A cylindrical bar, whose lateral surface is constrained so that there can be no lateral expansion, is then loaded with an axial compressive stress 01=-6. (a) Find o22 and o33 in terms of o and the Poisson's ratio v. (b) Show that the effective Young's modulus (Er)eff= o1/111 is given by: (EY)eff= E(1 - v)/(1 – v– 2v² ) where E and v are the elastic constant and Poisson's ratio in the case of isotropic elasticity.

A cylindrical bar, whose lateral surface is constrained so that there can be no lateral expansion, is then loaded with an axial compressive stress 01=-6. (a) Find o22 and o33 in terms of o and the Poisson's ratio v. (b) Show that the effective Young's modulus (Er)eff= o1/111 is given by: (EY)eff= E(1 - v)/(1 – v– 2v² ) where E and v are the elastic constant and Poisson's ratio in the case of isotropic elasticity.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Consider a one-element triangular mesh shown in Figure 2. The edge AC is fixed. The edge BC is subject to lin- early varying traction normal to the edge as shown in Figure 2. Assume plane-stress conditions with thickness 1 = 1 cm and Young's modulus E = 70 GPa and Poisson's ratio v = 0.3. 150 kN/m 50 kN/m C (0,0.3) B (0.4,0.3) a) Specify the boundary condi- tions. b) Construct the stiffness matrix. A (0,0) c) Calculate the global force ma- Figure 2: Triangular element. All coordinates are in meters. trix. d) Solve for the unknown displace- ments and compute the stress at (0.1, 0.2).
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FN = 50
Fined the stress in each segment and the displacement in each segment
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A steel ring at a room temperature has a radius of R, of 1.00 mm x 1.00 mm. One like to insert a bar of radius R, = 2.002 cm into the ring. The following data is known for steel: 2.00 cm and a cross section area • Young Modulus E = 2.00 × 1011 Pa. • Coefficient of length contraction a = 1.20 x 10-5 C-1 • Specific heat capacity c = 511 J.kg-1.C-1 • Mass density p= 8050 kg.m -3 (a) What is the amount of heat needed for heating the ring so that the rod can fitted into it. (b) Assume the rod is rigid, calculate the pressure on the surface of the rod as the steel cool down to the room temperature.
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