Page 324 - Mechanical Behavior of Materials

Problems and Questions 325

pressure of 20 MPa, a torque of 60 kN·m, and a compressive axial force of 200 kN. Determine
the safety factor against yielding.
7.18 A solid shaft of diameter d is made of ASTM A514, T1 structural steel and is subjected to
a tensile axial force of 200 kN and a torque of 1.5 kN.m. What is the safety factor against
yielding if the diameter is 50 mm? Use the octahedral shear stress yield criterion.
7.19 A solid shaft is subjected to a tensile axial force of 300 kN, a bending moment of 5.0 kN·m,
and a torque of 9.0 kN·m. A safety factor against yielding of 2.75 is required. What is the
smallest permissible value of diameter d if the material is 18 Ni (250) maraging steel?
7.20 A vertical force of 50 kN is applied at mid-span of a simply supported beam, as in Fig. A.4(a).
The beam is made of AISI 1020 steel (as rolled), it is 1.0 m long, and it has an I-shaped cross
section. The dimensions, as defined in Fig. A.2(d), are h 2 = 150, h 1 = 135, b 2 = 100, and
b 1 = 96 mm, with loading in the y-direction of Fig. A.2(d).
(a) For an arbitrary location along the beam length, qualitatively sketch the variations of
bending stress and of transverse shear stress through the depth of the beam.
(b) Determine the safety factor against yielding, checking any points of possible maximum
stress. (Suggestion: The transverse shear stress at the center of the beam, y = 0, may
be approximated as τ xy = V/A web .)
7.21 A circular tube must support a bending moment of 4.5 kN·m and a torque of 7.0 kN·m. It is
made of ASTM A514 (T1) structural steel and has a wall thickness of 3.0 mm.
(a) What is the safety factor against yielding if the outside diameter is 80 mm?
(b) For the situation of (a), what adjusted value of outside diameter with the same thickness
is required to obtain a safety factor against yielding of 1.5?
7.22 A circular tube must support an axial load of 60 kN tension and a torque of 1.0 kN·m. It is
made of 7075-T6 aluminum and has an inside diameter of 46.0 mm.
(a) What is the safety factor against yielding if the wall thickness is 2.5 mm?
(b) For the situation of (a), what adjusted value of thickness with the same inside diameter
is required to obtain a safety factor against yielding of 2.0?
7.23 Consider a solid circular shaft subjected to bending and torsion, so that the state of stress of
interest involves only a normal stress σ x and a shear stress τ xy , with all other stress components
being zero, as in Fig. P7.23. Develop a design equation for the shaft, giving diameter d as a
function of yield strength, safety factor, bending moment M, and torque T . Employ (a) the
maximum shear stress criterion, and (b) the octahedral shear stress criterion.

y
M

x σ
x
T
τ
xy
Figure P7.23

7.24 A thin-walled tube with closed ends has an inner diameter of 40 mm and a wall thickness of
2.5 mm. It contains a pressure of 10 MPa and is subjected to a torque of 3000 N·m.