A pipe heated from 20 °C to 170 °C grows by about 1.8 mm for every meter of its length. A straight run held rigidly at both ends cannot grow. In carbon steel, the stress needed to prevent growth is about 360 MPa, above its yield strength. Changes of direction let a line bend and absorb thermal growth at a small fraction of that stress.

Piping flexibility analysis asks whether the layout is flexible enough. It calculates movements, loads on attached equipment and structures, and stresses from movement and weight (Part II A).

Those questions concern the whole line. A piping system can be represented by its centerline, with components, supports, anchors and loads attached. SWBPIPE divides the centerline into beam elements that meet at nodes. Each node has three translational and three rotational degrees of freedom.

The native product entrypoint is run_linear_static_preview_with_mode. It solves the supported model and recovers movements, member forces and stresses. Ordinary preview-physics-1 publishes six signed support components where attribution is possible. It withholds ambiguous support actions and arc governing stress maxima (Part III).

1.What the program computes, and what comes from you.

This chapter describes source revision a72f994d89. The verification records identify their own source pins and execution paths (Part VI). SWBPIPE supplies no code tables and does not judge code compliance. Its results help readers develop and understand a design. The design is validated elsewhere (Part V).

A beam model does not resolve local shell behavior in the pipe wall. Under moment, a bend can flatten into an oval. Ovalization increases flexibility and concentrates stress at the flanks. A tee or nozzle transfers load through local shell bending.

Engineering flexibility models represent some local effects with flexibility factors k and stress intensification factors i (Part II E). These factors come from shell theory and tests. Their suitability strongly affects the analysis. They do not make a beam model a local shell analysis.

Current SWBPIPE behavior depends on the selected method and model contract. The ordinary route supports an explicit curved-bend mode with entered k. Its separate user equal-factor intensified bending measure is not a code stress. That measure does not apply to realized arcs. The route withholds arc governing stress maxima (Status).

The native entrypoint accepts pressure contract 2.0.0, exact_straight_pressure_v2, and contract 3.0.0, exact_pressure_v3. New authoring writes contract 3.0.0. Model 0.4.0 requires an explicit exact contract. Both require explicit pressure regions, terminal closure transfer, and homogeneous isotropic material properties with E/ν.

Contract 2.0.0 remains straight-only. Contract 3.0.0 also admits realized curved bends with entered k. It excludes Bourdon opening, pressure-dependent flexibility and SIFs, and ovalization. Legacy pressure is refused even at zero. Read the full input and result limits before modelling pressure (Part IV D).

Where the global model does not represent the local behavior, a detail may need a local model. Examples include vessel or tank nozzles, trunnions, lugs, large branch connections and other points where load enters the pipe locally. A local method can use WRC 107 or 297, or finite elements. The global model supplies boundary loads and movements for the local model. It does not replace that model.

A result describes the model as entered. It does not establish the behavior of the plant. Interpreting the result requires examination of the centerline, supports and restraints against the line as built. It also requires complete, correct inputs and assessment of details that need local analysis. Part IV explains how to build and examine a model.

Systematic study of pipe bends began in 1910. Bantlin reported that curved pipes flatten under bending and are much more flexible than beam theory predicts. A year later, von Kármán published the first theory of this behavior. Others continued the work. Clark and Reissner brought it to closed form in 1951, providing the basis for flexibility factors still used.

The first analytical methods for whole lines applied to pipe in one plane. In 1929, W. H. Shipman published a general solution for a single-plane line with two fixed ends. He integrated the quantities that depend only on line shape in advance. The method needed simple arithmetic and suited routine design.

Tingey introduced the elastic center: the centroid of the line’s elastic weight, about which the equations uncouple. Graphical constructions, charts and scale-model tests gave quicker answers for simple layouts and verified the calculations.

In 1932, the Engineering Department of the Standard Oil Company (Indiana) extended Shipman’s method to lines in space in a company report. The M. W. Kellogg Company developed and organized that work for its use during the 1930s. In 1941, it published Design of Piping Systems: Expansion Stresses and Reactions in Piping Systems.

D. B. Rossheim, A. R. C. Markl, H. V. Wallstrom and E. Slezak wrote the book. It presented the first general method for stresses, reactions and movements of a spatial piping system, with any number of legs, bends and restraints.

1.From stress to stress range.

In 1940, Rossheim and Markl argued that thermal stress is self-limiting. They argued that a line fails by fatigue rather than one overload. Thus, the line should be judged by its stress range through repeated cycles. They proposed an allowable range and began fatigue tests of piping components. Markl continued these tests through the 1940s and early 1950s. The tests provided the stress intensification factors.

Markl’s “Piping-Flexibility Analysis” of 1955 described this approach. The Code for Pressure Piping, ASA B31.1, adopted it in its 1955 edition. The B31 codes still follow the approach (Part II D).

The second edition of Design of Piping Systems (John Wiley & Sons, 1956) expanded the book to cover the whole design of piping systems. It included the new stress-range rules. This is the edition most stress engineers know.

2.The computer.

The general method used tabulated steps that suited machine calculation. Kellogg used machines for routine piping solutions from 1954. Matrix methods of structural analysis followed. Proprietary pipe stress programs developed in later decades.

SWBPIPE uses the stiffness method from that later family. Its bend element uses the same flexibility integrals as the Kellogg method. Readers can examine each step in the published source.

The 1941 manual opens with an acknowledgment of earlier investigators. It singles out three engineers. It pays particular tribute to W. H. Shipman. His systematic single-plane solution used preintegrated shape coefficients and prepared the way for later work. The acknowledgment credits G. W. Watts and W. R. Burrows, of the Engineering Department of the Standard Oil Company (Indiana), with

“the most significant step towards the general solution” Design of Piping Systems, 1941, Acknowledgment

by extending Shipman’s method to the three-plane problem with two fixed ends. Their work appeared only in a company report. They derived coefficients for the other planes from one basic plane by cyclic permutation of the coordinates. The acknowledgment states that these works underlie the manual’s general method.

SWBPIPE takes its name from these three engineers. For decades, engineers used the general method by hand, one coefficient at a time. The method later moved into programs whose internal mechanics are often unavailable. SWBPIPE publishes the mechanics, evidence and source for readers to study. The expansion loop in Part VI uses the force method that the 1941 manual made general. Its recorded comparison uses the bend element and frame kernel directly; it does not qualify the product-physics or desktop path.