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Pipe Expansion Loop (U-Bend) Sizing Calculator engineering
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Pipe Expansion Loop (U-Bend) Sizing Calculator

Calculate pipe thermal expansion U-loop leg length (H), loop width (W), developed piping length, and anchor guide reaction forces via the Kellogg formula.

Pipe Diameter & Thermal Growth

4.50" for 4" NPS, 6.625" for 6" NPS.
Typical: 20,000 to 25,000 psi for A106 Grade B.

Expansion Loop Dimensions

Required Leg Length (H)
-- ft
-- meters loop depth
Loop Width (W)
-- ft
Parallel pipe run
Developed Length
-- ft
2H + W total pipe
Approx Anchor Reaction: -- lbs force
Calculated Bending Stress: -- psi (≤ Allowable)
Pipe guides must be placed strictly on both sides of the expansion loop to direct straight axial thermal movement squarely into loop bending flexibility.

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Frequently Asked Questions

What is the M.W. Kellogg formula for expansion loop sizing?

The Kellogg equation (H = (1/12) · √(3·E·Do·ΔL / SA)) calculates the minimum perpendicular leg length (H) required for a symmetrical U-loop to safely absorb thermal expansion (ΔL) without exceeding code allowable bending stress range (SA).

Why are expansion loops preferred over mechanical expansion joints in critical lines?

Expansion loops are fabricated entirely from standard pipe and forged elbows with zero moving parts, zero gaskets, zero packing glands, and zero thin metal membranes. They eliminate failure points, require zero maintenance, and have infinite design lifespans.

Why are pipe alignment guides mandatory adjacent to expansion loops?

Without pipe guides, long thermal lines will buckle laterally or snake sideways across the pipe rack rather than pushing into the expansion loop legs. Standard practice places the first guide within 4 pipe diameters of the loop elbow.