Solution to Problem 350 | Helical Springs

Problem 350
As shown in Fig. P-350, a homogeneous 50-kg rigid block is suspended by the three springs whose lower ends were originally at the same level. Each steel spring has 24 turns of 10-mm-diameter on a mean diameter of 100 mm, and G = 83 GPa. The bronze spring has 48 turns of 20-mm-diameter wire on a mean diameter of 150 mm, and G = 42 GPa. Compute the maximum shearing stress in each spring using Eq. (3-9).
 

Bar supported by three springs

 

Solution to Problem 320 Torsion Jhun Vert Tue, 04/21/2020 - 12:47 pm

Problem 320
In Prob. 319, determine the ratio of lengths b/a so that each material will be stressed to its permissible limit. What torque T is required?
 

Solution to Problem 319 Torsion Jhun Vert Tue, 04/21/2020 - 12:43 pm

Problem 319
The compound shaft shown in Fig. P-319 is attached to rigid supports. For the bronze segment AB, the diameter is 75 mm, τ ≤ 60 MPa, and G = 35 GPa. For the steel segment BC, the diameter is 50 mm, τ ≤ 80 MPa, and G = 83 GPa. If a = 2 m and b = 1.5 m, compute the maximum torque T that can be applied.
 

Compound Shaft

 

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 272 Thermal Stress Jhun Vert Tue, 04/21/2020 - 09:55 am

Problem 272
For the assembly in Fig. 271, find the stress in each rod if the temperature rises 30°C after a load W = 120 kN is applied.
 

Figure P-271 and Figure P-272