Mechanics of Materials
11th Edition
ISBN: 9780137605514
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Textbook Question
Chapter 14, Problem 8RP
The truss is made from A992 steel rods each having a diameter of 1 in.
R14–7/8
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The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L.
Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).
The heated rod from Problem 3 is subject to a volumetric heatingh(x) = h0xLin units of [Wm−3], as shown in the figure below. Under theheat supply the temperature of the rod changes along x with thetemperature function T(x). The temperature T(x) is governed by thefollowing equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(4)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. Both ends of the bar are in contact with a heatreservoir at zero temperature.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
A heated rod of length L is subject to a volumetric heating h(x) = h0xLinunits of [Wm−3], as shown in the figure below. Under the heat supply thetemperature of the rod changes along x with the temperature functionT(x). The temperature T(x) is governed by the following equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(3)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. The left end of the bar is in contact with a heatreservoir at zero temperature, while the right end of the bar is thermallyinsulated.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
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 - The A-36 steel bar consists of two segments, one...Ch. 14.2 - If P = 10 kip, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - Consider the thin-walled tube of Fig.5-26 . Use...Ch. 14.2 - Determine the bending strain energy in the 2-in...Ch. 14.2 - Determine the bending strain energy in the...Ch. 14.2 - Determine the bending strain energy in the simply...Ch. 14.3 - Determine the horizontal displacement of joint A....
Ch. 14.3 - Determine the vertical displacement of point S on...Ch. 14.3 - Prob. 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. 44PCh. 14.4 - The collar has a weight of 50 lb and falls down...Ch. 14.4 - Prob. 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 - 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 vertical displacement of joint E....Ch. 14.6 - Determine the horizontal displacement of joint B...Ch. 14.6 - Determine the vertical displacement of joint C 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 - 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 at A of the 2014T6 aluminum...Ch. 14.7 - Prob. 104PCh. 14.7 - Prob. 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 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 - The beam is made of oak, for which Eo = 11 GPa....Ch. 14.7 - Determine the slope of the shaft at the bearing...Ch. 14.7 - The L-shaped frame is made from two segments, each...Ch. 14.7 - Determine the vertical displacement of the ring at...Ch. 14.7 - Determine the horizontal displacement at the...Ch. 14.9 - Solve Prob. 1473 using Castiglianos theorem. 1473....Ch. 14.9 - Solve Prob. 1474 using Castiglianos theorem. 1474....Ch. 14.9 - Prob. 125PCh. 14.9 - Prob. 126PCh. 14.9 - Prob. 127PCh. 14.9 - Solve Prob. 1478 using Castiglianos theorem. 1478....Ch. 14.9 - Solve Prob. 1481 using Castiglianos theorem. 1481....Ch. 14.9 - Solve Prob. 1482 using Castiglianos theorem. 1482....Ch. 14.9 - Solve Prob. 1485 using Castiglianos theorem. 1485....Ch. 14.9 - Solve Prob. 1486 using Castiglianos theorem. 1486....Ch. 14.10 - Solve Prob. 1490 using Castiglianos theorem. 1490....Ch. 14.10 - Solve Prob. 1491 using Castiglianos theorem. 1491....Ch. 14.10 - Prob. 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. 139PCh. 14.10 - Prob. 140PCh. 14.10 - Prob. 141PCh. 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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