Pipe Leg

It is not a flexibility analysis and it does not change a design.

Formula

L = sqrt(3 × E × D × Δ / Sa)

S = 3 × E × D × Δ / L²

Guided cantilever method, as given in M.W. Kellogg, Design of Piping Systems, and in standard piping textbooks. L is the leg length perpendicular to the movement. E and Sa use the same stress unit. D and Δ use the same length unit. This page converts the units you choose so the pair stays consistent. If L is wanted in feet while D and Δ are in inches and E and Sa are in psi, the textbook form divides by 144 inside the square root. That factor is a unit conversion, and this page does not apply it twice.

When you compute an expansion, Δ = α × L_run × ΔT. α is per degree, in the same degree as ΔT. Δ is in the same unit as the run length.

An L-bend uses the same formula on each leg. Leg A is perpendicular to run B and absorbs the expansion of run B. Leg B is perpendicular to run A and absorbs the expansion of run A. A Z-bend uses the same formula on the offset. The offset absorbs the sum of the absolute expansions of the two parallel runs. Anchors are at the far ends. The elbows add no flexibility. Friction is not included. The offset is the only absorbing leg.

Limits: the absorbing member is guided (it translates and does not rotate), the movement is perpendicular to that member, and the member has a constant section. Friction, pressure elongation, torsion, intermediate restraints, and multi-plane routing are not in this estimate. 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. Numbers on the result line are rounded for display with six significant figures.