Engineering Statics

A-13


The end of the transmission cable AE is attached to the pole, AB, which is strengthened by the guy wires AC and AD. Knowing that the tension in cable AC is 180 pounds and the resultant of the forces exerted at point A by wires AC and AE must be limited to the xy plane, determine the tension in wire AD. Determine the magnitude and direction the resultant makes with the x, y, and z axes.

A free body diagram. Notice that the origin is at point A.
All of the forces we are interested pass through this point.
We write ACxz in terms of what we know about AC, and then solve for it numerically.
Using ACxz we then solve for ACx.
Using AC we solve for ACy. Notice that the result is negative, indicating down.
Using the calculation of AC in the xz plane, we solve for AC in the z-direction.
Since the sum of forces in the z-direction must be zero, ADz must be 30.7 pounds.
Knowing ADz, we can solve for ADxz, or AD in the xz plane.
Knowing ADxz, we can solve for ADx, or the x-component of AD.
We can now easily solve for the tension in wire AD.
We use trig to solve for the y-component of AD, or ADy.
Summing the x and y-components of the two cables...
Simplifying using arithmetic...
The θx is the arc-cosine of the x-component divided by the magnitude.
The θy is the arc-cosine of the y-component divided by the magnitude.
Because the resultant has no z component, θz is 90°.