VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
11th Edition
ISBN: 9781259633133
Author: BEER
Publisher: MCG
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Chapter 7.4, Problem 7.117P
(a)
To determine
The maximum tension in the cable.
(b)
To determine
The slope at B.
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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 7 Solutions
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
Ch. 7.1 - Prob. 7.1PCh. 7.1 - Prob. 7.2PCh. 7.1 - 7.3 Determine the internal forces at point J when...Ch. 7.1 - Prob. 7.4PCh. 7.1 - Prob. 7.5PCh. 7.1 - Prob. 7.6PCh. 7.1 - An archer aiming at a target is pulling with a...Ch. 7.1 - For the bow of Prob. 7.7, determine the magnitude...Ch. 7.1 - A semicircular rod is loaded as shown. Determine...Ch. 7.1 - A semicircular rod is loaded as shown. Determine...
Ch. 7.1 - A semicircular rod is loaded as shown. Determine...Ch. 7.1 - Fig. P7.11 and P7.12 7.12 A semicircular rod is...Ch. 7.1 - The axis of the curved member AB is a parabola...Ch. 7.1 - Knowing that the axis of the curved member AB is a...Ch. 7.1 - Prob. 7.15PCh. 7.1 - 7.16 Knowing that the radius of each pulley is 200...Ch. 7.1 - Prob. 7.17PCh. 7.1 - For the frame of Prob. 7.17, determine the...Ch. 7.1 - Knowing that the radius of each pulley is 200 mm...Ch. 7.1 - Fig. P7.19 and P7.20 7.20 Knowing that the radius...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - Prob. 7.23PCh. 7.1 - For the rod of Prob. 7.23, determine the magnitude...Ch. 7.1 - A semicircular rod of weight W and uniform cross...Ch. 7.1 - Prob. 7.26PCh. 7.1 - Prob. 7.27PCh. 7.1 - 7.27 and 7.28 A half section of pipe rests on a...Ch. 7.2 - Prob. 7.29PCh. 7.2 - Prob. 7.30PCh. 7.2 - Prob. 7.31PCh. 7.2 - Prob. 7.32PCh. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.35 and 7.36 For the beam and loading shown, (a)...Ch. 7.2 - Prob. 7.36PCh. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - For the beam and loading shown, (a) draw the shear...Ch. 7.2 - 7.39 through 7.42 For the beam and loading shown,...Ch. 7.2 - Prob. 7.41PCh. 7.2 - 7.39 through 7.42 For the beam and loading shown,...Ch. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Solve Problem 7.43 knowing that P = 3wa. PROBLEM...Ch. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Prob. 7.46PCh. 7.2 - Prob. 7.47PCh. 7.2 - Prob. 7.48PCh. 7.2 - Prob. 7.49PCh. 7.2 - Prob. 7.50PCh. 7.2 - Prob. 7.51PCh. 7.2 - 7.51 and 7.52 Draw the shear and bending-moment...Ch. 7.2 - Two small channel sections DF and EH have been...Ch. 7.2 - Solve Prob. 7.53 when = 60. PROBLEM 7.53 Two...Ch. 7.2 - For the structural member of Prob. 7.53, determine...Ch. 7.2 - For the beam of Prob. 7.43, determine (a) the...Ch. 7.2 - Determine (a) the distance a for which the maximum...Ch. 7.2 - For the beam and loading shown, determine (a) the...Ch. 7.2 - A uniform beam is to be picked up by crane cables...Ch. 7.2 - Knowing that P = Q = 150 lb, determine (a) the...Ch. 7.2 - Prob. 7.61PCh. 7.2 - Prob. 7.62PCh. 7.3 - 7.63 Using the method of Sec, 73. solve Prob....Ch. 7.3 - Prob. 7.64PCh. 7.3 - Prob. 7.65PCh. 7.3 - Prob. 7.66PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.33....Ch. