Pipe Loop

It is a symmetrical U-loop sketch, not a flexibility analysis.

Formula

Δ = α × L_run × ΔT

L = sqrt(3 × E × D × Δ / Sa)

W + 2H = L

The leg length is the guided cantilever method, M.W. Kellogg, Design of Piping Systems, and standard piping textbooks. This page takes that length as the straight developed length of a symmetrical U-loop, W + 2H. That developed-length form is the one published for thermal expansion loops. The usual proportion with that form is height twice the width, so W = L/5 and H = 2L/5. The other two rows keep the same developed length and only change the proportion. They are layout options, not extra code requirements. Elbow arc length is not included.

Assumptions: anchors at both ends of the run, guides so the growth goes into the loop, and no friction. The loop is in one plane. E and Sa are the values you enter. A typical modulus is a near-ambient textbook figure, not a code allowable, and it is not adjusted for temperature. The coefficient must use the same degree as the temperature difference. Changing that degree converts the temperature difference and the coefficient. A coefficient per °F is the coefficient per °C times 5/9.