
(a)
Find whether the plate is completely, partially, or improperly constrained.
(a)

Answer to Problem 4.59P
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 size of the identical plates is
Number of plates is 8.
The mass of each plate is
Calculation:
Find the weight (W) of the plate using the relation.
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity as
Substitute 40 kg for m and
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 non-concurrent and non-parallel force system.
The plate figure 2 is
Figure 3:
Show the free-body diagram of the Figure 3.
The four 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 three reactions in the plate behave like concurrent force system.
The plate figure 4 is
Figure 5:
Show the free-body diagram of the Figure 5.
The two 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 three reactions in the plate behave like non-concurrent and non-parallel force system.
The plate figure 6 is
Figure 7:
Show the free-body diagram of the Figure 7.
The two reactions in the plate behave like concurrent 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.
(b)

Answer to Problem 4.59P
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.
The reactions in figure 2 is
Refer Figure 3:
The equilibrium equations are;
The equilibrium equations are not enough to determine the unknown reactions.
The reactions in figure 3 is
Refer Figure 4:
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 4 is
Refer Figure 5:
The equilibrium equations are;
The equilibrium equations are enough to determine the unknown reactions.
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.
But the plate is improperly constrained and the plate is not in equilibrium.
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.
(c)

Answer to Problem 4.59P
The reactions in the plate 1 are
The plate 1 is in
The reactions in the plate 2 are
The plate 2 is in
The reactions in the plate 3 are
The plate 3 is in
The plate 4 is in
The reactions in the plate 5 are
The plate 5 is in
The reactions in the plate 6 are
The plate 6 is in
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.
Therefore, the reactions in the plate 1 are
The plate 1 is in
Refer Figure 2:
The equilibrium equations are;
Take moment about point B.
Resolve the horizontal component of forces.
Resolve the vertical component of forces.
Therefore, the reactions in the plate 2 are
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;
The moment about point D is not equal to zero.
The plate 4 is in
Refer Figure 5:
The equilibrium equations are;
Take moment about point A.
Resolve the vertical component of forces.
Therefore, the reactions in the plate 5 are
The plate 5 is in
Refer Figure 6:
The equilibrium equations are;
Take moment about point A.
Resolve the vertical component of forces.
Resolve the horizontal component of forces.
Find the resultant force at D;
Find the angle
Therefore, the reactions in the plate 6 are
The plate 6 is in
Refer Figure 7:
The equilibrium equations are;
The plate 7 is in
Refer Figure 8:
The equilibrium equations are;
Take moment about point D.
Resolve the vertical component of forces.
Resolve the horizontal component of forces.
Therefore, the reactions in the plate 8 are
The plate 8 is in
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Chapter 4 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics
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