Restrained-Joint Length at a Pipe Bend
Run of restrained pipe each side of a bend that holds the thrust when a concrete block will not fit.
Example
You enter
- Pipe outside diameter (in) 12
- Design (test) pressure (psi) 150
- Horizontal bend angle (deg) 90
- Unit resistance per foot, Ff + Rs/2 (lb/ft; DIPRA counts half the bearing) 600
You get
- Area (in²) 113.097
- Thrust at the bend 23992 lb
- Restrained length each side 42.4 ft each side
Checked against published worked examples from: DIPRA.
Details, formula, and sources
Scopethrust = 2 x pressure x area x sin(bend/2); length each side = Sf x pressure x area x tan(bend/2) / unit resistance (DIPRA: friction plus half the bearing, Ff + Rs/2). A 12 in OD main at 150 psi through a 90-degree bend throws 24,000 lb, so at 600 lb/ft and Sf 1.5 the crew restrains about 42 ft each side; a 45-degree bend needs about 18 ft, since the length goes as tan(bend/2), not half. DIPRA's 30 in, 150 psi, 90-degree example prints 55.3 ft. The restraint manufacturer's tables (EBAA / AWWA M41) set the unit resistance.
Formula or tablearea_in2 = (PI/4) x od_in^2; thrust_lb = 2 x pressure_psi x area_in2 x sin(bend_angle_deg/2); length_each_side_ft = Sf x pressure_psi x area_in2 x tan(bend_angle_deg/2) / unit_resistance_plf (DIPRA / AWWA M41, Sf commonly 1.5).
Source and editionThrust and restrained-length identity by name (thrust = 2 P A sin(bend/2); length = Sf P A tan(bend/2) / (Ff + Rs/2), DIPRA Thrust Restraint Design, 7th ed.); the thrust itself is first-principles statics.
Free accessThe thrust geometry is public first-principles statics; the unit soil resistance comes from the restraint manufacturer's tables.
What governsEstimate. AHJ and licensed professional govern.
API field namespipe_od_in, pressure_psi, bend_angle_deg, unit_resistance_plf, area_in2, thrust_lb, length_each_side_ft
- Thrust the unbalanced hydrostatic thrust at the bend, 2 x pressure x pipe area x sin(bend/2)first-principles statics
- Unit resistance resistance per foot of restrained pipe, Ff + Rs/2 (friction plus half the bearing, as DIPRA counts it), from the restraint manufacturer's tablesEBAA / AWWA M41