Concept explainers
6.70 through 6.74 classify as determinate or indeterminate. (All members act both in tension and in compression.)
Fig. P6.74
(a)
Classify the given structure as completely, partially, or improperly constrained and if completely constrained, further classify as determinate or indeterminate.
Answer to Problem 6.74P
The given structure is completely constrained and determinate.
Explanation of Solution
The structure is shown in Fig. P6.74 (a). The arrangement can be redrawn by labeling different points in the truss and is given in Figure 1.
The free-body diagram of the section
Write the condition for a truss to be completely constrained.
Here,
Write the condition for a truss to be partially constrained.
Write the expression for a truss to be indeterminate.
Write the expression for the condition for equilibrium.
Here,
Conclusion:
For the given truss,
Compute
Compute
So, for the given system,
Apply the condition for equilibrium in equation (IV) about point
Apply the condition for equilibrium in equation (V) about various points of the structure in the free-body diagrams given in Figure 2.
So, the truss
Therefore, the given structure is completely constrained and determinate.
(b)
Classify the given structure as completely, partially, or improperly constrained and if completely constrained, further classify as determinate or indeterminate.
Answer to Problem 6.74P
The given structure is partially constrained.
Explanation of Solution
The structure is shown in Fig. P6.74 (b). The arrangement can be redrawn by labeling different points in the truss and is given in Figure 3.
From equations (I), (II), and (III), the conditions for the state of constrain of the structure is as follows,
Conclusion:
For the given truss,
Compute
Compute
So, for the given system,
Therefore, the given structure is partially constrained.
(c)
Classify the given structure as completely, partially, or improperly constrained and if completely constrained, further classify as determinate or indeterminate.
Answer to Problem 6.74P
The given structure is completely constrained and indeterminate.
Explanation of Solution
The structure is shown in Fig. P6.74 (c). The arrangement can be redrawn by labeling different points in the truss and is given in Figure 4.
From equations (I), (II), and (III), the conditions for the state of constrain of the structure is as follows,
Conclusion:
For the given truss,
Compute
Compute
So, for the given system,
Therefore, the given structure is completely constrained and indeterminate.
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