Vector Mechanics for Engineers: Statics and Dynamics
Vector Mechanics for Engineers: Statics and Dynamics
12th Edition
ISBN: 9781259638091
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Textbook Question
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Chapter 4.1, Problem 4.60P

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.

Chapter 4.1, Problem 4.60P, A truss can be supported in the eight different ways shown A connections consist of smooth pins,

Fig. P4.60

(a)

Expert Solution
Check Mark
To determine

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

Answer to Problem 4.60P

The plate in figure 1 is completelyconstrained_.

The plate figure 2 is improperlyconstrained_.

The plate figure 3 is completelyconstrained_.

The plate figure 4 is completelyconstrained_.

The plate figure 5 is improperlyconstrained_.

The plate figure 6 is partiallyconstrained_.

The plate figure 7 is completelyconstrained_.

The plate figure 8 is completelyconstrained_.

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.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  1

The three reactions in the plate behave like non-concurrent and non-parallel force system.

The plate in figure 1 is completelyconstrained_.

Figure 2:

Show the free-body diagram of the Figure 2.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  2

The three reactions in the plate behave like concurrent force system.

The plate figure 2 is improperlyconstrained_.

Figure 3:

Show the free-body diagram of the Figure 3.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  3

The three reactions in the plate behave like non-concurrent and non-parallel force system.

The plate figure 3 is completelyconstrained_.

Figure 4:

Show the free-body diagram of the Figure 4.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  4

The four reactions in the plate behave like non-concurrent and non-parallel force system.

The plate figure 4 is completelyconstrained_.

Figure 5:

Show the free-body diagram of the Figure 5.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  5

The four reactions in the plate behave like concurrent force system.

The plate figure 5 is improperlyconstrained_.

Figure 6:

Show the free-body diagram of the Figure 6.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  6

The two reactions in the plate behave like concurrent force system.

The plate figure 6 is partiallyconstrained_.

Figure 7:

Show the free-body diagram of the Figure 7.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  7

The three reactions in the plate behave like non-concurrent and non-parallel force system.

The plate figure 7 is completelyconstrained_.

Figure 8:

Show the free-body diagram of the Figure 8.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 4.1, Problem 4.60P , additional homework tip  8

The four reactions in the plate behave like non-concurrent and non-parallel force system.

The plate figure 8 is completelyconstrained_.

(b)

Expert Solution
Check Mark
To determine

Find whether the reactions are statically determinate or indeterminate.

Answer to Problem 4.60P

The reactions in figure 1 is determinate_.

The reactions in figure 2 is indeterminate_.

The reactions in figure 3 is determinate_.

The reactions in figure 4 is indeterminate_.

The reactions in figure 5 is indeterminate_.

The reactions in figure 6 is determinate_.

The reactions in figure 7 is determinate_.

The reactions in figure 8 is indeterminate_.

Explanation of Solution

Refer Figure 1:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknownsequilibriumequations.

The equilibrium equations are enough to determine the unknown reactions.

The reactions in figure 1 is determinate_.

Refer Figure 2:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknownsequilibriumequations.

The equilibrium equations are enough to determine the unknown reactions.

But the plate is improperly constrained and the plate is not in equilibrium. (MA0)

The reactions in figure 2 is indeterminate_.

Refer Figure 3:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknownsequilibriumequations.

The equilibrium equations are enough to determine the unknown reactions.

The reactions in figure 3 is determinate_.

Refer Figure 4:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknowns>equilibriumequations.

The equilibrium equations are not enough to determine the unknown reactions.

The reactions in figure 4 is indeterminate_.

Refer Figure 5:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknownsequilibriumequations.

The equilibrium equations are enough to determine the unknown reactions.

But the plate is improperly constrained and the plate is not in equilibrium. (MA0)

The reactions in figure 5 is indeterminate_.

Refer Figure 6:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknownsequilibriumequations.

The equilibrium equations are enough to determine the unknown reactions.

The reactions in figure 6 is determinate_.

Refer Figure 7:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknownsequilibriumequations.

The equilibrium equations are enough to determine the unknown reactions.

