Question

The planning commission of the college is proposing to erect the iron gate shown. Given the architectural drawing, calculate to the nearest foot the total length of I-beam needed for the vertical stringers, assuming that both arches are parabolic and that the stringers are 10 ft. apart.

16 ft 16 ft -80 ft-

Answer 1

Equation of Parabola: y = 4 hx/L^2 (L - X) For lower arch Y_1 = 4 times 16 x/80^2 (80 - X) For arch at higher level Y_2 = 4 times 32 X/80^2 (80 - X) Delta h = Y_2 - Y_1 = {4 X/80^2 (80 - X)} times (32 - 16) Delta h = 0.01 X (80 - X) at 10 ft: Delta h = 0 01 times 10 (80 - 10) = 7 ft at 20 ft: delta h = 0 01 times 20 (80 - 20) = 12 ft at 30 ft: delta h = 0 01 times 30 (80 - 30) = 15 ft at 40 ft: Delta h = 0 01 times 40 (80 - 40) = 16 ft at 50 ft: delta h = 0 01 times 50 (80 - 50) = 15 ft at 60 ft: delta h = 0 01 times 60 (80 - 60) = 12 ft at 70 ft: delta h = 0 01 times 70 (80 - 70) = 7 ft