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7.31 Draw the shear-force and bending-moment diagram for the beam shown in Fig. P7.31. Assume the upward reaction provided by the ground to be uniformly distributed. Label all significant points on each diagram. Determine the maximum value of (a) the internal shear force and (b) the internal bending moment. Fig. P7.31

Solution Beam equilibrium:

( )( ) ( )2 kips/ft 8 ft 25 kips 25 kips 16 ft 0

4.125 kips/ftyF w

wΣ = − − − + =

∴ =

Shear-force and bending-moment diagrams

(a) Maximum value of internal shear force:

V = 16.50 kips @ x = 4 ft Ans.

V = −16.50 kips @ x = 12 ft Ans.

(b) Maximum value of internal bending moment:

M = 33 kip-ft @ x = 4 ft, 12 ft Ans.

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.32 Draw the shear-force and bending-moment diagram for the beam shown in Fig. P7.32. Assume the upward reaction provided by the ground to be uniformly distributed. Label all significant points on each diagram. Determine the maximum value of (a) the internal shear force and (b) the internal bending moment. Fig. P7.32

Solution Beam equilibrium:

( )( )( )( ) ( )40 kN/m 1 m 50 kN

40 kN/m 1 m 4 m 0 32.5 kN/m

yF

ww

Σ = − −

− + =∴ =

Shear-force and bending-moment diagrams

(a) Maximum value of internal shear force:

V = ±25 kN @ x = 2 m Ans.

(b) Maximum value of internal bending moment:

M = −4.62 kN-m @ x = 1.23 m Ans.

M = −4.62 kN-m @ x = 2.77 m Ans.

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.33 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: (a) Determine V and M in the beam at a point located 0.75 m to the right of B. (b) Determine V and M in the beam at a point located 1.25 m to the left of C.

Fig. P7.33

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

Shear force V and bending moment M at specific locations: (a) At x = 3.75 m,

V = 20.35 kN Ans.

M = 214.03 kN-m Ans.

(b) At x = 13.75 m,

V = −49.65 kN Ans.

M = 67.53 kN-m Ans.

( )( ) ( )( )( )( )

( )( )( )( )

40 kN 3 m 7 kN/m 12 m 9 m

15 m 0

58.40 kN

40 kN 7 kN/m 12 m

58.4 kN 40 kN 7 kN/m 12 m 0

65.60 kN

A

y

y

y y y

y

y

M

CC

F A C

AA

Σ = − −

+ =

∴ =

Σ = + − −

= + − − =

∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.34 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: (a) Determine V and M in the beam at a point located 0.75 m to the right of B. (b) Determine V and M in the beam at a point located 1.25 m to the left of C.

Fig. P7.34

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

Shear force V and bending moment M at specific locations: (a) At x = 3.75 m,

V = 14.46 kN Ans.

M = −29.89 kN-m Ans.

(b) At x = 7.75 m,

V = −3.54 kN Ans.

M = −8.06 kN-m Ans.

( )( ) ( )( )( )( )( ) ( )

( )( )( )( )

14 kN 3 m 4.5 kN/m 6 m 3 m

4 kN 10 m 6 m 0

13.17 kN

14 kN 4.5 kN/m 6 m 4 kN

13.17 kN 14 kN 4.5 kN/m 6 m 4 kN 0

31.83 kN

B

y

y

y y y

y

y

M

CC

F B C

BB

Σ = −

− + =

∴ =

Σ = + − − −

= + − − − =

∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.35 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: (a) Determine V and M in the beam at a point located 0.75 m to the right of B. (b) Determine V and M in the beam at a point located 1.25 m to the left of C.

Fig. P7.35

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

Shear force V and bending moment M at specific locations: (a) At x = 3.75 m,

V = 6.95 kN Ans.

M = 15.62 kN-m Ans.

(b) At x = 6.75 m,

V = −8.05 kN Ans.

M = 13.97 kN-m Ans.

