The two-segment statically indeterminate bar in the following figure has a constant cross- sectional area A = 0.8 in². It is made entirely of material that has elastic, perfectly plastic behaviour with oy = 36 ksi and E = 30x103 ksi. If P=50kip is applied to the bar and then removed 20 in. (1) 40 in. (2) Ey (a) A two-segment bar. (b) A stress-strain diagram for an elastic, perfectly-plastic material. a) Determine the residual stress in each segment. b) Find the permanent deformation at point B. c) Determine the smallest load P needed to cause segment CB to yield. 1.5 ksi 5.67 ksi 7.5 ksi 10 ksi 20 ksi 36 ksi 65.15 ksi 0.002 in 0.003 in 0.007556 0.001 in 0.02 in 0.104242 in 57.6 kip 60 kip 48 kip 80 kip 600 kip

The two-segment statically indeterminate bar in the following figure has a constant cross- sectional area A = 0.8 in². It is made entirely of material that has elastic, perfectly plastic behaviour with oy = 36 ksi and E = 30x103 ksi. If P=50kip is applied to the bar and then removed 20 in. (1) 40 in. (2) Ey (a) A two-segment bar. (b) A stress-strain diagram for an elastic, perfectly-plastic material. a) Determine the residual stress in each segment. b) Find the permanent deformation at point B. c) Determine the smallest load P needed to cause segment CB to yield. 1.5 ksi 5.67 ksi 7.5 ksi 10 ksi 20 ksi 36 ksi 65.15 ksi 0.002 in 0.003 in 0.007556 0.001 in 0.02 in 0.104242 in 57.6 kip 60 kip 48 kip 80 kip 600 kip

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.3.21P: A slightly tapered bar AB of solid circular crass section and length L is supported at end B and...

See similar textbooks

Similar questions

A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
An elastomeric bearing pad consisting of two steel plates bonded to a chloroprene elastomer (an artificial rubber) is subjected to a shear force V during a static loading test (see figure). The pad has dimensions a = 125 mm and b = 240 mm, and the elastomer has a thickness t = 50 mm. When the Force V equals 12 kN, the top plate is found to have displaced laterally S.O mm with respect to the bottom plate. What is the shear modulus of elasticity G of the chloroprene?
A plastic rod AB of length L = 0.5 m has a diameter d1= 30 mm (see figure). A plastic sleeve CD of length c = 0.3 m and outer diameter d2= 45 mm is securely bonded to the rod so that no slippage can occur between the rod and the sleeve. The rod is made of an acrylic with a modulus of elasticity E1= 3.1 GPa, and the sleeve is made of a polyamide with E2= 2.5 GPa. (a) Calculate the elongation d of the rod when it is pulled by axial forces P = 12 kN. (b) If the sleeve is extended for the full length of the rod, what is the elongation? (c) If the sleeve is removed, what is the elongation?
Solve the preceding problem if the cube is granite (E = 80 GPa, v = 0.25) with dimensions E = 89 mm and compressive strains E = 690 X l0-6 and = = 255 X 10-6. For part (c) of Problem 7.6-5. find the maximum value of cr when the change in volume must be limited to 0.11%. For part. find the required value of when the strain energy must be 33 J.
*16 A prismatic bar AB of length L, cross-sectional area A, modulus of elasticity E, and weight Changs vertically under its own weight (see figure). (a) Derive a formula for the downward displacement Scof point E. located at distance It from the lower end of the bar. (b) What is the elongation SBof the entire bar? (c) What is the ratio £ of the elongation, of the upper half of the bar to the elongation of the lower half of the bar? (d) If bar A B is a riser pipe hanging from a drill rig at sea. what is the total elongation of the pipe? Let L = 1500 m, A - 0.ol57 m2, and E = 210 GPa. See Appendix 1 for weight densities of steel and sea water. (See Probs. 1.4-2 and J.7-13 for additional figures.)
The length of the end segments of the bar (see figure) is 20 in. and the length of the prismatic middle segment is 50 in. Also, the diameters at cross sections A. B, C, and D are 0.5, 1.0, 1.0, and 0.5 in., respectively, and the modulus of elasticity is 18 ,000 ksi. (a) Calculate the elongation of a copper bar of solid circular cross section with tapered ends when it is stretched by axial loads of magnitude 3.0 kips (see figure). (b) If the total elongation of the bar cannot exceed 0.025 in., what are the required diameters at B and C? Assume that diameters at A and D remain at 0.5 in.
A bimetallic bar (or composite bar) of square cross sec lion with dimensions 2b X lb is construe ted of two different metals having module of elasticity E2and E2(see figure). The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces P acting through rigid end plates. T h e line of action of t he loads has an eccentricity e of such magnitude that each part of the bar is stressed uniformly in compression. (a) Determine the axial forces Ptand P2in the two parts of the bar. (b} Determine the eccentricity e of the loads. (c) Determine the ratio C|/tr2 of the stresses in the two parts of the bar.
A slightly tapered bar AB of solid circular crass section and length L is supported at end B and subjected to a tensile load P at the free end A. The diameters of the bar at ends A and B are dAand dB. respectively. Determine the length of the bar if the elongation of the bar due to the load P = 45 kips is 0.02 in. Assume that E = 10,400 ksi.
A vertical bar is loaded with axial loads at points B, C, and D. as shown in the figure. The bar is made of steel with a modulus of elasticity E = 29,000 ksi., The bar has a cross-sectional area of 8.24 in2. Calculate the displacements at points B, C, and D. Ignore the weight of the bar
(a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressure
An aluminum bar subjected to tensile Forces P has a length L = 150 in. and cross-sectional area A = 2.0 in2 The stress-strain behavior of the aluminum may be represented approximately by the bilinear stress-strain diagram shown in the figure. Calculate the elongation S of the bar for each of the following axial loads: p = 8 kips, 16 kips. 24 kips, 32 kips, and 40 kips. From these results, plot a diagram of load P versus elongation S (load-displacement diagram).
A round bar ABC of length 2L (see figure) rotates about an axis through the midpoint C with constant angular speed w (radians per second). The material of the bar has weight density y. (a) Derive a formula for the tensile stress a’ in the bar as a function of the distance x from the midpoint C. (b) What is the maximum tensile stress a max?