bronze

Solution to Problem 320 Torsion

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

319-320 Compound Shaft

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.

 

Solution to Problem 272 Thermal Stress

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.

 

Solution 272

\Sigma M_A = 0
4P_{br} + P_{st} = 2.5(80\,000)
4\sigma_{br}(1300) + \sigma_{st}(320) = 2.5(80\,000)
16.25\sigma_{br} + \sigma_{st} = 625
\sigma_{st} = 625 – 16.25\sigma_{br} \, \to \, Equation (1)

 

Solution to Problem 271 Thermal Stress

271-272 Rigid bar supported by bronze and steel rods

Problem 271

A rigid bar of negligible weight is supported as shown in Fig. P-271. If W = 80 kN, compute the temperature change that will cause the stress in the steel rod to be 55 MPa. Assume the coefficients of linear expansion are 11.7 µm/(m·°C) for steel and 18.9 µm/(m·°C) for bronze.

Solution to Problem 270 Thermal Stress

270 Bronze sleeve slipped over a steel bolt

Problem 270

A bronze sleeve is slipped over a steel bolt and held in place by a nut that is turned to produce an initial stress of 2000 psi in the bronze. For the steel bolt, A = 0.75 in2, E = 29 × 106 psi, and α = 6.5 × 10–6 in/(in·°F). For the bronze sleeve, A = 1.5 in2, E = 12 × 106 psi and α = 10.5 × 10–6 in/(in·°F). After a temperature rise of 100°F, find the final stress in each material.

Solution to Problem 265 Thermal Stress

265 Bronze bar between rigid walls

Problem 265

A bronze bar 3 m long with a cross sectional area of 320 mm2 is placed between two rigid walls as shown in Fig. P-265. At a temperature of −20°C, the gap Δ = 25 mm. Find the temperature at which the compressive stress in the bar will be 35 MPa. Use α = 18.0 × 10−6 m/(m·°C) and E = 80 GPa.

Solution to Problem 256 Statically Indeterminate

256 Load supported by three rods

Problem 256

Three rods, each of area 250 mm2, jointly support a 7.5 kN load, as shown in Fig. P-256. Assuming that there was no slack or stress in the rods before the load was applied, find the stress in each rod. Use Est = 200 GPa and Ebr = 83 GPa.

Solution to Problem 254 Statically Indeterminate

254 Pinned rigid bar

Problem 254

As shown in Fig. P-254, a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assuming that the rods were initially stress-free, what maximum load P can be applied without exceeding stresses of 150 MPa in the steel rod and 70 MPa in the bronze rod.

Solution to Problem 253 Statically Indeterminate

253 Rigid beam supported by pin and rods

Problem 253

As shown in Fig. P-253, a rigid beam with negligible weight is pinned at one end and attached to two vertical rods. The beam was initially horizontal before the load W = 50 kips was applied. Find the vertical movement of W.

Solution to Problem 250 Statically Indeterminate

250 Bolt and tube assembly

Problem 250

In the assembly of the bronze tube and steel bolt shown in Fig. P-250, the pitch of the bolt thread is p = 1/32 in.; the cross-sectional area of the bronze tube is 1.5 in.2 and of steel bolt is 3/4 in.2 The nut is turned until there is a compressive stress of 4000 psi in the bronze tube. Find the stresses if the nut is given one additional turn. How many turns of the nut will reduce these stresses to zero? Use Ebr = 12 × 106 psi and Est = 29 × 106 psi.

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