6.119 through 6.121 Each of the frames shown consists of two L-shaped members connected by two rigid links. For each frame, determine the reactions at the supports and indicate whether the frame is rigid.
Fig. P6.121
The reactions at the frame and the rigidness of the frame.
Answer to Problem 6.121P
The reactions at the frame for figure (a) is
Explanation of Solution
The following figure gives the free body diagram of the first part of the member in figure P6.121(a).
Write the equation to find the moment of force.
Here,
Write the equation to find the total moment about the point
Write the equations for equilibrium for the free body diagram in figure 1.
Here,
The following figure gives the free body diagram of the second part of the member in figure P6.121(a).
Write the equations for equilibrium for the free body diagram in figure 2.
Here,
The following figure gives the free body diagram of the first part of the member in figure P6.119(b).
Write the equations for equilibrium for the free body diagram in figure 3.
Here,
The following figure gives the free body diagram of the second part of the member in figure P6.119(b).
Write the equations for equilibrium for the free body diagram in figure 4.
Here,
The following figure gives the free body diagram of the member in figure P6.119(c).
Write the equations for equilibrium for the free body diagram in figure 5.
Here,
The following figure gives the free body diagram of right part of the member in figure P6.119(c).
Write the equations for equilibrium for the free body diagram in figure 6.
Here,
Write the expression to find the magnitude of the vector from its components.
Here,
Write the equation to find the angle of orientation of the vector
Conclusion:
Solve equation (I) using figure 1.
Rewrite the above equation.
Solve equation (III) using figure 1.
Rewrite the above equation.
Solve equation (IV) using figure 2.
Rewrite the above equation.
Solve equation (V) using figure 2.
Substitute
Solve equation (VI) using figure 2.
Substitute
Rewrite equation (XIV) in terms of the vector
Substitute
Rewrite equation (XV) in terms of the vector
Substitute
Rewrite equation (XIV) in terms of the vector
Substitute
Solve equation (VII) using figure 3.
Rewrite the above equation.
Solve equation (VIII) using figure 4.
Rewrite the above equation.
Solve the conditions obtained from figure 3 and 4.
Solve equation (IX) using figure 5.
Rewrite the above equation to find
Solve equation (X) using figure 5.
Substitute
Solve equation (XI) using figure 5.
Substitute
Solve equation (XII) using figure 6.
Substitute
Solve equation (XII) to the right using figure 6.
Substitute
Solve equation (XII) upwards using figure 6.
Substitute
Therefore, the reactions at the frame for figure (a) is
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Chapter 6 Solutions
Vector Mechanics for Engineers: Statics
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