Engineering task and calculation objective
Horizontal pressure vessels normally rest on two saddle supports. In addition to the internal pressure, the dead weight plus contents generates bending moments over the vessel length, shear forces at the saddles and local circumferential stresses at the saddle horn — loads that a pure wall thickness calculation does not capture. This module performs the strength verification of horizontal vessels on saddles to ASME BPVC Section VIII Division 2, Paragraph 4.15.3, the design method going back to L. P. Zick.
The module calculates the internal moments M1 (over the saddle) and M2 (at midspan), the shear force T at the saddle, and from these the longitudinal stresses in shell and head, the shear stresses and the circumferential stresses at the saddle horn and at the lowest shell line — each superimposed with the pressure condition. Stiffening rings in or on the shell and the horizontal saddle force Fh with its acceptance criteria are verified as well. The module evaluates the stress coefficients K1 to K10 of Table 4.15.1 as closed-form functions of the saddle contact angle.
You need to calculate the saddle support check to ASME VIII-2 for practically every horizontal storage, process or transport vessel — especially with large diameter-to-thickness ratios, long vessels, high fill density, or when checking whether stiffening rings are required.
Standard and calculation basis: ASME BPVC Sec. VIII Div. 2, Part 4.15.3: 2025
Calculation workflow
- Define geometry and load data: The inputs are shell diameter and wall thickness, head shape and head depth, vessel length, saddle distance from the head tangent line a, saddle width b and contact angle θ (typically 120° to 150°), together with the total load from dead weight, contents (operation and water fill during the pressure test) and attachments.
- Determine section forces per Zick: The vessel is treated as a beam on two supports with overhanging ends. This yields the moment M1 over the saddle, the moment M2 at midspan and the shear force T at the saddle; the dished heads act as load-sharing end stiffening.
- Evaluate stress coefficients: The coefficients K1 to K10 per Table 4.15.1 depend on the contact angle and on whether the shell at the saddle is stiffened by head proximity or rings. The module evaluates them as closed-form functions of θ instead of reading them from charts.
- Calculate stresses and superimpose with the pressure condition: From M1, M2 and T follow the longitudinal stresses at the top and bottom of the shell, the shear stress in the shell or head, and the circumferential stresses at the saddle horn and at the lowest point. These are superimposed with the membrane stresses from internal pressure (or test pressure).
- Verify stiffening rings and the horizontal saddle force: If the circumferential stress at the saddle horn is inadmissible, stiffening rings in or adjacent to the saddle plane are sized and their stresses verified. In addition, the horizontal force Fh is checked, which tends to spread the saddle apart and loads the low-lying saddle cross-section.
- Check acceptance criteria: All stresses are checked against the allowable values per Part 4.15.3: tensile longitudinal stresses against S·E, compressive longitudinal stresses additionally against the buckling limit per Paragraph 4.4, shear and circumferential stresses against their respective factors of the allowable stress value.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Shell inside diameter Di | – | – |
| Shell wall thickness tn | – | – |
| Corrosion allowance c | – | – |
| Design temperature T | – | – |
| Design pressure P | – | – |
| Shell material | – | – |
| Head wall thickness th | – | – |
| Mean head radius Rmh | – | – |
| Length tangent-tangent L | – | – |
| Saddle to tangent a | – | – |
| Saddle width b | – | – |
| Saddle angle theta | – | – |
| Mean head depth hm | – | – |
| Reaction per saddle Q | – | – |
| Head type | – | – |
| Stiffening configuration | – | – |
| Wear plate present | – | – |
| Wear plate thickness tr | – | – |
| Wear plate width b1 | – | – |
| Plate arc angle theta1 | – | – |
| Load factor K | – | – |
| Support condition k | – | – |
| Weld joint efficiency E | – | – |
| Ring area A | – | – |
Calculation options
Head type
1 · 2 · 3 · 4
Stiffening configuration
1 · 2 · 3 · 4
Load factor K
1 · 2
Support condition k
1 · 2
Frequently asked questions
Why is the ideal saddle located near the heads (a ≤ 0.25·L)?
Dished heads stiffen the shell cross-section against ovalization. If the saddle is close to the head (typical recommendation a ≤ 0.25·L, often a ≈ 0.2·Rm), the cross-section over the saddle remains nearly round, the effective shell width is larger and the circumferential stress at the saddle horn drops significantly. Saddles far from the heads frequently require stiffening rings.
When are stiffening rings required?
When the circumferential stress at the saddle horn exceeds the acceptance criterion — typically for thin-walled, large-diameter vessels, small contact angles or a large distance between the saddles and the heads. Rings in the saddle plane or on both sides of it distribute the saddle load around the circumference; the module verifies the ring stresses separately per 4.15.3.
Does the water-filled load case during the pressure test have to be considered separately?
Yes. During the hydrostatic test the vessel is completely filled with water, which — particularly for gas or vapor vessels — can mean several times the operating load. Since the test pressure is applied at the same time, the combination of maximum saddle load and test pressure is often the governing load case for the saddle horn and the longitudinal stresses.
Does the Zick method also apply to more than two saddles?
The method of 4.15.3 is derived for two symmetrically arranged saddles; the section forces are based on the statically determinate two-support model. With three or more saddles the system is statically indeterminate, differential settlement changes the load distribution considerably, and the code does not cover this case — a separate analysis (e.g. FEM with an elastic-foundation approach) is required.