG-16(b) | All | Minimum 0.0625 in |
| UG-23 | All | Allowable stresses |
| UG-25 | All | Corrosion allowance |
| UG-27(c)(1) | Shell, channel | Internal pressure |
| UG-31 | Tubes | Internal pressure on small-diameter pipe, with UG-31(c)(2) external-pressure check for cases where shell-side P exceeds tube-side P |
| UG-32(d) | Channel 2:1 SE head | Internal pressure |
| Clause | Use |
|---|---|
| UW-20 | Tube-to-tubesheet joint, expanded + seal-welded, qualified per UW-20 strength-weld rules |
| UG-36(c)(3)(a) | Exempts the NPS 4 shell-side nozzles and the NPS 1 instrument taps from UG-37; the NPS 6 tube-side nozzles require UG-37 |
| UG-37 | Area replacement on NPS 6 inlet/outlet |
| UG-44 | NPS 24 Cl 300 girth flange custom forging, with the tubesheet as the mating face. Process nozzles use B16.5 Cl 300 RFWN. |
| Clause | Use |
|---|---|
| UW-9 / UW-11(a)(1) / Table UW-12 | Cat. A welds, full RT, E = 1.00 |
| UCS-66 / UCS-66.1 | MDMT qualification, with 1.500 in tubesheet at -15 F required (close to but inside the -20 F design MDMT) |
| UG-99(b) / Note 35 | Shell-side and tube-side hydrotests, sequentially, with simultaneous-pressure verification |
| UG-116 / UG-118 / UG-120(c) | Nameplate, location, U-1A data report (Form U-1A) with shell-side and tube-side MAWPs marked separately |
Five worked examples. The UHX-12 case 6 walkthrough (example 4) is the central content.
Required thickness with CA is 0.230 in. Shell t_avail 0.375 in (0.500 nom less mill + CA). PASS with 0.146 in margin. Shell MAWP 625 psig.
| Symbol | Value |
|---|---|
| P | 150 psig |
| R (tube inside radius) | 0.292 in |
| S | 13,400 psi (SA-179 at 200 F) |
| E | 1.00 (seamless tube) |
Required tube wall is 0.003 in, far below the 0.083 in (14 BWG) supplied wall. PASS with very large margin. The tube wall is governed by mechanical-handling and tube-to-tubesheet joint expansion requirements, not by pressure.
Both PASS by very large margin. Channel MAWP 625 psig (matches shell capacity).
This is the typical governing case for fixed-tubesheet exchangers in cooling service. Shell side is at design pressure (285 psig), tube side is at 0 psig, and there is a thermal differential between the hot shell and the cool tubes (a typical condensing service condition, for example after shell-side flooding during a startup transient).
| Symbol | Value | Source |
|---|---|---|
| P_s | 285 psig | Shell-side design pressure |
| P_t | 0 psig | Tube-side at zero (case 6) |
| T_s | 200 °F | Shell-side metal temperature |
| T_t | 100 °F | Tube-side metal temperature (assumed) |
| ΔT (differential) | 100 °F | T_s - T_t |
| α (CTE, carbon steel) | 6.5 x 10&sup-6; per °F | Both shell and tubes are carbon steel; differential is from temperature difference only |
| L (tube length between tubesheets) | 96 in | |
| E_t (modulus, tubes at 100 F) | 29.5 x 10&sup6; psi | |
| A_t (total tube metal area) | 109 tubes × 0.1731 in² per tube = 18.87 in² | 14 BWG ring area |
| A_s (shell metal area) | π × (R_o + R_i) × t = π × 23.75 × 0.375 = 27.98 in² | 0.375 in corroded shell wall |
Tube-side pressure is 0 (case 6), so no pressure end load. Total tube stress is the thermal-induced 11,685 psi tension.
PASS. The tube-stress check is the binding constraint in case 6 on this exchanger. If the differential temperature were higher (e.g., a sour-gas service with 400 F shell-side and 100 F tube-side, ΔT = 300 F), the tube stress would scale linearly, the case 6 ratio would climb to 35,000 psi, and the design would need an expansion joint or a U-tube configuration to relieve the thermal stress.
Shell axial stress in case 6 is approximately F_t / A_s = 220,500 / 27.98 = 7,880 psi compression (added to the shell hoop stress of P_s × R / t = 285 × 11.625 / 0.375 = 8,840 psi). Combined: shell sees 7,880 psi axial compression and 8,840 psi hoop tension. Both well below the SA-516-70 N allowable of 20,000 psi. The shell is not the governing component.
Tubesheet bending stress in case 6 (from the simultaneous-load formula in UHX-12.5.3, computed in a commercial program in production): approximately 16,500 psi bending across the deepest ligament, against an allowable of 1.5 S = 30,000 psi. PASS with 45% margin on the 1.500 in tubesheet thickness.
The tube-to-tubesheet joint per UW-20 must carry the larger of the pressure end load and the thermal-induced tension found in worked example 4.
| Source | Per-tube load (lb) |
|---|---|
| Tube-side pressure end load: P_t × A_t,bore = 150 × (π/4 × 0.521²) = 32.0 lb | 32 lb |
| Thermal tension from worked example 4 | 220,500 / 109 = 2,023 lb |
| Governing per-tube joint load | 2,023 lb |
The seal-welded expanded joint (tube rolled to 75% of tube OD into the tubesheet plus a fillet seal weld around the perimeter) is qualified per UW-20 to carry approximately 4 times the rolling joint friction strength as a baseline. For a 3/4 in OD tube on a 1 in pitch in a 1.500 in tubesheet, the published joint strength is approximately 6,500 lb per tube (varies by tubesheet hardness and rolling expansion ratio). The 2,023 lb thermal load is 31% of the joint capacity. PASS.
24 in OD fixed-tubesheet heat exchangers are common as gas coolers, intercoolers, and condensers in compression service. The teaching value of the example is the chain from Part UHX-11 load definitions through the UHX-12 calc for the governing case (case 6, shell-side pressure plus thermal differential). The thermal-expansion compatibility analysis is the engineering content that distinguishes a fixed-tubesheet exchanger from a separate shell and channel. If the calculated tube stress exceeds the UG-23 allowable, the response is to add a shell-side expansion joint (UHX-12 modified rules) or to switch to a U-tube or floating-head configuration that relieves the differential thermal load.