Page 408 - Mechanical Behavior of Materials

Problems and Questions 409

(b) If an axial tensile force of 120 kN is combined with the bending moment, what is the
safety factor?
8.29 A solid circular shaft has a diameter of 50 mm and is made of 7075-T651 aluminum. The
shaft contains a half-circular surface crack, as in Fig. 8.17(d), of depth a = 10 mm, and it is
subjected to a bending moment of M = 600 N·m. What is the largest axial force P that can
be applied along with M such that the safety factor against brittle fracture is not less than 4.0?
8.30 A tension member made of the AISI 4130 steel of Table 8.1 has dimensions, as defined
in Fig. 8.12(c), of b = 50 and t = 10 mm. A safety factor of 3.5 against brittle fracture is
required.
(a) If there is a through-thickness crack in one edge of length a = 5 mm, what is the
highest tension force P that can be permitted in service?
(b) The force P may be off the center of the width dimension b of the member (eccentric)
by as much as 5 mm. In this case, and for the same a = 5 mm, what is the highest
force P that can be permitted in service?
8.31 A tube made of soda-lime glass has an inner radius r 1 = 38 mm and a wall thickness
t = 4 mm. A half-circular surface crack of depth a = 2 mm is present as shown in Fig. P8.31.
What internal pressure will cause fracture of the tube?

t
a crack
r 1

pressure

Figure P8.31

8.32 Consider the case of an infinite array of collinear cracks of Fig. 8.23(b), specifically, the K 2
case where the crack faces are loaded on one side.
(a) For α = a/b in the range 0.01 to 0.99, calculate a number of values of the
√
dimensionless function F P2 = K 2 t b/P. Plot these as a function of α, and comment
on the somewhat unusual trend observed.
(b) Verify that the two approximations given near the bottom of Fig. 8.23 are indeed
within 10% over the ranges indicated.
8.33 In joining plates of 2024-T351 aluminum, a row of bolt holes is loaded on one side by
concentrated forces, as in Fig. 8.24. The remotely applied stress is S = 60 MPa, the hole
spacing is 2b = 24 mm, and the hole diameters are 4 mm. Cracks of length l = 3mm are
present on each side of each hole. What is the safety factor against failure? Consider both
brittle fracture and fully plastic yielding.