Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)
5th Edition
ISBN: 9780134301006
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 13.1, Problem 15P
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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).
Chapter 13 Solutions
Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)
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Ch. 13.1 - The gas pipe line is supported every 20 ft by...Ch. 13.1 - Prob. 12PCh. 13.1 - An A-36-steel hoop has an inner diameter of 23.99...Ch. 13.1 - The ring, having the dimensions shown, is placed...Ch. 13.1 - Prob. 15PCh. 13.1 - Prob. 16PCh. 13.1 - Prob. 17PCh. 13.2 - In each case, determine the internal loadings that...Ch. 13.2 - The internal loadings act on the section. Show the...Ch. 13.2 - Determine the normal stress at comers A and B of...Ch. 13.2 - Determine the state of stress at point A on the...Ch. 13.2 - Determine the state of stress at point A on the...Ch. 13.2 - Determine the magnitude of the load P that will...Ch. 13.2 - Prob. 5FPCh. 13.2 - Determine the state of stress at point A on the...Ch. 13.2 - Determine the state of stress at point A on the...Ch. 13.2 - Determine the state of stress at point A on the...Ch. 13.2 - Determine the shortest distance d to the edge of...Ch. 13.2 - Determine the maximum distance d to the edge of...Ch. 13.2 - The plate has a thickness of 20 mm and the force P...Ch. 13.2 - If the load has a weight of 600 lb, determine the...Ch. 13.2 - The steel bracket is used to connect the ends of...Ch. 13.2 - Prob. 23PCh. 13.2 - The column is built up by gluing the two boards...Ch. 13.2 - Prob. 25PCh. 13.2 - The screw of the clamp exerts a compressive force...Ch. 13.2 - Prob. 27PCh. 13.2 - Prob. 28PCh. 13.2 - The joint is subjected to the force system shown....Ch. 13.2 - Prob. 30PCh. 13.2 - The 12-in.-diameter holt hook is subjected to the...Ch. 13.2 - Prob. 32PCh. 13.2 - Prob. 33PCh. 13.2 - Prob. 34PCh. 13.2 - Prob. 35PCh. 13.2 - The drill is jammed in the wall and is subjected...Ch. 13.2 - The drill is jammed in the wall and is subjected...Ch. 13.2 - The frame supports the distributed load shown....Ch. 13.2 - Prob. 39PCh. 13.2 - The rod has a diameter of 40 mm. If it is...Ch. 13.2 - The rod has a diameter of 40 mm. If it is...Ch. 13.2 - The beveled gear is subjected to the loads shown....Ch. 13.2 - The beveled gear is subjected to the loads shown....Ch. 13.2 - Determine the normal-stress developed at points A...Ch. 13.2 - Sketch the normal-stress distribution acting over...Ch. 13.2 - Prob. 46PCh. 13.2 - The solid rod is subjected to the loading shown....Ch. 13.2 - Prob. 48PCh. 13.2 - Prob. 49PCh. 13.2 - The C-frame is used in a riveting machine. If the...Ch. 13.2 - Prob. 51PCh. 13.2 - The uniform sign has a weight of 1500 lb and is...Ch. 13.2 - The uniform sign has a weight of 1500 lb and is...Ch. 13 - The post has a circular cross section of radius c....Ch. 13 - The 20-kg drum is suspended from the hook mounted...Ch. 13 - The 20-kg drum is suspended from the hook mounted...Ch. 13 - Prob. 4RPCh. 13 - If the cross section of the femur at section aa...Ch. 13 - Prob. 6RPCh. 13 - Prob. 7RPCh. 13 - Prob. 8RP
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- 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).arrow_forwardCalculate the mean piston speed (in mph) for a Formula 1 engine running at 14,750 rpm with a bore of 80mm and a stroke of 53mm. Estimate the average acceleration imparted on the piston as it moves from TDC to 90 degrees ATDCarrow_forwardCalculate the compression ratio of an engine with a stroke of 4.2inches a bore of 4.5 inches and a clearance volume of 6.15 cubic inches. Discuss whether or not this is a realistic compression ratio for a street engine and what octane rating of fuel it would need to run correctlyarrow_forward
- Draw the free-body diagram for the pinned assembly shown. Find the magnitude of the forces acting on each member of the assembly. 1500 N 1500 N C 45° 45° 45° 45° 1000 mmarrow_forwardAn elastic bar of length L 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. Due to 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 (1) 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 free at x = L. Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).arrow_forwardWith reference to the given figure: a) Draw a free-body diagram of the structure supporting the pulley. b) Draw shear and bending moment diagrams for both the vertical and horizontal portions of the structure. 48 in. 100 lb 12 in. Cable 27 in. 12-in. pulley radius 100 lb Cablearrow_forward
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