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
- Soil resistance per foot (lb/ft) 600
You get
- Area (in²) 113.097
- Thrust at the bend 23992 lb
- Restrained length each side 40.0 ft each side
Details, formula, and sources
thrust = 2 x pressure x area x sin(bend/2); length each side = thrust / soil resistance per foot. A 12 in main at 150 psi through a 90-degree bend throws 24,000 lb, so at 600 lb/ft the crew restrains ~40 ft each side; a 45-degree bend needs half that. The restraint manufacturer's tables (EBAA / AWWA M41) set the unit resistance.
area_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 = thrust_lb / unit_resistance_plf.
Thrust and restrained-length identity by name (thrust = 2 P A sin(bend/2); length = thrust / unit resistance); first-principles statics.
The thrust geometry is public first-principles statics; the unit soil resistance comes from the restraint manufacturer's tables.
Estimate. AHJ and licensed professional govern.
Field names used by the API: pipe_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 soil resistance per foot of restrained pipe (pipe friction + fitting bearing), from the restraint manufacturer's tablesEBAA / AWWA M41