5.15 Rigid bar ABCD is loaded and supported as
shown in Fig. P5.15. Bars (1) and (2) are
unstressed before the load P is applied. Bar (1) is
made of bronze [E = 100 GPa] and has a crosssectional area of 520 mm2. Bar (2) is made of
aluminum [E = 70 GPa] an
6.25 A compound shaft drives several pulleys, as shown in Fig. P6.25. Segments (1) and (2) of the compound shaft are hollow aluminum [G = 4,000 ksi] tubes, which have an outside diameter of 3.00 in. and a wall thickness of 0.125 in. Segments (3) and (4) a
5.28 The concrete [E = 29 GPa] pier shown in
Fig. P5.28 is reinforced using four steel [E =
200 GPa] reinforcing rods, each having a
diameter of 19 mm. If the pier is subjected to an
axial load of 670 kN, determine:
(a) the normal stress in the concrete a
5.68 A 100-mm-wide by 8-mm-thick steel
bar is transmitting an axial tensile load of
3,000 N. After the load is applied, a 4mm-diameter hole is drilled through the
bar, as shown in Fig. P5.68. The hole is
centered in the bar.
(a) Determine the stress at po
5.48 The assembly shown in Fig. P5.48 consists of a brass shell
(1) fully bonded to a solid ceramic core (2). The brass shell [E
= 115 GPa, = 18.7 106/C] has an outside diameter of 50
mm and an inside diameter of 35 mm. The ceramic core [E =
290 GPa, = 3.
5.17 Rigid bar ABC is supported by bronze rod (1) and aluminum
rod (2), as shown in Fig P5-17. A concentrated load P is applied
to the free end of aluminum rod (3). Bronze rod (1) has an elastic
modulus of E1 = 15,000 ksi and a diameter of d1 = 0.50 in.
5.35 The pin-connected structure shown in Fig.
P5.35 consists of a rigid beam ABCD and two
supporting bars. Bar (1) is an aluminum alloy [E =
70 GPa] with a cross-sectional area of A1 = 800
mm2. Bar (2) is a bronze alloy [E = 100 GPa] with
5.49 At a temperature of 60F, a 0.04-in. gap exists between the ends of the two bars shown in Fig. P5.49. Bar (1) is an aluminum alloy [E = 10,000 ksi, = 0.32, = 12.5 10-6/F] bar with a width of 3 in. and a thickness of 0.75 in. Bar (2) is a stainless ste
12.12 A 2.5-in.-diameter solid aluminum post is
subjected to a horizontal force of V = 6 kips, a
vertical force of P = 15 kips, and a concentrated
torque of T = 22 kip-in., acting in the directions
shown in Fig. P12.12. Assume L = 4.5 in.
Determine the no
12.5 A tee-shaped flexural member (Fig. P12.5b) is subjected to an internal axial force of 2,200
lb, an internal shear force of 1,600 lb, and an internal bending moment of 4,000 lb-ft, as shown
in Fig. P12.5a. Determine the normal and shear stresses at po
9.3 For the following problems, a beam segment subjected to internal bending moments at sections A
and B is shown along with a sketch of the cross-sectional dimensions. For each problem:
(a) Sketch a side view of the beam segment and plot the distribution
8.62 The tee shape shown in Fig. P8.62b is used as a post that supports a load of P = 25 kN. Note
that the load P is applied 400 mm from the flange of the tee shape, as shown in Fig. P8.62a.
Determine the normal stresses at points H and K.
8.40 The beam shown in Fig. P8.40 will be constructed from a
standard steel W-shape using an allowable bending stress of 165
(a) Develop a list of four acceptable shapes that could be used for
this beam. Include the most economical W310, W360, W410,
8.30 A W410 60 standard steel shape
is used to support the loads shown on
the beam in Fig. P8.30. The shape is
oriented so that bending occurs about
the strong axis. Determine the
magnitude and location of the
maximum bending stress in the beam.
(270 lb-ft)(1.4747 in.)(12 in./ft)
= 4,698.164 psi = 4,700 psi (C)
8.17 Two vertical forces are applied to a simply supported beam (Fig. P8.17a) having the cross section
shown in Fig. P8.17b. Determine the maximum tension a
6.61 The motor shown in Fig. P6.61 supplies 10 hp
at 1,500 rpm at A. The bearings shown permit free
rotation of the shafts.
(a) Shaft (1) is a solid 0.875-in.-diameter steel
shaft. Determine the maximum shear stress
produced in shaft (1).
(b) If the shear
6.44 A tubular steel shaft is being designed to transmit 225 kW at 1,700 rpm. The maximum
shear stress in the shaft must not exceed 30 MPa. If the outside diameter of the shaft is D = 75
mm, determine the minimum wall thickness for the shaft.
6.16 A compound steel [G = 80 GPa] shaft
(Fig. P6.16) consists of a solid 55-mmdiameter segment (1) and a solid 40-mmdiameter segment (2). The allowable shear
stress of the steel is 70 MPa, and the
maximum rotation angle at the free end of
the compound sh
6.5 A compound shaft consists of two pipe
segments. Segment (1) has an outside diameter of
10.75 in. and a wall thickness of 0.365 in. Segment
(2) has an outside diameter of 6.625 in. and a wall
thickness of 0.280 in. The shaft is subjected to