Solution to Problem 506 | Flexure Formula Jhun Vert Tue, 04/21/2020 - 11:20 pm

Problem 506
A flat steel bar, 1 inch wide by ¼ inch thick and 40 inches long, is bent by couples applied at the ends so that the midpoint deflection is 1.0 inch. Compute the stress in the bar and the magnitude of the couples. Use E = 29 × 106 psi.
 

Solution to Problem 276 Thermal Stress Jhun Vert Tue, 04/21/2020 - 10:06 am

Problem 276
Four steel bars jointly support a mass of 15 Mg as shown in Fig. P-276. Each bar has a cross-sectional area of 600 mm2. Find the load carried by each bar after a temperature rise of 50°C. Assume α = 11.7 µm/(m·°C) and E = 200 GPa.
 

Load supported by four steel bars

 

Solution to Problem 275 Thermal Stress Jhun Vert Tue, 04/21/2020 - 10:03 am

Problem 275
A rigid horizontal bar of negligible mass is connected to two rods as shown in Fig. P-275. If the system is initially stress-free. Calculate the temperature change that will cause a tensile stress of 90 MPa in the brass rod. Assume that both rods are subjected to the change in temperature.
 

Bar connected in two rods

 

Solution to Problem 274 Thermal Stress Jhun Vert Tue, 04/21/2020 - 10:00 am

Problem 274
At what temperature will the aluminum and steel segments in Prob. 273 have numerically equal stress?
 

Solution to Problem 273 Thermal Stress Jhun Vert Tue, 04/21/2020 - 09:59 am

Problem 273
The composite bar shown in Fig. P-273 is firmly attached to unyielding supports. An axial force P = 50 kips is applied at 60°F. Compute the stress in each material at 120°F. Assume α = 6.5 × 10-6 in/(in·°F) for steel and 12.8 × 10-6 in/(in·°F) for aluminum.
 

Composite aluminum and steel bar

 

Solution to Problem 257 Statically Indeterminate Jhun Vert Mon, 04/20/2020 - 11:39 pm

Problem 257
Three bars AB, AC, and AD are pinned together as shown in Fig. P-257. Initially, the assembly is stress free. Horizontal movement of the joint at A is prevented by a short horizontal strut AE. Calculate the stress in each bar and the force in the strut AE when the assembly is used to support the load W = 10 kips. For each steel bar, A = 0.3 in.2 and E = 29 × 106 psi. For the aluminum bar, A = 0.6 in.2 and E = 10 × 106 psi.
 

Figure 257

 

Solution to Problem 239 Statically Indeterminate Jhun Vert Mon, 04/20/2020 - 10:24 pm

Problem 239
The rigid platform in Fig. P-239 has negligible mass and rests on two steel bars, each 250.00 mm long. The center bar is aluminum and 249.90 mm long. Compute the stress in the aluminum bar after the center load P = 400 kN has been applied. For each steel bar, the area is 1200 mm2 and E = 200 GPa. For the aluminum bar, the area is 2400 mm2 and E = 70 GPa.
 

Figure 239

 

Solution to Problem 238 Statically Indeterminate Jhun Vert Mon, 04/20/2020 - 10:00 pm

Problem 238
The lower ends of the three bars in Fig. P-238 are at the same level before the uniform rigid block weighing 40 kips is attached. Each steel bar has a length of 3 ft, and area of 1.0 in.2, and E = 29 × 106 psi. For the bronze bar, the area is 1.5 in.2 and E = 12 × 106 psi. Determine (a) the length of the bronze bar so that the load on each steel bar is twice the load on the bronze bar, and (b) the length of the bronze that will make the steel stress twice the bronze stress.
 

Rigid bar supported by three rods

 

Solution to Problem 233 Statically Indeterminate Jhun Vert Mon, 04/20/2020 - 09:06 pm

Problem 233
A steel bar 50 mm in diameter and 2 m long is surrounded by a shell of a cast iron 5 mm thick. Compute the load that will compress the combined bar a total of 0.8 mm in the length of 2 m. For steel, E = 200 GPa, and for cast iron, E = 100 GPa.