Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 14.2, Problem 14.1P
A material is subjected to a general state of plane stress. Express the strain energy density in terms of the elastic constants E, G, and ν and the stress components σx, σy, and τxy.
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The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression γy/3E where γ = 2.9 lb/in.3 is the specific weight of the material, y = 3.4 in. is the distance from the free (i.e., bottom) end of the bar, L = 17 in. is the length of the bar, and E = 24000 ksi is a material constant. Determine,
(a) the change in length of the bar due to its own weight.
(b) the average normal strain over the length L of the bar.
(c) the maximum normal strain in the bar.
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Chapter 14 Solutions
Mechanics of Materials
Ch. 14.2 - A material is subjected to a general state of...Ch. 14.2 - The strain-energy density for plane stress must be...Ch. 14.2 - 14–3. Determine the strain energy in the stepped...Ch. 14.2 - Prob. 14.4PCh. 14.2 - Using bolts of the same material and...Ch. 14.2 - If P = 60 kN, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - *14–8. Determine the torsional strain energy in...Ch. 14.2 - Determine the torsional strain energy in the A-36...Ch. 14.2 - The shaft assembly is fixed at C. The hollow...
Ch. 14.2 - Prob. 14.11PCh. 14.2 - If P = 10 kip, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - Prob. 14.14PCh. 14.2 - 14–15. Determine the bending strain energy stored...Ch. 14.2 - Prob. 14.16PCh. 14.2 - Prob. 14.17PCh. 14.2 - 14–18. Determine the bending strain energy stored...Ch. 14.2 - Prob. 14.19PCh. 14.2 - Prob. 14.20PCh. 14.2 - Prob. 14.21PCh. 14.2 - 14–22. Determine the bending strain energy in the...Ch. 14.2 - Determine the bending strain energy in the...Ch. 14.2 - Determine the bending strain energy in the simply...Ch. 14.3 - 14–25. Determine the horizontal displacement of...Ch. 14.3 - Prob. 14.26PCh. 14.3 - 14–27. Determine the horizontal displacement of...Ch. 14.3 - *14–28. Determine the vertical displacement of...Ch. 14.3 - 14–29. Determine the displacement of point B on...Ch. 14.3 - Determine the vertical displacement of end B of...Ch. 14.3 - Determine the vertical displacement of point S on...Ch. 14.3 - EI is constant. Prob. 1432Ch. 14.3 - The A992 steel bars are pin connected at C and D....Ch. 14.3 - The A992 steel bars are pin connected at C. If...Ch. 14.3 - Determine the slope of the beam at the pin support...Ch. 14.3 - Prob. 14.36PCh. 14.3 - Prob. 14.37PCh. 14.3 - Prob. 14.38PCh. 14.3 - Prob. 14.39PCh. 14.3 - Prob. 14.40PCh. 14.3 - Determine the vertical displacement of end B of...Ch. 14.4 - A bar is 4 m long and has a diameter of 30 mm....Ch. 14.4 - Determine the diameter of a red brass C83400 bar...Ch. 14.4 - Prob. 14.44PCh. 14.4 - The collar has a weight of 50 lb and falls down...Ch. 14.4 - The collar has a weight of 50 lb and falls down...Ch. 14.4 - Prob. 14.47PCh. 14.4 - Prob. 14.48PCh. 14.4 - Prob. 14.49PCh. 14.4 - Prob. 14.50PCh. 14.4 - 14-51. Rods AB and AC have a diameter of 20 mm and...Ch. 14.4 - Prob. 14.52PCh. 14.4 - The composite aluminum 2014T6 bar is made from two...Ch. 14.4 - The composite aluminum 2014-T6 bar is made from...Ch. 14.4 - When the 100-lb block is at h = 3 ft above the...Ch. 14.4 - Prob. 14.56PCh. 14.4 - Prob. 14.57PCh. 14.4 - The tugboat has a weight of 120 000 lb and is...Ch. 14.4 - Prob. 14.59PCh. 14.4 - The weight of 175 lb is dropped from a height of 4...Ch. 14.4 - The weight of 175 lb, is dropped from a height of...Ch. 14.4 - Prob. 14.62PCh. 14.4 - Prob. 14.63PCh. 14.4 - Prob. 14.64PCh. 14.4 - * 14-65. Determine the maximum height h from which...Ch. 14.4 - Prob. 14.66PCh. 14.4 - The overhang beam is made of 2014T6 aluminum....Ch. 14.4 - If the beam is a W1015, determine the maximum...Ch. 14.4 - If the maximum allowable bending stress for the...Ch. 14.4 - A 40-lb weight is dropped from a height of h = 2...Ch. 14.4 - The car bumper is made of...Ch. 14.6 - Determine the vertical displacement of joint A....Ch. 14.6 - Determine the horizontal displacement of joint B....Ch. 14.6 - Determine the vertical displacement of