1. The angular orientation, θ, of a "rigid" mirror is controlled by the lengths of rods (1) and (2), as shown in Fig. P2.3-17. At the reference temperature, the rods are the same length: L1 = L2 = 2.00 m. The distance between the rods is a = 1.2 m.
(a) If the thermal coefficient of the rods is α1 = α2 = 14 x 10-6/0c, determine an expression for the angle θ (in radians) as a function of ΔT1 and ΔT2.
(b) If the maximum temperature difference that can be achieved between the temperature changes ΔT1 and ΔT2 of the rods is 30°C, what is the maximum mirror rotation angle that can be achieved? (Assume that the rods are uniformly heated or cooled along their lengths.)
2. A tension specimen (diameter = do = 0.500 in., gage length = Lo = 2.0 in.) was used to obtain the load-elongation data given in Table.
TABLE. Tension-test Data
|
P (kips)
|
AL (in.)
|
P (kips)
|
AL (in.)
|
|
0.0
|
0.000
|
12.5
|
0.060
|
|
5.2
|
0.005
|
12.7
|
0.070
|
|
9.4
|
0.009
|
12.9
|
0.080
|
|
9.7
|
0.010
|
13.0
|
0.090
|
|
10.0
|
0.013
|
13.1
|
0.100
|
|
10.6
|
0.020
|
13.2
|
0.110
|
|
11.3
|
0.030
|
13.2
|
0.120
|
|
11.8
|
0.040
|
13.0
|
0.130
|
|
12.2
|
0.050
|
12.6
|
0.138
|
(a) Plot a curve of engineering stress, σ, versus engineering strain, ε, using the given data.
(b) Determine the modulus of elasticity of this material.
(c) Use the 0.2%-offset method to determine the yield strength of this material, σys.
(d) Determine the tensile ultimate stress, σTU
3. A rectangular aluminum bar (wo = 2.0 in., to = 0.5 in.) is subjected to a tensile load P by pins at A and B (Fig. P2.6-9), Strain gages (which are described in Section 8.10) measure the following strains in the longitudinal (x) and transverse (y) directions: εx= 566μ, and εy = -187μ.
(a) What is the value of Poisson's ratio for this specimen?
(b) If the load P that produces these values of εx and εy is P = 6 kips, what is the modulus of elasticity, E, for this specimen?
(c) What is the change in volume, ΔV, of a segment of bar that is initially 2 in. long? (Hint: εz= εy.)
4. Two bolts are used to form a joint connecting rectangular bars in tension, as shown in Fig. P2.7-1. If the bolts have a diameter of 3/8 in., and the load is P = 20 kips, determine the average shear stress on the bolt surfaces that are subjected to direct shear.
5. A 100-kip capacity hydraulic punch press is used to punch circular holes in a 3/8-in.-thick aluminum plate, as illustrated in Fig. P2.7-4. If the average punching shear resistance of this plate is 30 ksi, what is the maximum diameter of hole that can be punched?
6. An angle bracket ABC is restrained by a high-strength steel wire CD, and it supports a load P at A, as shown inFig. P2.7-8. The diameter of the wire CD is dw - 1/8 = in., and the diameter of the in at B is dp = 1/8 in. Determine, the tensile stress in wire CD and the average direct shear stress in the pin at B.
