Concept explainers
A truss can be supported in the eight different ways shown A connections consist of smooth pins, rollers, or short links. For case, answer the questions listed in Prob. 4.59, and, wherever possible, compute the reactions, assuming that the magnitude force P is 12 kips.
Fig. P4.60
(a)
Find whether the plate is completely, partially, or improperly constrained.
Answer to Problem 4.60P
The plate in figure 1 is
The plate figure 2 is
The plate figure 3 is
The plate figure 4 is
The plate figure 5 is
The plate figure 6 is
The plate figure 7 is
The plate figure 8 is
Explanation of Solution
Given information:
The magnitude of the force P is 12 kips.
Calculation:
Figure 1:
Show the free-body diagram of the Figure 1.
The three reactions in the plate behave like non-concurrent and non-parallel force system.
The plate in figure 1 is
Figure 2:
Show the free-body diagram of the Figure 2.
The three reactions in the plate behave like concurrent force system.
The plate figure 2 is
Figure 3:
Show the free-body diagram of the Figure 3.
The three reactions in the plate behave like non-concurrent and non-parallel force system.
The plate figure 3 is
Figure 4:
Show the free-body diagram of the Figure 4.
The four reactions in the plate behave like non-concurrent and non-parallel force system.
The plate figure 4 is
Figure 5:
Show the free-body diagram of the Figure 5.
The four reactions in the plate behave like concurrent force system.
The plate figure 5 is
Figure 6:
Show the free-body diagram of the Figure 6.
The two reactions in the plate behave like concurrent force system.
The plate figure 6 is
Figure 7:
Show the free-body diagram of the Figure 7.
The three reactions in the plate behave like non-concurrent and non-parallel force system.
The plate figure 7 is
Figure 8:
Show the free-body diagram of the Figure 8.
The four reactions in the plate behave like non-concurrent and non-parallel force system.
The plate figure 8 is
(b)
Find whether the reactions are statically determinate or indeterminate.
Answer to Problem 4.60P
The reactions in figure 1 is
The reactions in figure 2 is
The reactions in figure 3 is
The reactions in figure 4 is
The reactions in figure 5 is
The reactions in figure 6 is
The reactions in figure 7 is
The reactions in figure 8 is
Explanation of Solution
Refer Figure 1:
The equilibrium equations are;
The equilibrium equations are enough to determine the unknown reactions.
The reactions in figure 1 is
Refer Figure 2:
The equilibrium equations are;
The equilibrium equations are enough to determine the unknown reactions.
But the plate is improperly constrained and the plate is not in equilibrium.
The reactions in figure 2 is
Refer Figure 3:
The equilibrium equations are;
The equilibrium equations are enough to determine the unknown reactions.
The reactions in figure 3 is
Refer Figure 4:
The equilibrium equations are;
The equilibrium equations are not enough to determine the unknown reactions.
The reactions in figure 4 is
Refer Figure 5:
The equilibrium equations are;
The equilibrium equations are enough to determine the unknown reactions.
But the plate is improperly constrained and the plate is not in equilibrium.
The reactions in figure 5 is
Refer Figure 6:
The equilibrium equations are;
The equilibrium equations are enough to determine the unknown reactions.
The reactions in figure 6 is
Refer Figure 7:
The equilibrium equations are;
The equilibrium equations are enough to determine the unknown reactions.
The reactions in figure 7 is
Refer Figure 8:
The equilibrium equations are;
The equilibrium equations are not enough to determine the unknown reactions.
The reactions in figure 8 is
(c)
Find whether the equilibrium of the plate is maintained.
Answer to Problem 4.60P
The reactions in the plate 1 are
The plate 1 is in
The plate 2 is in
The reactions in the plate 3 are
The plate 3 is in
The reactions in the plate 4 are
The plate 4 is in
The plate 5 is in
The reactions in the plate 6 are
The plate 6 is in
The reactions in the plate 7 are
The plate 7 is in
The reactions in the plate 8 are
The plate 8 is in
Explanation of Solution
Refer Figure 1:
The equilibrium equations are;
Take moment about point A.
Resolve the horizontal component of forces.
Resolve the vertical component of forces.
Find the resultant force at A;
Find the angle
Therefore, the reactions in the plate 1 are
The plate 1 is in
Refer Figure 2:
The equilibrium equations are;
The moment about point A is not equal to zero.
The plate 2 is in
Refer Figure 3:
The equilibrium equations are;
Take moment about point A.
Resolve the horizontal component of forces.
Resolve the vertical component of forces.
Therefore, the reactions in the plate 3 are
The plate 3 is in
Refer Figure 4:
The equilibrium equations are;
Take moment about point A.
Resolve the horizontal component of forces.
Resolve the vertical component of forces.
Therefore, the reactions in the plate 4 are
The plate 4 is in
Refer Figure 5:
The equilibrium equations are;
The moment about point A is not equal to zero.
The plate 5 is in
Refer Figure 6:
The equilibrium equations are;
Take moment about point A.
Resolve the vertical component of forces.
Therefore, the reactions in the plate 6 are
The plate 6 is in
Refer Figure 7:
The equilibrium equations are;
Find the angle
Take moment about point A.
Resolve the horizontal component of forces.
Resolve the vertical component of forces.
Therefore, the reactions in the plate 7 are
The plate 7 is in
Refer Figure 8:
The equilibrium equations are;
Take moment about point C.
Therefore, the reactions in the plate 8 are
The plate 8 is in
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