Concept explainers
Two shafts AC and CF, which lie in the vertical xy plane, are connected by a universal joint at C. The bearings at B and D do not exert any axial force. A couple with a magnitude of 500 lb·in. (clockwise when viewed from the positive x axis) is applied to shaft CF at F. At a time when the arm of the crosspiece attached to shaft CF is horizontal, determine (a) the magnitude of the couple that must be applied to shaft AC at A to maintain equilibrium, (b) the reactions at B, D, and E. (Hint: The sum of the couples exerted on the crosspiece must be zero.)
Fig. P6.161
(a)
The magnitude of the couple that must be applied to shaft
Answer to Problem 6.161P
The magnitude of the couple that must be applied to shaft
Explanation of Solution
Take all vectors along the
The free body diagram of the shaft
Here,
At equilibrium total moment will be zero.
Write the expression for the equilibrium moment about
Here,
The moment along the
From free body diagram in figure1, write the complete equilibrium expression of moment about
Here,
The free body diagram of the shaft
Here,
Write the expression for the equilibrium moment about
Here,
From free body diagram in figure2, write the complete equilibrium expression of moment about
Here,
Calculation:
Rearrange equation (II) to get
Equate coefficient of
Therefore, the magnitude of the couple that must be applied to shaft
(b)
The reaction at
Answer to Problem 6.161P
The reaction at
Explanation of Solution
From free body diagram in figure2, write the complete equilibrium expression of moment about
Here,
Since the net force at the shaft
Using free body diagram in figure1, apply the equilibrium condition for moment about
Here,
From figure1, write the complete expression of moment
Since net force at shaft
Calculation:
Equate coefficient of
Equate coefficient of
Therefore
Substitute
Equate coefficient of
Equate coefficient of
Equate coefficient of
Therefore, net reaction at
Equate coefficient of
Substitute
Therefore, total reaction at
Therefore, the reaction at
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Chapter 6 Solutions
EBK VECTOR MECHANICS FOR ENGINEERS: STA
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