Mechanical Engineering Chapter 6 Homework We will use the above result to analyze the equilibrium of joints Cand A,

481

SOLUTION

Method of Joints. Start at joint C and then proceed to join D.

Joint C. Fig. a

Joint D. Fig. b

6–1.

CB

A

D

1.5 m

2 m

P2

482

SOLUTION

Method of Joints. Start at joint C and then proceed to joint D.

Joint C. Fig. a

6–2.

Determine the force in each member of the truss and state

if the members are in tension or compression. Set

P1 = 45 kN, P2 = 30 kN.

CB

A

D

1.5 m

2 m

P1

P2

483

6–3.

SOLUTION

Joint A:

Joint B:

Joint C:

Joint D:

FAB =140

lb (T)

FBD =140

lb

Determine the force in each member of the truss. State if

the members are in tension or compression.

3ft3ft3ft

12

5

13

130 lb

AB

C

E

D

F

4 ft 4 ft

FAC =150

lb (C)

484

*6–4.

SOLUTION

Joint A:

Joint B:

Joint D:

Joint F:

Joint H:

Determ

i

ne t

h

e force

i

n eac

h

mem

b

er of t

h

e truss an

d

state

if the members are in tension or compression. 2kip

1.5 kip

4ft

10 ft 10 ft 10 ft

3kip

10 ft

AB

I

H

G

F

CD

E

8ft

485

*6–4. Continued

Joint C:

J

oint G:

Ans:

486

6–5.

Determine the force in each member of the truss, and state

if the members are in tension or compression. Set .

SOLUTION

Support Reactions: Applying the equations of equilibrium to the free-body diagram

of the entire truss,Fig.a, we have

Method of Joints: We will use the above result to analyze the equilibrium of

joints Cand A, and then proceed to analyze of joint B.

Joint A:From the free-body diagram in Fig. c, we can write

Joint B:From the free-body diagram in Fig. d, we can write

u=0°

AC

B

D

2 m

3 kN

2 m

1.5 m

u

487

6–6.

Determine the force in each member of the truss, and state

if the members are in tension or compression. Set .

SOLUTION

Support Reactions: From the free-body diagram of the truss,Fig. a, and applying

the equations of equilibrium, we have

Joint A:From the free-body diagram in Fig. c, we can write

u=30°

AC

B

D

2 m

3 kN

2 m

1.5 m

u

488

6–7.

SOLUTION

Support Reactions:

Method of Joints:

Joint C:

Determine the force in each member of the truss and state

if the members are in tension or compression.

E

D

C

B

F

A5m

3m

5kN

4kN

3m 3m 3m

489

6–7. Continued

Joint B:

Ans:

490

*6–8.

Determine the force in each member of the truss, and state

if the members are in tension or compression.

SOLUTION

Method of Joints: We will begin by analyzing the equilibrium of joint D, and then

proceed to analyze joints Cand E.

Joint C:From the free-body diagram in Fig. b,

Joint E:From the free-body diagram in Fig. c,

E

D

C

600 N

900 N

4 m

Ans:

FDE =1.00 kN (C)

491

SOLUTION

Support Reactions. Referring to the FBD of the entire truss shown in Fig. a,

6–9.

Determine the force in each member of the truss and state

if the members are in tension or compression. Set

P1 = 3 kN, P2 = 6 kN.

AD

E

B C

P1P2

4 m4 m4 m

6 m

492

6–9. Continued

Joint D. Fig. c

Ans:

493

SOLUTION

Support Reactions. Referring to the FBD of the entire truss shown in Fig. a,

sequence of joints A, D, B and C.

Joint A. Fig. a

Joint D. Fig. c

6–10.

Determine the force in each member of the truss and state

if the members are in tension or compression. Set P1 = 6 kN,

P2 = 9 kN.

AD

E

B C

P1P2

4 m4 m4 m

6 m

494

Joint B. Fig. d

6–10. Continued

Ans:

495

6–11.

Determine the force in each member of the Pratt truss, and

state if the members are in tension or compression.

SOLUTION

Joint A:

Joint L:

Joint C:

Joint K:

Joint J:

Due to Symmetry

CK =10 kN (T)

H

I

J

K

L

2 m

496

*6–12.

SOLUTION

Joint D:

Joint E:

Joint B:

Determine the force in each member of the truss and state

if the members are in tension or compression.

500 lb

3 ft

500 lb

C

B

E

D

6 ft

3 ft 3 ft

Ans:

497

6–13.

SOLUTION

Joint A:

Joint D:

Determine the force in each member of the truss in terms of

the load Pand state if the members are in tension or

compression.

B

D

A

C

a a

a

3

—

4

1

—

4

498

6–14.

Members AB and BC can each support a maximum

compressive force of 800 lb,and members AD,DC,and BD

can support a maximum tensile force of 1500 lb.If ,

determine the greatest load Pthe truss can support.

a=10 ft

SOLUTION

Joint D:

B

D

A

C

a

3

—

4

1

—

4

Ans:

6–15.

Members AB and BC can each support a maximum

compressive force of 800 lb, and members AD, DC, and BD

can support a maximum tensile force of 2000 lb. If a = 6 ft,

determine the greatest load P the truss can support.

B

D

3

A

C

a a

a

3

—

4

1

—

4

SOLUTION

1) Assume

FAB =800 lb (C)

Joint A:

500

*6–16.

SOLUTION

Method of Joints: In this case, the support reactions are not required for

determining the member forces.

Joint C:

Joint B:

Determine the force in each member of the truss. State

whether the members are in tension or compression. Set

P=8 kN.

60••

4m 4m

B

ED

C

A

4m

P