( )( )( )( )( )( ) ( )

( )( ) ( )( )( )( ) ( )( )

2 kN/m 3 m 1.5 m

5 kN/m 5 m 2.5 m 5 m 0

14.30 kN

2 kN/m 3 m 5 kN/m 5 m

14.30 kN 2 kN/m 3 m 5 kN/m 5 m 0

4.70 kN

B

y

y

y y y

y

y

M

CC

F B C

BB

Σ = −

− + =

∴ =

Σ = + + −

= + + − =

∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.36 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: (a) Determine V and M in the beam at a point located 0.75 m to the right of B. (b) Determine V and M in the beam at a point located 1.25 m to the left of C. Fig. P7.36

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

Shear force V and bending moment M at specific locations: (a) At x = 3.25 m,

V = −4.00 kN Ans.

M = 3.38 kN-m Ans.

(b) At x = 4.75 m,

V = 2.00 kN Ans.

M = 1.88 kN-m Ans.

( )( )

( )( ) ( )( )( )( )( )

10 kN 7 kN 4 kN/m 6 m 0

7.00 kN

10 kN 6 m 7 kN 3.5 m 20 kN-m

4 kN/m 6 m 3 m 0 7.50 kN-m

y y

y

C

C

C

F CC

M

MM

Σ = − − + + =

∴ = −

Σ = + −

− + =∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.37 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: (a) Determine V and M in the beam at a point located 1.50 m to the right of B. (b) Determine V and M in the beam at a point located 1.25 m to the left of D.

Fig. P7.37

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

Shear force V and bending moment M at specific locations: (a) At x = 3.75 m,

V = 15.00 kN Ans.

M = −41.62 kN-m Ans.

(b) At x = 10.75 m,

V = −28.75 kN Ans.

M = 5.41 kN-m Ans.

( )( ) ( )( )( )( )( ) ( )

( )( )( )( )

24 kN 3 m 7 kN/m 9 m 4.5 m

90 kN-m 12 kN 12 m 9 m 0

49.50 kN

24 kN 7 kN/m 9 m 12 kN

49.50 kN 24 kN 7 kN/m 9 m 12 kN 0

49.5 kN

B

y

y

y y y

y

y

M

DD

F B D

BB

Σ = −

− − + =

∴ =

Σ = + − − −

= + − − − =

∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.38 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: (a) Determine V and M in the beam at a point located 1.50 m to the right of B. (b) Determine V and M in the beam at a point located 1.25 m to the left of D.

Fig. P7.38

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

Shear force V and bending moment M at specific locations: (a) At x = 4.25 m,

V = 14.80 kN Ans.

M = −7.80 kN-m Ans.

(b) At x = 12.25 m,

V = −13.70 kN Ans.

M = −9.44 kN-m Ans.

( )( )( )( )( )( ) ( )( )( )( ) ( )

( )( )( )( )

6 kN/m 3.5 m 1.75 m

6 kN/m 12.5 m 6.25 m 15 kN 5.5 m

5 kN 12.5 m 10 m 0

41.20 kN

6 kN/m 16 m 15 kN 5 kN

41.20 kN 6 kN/m 16 m 15 kN 5 kN 0

B

y

y

y y y

y

M

DD

F B D

B

Σ =

− +

− + =

∴ =

Σ = + − + −

= + − + − =

44.80 kNyB∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.39 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Additionally: (a) Determine V and M in the beam at a point located 1.50 m to the right of B. (b) Determine V and M in the beam at a point located 1.25 m to the left of D.

Fig. P7.39

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

Shear force V and bending moment M at specific locations: (a) At x = 3.50 m,

V = 285.00 kN Ans.

M = 63.75 kN-m Ans.

(b) At x = 7.75 m,

V = −190.00 kN Ans.

M = 331.25 kN-m Ans.

( )( ) ( )( )( )( )( )( )( )( )( ) ( )

( )( )( )( )

( )( )

160 kN 2 m 50 kN/m 2 m 1 m

50 kN/m 2 m 1 m

120 kN/m 5 m 4.5 m 7 m 0

340 kN

160 kN 50 kN/m 4 m

120 kN/m 5 m

340 kN 160 kN 50 kN/m 4 m

B

y

y

y y y

y

M

DD

F B D

B

Σ = +

−

− + =

∴ =

Σ = + − −

−

= + − −

( )( ) 120 kN/m 5 m 0 620 kNyB

− =∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.40 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Fig. P7.40

