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: 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.
Formula and source
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.
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