Concept explainers
3–1* to 3–4 Sketch a free-body diagram of each element in the figure. Compute the magnitude and direction of each force using an algebraic or
The free body diagram of each element of the given figure.
The magnitude and direction of each force.
Answer to Problem 1P
The free body diagram of element OB is shown in Figure (1).
The free body diagram of element BC is shown in Figure (2).
The free body diagram of pin joint C is shown in Figure (3).
The free body diagram of pin joint O is shown in Figure (4).
The magnitude of force at O is
The magnitude of force at B is
The magnitude of force at C is
Explanation of Solution
Figure (1) shows the free body diagram of the element OB.
Figure (1)
Write the net moment at point O on the link OB.
Here, perpendicular distance between point O and
Write the net reaction force in the vertical direction on the link OB.
Here, force acting at point O is
Write the net reaction force in the horizontal direction on the link OB.
Here, force acting at point O is
Figure (2) shows the free body diagram of element BC.
Figure (2)
Write the net reaction force in the horizontal direction on the link BC.
Here, force acting at point B is
Write the net reaction force in the vertical direction on the link OB.
Here, force acting at point C is
Figure (3) shows the free body diagram of pin joint C.
Figure (3)
Write the expression of net reaction force at pin joint C in horizontal direction.
Here, force acting at point C in the horizontal direction is
The force acting in the vertical direction at point C is balanced by the reaction force by link BC at point C.
Figure (4) shows the free body diagram of the pivot point O.
Figure (4)
Write the expression of net reaction force at pin joint O in horizontal direction.
Here, force acting at point O in the horizontal direction is
The force acting in the vertical direction at point O is balanced by the reaction force by link OB at point O.
Conclusion
Substitute
Thus, the vertical component of the force at point
Substitute
Thus, the vertical component of the force at point
Substitute
Thus, the vertical component of the force at point
Substitute
Thus, the horizontal component of the force at point
Substitute
Thus, the horizontal component of the force at point
Thus, the magnitude of force at O is
Thus, the magnitude of force at B is
Thus, the magnitude of force at C is
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