Concept explainers
Space Frame ABC is clamped at A, except it is free to rotate at A about the x and y axes. Cables DC and EC support the frame at C. Force Py= - 50 lb is applied at the mid-span of AS, and a concentrated moment Mx= -20 in-lb acts at joint B.
(a) Find reactions at support A.
(b) Find cable tension Forces.
(a)
Reactions at support A.
Answer to Problem 1.3.31P
The correct answers are:
Explanation of Solution
Given Information:
You have following figure with all relevant information,
and
Draw free body diagram of joints and use equilibrium of forces to determine the unknowns.
Calculation:
Draw free body diagram as shown in the following figure,
Analyze the free body diagram of member ABC.
The forces and corresponding position vectors are,
Force | Position vector |
|
|
|
|
|
|
|
|
Take equilibrium of forces vector form,
The vector equation yields three equations in components form as below,
Now take equilibrium of moments about A in vector form as,
Evaluate the cross products to get,
The vector equation yields three equations in components form as below,
Solve equations (1-6) to get,
Conclusion:
Therefore the forces and moments are:
(a)
Cable forces.
Answer to Problem 1.3.31P
The correct answers are:
Explanation of Solution
Given Information:
You have following figure with all relevant information,
and
Draw free body diagram of joints and use equilibrium of forces to determine the unknowns.
Calculation:
Draw free body diagram as shown in the following figure,
Analyze the free body diagram of member ABC.
The forces and corresponding position vectors are,
Force | Position vector |
|
|
|
|
|
|
|
|
Take equilibrium of forces vector form,
The vector equation yields three equations in components form as below,
Now take equilibrium of moments about A in vector form as,
Evaluate the cross products to get,
The vector equation yields three equations in components form as below,
Solve equations (1-6) to get,
Conclusion:
Therefore cable forces are:
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