The reactions in figure 7 is determinate_.

Refer Figure 8:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

numberofunknowns>equilibriumequations.

The equilibrium equations are not enough to determine the unknown reactions.

The reactions in figure 8 is indeterminate_.

(c)

Expert Solution
Check Mark
To determine

Find whether the equilibrium of the plate is maintained.

Answer to Problem 4.60P

The reactions in the plate 1 are B=8kips();A=14.42kips(56.3°)_.

The plate 1 is in equilibrium_.

The plate 2 is in notequilibrium_.

The reactions in the plate 3 are C=6kips();A=6kips()_.

The plate 3 is in equilibrium_.

The reactions in the plate 4 are Bx=8kips();Ax=8kips()_.

The plate 4 is in equilibrium_.

The plate 5 is in notequilibrium_.

The reactions in the plate 6 are C=6kips();A=6kips()_.

The plate 6 is in equilibrium_.

The reactions in the plate 7 are A=6kips();B=10kips(36.9°);C=8kips()_.

The plate 7 is in equilibrium_.

The reactions in the plate 8 are Ay=6kips()_.

The plate 8 is in equilibrium_.

Explanation of Solution

Refer Figure 1:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

Take moment about point A.

MA=0B(9)12(6)=0B=8kips()

Resolve the horizontal component of forces.

Fx=0B+Ax=08+Ax=0Ax=8kips()

Resolve the vertical component of forces.

Fy=0Ay12=0Ay=12kips()

Find the resultant force at A;

A=Ax2+Ay2=82+122=14.42kips

Find the angle θ at which the resultant passes from the horizontal axis.

tanθ=AyAx=128θ=56.3°

Therefore, the reactions in the plate 1 are B=8kips();A=14.42kips(56.3°)_.

The plate 1 is in equilibrium_.

Refer Figure 2:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

The moment about point A is not equal to zero.

The plate 2 is in notequilibrium_.

Refer Figure 3:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

Take moment about point A.

MA=0C(12)12(6)=0C=6kips()

Resolve the horizontal component of forces.

Fx=0Ax=0

Resolve the vertical component of forces.

Fy=0Ay+C12=0Ay+612=0Ay=6kips()

Therefore, the reactions in the plate 3 are C=6kips();A=6kips()_.

The plate 3 is in equilibrium_.

Refer Figure 4:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

Take moment about point A.

MA=0Bx(9)12(6)=0Bx=8kips()

Resolve the horizontal component of forces.

Fx=0Bx+Ax=08+Ax=0Ax=8kips()

Resolve the vertical component of forces.

Fy=0Ay+By12=0

Therefore, the reactions in the plate 4 are Bx=8kips();Ax=8kips()_.

The plate 4 is in equilibrium_.

Refer Figure 5:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

The moment about point A is not equal to zero.

The plate 5 is in notequilibrium_.

Refer Figure 6:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

Take moment about point A.

MA=0C(12)12(6)=0C=6kips()

Resolve the vertical component of forces.

Fy=0A12+C=0A12+6=0A=6kips()

Therefore, the reactions in the plate 6 are C=6kips();A=6kips()_.

The plate 6 is in equilibrium_.

Refer Figure 7:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

Find the angle θ.

tanθ=oppositesideadjacentside=912θ=36.9°

Take moment about point A.

MA=0Bcos36.9°(9)12(6)=0B=10kips(36.9°)

Resolve the horizontal component of forces.

Fx=0Bx+C=08+C=0C=8kips()

Resolve the vertical component of forces.

Fy=0A12+10sin36.9°=0A=6kips()

Therefore, the reactions in the plate 7 are A=6kips();B=10kips(36.9°);C=8kips()_.

The plate 7 is in equilibrium_.

Refer Figure 8:

The equilibrium equations are;

Fx=0;Fy=0;M=0;

Take moment about point C.

MC=012(6)Ay(12)=0Ay=6kips()

Therefore, the reactions in the plate 8 are Ay=6kips()_.

The plate 8 is in equilibrium_.

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Chapter 4 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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