Expansion Loop Leg Length (Guided Cantilever)

Heat a straight anchored pipe and it must grow somewhere; if it cannot, it buckles or tears out its anchors. The standard remedy is to build flexibility in — a U-loop, an L-bend or a Z-offset — and the guided-cantilever method treats the offset leg as a beam with both ends guided, giving the required length directly from the movement it must swallow. A 6.625 in steel line growing 2 in, with E = 27.9 × 10⁶ psi and an allowable stress of 22 000 psi, needs a leg of $\sqrt{3 \times 27.9 \times 10^{6} \times 6.625 \times 2 / 22\,000} \approx 225$ in, about 18.7 ft.

Notice the square root and the D term together: doubling the movement only asks for 41% more leg, but doubling the pipe size asks for 41% more too — large pipe is stiff, and that is why an 18 in steam header needs enormous loops while ¾ in tubing can absorb the same growth in a single offset. The classic mistake is forgetting the anchors. A loop only works between two solid anchors with proper guides on the approach legs; drop in a loop and let the pipe slide freely through the hangers instead, and the expansion simply goes somewhere else and breaks a branch connection.