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.34....Ch. 7.3 - Prob. 7.69PCh. 7.3 - 7.69 and 7.70 For the beam and loading shown, (a)...Ch. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.39....Ch. 7.3 - Prob. 7.72PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.41....Ch. 7.3 - Prob. 7.74PCh. 7.3 - Prob. 7.75PCh. 7.3 - Prob. 7.76PCh. 7.3 - 7.77 and 7.78 For the beam and loading shown. (a)...Ch. 7.3 - 7.77 and 7.78 For the beam and loading shown, (a)...Ch. 7.3 - 7.79 and 7.80 For the beam and loading shown, (a)...Ch. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - 7.81 and 7.82 For the beam and loading shown, (a)...Ch. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - (a) Draw the shear and bending-moment diagrams for...Ch. 7.3 - Solve Prob. 7.83 assuming that the 300-lb force...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - Prob. 7.86PCh. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - Prob. 7.88PCh. 7.3 - Prob. 7.89PCh. 7.3 - Prob. 7.90PCh. 7.3 - Prob. 7.91PCh. 7.3 - Prob. 7.92PCh. 7.4 - Three loads are suspended as shown from the cable...Ch. 7.4 - Knowing that the maximum tension in cable ABCDE is...Ch. 7.4 - Prob. 7.95PCh. 7.4 - Prob. 7.96PCh. 7.4 - 7.97 Knowing that dC = 3 m, determine (a) the...Ch. 7.4 - Prob. 7.98PCh. 7.4 - Prob. 7.99PCh. 7.4 - Prob. 7.100PCh. 7.4 - Knowing that mB = 70 kg and mC = 25 kg, determine...Ch. 7.4 - Prob. 7.102PCh. 7.4 - Prob. 7.103PCh. 7.4 - Prob. 7.104PCh. 7.4 - Prob. 7.105PCh. 7.4 - If a = 4 m, determine the magnitudes of P and Q...Ch. 7.4 - An electric wire having a mass per unit length of...Ch. 7.4 - Prob. 7.108PCh. 7.4 - Prob. 7.109PCh. 7.4 - Prob. 7.110PCh. 7.4 - Prob. 7.111PCh. 7.4 - Two cables of the same gauge are attached to a...Ch. 7.4 - Prob. 7.113PCh. 7.4 - Prob. 7.114PCh. 7.4 - Prob. 7.115PCh. 7.4 - Prob. 7.116PCh. 7.4 - Prob. 7.117PCh. 7.4 - Prob. 7.118PCh. 7.4 - Prob. 7.119PCh. 7.4 - Prob. 7.120PCh. 7.4 - Prob. 7.121PCh. 7.4 - Prob. 7.122PCh. 7.4 - Prob. 7.123PCh. 7.4 - Prob. 7.124PCh. 7.4 - Prob. 7.125PCh. 7.4 - Prob. 7.126PCh. 7.5 - A 25-ft chain with a weight of 30 lb is suspended...Ch. 7.5 - A 500-ft-long aerial tramway cable having a weight...Ch. 7.5 - Prob. 7.129PCh. 7.5 - Prob. 7.130PCh. 7.5 - Prob. 7.131PCh. 7.5 - Prob. 7.132PCh. 7.5 - Prob. 7.133PCh. 7.5 - Prob. 7.134PCh. 7.5 - Prob. 7.135PCh. 7.5 - Prob. 7.136PCh. 7.5 - Prob. 7.137PCh. 7.5 - Prob. 7.138PCh. 7.5 - Prob. 7.139PCh. 7.5 - Prob. 7.140PCh. 7.5 - Prob. 7.141PCh. 7.5 - Prob. 7.142PCh. 7.5 - Prob. 7.143PCh. 7.5 - Prob. 7.144PCh. 7.5 - Prob. 7.145PCh. 7.5 - Prob. 7.146PCh. 7.5 - Prob. 7.147PCh. 7.5 - Prob. 7.148PCh. 7.5 - Prob. 7.149PCh. 7.5 - Prob. 7.150PCh. 7.5 - A cable has a mass per unit length of 3 kg/m and...Ch. 7.5 - Prob. 7.152PCh. 7.5 - Prob. 7.153PCh. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Two members, each consisting of a straight and a...Ch. 7 - Knowing that the radius of each pulley is 150 mm,...Ch. 7 - Prob. 7.158RPCh. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - Prob. 7.161RPCh. 7 - Prob. 7.162RPCh. 7 - Prob. 7.163RPCh. 7 - Prob. 7.164RPCh. 7 - A 10-ft rope is attached to two supports A and B...
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