Concept explainers
The 48-lb load is removed and a 288-lb · in. clockwise couple is applied successively at A, D, and E. Determine the components of the reactions at Band F if the couple is applied (a) at A, (b) at D, (c) at E.
(a)
The component of reactions at point B and F when the couple is applied at A.
Answer to Problem 6.89P
The x component of the reaction force at point B is
The x component of force applied is
Explanation of Solution
The free body diagram of the problem 6.89P is shown in figure 1 below.
A clockwise couple is applied at A,D, and E. Due to this couple, resultant reaction forces are experienced in points A, D, and E.
First consider the couple applied at point A.
Write the equation to find the sum of moments of force at point F.
Here,
Since the sum of moments of force at a point of a system in equilibrium is zero, rewrite the equation for the sum of moments.
Write the equation to find the x components of force.
Here,
Since the sum of forces at a point is zero in equilibrium, the above equation is rewritten.
Substitute
Write the equation to find the sum of y component of forces.
Here,
No force is applied in the y direction, therefore there will be no reaction also.
Consider figure 2.
Write the equation to find the y component of reaction force at point B.
Here,
Rewrite equation (I) to find the value of
Conclusion:
Observe figure 2.
Substitute
The y component of reaction force at point B is having a magnitude of
Substitute
The y component of the force applied at point b is
Therefore, the x component of the reaction force at point B is
The x component of force applied is
(b)
The component of reactions at point B and F when the couple is applied at D.
Answer to Problem 6.89P
The x component of the reaction force at point B is
The x component of force applied is
Explanation of Solution
The free body diagram of the problem 6.89P is shown in figure 1.
A clockwise couple is applied at A,D, and E. Due to this couple, resultant reaction forces are experienced in points A, D, and E.
Consider the couple applied at point D.
Write the equation to find the sum of moments of force at point F.
Here,
Since the sum of moments of force at a point of a system in equilibrium is zero, rewrite the equation for the sum of moments.
Write the equation to find the x components of force.
Here,
Since the sum of forces at a point is zero in equilibrium, the above equation is rewritten.
Substitute
Write the equation to find the sum of y component of forces.
Here,
No force is applied in the y direction, therefore there will be no reaction also.
Consider figure 3.
Write the equation to find the y component of reaction force at point B.
Here,
Rewrite equation (I) to find the value of
Conclusion:
Observe figure 3.
Substitute
The y component of force at point B is having a magnitude of
Substitute
The y component of the reaction force applied at point B is
Therefore, the x component of the reaction force at point B is
The x component of force applied is
(c)
The component of reactions at point B and F when the couple is applied at E.
Answer to Problem 6.89P
The x component of the reaction force at point B is
The x component of force applied is
Explanation of Solution
The free body diagram of the problem 6.89P is shown in figure 1.
A clockwise couple is applied at A,D, and E. Due to this couple, resultant reaction forces are experienced in points A, D, and E.
First consider the couple applied at point E.
Write the equation to find the sum of moments of force at point F.
Here,
Since the sum of moments of force at a point of a system in equilibrium is zero, rewrite the equation for the sum of moments.
Write the equation to find the x components of force.
Here,
Since the sum of forces at a point is zero in equilibrium, the above equation is rewritten.
Substitute
Write the equation to find the sum of y component of forces.
Here,
No force is applied in the y direction, therefore there will be no reaction also.
Consider figure 4.
Write the equation to find the y component of reaction force at point B.
Here,
Rewrite equation (VII) to find the value of
Conclusion:
Observe figure 4.
Substitute
The y component of reaction force at point B is having a magnitude of
Substitute
The y component of the force applied at point b is
Therefore, the x component of the reaction force at point B is
The x component of force applied is
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Chapter 6 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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