Mechanics of Materials
11th Edition
ISBN: 9780137605514
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 8.2, Problem 45P
Neglect the weight of the block.
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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) = ω2x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement d u(x) is governed by the following equations: 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). SIDE QUESTION: I saw a tutor solve it before but I didn't understand why the tutor did not divide E under the second term (c1x) before finding u(x). The tutor only divided E under first term. please explain and thank you
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Chapter 8 Solutions
Mechanics of Materials
Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - The thin-walled cylinder can be supported in one...Ch. 8.1 - If the inner diameter of the tank is 22 in., and...Ch. 8.1 - Prob. 5PCh. 8.1 - 88. The steel water pipe has an inner diameter of...Ch. 8.1 - The steel water pipe has an inner diameter of 12...Ch. 8.2 - Fundamental Problems F81. Determine the normal...Ch. 8.2 - Show the results in a differential element at the...Ch. 8.2 - Determine the state of stress at point A on the...
Ch. 8.2 - Determine the magnitude of the load P that will...Ch. 8.2 - Determine the state of stress at point B. Show the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Show the results in a differential element at the...Ch. 8.2 - The plate has a thickness of 20 mm and P acts...Ch. 8.2 - Plot the distribution of normal stress acting...Ch. 8.2 - Also, plot the normal-stress distribution over the...Ch. 8.2 - Determine the stress components at point A on the...Ch. 8.2 - Determine the stress components at point B on the...Ch. 8.2 - If it is subjected to the force system shown,...Ch. 8.2 - Neglect the weight of the block.Ch. 8.2 - Neglect the weight of the block.Ch. 8.2 - He is supported uniformly by two bars, each having...Ch. 8.2 - Specify the region to which this load can be...Ch. 8.2 - The pins at C and D are at the same location as...Ch. 8.2 - If the force at the ram on the clamp at D is P= 8...Ch. 8.2 - Determine the maximum ram force P that can be...Ch. 8.2 - and an outer radius of 3.00 in. If the face of the...Ch. 8 - If it supports a cable loading of 800 lb,...Ch. 8 - Determine the state of stress at point E on the...Ch. 8 - Determine the state of stress at point F on the...Ch. 8 - The suspender arm AE has a square cross-sectional...Ch. 8 - If the cross section of the femur at section aa...Ch. 8 - If it has a mass of 5 kg/m, determine the largest...Ch. 8 - and is used to support the vertical reactions of...Ch. 8 - and is used to support the vertical reactions of...
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- 6. Consider a 10N step input to the mechanical system shown below, take M = 15kg, K = 135N/m, and b = 0.4 Ns/m. (a) Assume zero initial condition, calculate the (i) System pole (ii) System characterization, and (iii) The time domain response (b) Calculate the steady-state value of the system b [ www K 个 х M -F(+)arrow_forward2. Solve the following linear time invariant differential equations using Laplace transforms subject to different initial conditions (a) y-y=t for y(0) = 1 and y(0) = 1 (b) ÿ+4y+ 4y = u(t) for y(0) = 0 and y(0) = 1 (c) y-y-2y=0 for y(0) = 1 and y(0) = 0arrow_forward3. For the mechanical systems shown below, the springs are undeflected when x₁ = x2 = x3 = 0 and the input is given as fa(t). Draw the free-body diagrams and write the modeling equations governing each of the systems. K₁ 000 K₂ 000 M₁ M2 -fa(t) B₂ B₁ (a) fa(t) M2 K₂ 000 B K₁ x1 000 M₁ (b)arrow_forward
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