### A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D . If the tension in wire AC is 590 lb, determine the vertical force P exerted by the tower on the pin at A.

1 Answers

Step 1

we solve this question by resolution of component of force in 3D ( 3 dimensions).

given

dimensions of all 3 wires from the origin O is given.

Step 2

Similarly dB=105 ft; dD=126 ft

Similarly, for pin at point B

and

For pin at point D

Boundary Condition- **Resultant Sum of force in x and y direction is 0**

**this above constraint is used to find FB and FD**

(60/118)590+(-20/105)FB+(-20/126)FD=0Â Â

& (18/118)590+(25/105)FB+(-74/126)FD=0

i.e (20/105)FB+(20/126)FD=(60/118)590

& (25/105)FB+(-74/126)FD=-(18/118)590

solving above two equations we get

FB=1081.82 lb

FD=591.82 lb

Step 3

we need to find vertical force P exerted by the tower on the pin at A

=Fcy+FBY+FDY

=2000 lb

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