Strength of Materials
1.
A shop crane consists of a boom AC that is supported by a pin at A and by a rectangular
tension bar BD, as shown in the figure. Details of the pin joints at A and B are shown
in Views a–a and b–b, respectively. The tension bar BD has a width w = 1.5 in. and a
thickness t = 0.5 in. If the vertical load at C is P = 5 kips, what is the average tensile
stress in the bar BD? (𝜎𝑎𝑣𝑒 = 13.3 𝑘𝑠𝑖 (𝑇))
2.
The Washington Monument (Fig. 1a) stands 555 ft high and weighs 181,700 kips (i.e.,
approximately 182 million pounds). The monument was made from over 36,000 blocks
of marble and granite. As shown in Fig. 1b, the base of the monument is a square that
is 665.5 in. long on each side, and the stone walls at the base are 180 in. thick. (𝜎𝑎𝑣𝑒 =
520 𝑝𝑠𝑖 (𝐶))
3.
Two solid circular rods are welded to a plate at B to form a single rod, as shown in the
figure. Consider the 30-kN force at B to be uniformly distributed around the
circumference of the collar at B and the 10 kN load at C to be applied at the centroid
of the end cross section. Determine the axial stress in each portion of the rod. (𝜎1 =
63.7 𝑀𝑃𝑎 (𝐶), 𝜎2 = 56.6 𝑀𝑃𝑎 (𝑇))
Strength of Materials
4.
When the bungee jumper in the figure stands on the jump platform, the unstretched
length of the bungee cord is 12.0 ft. Assuming that the bungee cord stretches uniformly
along its length, determine the extensional strain in the bungee cord when the jumper
“hits bottom,” where the extended length of the cord is 37.1 ft. (𝜀 = 2.09)
5.
The bar ABCD in the figure consists of three cylindrical steel segments with diffrent
lengths and cross-sectional areas. Axial loads are applied as shown. Calculate the
normal stress in each segment. (𝜎𝐴𝐵 = 3330 𝑝𝑠𝑖 (𝑇), 𝜎𝐵𝐶 = 2780 𝑝𝑠𝑖 (𝐶), 𝜎𝐶𝐷 =
4380 𝑝𝑠𝑖 (𝐶))
6.
For the truss shown in the figure, calculate the normal stresses in (1) member AC; and
(2) member BD. The cross-sectional area of each member is 900 mm2. (𝜎𝐴𝐶 =
53.9 𝑀𝑃𝑎 (𝑇), 𝜎𝐵𝐷 = 74.1 𝑀𝑃𝑎 (𝐶))
7.
The figure shows a two-member truss supporting a block of weight W. The crosssectional areas of the members are 800 mm2 for AB and 400 mm2 for AC. Determine
the maximum safe value of W if the working stresses are 110 MPa for AB and 120
MPa for AC. (𝑊 = 61.7 𝑘𝑁)
Strength of Materials
8.
The rectangular wood panel is formed by gluing together two boards along the 30degree seam as shown in the figure. Determine the largest axial force P that can be
carried safely by the panel if the working stress for the wood is 1120 psi, and the normal
and shear stresses in the glue are limited to 700 psi and 450 psi, respectively. (𝑃 =
3730 𝑙𝑏)
9.
A solid steel bar of circular cross section has diameter d = 1.5 in., length L = 54 in.,
and shear modulus of elasticity G = 11.5x106 psi. The bar is subjected to torques T
acting at the ends.
(a) If the torques have magnitude T = 250 lb-ft, what is the maximum shear stress in
the bar? What is the angle of twist between the ends? (𝜏𝑚𝑎𝑥 = 4530 𝑝𝑠𝑖, 𝜃 = 1.62°)
(b) If the allowable shear stress is 6000 psi and the allowable angle of twist is 2.5°,
what is the maximum permissible torque? (𝑇𝑚𝑎𝑥 = 331 𝑙𝑏 − 𝑓𝑡)
10. A steel shaft is to be manufactured either as a solid circular bar or as a circular tube.
The shaft is required to transmit a torque of 1200 Nm without exceeding an allowable
shear stress of 40 MPa nor an allowable rate of twist of 0.75°/m. (The shear modulus
of elasticity of the steel is 78 GPa.)
(a) Determine the required diameter 𝑑𝑜 of the solid shaft. (58.8 𝑚𝑚)
(b) Determine the required outer diameter 𝑑2 of the hollow shaft if the thickness 𝑡 of
the shaft is specified as one-tenth of the outer diameter. (67.1 𝑚𝑚)
(c) Determine the ratio of diameters (that is, the ratio 𝑑2 /𝑑𝑜 ) and the ratio of weights
of the hollow and solid shafts. (1.14)