534 Principal Stresses under a Given Loading 8.37 Several forces are applied to the pipe assembly shown. Knowing that the pipe has inner and outer diameters equal to 1.61 and 1.90 in., respectively, determine the normal and shearing stresses at (a) point H, (b) point K.

4 in.

6 in.

4 in.

H

y

zK

150 lb

50 lbx

10 in.

150 lb

200 lb

D

Fig. P8.37

8.38 The steel pile AB has a 100-mm outer diameter and an 8-mm wall thickness. Knowing that the tension in the cable is 40 kN, deter-mine the normal and shearing stresses at point H.

8.39 The billboard shown weighs 8000 lb and is supported by a struc-tural tube that has a 15-in. outer diameter and a 0.5-in. wall thick-ness. At a time when the resultant of the wind pressure is 3 kips, located at the center C of the billboard, determine the normal and shearing stresses at point H.

50 mm

225 mm

20 mm

A

HE

D

B

z

x

y

t � 8 mm

60�

Fig. P8.38

2 ft

8 ft

H

xx

zH

z

3 ft

6 ft3 ft

9 ft

3 ft

3 kips

8 kips

C

y

Fig. P8.39

F

c

K

H

l

Fig. P8.40

8.40 A thin strap is wrapped around a solid rod of radius c 5 20 mm as shown. Knowing that l 5 100 mm and F 5 5 kN, determine the normal and shearing stresses at (a) point H, (b) point K.

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535Problems 8.41 A vertical force P of magnitude 60 lb is applied to the crank at point A. Knowing that the shaft BDE has a diameter of 0.75 in., determine the principal stresses and the maximum shearing stress at point H located at the top of the shaft, 2 in. to the right of support D.

8.42 A 13-kN force is applied as shown to the 60-mm-diameter cast-iron post ABD. At point H, determine (a) the principal stresses and principal planes, (b) the maximum shearing stress.

8.43 A 10-kN force and a 1.4-kN ? m couple are applied at the top of the 65-mm diameter brass post shown. Determine the principal stresses and maximum shearing stress at (a) point H, (b) point K.

8.44 Forces are applied at points A and B of the solid cast-iron bracket shown. Knowing that the bracket has a diameter of 0.8 in., deter-mine the principal stresses and the maximum shearing stress at (a) point H, (b) point K.

60°

8 in.

2 in.

5 in.

1 in.

z

ED

H

A

xB

yP

Fig. P8.41

H

A

B

D

x

z

E

13 kN 300 mm

125 mm150 mm

100 mm

y

Fig. P8.42

C

240 mm

1.4 kN · m

10 kN

H K

Fig. P8.43

H

B

Az

y

xK

600 lb

3.5 in.2.5 in.

1 in.

2500 lb

Fig. P8.44

8.45 Three forces are applied to the bar shown. Determine the normal and shearing stresses at (a) point a, (b) point b, (c) point c.

8.46 Solve Prob. 8.45, assuming that h 5 12 in.

h � 10.5 in.

0.9 in.

4.8 in.1.8 in.

0.9 in. 2.4 in.

50 kips

2 kips

6 kips

2 in.

1.2 in.

1.2 in.

ab c

C

Fig. P8.45

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536 Principal Stresses under a Given Loading 8.47 Three forces are applied to the bar shown. Determine the normal and shearing stresses at (a) point a, (b) point b, (c) point c.

8.48 Solve Prob. 8.47, assuming that the 750-N force is directed verti-cally upward.

8.49 For the post and loading shown, determine the principal stresses, principal planes, and maximum shearing stress at point H.

8.50 For the post and loading shown, determine the principal stresses, principal planes, and maximum shearing stress at point K.

8.51 Two forces are applied to the small post BD as shown. Knowing that the vertical portion of the post has a cross section of 1.5 3 2.4 in., determine the principal stresses, principal planes, and maxi-mum shearing stress at point H.

24 mm

15 mm

32 mm

60 mm

180 mma

b c

C

40 mm

30 mm

500 N

750 N

10 kN

16 mm

Fig. P8.47

50 mm50 mm

75 mm75 mm

50 kN

120 kN

y

z x

30�

C

375 mm

H K

Fig. P8.49 and P8.50

6000 lb

500 lb

4 in.

6 in.

3.25 in.

1.75 in.

2.4 in.1.5 in.

y

H

B

D

z

x

1 in.

Fig. P8.51

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