Question

After an unfortunate accident at a local warehouse you have been contracted to determine the cause. A jib crane collapsed and injured a worker. An image of this type of crane is shown in the figure below. The horizontal steel beam had a mass of 95.30 kg per meter of length and the tension in the cable was T = 1.100 × 104 N. The crane was rated for a maximum load of 454.5 kg. If d = 6.160 m, s = 0.594 m, x = 1.250 m and h = 1.980 m, what was the magnitude of WL (the load on the crane) before the collapse? What was the magnitude of force at the attachment point P? The acceleration due to gravity is g = 9.810 m/s2

What is WL and Fp?

Answer 1

Sum the moments about P:
0 = T(d - s)sinΘ - W(d - x) - F(d/2)
Θ = arctan(h/(d-s)) = arctan(1.98 / 5.566) = 19.58⁰
where F is the weight of the beam.
0 = 11000N*5.566m*sin19.58º - W*4.91m - 95.3kg/m*6.16m*9.8m/s²*(6.16m/2)

0=20518.22-W*4.91-17737.53
4.43W = 2780.68 N
W = 566.33 N ← load

(b) sum the vertical forces:
Fv + TsinΘ - W - 95.3kg/m*6.16m*9.8m/s² = 0
Fv + 11000N*sin19.58 - 566.33N - 5759N = 0
Fv = 2639 N ← vertical force at P

sum the horizontal forces:
Fh - TcosΘ = 0
Fh - 11000N*cos19.58º = 0
Fh = 10364 N ← horizontal force at P

mag P = √(10364² + 2639²) N = 10694.6 N ← total reaction at P

This is approx value. But method is correct