joint B....Ch. 14.6 - Determine the vertical displacement of joint B....Ch. 14.6 - Determine the vertical displacement of joint E....Ch. 14.6 - Prob. 14.77PCh. 14.6 - Prob. 14.78PCh. 14.6 - Determine the horizontal displacement of joint B...Ch. 14.6 - Determine the vertical displacement of joint C of...Ch. 14.6 - 14-81. Determine the horizontal displacement of...Ch. 14.6 - 14-82. Determine the horizontal displacement of...Ch. 14.6 - Determine the vertical displacement of joint A....Ch. 14.6 - The truss is made from A992 steel rods having a...Ch. 14.6 - 14-85. Determine the vertical displacement of...Ch. 14.6 - 14-86. Determine the vertical displacement of...Ch. 14.7 - Determine the displacement at point C. El is...Ch. 14.7 - The beam is made of southern pine for which Ep =...Ch. 14.7 - Determine the displacement at point C. El is...Ch. 14.7 - Determine the slope at point C. El is constant....Ch. 14.7 - Determine the slope at point A. El is constant....Ch. 14.7 - Determine the displacement of point C of the beam...Ch. 14.7 - Determine the slope at B of the beam made from...Ch. 14.7 - The beam is made of Douglas fir. Determine the...Ch. 14.7 - Determine the displacement at pulley B. The A992...Ch. 14.7 - The A992 steel beam has a moment of inertia of I =...Ch. 14.7 - The A992 steel beam has a moment of inertia of I =...Ch. 14.7 - The A992 structural steel beam has a moment of...Ch. 14.7 - Determine the displacement at point C of the...Ch. 14.7 - Determine the slope at A of the shaft. El is...Ch. 14.7 - Determine the slope of end C of the overhang beam....Ch. 14.7 - Determine the displacement of point D of the...Ch. 14.7 - Determine the slope at A of the 2014T6 aluminum...Ch. 14.7 - Prob. 14.104PCh. 14.7 - Prob. 14.105PCh. 14.7 - Determine the displacement at point C of the W14 ...Ch. 14.7 - Determine the slope at A of the W14 26 beam made...Ch. 14.7 - Determine the slope at A. El is constant. Prob....Ch. 14.7 - Determine the slope at C of the overhang white...Ch. 14.7 - Determine the displacement at point D of the...Ch. 14.7 - Determine the maximum deflection of the beam...Ch. 14.7 - Prob. 14.112PCh. 14.7 - Determine the slope of the shaft at the bearing...Ch. 14.7 - Prob. 14.114PCh. 14.7 - Beam AB has a square cross section of 100 mm by...Ch. 14.7 - Beam AB has a square cross section of 100 mm by...Ch. 14.7 - Bar ABC has a rectangular cross section of 300 mm...Ch. 14.7 - Bar ABC has a rectangular cross section of 300 mm...Ch. 14.7 - The L-shaped frame is made from two segments, each...Ch. 14.7 - The L-shaped frame is made from two segments, each...Ch. 14.7 - Prob. 14.121PCh. 14.7 - Prob. 14.122PCh. 14.9 - Solve Prob. 1473 using Castiglianos theorem. 1473....Ch. 14.9 - Solve Prob. 1474 using Castiglianos theorem. 1474....Ch. 14.9 - Prob. 14.125PCh. 14.9 - Prob. 14.126PCh. 14.9 - Prob. 14.127PCh. 14.9 - Prob. 14.128PCh. 14.9 - Prob. 14.129PCh. 14.9 - Prob. 14.130PCh. 14.9 - Prob. 14.131PCh. 14.9 - *14-132. Solve Prob. 14-86 using Castigliano’s...Ch. 14.10 - Solve Prob. 1490 using Castiglianos theorem. 1490....Ch. 14.10 - Solve Prob. 1491 using Castiglianos theorem. 1491....Ch. 14.10 - Prob. 14.135PCh. 14.10 - Solve Prob. 1493 using Castiglianos theorem. 1493....Ch. 14.10 - Solve Prob. 1495 using Castiglianos theorem. 1495....Ch. 14.10 - Solve Prob. 1496 using Castiglianos theorem. 1496....Ch. 14.10 - Prob. 14.139PCh. 14.10 - Prob. 14.140PCh. 14.10 - Prob. 14.141PCh. 14.10 - Solve Prob. 14119 using Castiglianos theorem....Ch. 14.10 - Prob. 14.143PCh. 14.10 - Prob. 14.144PCh. 14.10 - Prob. 14.145PCh. 14 - A = 2300 mm2, I = 9.5(106) mm4. R141Ch. 14 - If the spring at B has a stiffness k = 200 kN/m....Ch. 14 - The spring at B has a stiffness k = 200 kN/m....Ch. 14 - If they each have a diameter of 30 mm, determine...Ch. 14 - and a length of 10 in. It is struck by a hammer...Ch. 14 - Determine the total axial and bending strain...Ch. 14 - The truss is made from A992 steel rods each having...Ch. 14 - The truss is made from A992 steel rods each having...Ch. 14 - El is constant. Use the method of virtual work....Ch. 14 - using Castiglianos theorem. R149. The cantilevered...
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