Concept explainers
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
The vertical force
Answer to Problem 2.112P
The vertical force
Explanation of Solution
Free body diagram at
Here,
The tension in the cable
The sketch of plate supported by three cables is shown in figure2.
Let
Let
Write the equation of vector distance
Here,
Write the vector distance of the cable
Here,
Write the vector distance of the cable
Here,
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of force exerting at point
Here,
Write the equilibrium condition for the forces at
Here, F is the force
The above equation implies that at equilibrium, total force acting on the cable at
Refer figure 2 and write the equation of equilibrium of forces at
Conclusion:
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Substitute
Substitute
(VII) to get
Substitute
Substitute
Substitute
Substitute
Since total force is zero. Equate force along each direction as zero.
Substitute
Multiply equation (XV) by
Substitute
Substitute
Therefore, the force
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Chapter 2 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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