534Principal 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. y 200 lb y 50 mm t ϭ 8 mm A D 20 mm z 4 in. 4 in. 150 lb 6 in. 225 mm Fig. P8.37 50 lb H K D 150 lb 10 in. x H 60Њ B E x 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, determine the normal and shearing stresses at point H. 8.39 The billboard shown weighs 8000 lb and is supported by a structural tube that has a 15-in. outer diameter and a 0.5-in. wall thickness. 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. y 6 ft 3 ft 9 ft 8 kips z Fig. P8.38 C l H H K H c z Fig. P8.39 2 ft x x z 8 ft 3 kips 3 ft 3 ft F 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. Fig. a 4.42 A 13-kN force is applied as shown to the 60-mm-diameter cast-iron post ABD. 1. 8. to the right of support D.43 A 10-kN force and a 1. 8.45. 2 in.5 in. Determine the principal stresses and maximum shearing stress at (a) point H. y B D Fig.43 50 kips 0. determine (a) the principal stresses and principal planes. P8. Knowing that the shaft BDE has a diameter of 0. 8.2 in.44 K x 6 kips A 3. determine the principal stresses and the maximum shearing stress at point H located at the top of the shaft.9 in.41 z Problems 535 y 1 in. (b) the maximum shearing stress.2 in. H 2500 lb B z 2. (b) point b. Knowing that the bracket has a diameter of 0. 600 lb Fig.41 A vertical force P of magnitude 60 lb is applied to the crank at point A. 2 in. Determine the normal and shearing stresses at (a) point a. P8.9 in.. At point H. Fig. 2 kips C 2. determine the principal stresses and the maximum shearing stress at (a) point H. B 60° P A 5 in. (b) point K.4 in. (b) point K.5 in..46 Solve Prob. P8.42 H K 1.5 in.45 . x 13 kN 300 mm H 100 mm E 125 mm x Fig. h ϭ 10.75 in. 8. 0.44 Forces are applied at points A and B of the solid cast-iron bracket shown.8 in.4-kN ? m couple are applied at the top of the 65-mm diameter brass post shown. y 1 in. 8. 1. 2 in. P8. (c) point c.4 kN · m C 10 kN A z 150 mm 240 mm 8.45 Three forces are applied to the bar shown. b c 1. assuming that h 5 12 in. P8. D E H 8 in.8 in.8.8 in. principal planes.25 in. Fig.47 Three forces are applied to the bar shown.50 8. P8.51 6 in. 4 in. Determine the normal and shearing stresses at (a) point a.47.48 Solve Prob. and maximum shearing stress at point H. z .51 Two forces are applied to the small post BD as shown.49 and P8. 8. 8. H D 3. and maximum shearing stress at point K. H K 8.5 3 2. and maximum shearing stress at point H. determine the principal stresses. 60 mm 24 mm a b c 15 mm 180 mm 750 N 30 mm 40 mm 16 mm 500 N 10 kN Fig.4 in. x z Fig. P8. P8. (c) point c. 2. principal planes.4 in. assuming that the 750-N force is directed vertically upward. y B 6000 lb 500 lb 1.536 Principal Stresses under a Given Loading 8.75 in.49 For the post and loading shown.47 32 mm y 50 mm 50 mm C 120 kN 75 mm 75 mm 50 kN 30Њ 375 mm C 8. determine the principal stresses.. determine the principal stresses.50 For the post and loading shown. principal planes. x 1. 1 in. (b) point b. Knowing that the vertical portion of the post has a cross section of 1.5 in.