Tools › Fluids and Heat Transfer › Pipe Flow › Pipe Stress and Support Spans › Example
100 ft run of 6 in steel pipe with a 30 ft leg heated 300 °F: guided cantilever against a stiffness solution with a flexible elbow
| Tool | Pipe Stress and Support Spans |
| Source | McKeon, J. T. (1965). Primary Piping Flexibility Analysis for Liquid-Metal-Cooled Fast Breeder Reactors. COO-1454-1, M. W. Kellogg Company for the U.S. Atomic Energy Commission, pp. 22–25 (Eq. 6 and 7: expansion stress and allowable range). Wais, E. A., and Rodabaugh, E. C. (2005). Background of SIFs and Stress Indices for Moment Loadings of Piping Components. EPRI Report 1012078, section 2.2 (h and i of an elbow). Pan, Y., Rafer, A., and Ahmed, H. (1980). A Study of Piping Configurations. ANL/ENG-80-02, p. 5 (k = 1.65/h). The layout and its numbers are an illustrative case computed by the tool, not a printed example. |
| Level | Professional |
Problem
A 6 in Schedule 40 carbon steel line (168.3 mm outside diameter, 7.11 mm wall, E = 200 GPa, α = 11.7 µm/m/°C) runs 30.48 m (100 ft) from anchor A, turns through a long-radius elbow (bend radius 228.6 mm) and ends 9.144 m (30 ft) further on at anchor B. It is heated by 166.67 °C (300 °F). The cold and hot allowable stresses are 138 MPa (20 ksi) and the line sees fewer than 7,000 cycles. Find the expansion to be absorbed, the flexibility and stress intensification factors of the elbow, the allowable stress range, the guided-cantilever estimate of the expansion stress, the screening criterion, and the anchor reactions and expansion stress range from a stiffness solution of the layout.
Inputs to Enter
- Analysis: thermal expansion and flexibility; pipe 6 in Sch 40; carbon steel, E 200 GPa, α 11.7 µm/m/°C
- Temperature change 166.67 °C; layout L-bend, run 30.48 m, leg 9.144 m; bend radius 228.6 mm
- Cold allowable 138 MPa, hot allowable 138 MPa, 7,000 cycles, no cold spring
Answers
- Free expansion 1.950 mm per m: the run grows 59.44 mm and the leg 17.83 mm; anchors 31.82 m apart, growth to absorb y = 62.05 mm
- Elbow: h = t R/r² = 0.2504, flexibility factor k = 1.65/h = 6.590, stress intensification factor i = 0.9/h^(2/3) = 2.266
- Allowable range S_A = 1.0 × (1.25 × 138 + 0.25 × 138) = 207 MPa
- Guided cantilever: the leg takes 59.44 mm with end moments 6 E I δ/L² = 9.992 kN·m, stress 71.77 MPa, 162.6 MPa with i; anchor force 12 E I δ/L³ = 2.186 kN; an 8.10 m leg would just reach S_A
- Screening criterion D y/(L − U)² = 0.0001715 against 0.2083 S_A/E = 0.0002156: passes
- Stiffness solution with the elbow as a flexible arc: anchor A 0.8963 kN, 0.1091 kN, 1.199 kN·m; anchor B −0.8963 kN, −0.1091 kN, −6.069 kN·m; largest moment in the elbow 2.103 kN·m (34.23 MPa with i)
- Expansion stress range S_E = 43.59 MPa at anchor B, 0.211 of S_A; 44.88 MPa with a square rigid corner; the guided cantilever is 3.73 times the stiffness result
Notes
The tool's default inputs are this case; press Submit. The guided cantilever assumes that the corner cannot rotate; on a 30 m run it rotates freely, so the estimate is far on the safe side here. The stiffness solver is checked by test_pipe_stress_support_spans.php (586 checks) against an independent flexibility-method solution with exact circular arcs (scipy) on ten layouts: this layout in US units gives the same reactions to 2 parts in 100,000. The screening criterion is cited from ASME B31.3 and was not verified against a public document; the allowable stresses are illustrative entries, not code values for a particular steel.