Concept explainers
A 150-lb rigid bar AB. with friction less rollers al each end. is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A.
(a) Find reactions at supports A and B.
(b) Find the force in the cable.
(a)
Reactions at supports A, and B.
Answer to Problem 1.3.27P
The correct answers are:
Explanation of Solution
Given Information:
You have a 150 lb rigid bar AB, with frictionless rollers at each end held with cables as shown in the figure below:
Calculation:
Consider the following diagram,
Calculate the position of D as,
Calculate the position of B as,
Calculate the position of C as,
Calculate the position of center of gravity as,
Calculate angle
Calculate the angle
Consider the following free body diagram,
Member AB :
Take equilibrium of moments about point A,
Take equilibrium of forces in
Take equilibrium of forces in
Analyze Joint C :
Consider free body diagram at C.
Take equilibrium of forces in
Take equilibrium of forces in
Analyze Joint D :
Consider free body diagram at D.
Take equilibrium of forces in
Take equilibrium of forces in
Also since the same cable rolls, hence
Also take equilibrium of the forces along AD for member AB as,
Now, solve equations (1-9) to get
Conclusion:
Thus the reaction forces are:
(b)
Reaction force in cable.
Answer to Problem 1.3.27P
The tension force in cable is 71.6 lb.
Explanation of Solution
Given Information:
You have a 150 lb rigid bar AB, with frictionless rollers at each end held with cables as shown in figure below,
Calculation:
Consider the following diagram,
Calculate position of D as,
Calculate position of B as,
Calculate position of C as,
Calculate position of center of gravity as,
Calculate angle
Calculate angle
Consider the following free body diagram,
Member AB :
Take equilibrium of moments about point A,
Take equilibrium of forces in
Take equilibrium of forces in
Analyze Joint C :
Consider free body diagram at C.
Take equilibrium of forces in
Take equilibrium of forces in
Analyze Joint D :
Consider free body diagram at D.
Take equilibrium of forces in
Take equilibrium of forces in
Also since the same cable rolls, hence
Also take equilibrium of the forces along AD for member AB as,
Now, solve equations (1-9) to get
Conclusion:
The tension force in cable is 71.6 lb.
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