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

( )( )( )( )( )( ) ( )

( )( ) ( )( )( )( )

( )( )

225 kN-m 120 kN/m 4 m 2 m

60 kN/m 2.5 m 8.75 m 7.5 m 0

273 kN

120 kN/m 4 m 60 kN/m 2.5 m

273 kN 120 kN/m 4 m

60 kN/m 2.5 m 0 357 kN

A

y

y

y y y

y

y

M

CC

F A C

A

A

Σ = −

− + =

∴ =

Σ = + − −

= + −

− =∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.41 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Fig. P7.41

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

( )( )( )( )( )( ) ( )( )

( )

( )( )( )( )

25 kip-ft 5 kips/ft 3 ft 1.5 ft

5 kips/ft 5 ft 2.5 ft 25 kips 10 ft

15 ft 0

17.67 kips

5 kips/ft 8 ft 25 kips

17.67 kips 5 kips/ft 8 ft 25 kips 0

B

y

y

y y y

y

M

EE

F B E

B

Σ = +

− −

+ =

∴ =

Σ = + − −

= + − − =

47.33 kipsyB∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.42 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Fig. P7.42

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

( )( )( )( )( ) ( )

( )( )( )( )

35 kip-ft 8 kips/ft 9 ft 4.5 ft

17 kips 12 ft 9 ft 0

62.56 kips

8 kips/ft 9 ft 17 kips

62.56 kips 8 kips/ft 9 ft 17 kips 0

26.44 kips

B

y

y

y y y

y

y

M

CC

F B C

BB

Σ = − −

− + =

∴ =

Σ = + − −

= + − − =

∴ =

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7.43 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams.

Fig. P7.43

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

( )( )( ) ( )( )( )( ) ( )( )( )

( )

( )( ) ( )( )

6 kips/ft 30 ft 15 ft 60 kips 10 ft

60 kips 20 ft 3 kips/ft 10 ft 35 ft

90 kip-ft 30 ft 0

62.00 kips

6 kips/ft 30 ft 10 ft3 kips/ft 60 kips 60 k

A

y

y

y y y

M

DD

F A D

Σ = − +

+ −

+ + =

∴ =

Σ = + − −

+ +

( )( ) ( )( )ips

62.00 kips 6 kips/ft 30 ft 10 ft3 kips/ft 60 kips 60 kips 0 28.00 kips

y

y

A

A

= + − −

+ + =∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.44 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Fig. P7.44

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

( )( ) ( )( )( )( )( ) ( )( ) ( )

( )( )( )( )

5 kips 5 ft 2 kips/ft 20 ft 10 ft 25 kip-ft

15 kips 8 ft 10 kips 23 ft 20 ft 0

23 kips

5 kips 2 kips/ft 20 ft 15 kips 10 kips

23 kips 5 kips 2 kips/ft 20 ft

B

y

y

y y y

y

M

DD

F B D

B

Σ = − +

+ − + =

∴ =

Σ = + − − + −

= + − −

15 kips 10 kips 0 17 kipsyB

+ − =∴ =

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7.45 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Fig. P7.45

Solution Beam equilibrium:

Shear-force and bending-moment diagrams

( )( )( ) ( )( )( )( )( ) ( )( )

( )( )( )( )

50 kN/m 2 m 1 m 20 kN 2 m

25 kN/m 3 m 3.5 m 50 kN 5 m 0 47.50 kN-m

50 kN/m 2 m 20 kN

25 kN/m 3 m 50 kN 0 55 kN

A A

A

y y

y

M M

MF A

A

Σ = − − +

+ − =∴ = −

Σ = − +

+ − =∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.46 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Fig. P7.46

Solution Beam equilibrium:

( )( ) ( )( )( )( )( )( )( )( )

( )( )( )( )

20 kips 15 ft 6 kips/ft 8 ft 11 ft

12 kips/ft 7 ft 3.5 ft

70 kips 7 ft 0 32.00 kip-ft

20 kips 6 kips/ft 8 ft 70 kips

12 kips/ft 7 ft 0

C

C

C

y

y

M

MM

F

CC

Σ = −

−

+ + =∴ =

Σ = − + −

+ + =

∴ 42.00 kipsy = −

Shear-force and bending-moment diagrams

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.47 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Fig. P7.47

