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Unformatted text preview: internal pressure p (see Table 1.1). Given a small circular
hole in the vessel wall, show that the maximum tangential and axial
= 5pd/4t and a = pd/4t, respectively.
stresses at the hole are
The shaft shown in Fig. D of Table 3.2 has the following dimensions:
a = 6 mm, h = 12 mm, and b = 200 mm. The shaft is subjected simultaneously to a torque T = 4 kN # m, a bending moment M = 2 kN # m, and an
axial force P = 10 kN. Calculate at the root of the notch (a) the maximum
principal stress, (b) the maximum shear stress, and (c) the octahedral stresses.
Redo Prob. 3.41 for a = 4 mm, h = 6 mm, b = 120 mm, T = 3 kN # m,
M = 1.5 kN # m, and P = 0. 3.43. A 50mmdiameter ball is pressed into a spherical seat of diameter 75 mm
by a force of 500 N. The material is steel 1E = 200 GPa, = 0.32. Calculate (a) the radius of the contact area; (b) the maximum contact pressure;
and (c) the relative displacement of the centers of the ball and seat.
3.44. Calculate the maximum contact pressure c in Prob. 3.43 for the cases
when the 50mmdiameter ball is pressed against (a) a flat surface, and (b)
an identical ball.
3.45. Calculate the maximum pressure between a steel wheel of radius
r1 = 400 mm and a steel rail of crown radius of the head r2 = 250 mm (Fig.
3.22b) for P = 4 kN. Use E = 200 GPa and = 0.3.
3.46. A concentrated load of 2.5 kN at the center of a deep steel beam is applied
through a 10mmdiameter steel rod laid across the 100mm beam width.
50 mm
150 mm P
slot FIGURE P3.38.
Problems 143 ch03.qxd 12/20/02 7:21 AM Page 144 Compute the maximum contact pressure and the width of the contact between rod and beam surface. Use E = 200 GPa and = 0.3.
3.47. Two identical 400mmdiameter steel rollers of a rolling mill are pressed
together with a force of 2 MN/m. Using E = 200 GPa and = 0.25, compute the maximum contact pressure and width of contact.
3.48. Determine the size of the contact area and the maximum pressure between
two circular cylinders with mutually perpendicular axes. Denote by r1 and
r2 the radii of the cylinders. Use r1 = 500 mm, r2 = 200 mm, P = 5 kN,
E = 210 GPa, and = 0.25.
3.49. Solve Prob. 3.48 for the case of two cylinders of equal radii,
r1 = r2 = 200 mm.
3.50. Determine the maximum pressure at the contact point between the outer
race and a ball in the singlerow ball bearing assembly shown in Fig. 3.22a.
The ball diameter is 50 mm; the radius of the grooves, 30 mm; the diameter
of the outer race, 250 mm; and the highest compressive force on the ball,
P = 1.8 kN. Take E = 200 GPa and = 0.3.
3.51. Redo Prob. 3.50 for a ball diameter of 40 mm and a groove radius of
22 mm. Assume the remaining data to be unchanged. 144 Chapter 3 TwoDimensional Problems in Elasticity...
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This note was uploaded on 01/09/2011 for the course ME 201 taught by Professor Yok during the Spring '08 term at Boğaziçi University.
 Spring '08
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