Knowing that P = 25 lb and Q = 55 lb, determine the components of the forces exerted (a) on member BCDF at C and D, (b) on member ACEG at E.
(a)
The components of the forces exerted on member BCDF at C and D.
Answer to Problem 6.104P
The x component of force at D,
Explanation of Solution
Figure 1 is the free body diagram of the entire frame of the system.
Write the equation to find the sum of the moments about point E.
Here,
Write the equation to find the sum of x components of force.
Here,
Consider the member BCDF of the system.
Figure 2 shown below is the free body diagram of member BCDF.
Write the equation to find the sum of x component of force.
Here,
Write the equation to find the sum of moments at D.
Here,
Write the equation to find the sum of y components of force.
Here,
Consider the free body diagram of member ACEG. The free body diagram of ACEG is given in figure 3.
Write the equation to find the sum of y component of force.
Here,
Conclusion:
Solve equation (I) to get the value of
Substitute
Solve equation (III) to get the value of
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, The x component of force at D,
(b)
The component of force on member ACEG at E.
Answer to Problem 6.104P
The x component of force at E,
Explanation of Solution
Rewrite equation (II) to find the x component of force at E.
Here,
Rewrite equation (VI) to get the y component of force at E.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, The x component of force at E,
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Chapter 6 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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