Solution Beam equilibrium:

( )( )( )( )( )( )

( )( ) ( )

4,000 lb-ft 800 lb/ft 4 ft 2 ft

9,000 lb-ft 600 lb/ft 10 ft 10 ft

3,600 lb 10 ft 15 ft 0

5,640 lb

B

y

y

M

EE

Σ = − +

+ −

− + =

∴ =

( )( ) ( )( )( )( ) ( )( )

800 lb/ft 4 ft 600 lb/ft 10 ft 3,600 lb

5,640 lb 800 lb/ft 4 ft 600 lb/ft 10 ft 3,600 lb 0

7,160 lb

y y y

y

y

F B E

BB

Σ = + − − −

= + − − − =

∴ =

Shear-force and bending-moment diagrams

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.48 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams.

Fig. P7.48

Solution Beam equilibrium:

( )( )( ) ( )( )( )( )( )( ) ( )( ) ( )

400 kN-m 500 kN-m 600 kN-m 60 kN 2 m 1 m 120 kN/m 4 m 4 m

60 kN/m 2 m 7 m 150 kN 6 m 8 m 0

530 kN

B

y

y

M

EE

Σ = − −+ −

− − + =

∴ =

( )( ) ( )( )( )( )

( )( ) ( )( )( )( )

60 kN 2 m 120 kN/m 4 m

60 kN 2 m 150 kN

530 kN 60 kN 2 m 120 kN/m 4 m

60 kN 2 m 150 kN 340 kN

y y y

y

y

F B E

B

B

Σ = + − −

− −

= + − −

− −∴ =

Shear-force and bending-moment diagrams

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.49 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams.

Fig. P7.49

Solution Beam equilibrium:

Consider free-body diagram of DE:

( )( )( ) ( )

( )( )( )( )

55 kN/m 3 m 1.5 m 3 m 0

82.5 kN

55 kN/m 3 m

82.5 kN 55 kN/m 3 m 0

82.5 kN

D y

y

y y y

y

y

M EE

F D E

DD

Σ = − + =

∴ =

Σ = + −

= + − =

∴ =

Consider free-body diagram of ABCD:

( )( )( )( )( ) ( ) ( )

( )( )( )( )( ) ( )( ) ( )

( )( )

60 kN-m 75 kN/m 5 m 2.5 m

100 kN 2.5 m 5 m 3.5 m

60 kN-m 75 kN/m 5 m 2.5 m

100 kN 2.5 m 82.5 kN 5 m 3.5 m 0

440 kN

75 kN/m 5 m 100 kN

A

y y

y

y

y y y y

M

D C

CC

F A C D

A

Σ = −

− − +

= −

− − + =

∴ =

Σ = + − − −

= ( )( )440 kN 75 kN/m 5 m 100 kN 82.5 kN 0

117.5 kNy

yA+ − − − =

∴ =

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

Shear-force and bending-moment diagrams

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

7.50 Use the graphical method to construct the shear-force and bending-moment diagrams for the beams shown. Label all significant points on each diagram and identify the maximum moments along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams.

Fig. P7.50

Solution Beam equilibrium:

Consider free-body diagram of ABC:

( )( )( ) ( )

( )( )( )( )

500 lb/ft 10 ft 5 ft 15 ft 0

1,666.67 lb

500 lb/ft 10 ft

1,666.67 lb 500 lb/ft 10 ft 0

3,333.33 lb

A y

y

y y y

y

y

M CC

F A C

AA

Σ = − + =

∴ =

Σ = + −

= + − =

∴ =

Consider free-body diagram of CDE:

( )

( ) ( )( )( )( ) ( )( )

1,200 lb

1,666.67 lb 1,200 lb 0

2,866.67 lb

10 ft 1,200 lb 8 ft

1,666.67 lb 10 ft 1,200 lb 8 ft 0 26,266.67 lb-ft

y y y

y

y

E y E

E

E

F C E

EE

M C M

MM

Σ = − + −

= − + − =

∴ =

Σ = + +

= + + =∴ =

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Shear-force and bending-moment diagrams