Concept explainers
Knowing that dc = 9 ft, determine (a) the distances dB and dD (b) the reaction at E.
Fig. P7.99 and P7.100
(a)
The distances
Answer to Problem 7.99P
The distance
Explanation of Solution
Refer Fig P7.99.
The figure 1 below shows the free body diagram of the portion ABC.
The total moment about the point C is zero.
Refer the free body diagram and write the equation for the moment about point C.
Here
Re-write the above equation to get an expression for
The figure 2 below shows the free body diagram of the entire cable.
The moment about point E is zero.
Refer the free body diagram of the entire cable and write the equation of the moment about point E.
Simplify the above equation.
Since the system is in equilibrium the total vertical and horizontal components will be zero.
Refer figure 2 and write the equation for total horizontal force.
Here
Refer figure 2 and write the equation for the total vertical force.
The figure 4 below shows the free body diagram of the portion AB.
The moment about point B is zero.
Refer figure 4 and write the equation for the moment about point B.
The figure 5 below shows the free body diagram of the portion DE.
Refer figure 5 and write the formula for the distance
Here
Refer figure 5 and write the formula for distance
Conclusion:
Substitute equation (I) in equation (II).
Substitute
Substitute
Substitute
Substitute
Calculate
Substitute
The distance
(b)
The reaction at point E.
Answer to Problem 7.99P
The reaction at point E is
Explanation of Solution
Refer Fig P7.99.
The figure 1 below shows the free body diagram of the portion ABC.
The total moment about the point C is zero.
Refer the free body diagram and write the equation for the moment about point C.
Here
Re-write the above equation to get an expression for
The figure 2 below shows the free body diagram of the entire cable.
The moment about point E is zero.
Refer the free body diagram of the entire cable and write the equation of the moment about point E.
Simplify the above equation.
Since the system is in equilibrium the total vertical and horizontal components will be zero.
Refer figure 2 and write the equation for total horizontal force.
Here
Refer figure 2 and write the equation for the total vertical force.
Write the formula for the magnitude of the reaction at point E.
Here
Write the formula for the angle made by the reaction at point E with horizontal.
Here
Conclusion:
Substitute equation (I) in equation (II).
Substitute
Substitute
Substitute
Substitute
Substitute
Thus the reaction at point E is
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