Engineering Mathematics
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rigid support

Solution to Problem 325 Torsion

Problem 325
The two steel shaft shown in Fig. P-325, each with one end built into a rigid support have flanges rigidly attached to their free ends. The shafts are to be bolted together at their flanges. However, initially there is a 6° mismatch in the location of the bolt holes as shown in the figure. Determine the maximum shearing stress in each shaft after the shafts are bolted together. Use G = 12 × 106 psi and neglect deformations of the bolts and flanges.
 

Shafts connected through flanges

 

Solution to Problem 324 Torsion

Problem 324
The compound shaft shown in Fig. P-324 is attached to rigid supports. For the bronze segment AB, the maximum shearing stress is limited to 8000 psi and for the steel segment BC, it is limited to 12 ksi. Determine the diameters of each segment so that each material will be simultaneously stressed to its permissible limit when a torque T = 12 kip·ft is applied. For bronze, G = 6 × 106 psi and for steel, G = 12 × 106 psi.
 

Solution to Problem 323 Torsion

Problem 323
A shaft composed of segments AC, CD, and DB is fastened to rigid supports and loaded as shown in Fig. P-323. For bronze, G = 35 GPa; aluminum, G = 28 GPa, and for steel, G = 83 GPa. Determine the maximum shearing stress developed in each segment.
 

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

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 246 Statically Indeterminate

Problem 246
Referring to the composite bar in Problem 245, what maximum axial load P can be applied if the allowable stresses are 10 ksi for aluminum and 18 ksi for steel.
 

Solution to Problem 245 Statically Indeterminate

Problem 245
The composite bar in Fig. P-245 is firmly attached to unyielding supports. Compute the stress in each material caused by the application of the axial load P = 50 kips.
 

Figure 245

 

Solution to Problem 244 Statically Indeterminate

Problem 244
A homogeneous bar with a cross sectional area of 500 mm2 is attached to rigid supports. It carries the axial loads P1 = 25 kN and P2 = 50 kN, applied as shown in Fig. P-244. Determine the stress in segment BC. (Hint: Use the results of Prob. 243, and compute the reactions caused by P1 and P2 acting separately. Then use the principle of superposition to compute the reactions when both loads are applied.)
 

Figure 244

 

Solution to Problem 243 Statically Indeterminate

Problem 243
A homogeneous rod of constant cross section is attached to unyielding supports. It carries an axial load P applied as shown in Fig. P-243. Prove that the reactions are given by R1 = Pb/L and R2 = Pa/L.
 

Rod between rigid walls

 

Solution to Problem 217 Axial Deformation

Problem 217
Solve Prob. 216 if rod AB is of steel, with E = 29 × 106 psi. Assume α = 45° and θ = 30°; all other data remain unchanged.
 

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