Solution to Problem 213 Axial Deformation

Problem 213
The rigid bar AB, attached to two vertical rods as shown in Fig. P-213, is horizontal before the load P is applied. Determine the vertical movement of P if its magnitude is 50 kN.
 

Figure P-213

 

Solution to Problem 212 Axial Deformation

Problem 212
The rigid bar ABC shown in Fig. P-212 is hinged at A and supported by a steel rod at B. Determine the largest load P that can be applied at C if the stress in the steel rod is limited to 30 ksi and the vertical movement of end C must not exceed 0.10 in.
 

Figure P-212

 

Solution to Problem 211 Axial Deformation

Problem 211
A bronze bar is fastened between a steel bar and an aluminum bar as shown in Fig. p-211. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa.
 

Figure P-211

 

Solution to Problem 210 Axial Deformation

Problem 210
Solve Prob. 209 if the points of application of the 6000-lb and the 4000-lb forces are interchanged.
 

Solution 210
P1 = 4000 lb compression
P2 = 11000 lb compression
P3 = 6000 lb compression
 

Solution to Problem 209 Axial Deformation

Problem 209
An aluminum bar having a cross-sectional area of 0.5 in2 carries the axial loads applied at the positions shown in Fig. P-209. Compute the total change in length of the bar if E = 10 × 106 psi. Assume the bar is suitably braced to prevent lateral buckling.
 

Aluminum bar loaded as indicated

 

Solution to Problem 208 Axial Deformation

Problem 208
A steel tire, 10 mm thick, 80 mm wide, and 1500.0 mm inside diameter, is heated and shrunk onto a steel wheel 1500.5 mm in diameter. If the coefficient of static friction is 0.30, what torque is required to twist the tire relative to the wheel? Neglect the deformation of the wheel. Use E = 200 GPa.
 

Solution to Problem 207 Axial Deformation

Problem 207
A steel wire 30 ft long, hanging vertically, supports a load of 500 lb. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20 ksi and the total elongation is not to exceed 0.20 in. Assume E = 29 × 106 psi.
 

Solution to Problem 206 Axial Deformation

Problem 206
A steel rod having a cross-sectional area of 300 mm2 and a length of 150 m is suspended vertically from one end. It supports a tensile load of 20 kN at the lower end. If the unit mass of steel is 7850 kg/m3 and E = 200 × 103 MN/m2, find the total elongation of the rod.
 

Solution to Problem 205 Axial Deformation

Problem 205
A uniform bar of length L, cross-sectional area A, and unit mass ρ is suspended vertically from one end. Show that its total elongation is δ = ρgL2/2E. If the total mass of the bar is M, show also that δ = MgL/2AE.
 

Solution to Problem 204 Stress-strain Diagram

Problem 204
The following data were obtained during a tension test of an aluminum alloy. The initial diameter of the test specimen was 0.505 in. and the gage length was 2.0 in.
 

Load (lb) Elongation (in.) Load (lb) Elongation (in.)
0 0 14 000 0.020
2 310 0.00220 14 400 0.025
4 640 0.00440 14 500 0.060
6 950 0.00660 14 600 0.080
9 290 0.00880 14 800 0.100
11 600 0.0110 14 600 0.120
12 600 0.0150 13 600 Fracture

 

Plot the stress-strain diagram and determine the following mechanical properties: (a) proportional limit; (b) modulus of elasticity; (c) yield point; (d) yield strength at 0.2% offset; (e) ultimate strength; and (f) rupture strength.
 

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