Question

A V-canyon supports a 100-ft high, constant-angle (120°) arch dam. If the canyon is 60 ft wide at the top and the design freeboard is 6 ft (ie., the water level is 6 ft below the top of the dam), determine the abutment reactions at dam heights of 25, 50, and 75 ft above the bottom of the canyon.

Answer 1

$F_i=\rho g V_i=\rho g\sqrt{a^2+b^2}lh_i\sin\alpha,$

$F_1=33~kN,$

$F_2=67~kN,$

$F_3=100~kN.$