Solution to Problem 228 Biaxial Deformation

Problem 228
A 6-in.-long bronze tube, with closed ends, is 3 in. in diameter with a wall thickness of 0.10 in. With no internal pressure, the tube just fits between two rigid end walls. Calculate the longitudinal and tangential stresses for an internal pressure of 6000 psi. Assume ν = 1/3 and E = 12 × 106 psi.
 

Solution 228
$\varepsilon = \dfrac{\sigma_x}{E} - \nu \dfrac{\sigma_y}{E} = 0$

Solution to Problem 227 Biaxial Deformation

Problem 227
A 150-mm-long bronze tube, closed at its ends, is 80 mm in diameter and has a wall thickness of 3 mm. It fits without clearance in an 80-mm hole in a rigid block. The tube is then subjected to an internal pressure of 4.00 MPa. Assuming ν = 1/3 and E = 83 GPa, determine the tangential stress in the tube.
 

Solution to Problem 226 Biaxial Deformation

Problem 226
A 2-in.-diameter steel tube with a wall thickness of 0.05 inch just fits in a rigid hole. Find the tangential stress if an axial compressive load of 3140 lb is applied. Assume ν = 0.30 and neglect the possibility of buckling.
 

Solution to Problem 225 Biaxial Deformation

Problem 225
A welded steel cylindrical drum made of a 10-mm plate has an internal diameter of 1.20 m. Compute the change in diameter that would be caused by an internal pressure of 1.5 MPa. Assume that Poisson's ratio is 0.30 and E = 200 GPa.
 

Solution to Problem 224 Triaxial Deformation

Problem 224
For the block loaded triaxially as described in Prob. 223, find the uniformly distributed load that must be added in the x direction to produce no deformation in the z direction.
 

Solution to Problem 222 Poisson's Ratio

Problem 222
A solid cylinder of diameter d carries an axial load P. Show that its change in diameter is 4Pν / πEd.
 

Solution to Problem 219 Axial Deformation

Problem 219
A round bar of length L, which tapers uniformly from a diameter D at one end to a smaller diameter d at the other, is suspended vertically from the large end. If w is the weight per unit volume, find the elongation of ω the rod caused by its own weight. Use this result to determine the elongation of a cone suspended from its base.
 

Solution to Problem 218 Axial Deformation

Problem 218
A uniform slender rod of length L and cross sectional area A is rotating in a horizontal plane about a vertical axis through one end. If the unit mass of the rod is ρ, and it is rotating at a constant angular velocity of ω rad/sec, show that the total elongation of the rod is ρω2 L3/3E.
 

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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