Imagine you have used several straingages to measure a 2D strain field on the surface of a material, which you find to be5+2xy(x² + y² + 2),4=€xx = 5+x² + y² +xª+yª, €yy = 6 + 3x² + 3y² + x² + y², €xyExz = Eyz = Ezz = 0.where x, y are coordinates. Verify compatibility and determine the displacement field, assum-ing displacement and rotation at the origin are zero.

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Answered: gages to measure a 2D strain field on…

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 the following strain state: [0.0016 0.0003 [0] = 0.0003 0.0008 0 0 0 0 0.0004] a. Determine the strain matrix for this strain state if the axes are rotated 30° counterclockwise around z-axis. b. Plot Mohr's circle for this strain state.
Determine whether the following strain field is compatible: Ex = 3y² + xy, Ey₁ = 2y + 4z + 3, ₂ = 3zx + 2xy, Yxy = 4xy, Yyz = 2xz, and Yxz = 2xyz.
3) The displacement field of a screw dislocation of Burger's vector b is given by u = v = 0, W = tan -1y 2n Find the Cartesian and polar components of the strain tensor.
3.11e If the deformation mapping of a body in a naval machine is given by X(X) = (X₁ + AX₂)ê₁ + (X₂ + BX₁)êz + X3ê3, where A and B are constants. Determine the components of the Euler strain tensors.
Q3 coordinates is given by: The 3-dimensional state of strain at a material point in x, y, z xx [ε] = &₁ Ex Exy Evy zy E XZ E 0 0 0 = 0 -1 -3 *10* 0 -3 5 (a) Calculate the characteristic equation and determine the principal strains for the three-dimensional state of strain (b) Calculate the volumetric strain and the deviatoric strain invariants
Solve the differential equation dy-xdx = 0 if the curve passes through (1,0).
Given the stress tensor: Find: 3 36 27 0 σ = 27-36 00 0 18 (a) The components of the traction (force per unit area) acting on a plane with unit normal n= 2 21 3 3'3 T (b) The component of the traction in the direction of the normal (c) The angle between the traction and the normal vector (d) The magnitude of the traction vector (e) The net force acting on a cube with corners at (x,y,z)=(±1,±1,±1)
A 60º strain rosette, or delta rosette, is composed of three electrical resistance strain gauges arranged as shown in figure 5. Strain gauge A measures the normal strain εa in the x-axis direction. Strain gauges B and C measure the strains εb and εc in the indicated inclined directions. Using Mohr's Circle, obtain the equations for the strains εxx, εyy and γxy associated with the x and y axes.
Consider that l'm pulling a material with a 5N force as below: Material Hanging 5N mass And I get the following force vs strain curves below (showing how the material stretches) depending on how long the force is applied. 5N 5 N 10 12 3 4 5 6 7 89 10 to 1 2 3 4 5 6 7 89 10 0.05 0.05 0.02 0 12 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time (s) Time (s) What sort of material is this? What are the viscosity and spring constant of the material? What is the time threshold that determines whether the material acts as a liquid or solid? What is the characteristic frequency of the material? What real world material property does this model describe? Strain Force Strain Force
۱:۳۵ ۱ ص STATIC QU... -> FIND moments around O, A and B 500N 1 900N 60° В 4m A 5m CU
Consider an offset field given by: u(x, y) ;(-4x³y + 6Lx²y – L³y) (m) v(x, y) = (-x* + 2Lx² – L°x) (m) 24EI 24EI where q, E, and I are known positive real numbers. (a) Determine the components of the strain field. (b) Determine the strain tensor components for x = L mm and y = 10 mm %3D
Q1 The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: xy [0]=0x0y 0 zy [100 0 of 0₂2 0 70 50 6 0 0 -90 70 MPa The material is linear elastic (E=210 GPa, v=0.3)

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