# The Benefits of Nonlinear Pipe Stress Analysis Method

In plant design, it is important to perform pipe stress analyses to examine different loading scenarios, such as thermal, seismic, wind and dynamic loads. This process brings significant benefits, but to understand what those benefits are, it is important to distinguish between a linear and a nonlinear analysis. A linear analysis is characterized by constant pipe properties, small deflections, and elastic deformation when the pipe reverts to its original shape. For example, for every pound of force applied one inch of displacement is created. Initial states are not required for the analysis – all gaps are assumed closed; friction is ignored; linear soil properties are used; and soil yielding is not considered.

A nonlinear analysis is characterized by changes in pipe properties over time, large deflections, and plastic – or permanent – deformations. The analysis is called nonlinear because the amount of force that creates a given amount of displacement is variable. It is important to run a nonlinear analysis because supports that have gaps and friction do not behave in a linear manner. Users gain significant benefits from a nonlinear analysis method. For example, a nonlinear analysis gives project teams the ability to better engineer designs by analyzing more realistic models. State-of-the-art nonlinear analysis engines use tangent stiffness and secant stiffness methods – both of which are found in finite element analysis (FEA) programs such as ANSYS and Abaqus – to handle piping models.

Tangent Stiffness vs. Secant Stiffness Strategies

A tangent stiffness strategy, which handles all the supports and their gaps, involves performing a linear analysis for the nonlinear supports. The starting point equation for the analysis is an initial state. If the support gap in that direction doesn’t close after the initial load case, the support in that direction is ignored. If the gap does close, the specified stiffness is used for the entire analysis. A secant stiffness strategy, which handles friction, derives the initial stiffness from the ratio of support forces – i.e., the friction force – to the support deformation – i.e., the amount of friction slip – and also starts with an initial state. There is some question, however, about whether or not friction should be considered for seismic loads.

According to design codes such as the Uniform Building Code (UBC) and the International Building Code (IBC), friction ought to be ignored – a situation that’s only possible with incremental load case analysis engines. The total load approach offered by most pipe-stress software vendors fails to understand either boundary conditions or how the direction of the pipe movement can change the bearing force. That kind of change can possibly double the stress and load range when, for example, the magnitude of the friction force from an operating condition stays the same when the pipe returns to ambient conditions, yet operates in the reverse direction. Instead, it is better to do an incremental analysis to ensure that no extreme load is overlooked – and to conform with American Society of Mechanical Engineers (ASME) code philosophy.