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Answer: CSiPlant calculates loads using the assigned pressure loading and pipe-section dimensions as defined in the section property (without any material allowance consideration). Pressure loads on piping are comprised of two parts:
- Pressure-thrust/End Cap -cap type load effects.
- Poisson contraction/elongation load effects.
Both sets of loads are applied simultaneously , whenever there is a pressure assignment other than ambient. The distribution of internal forces and deformations depends on the structure flexibility and boundary conditions.
Pressure Thrust/End Cap
Pressure-thrust/end-cap loads are self-equilibrating loads. This means that for any given piping component, the distribution of pressure load is in equilibrium. The pressure load at the inlets/outlets is commonly referred to as "End-Cap cap forces", calculated as shown in Figure 1, and follows a sign convention that a positive end-cap force induces tension on the pipe. Note that for the calculation of analysis loads, no material allowances are considered.
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Figure 1: Internal and external pressure acting on a straight pipe with end caps.
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For pipes with variable cross section (reducers or reducing elbows) there is a pressure thrust in addition to the end-cap force. Only the component of pressure acting parallel to the longitudinal axis of the pipe contributes to the pressure thrust. The end-cap forces are calculated as previously using the inside and outside diameters at each end of the reducer. The pressure thrust acts as a uniformly distributed axial load and is equivalent to the pressure acting on projected area of a pipe segment of length 'dx'. The small side end-cap force combined with the total pressure-thrust load is equal and opposite to the large side end-cap force. Figure 2 shows the End-Capcap/Pressure Thrust -thrust forces on a reducer.
Figure 2: Internal and external pressure acting on linear reducer showing end-cap force and pressure thrust.
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A special case of pressure-thrust forces is for flexible expansion joints, ; in these cases the pressure-thrust force is calculated using the provided pressure-thrust area (typically from vendor catalogue data) along with the applied pressure.
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When a pipe experiences pressure load, it expands or contracts radially (under internal or external pressure, respectively). An internal circumferential force develops to resist the expansion/contraction of the cross section, and is equal to the applied pressure acting on the projected area, dividing . Dividing by the pipe wall thickness returns the average hoop stress. For thin-walled structures (D/t > 30) this is a reasonable approximation of the hoop stress. For thick-walled structures, there is a more significant variation through the thickness, and the Lame' equations are necessary to calculate the peak hoop stress. Regardless of thin- or thick-walled structures, the total longitudinal force due to Poisson contraction follows the average hoop stress. Figure 3 shows how the average hoop stress can be calculated.
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Figure 3: Calculation of average hoop stress
Due to the Poisson effect, there will be a corresponding change in length (contraction for internal pressure and elongation for external pressure). The unrestrained pressure elongation strain, εp, is proportional to the the average hoop strain by the Poisson ratio (≈ 0.3 for most metals). Figure 4 illustrates the relationship between changing pipe radius and the corresponding change in length (for internal pressure only).
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For systems that ARE free to deform (unrestrained), pressure stresses are from the end-cap/pressure-thrust forces as since the Pressure pressure elongation can occur. Examples of systems that can be considered unrestrained include:
- Straight pipe, fixed/line-stop at one end, and free or guided at the other;
- Straight pipe, fixed/line-stop at the center, and both ends free or guided.
- Non-buried piping with elbows or other components that allow the elongation to occur.
For systems that are NOT free to deform (restrained), pressure stresses are from the Poisson effects. Examples of systems that can be considered unrestrained include:
- Straight pipe, fixed or with line stops at each end.
- Buried piping where the soil is sufficiently stiff to prevent the pressure elongation from occurring.
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