Two cranes are attempting to pull a precast pile from an excavation. The tension

Question

Two cranes are attempting to pull a precast pile from an excavation. The tension in cable AB attached to the ring at B is 3 kN. Determine by trigonometry:
a) the magnitude and direction of the smallest tension force in cable BC attached to the second crane such that the resultant R of the two forces applied
to the pile at B is vertical
b) the corresponding magnitude of R

Two cranes are attempting to pull a precast pile from an excavation cable AB attached to the ring at B is 3 kN. Determine by trigonomet rection of the smallest tension force in cableiB the magnitude and di the second crane such that the resultant R of the two force applied t is vertical. the corresponding magnitude of R 30°

Explanation / Answer

Let do force balance in X dir, Y dir at point B

3 cos(30) = T cos(alpha)

=> T = 3 cos(30)/cos(alpha)

for min T condition

cos(alpha) = 1

=> T = 3cos(30) = 2.59 kN

R = Tsin(90) + 3sin(30) = 2.59 + 3/2 = 4.09 in vertical direction

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