1.5-8 A steel pipe of length L = 2 m, outside diameter d=110 mm, and wall thickness t = 8 mm is subjected to an axial compressive load P = 160 kN (see figure). Assuming that E 200 GPa and v= 0.3, find (a) the shortening & of the pipe, (b) the increase Ad in outside diameter, and (c) the increase At in wall thickness. =

1.5-8 A steel pipe of length L = 2 m, outside diameter d=110 mm, and wall thickness t = 8 mm is subjected to an axial compressive load P = 160 kN (see figure). Assuming that E 200 GPa and v= 0.3, find (a) the shortening & of the pipe, (b) the increase Ad in outside diameter, and (c) the increase At in wall thickness. =

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.5.2P: A steel wire (E = 200 GPa) of a diameter d = L25 mm is bent around a pulley of a radius i/o = 500 mm...

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A thin-walled circular tube and a solid circular bar of the same material (see figure) are subjected to torsion. The tube and bar have the same cross-sectional area and the same length. What is the ratio of the strain energy U1in the tube to the strain energy U2in the solid bar if the maximum shear stresses are the same in both cases? (For the tube, use the approximate theory for thin-walled bars.)
A hollow circular pipe (see figure} support s a load P that is uniformly distributed around a cap plate at the top of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are d1= 50 mm, d2= 60 mm, rf3 = 57 mm, and d1= 64 mm, respectively. Pipe lengths are Lt= 2 m and L, = 3 m. Neglect the self-weight of the pipes. Assume that cap plate thickness is small compared to I, and E,. Let E = 110 MPa. (a) If the tensile stress in the upper part is d = 10.5 MPa. what is load PI Also, what are reactions ft, at the upper support and R-, at the lower support? What is the stress ar(MPa) in the lower part? (b) Find displacement S(mm) at the cap plate. Plot the axial force diagram (AFD) [Ar(.f)] and axial displacement diagram (ADD)[5(.t)]. (c) Add the uniformly distributed load q along the censorial axis of pipe segment 2. Find q (kN/m) so that It, = 0. Assume that load P from part (a) is also applied.
-3 An element of aluminum in the form of a rectangular parallelepiped (see figure) of dimensions a = 5.5 in., h = 4.5 in, and c = 3.5 in. is subjected to iriaxial stresses = 12,500 psi, o. = —5000 psi, and ci. = —1400 psi acting on the x,i, and z faces, respectively. Determine the following quantities: (a) the maxim um shear stress in the material; (b) the changes ..la, .11. and 1c in the dimensions of the element: (C) the change .IJ’ in the volume: (d) the strain energy U stored in the element: (e) the maximum value of cr1 when the change in volume must be limited to 0.021%; and (f) the required value of o when the strain energy must be 900 in.-lb. (Assume E = 10,400 ksi and v = 0.33.)
A steel pipe is subjected to a quadratic distributed load over its height with the peak intensity q0at the base (see figure). Assume the following pipe properties and dimensions: height L, outside diameter d = 200 mm, and wall thickness f = 10 mm. Allowable stresses for flexure and shear are o~a=125 MPa and Ta= 30 MPa, If L = 2.6 m, Fmd^0ayM (kN/m), assuming that allowable flexure and shear stresses in the pipe are not to be exceeded. If q0= 60 kN/m, find the maximum height Lraajl(m) of the pipe if the allowable flexure and shear stresses in the pipe arc not to be exceeded.
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