Concept explainers
Classify each of the structures shown as completely, partially, or improperly constrained; if completely constrained, further classify as determinate or indeterminate. (All members can act both in tension and in compression.)
(a)
Classify the given structure as completely, partially, or improperly constrained and if completely constrained, further classify as determinate or indeterminate.
Answer to Problem 6.70P
The given structure is completely constrained and determinate.
Explanation of Solution
The structure is shown in Fig. P6.70 (a). The free-body diagram of the truss is given in Figure 1.
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 various points of the structure in the free-body diagrams
Apply the condition for equilibrium in equation (V) about various points of the structure in the free-body diagrams
Since each section is a simple truss with reactions determined, the given structure is completely constrained and determinate.
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 6.70P
The given structure is partially constrained.
Explanation of Solution
The structure is shown in Fig. P6.70 (b). It is a non-simple truss.
From equations (I), and (II), 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 6.70P
The given structure is improperly constrained and indeterminate.
Explanation of Solution
The structure is shown in Fig. P6.70 (c). The free-body diagram of the truss is given in Figure 2.
From equations (I), and (II), the conditions for the state of constrain of the structure is as follows,
Conclusion:
For the given truss,
Compute
Compute
It is clear that for the given system, the condition in equation (I) is satisfied, but the horizontal reaction forces
Therefore, the given structure is improperly constrained and indeterminate.
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Chapter 6 Solutions
EBK VECTOR MECHANICS FOR ENGINEERS: STA
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