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Concept explainers
*16 A prismatic bar AB of length L, cross-sectional area A, modulus of elasticity E, and weight Changs vertically under its own weight (see figure).
(a) Derive a formula for the downward displacement Scof point E. located at distance It from the lower end of the bar.
(b) What is the elongation SBof the entire bar?
(c) What is the ratio £ of the elongation, of the upper half of the bar to the elongation of the lower half of the bar?
(d) If bar A B is a riser pipe hanging from a drill rig at sea. what is the total elongation of the pipe? Let L = 1500 m, A - 0.ol57 m2, and E = 210 GPa. See Appendix 1 for weight densities of steel and sea water. (See Probs. 1.4-2 and J.7-13 for additional figures.)
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Chapter 2 Solutions
Mechanics of Materials, SI Edition
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- Generate the kinematic diagram of the following mechanism. Then, draw their graphs and calculate their degrees of freedom (DoF) using Gruebler's formula.arrow_forwardAn elastic bar of length L = 1m and cross section A = 1cm2 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, where ω= 100rad/s is the angular velocity. The bar is pinned on the rotation axis at x = 0. A mass M = 1kg is attached to the right end of the bar. Due to the radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) solves the BVP (strong form) sketched below: d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (1) u(0) =?? essential BC σ(L) =?? natural BC where σ(x) is the axial stress in the rod, ρ= 2700kg /m3 is the mass density, and E = 70GPa is the Young’s modulus 1. Define appropriate BCs for the strong BVP 2. Find the solution of the strong BVP analytically 3. Derive the weak form of the BVP.arrow_forwardGruebler's formula for the following mechanism?arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
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