2. The displacements, in meters, at an arbitrary point (x,y,z) in a given body are: u(x, y,2) = (x*y+xy*)×104 v(x, y,2) = x³y³ x104 w(x, y, z) = 0 (a) Determine all the strains in x-y-z coordinates at any point (x,y,z). (b) Is the body in plane strain? Explain why or why not. (c) Determine by a calculation whether or not compatibility holds for this strain field. (d) From (a) what is the strain tensor at the point (1,2,1)? (e) Compute the principal normal strains at the point (1,2,1). (f) What is the maximum shear strain at the point (1,2,1)? (g) If the shear modulus of the material is 80 MPa, find the difference between the two principal stresses.

2. The displacements, in meters, at an arbitrary point (x,y,z) in a given body are: u(x, y,2) = (xy+xy)×104 v(x, y,2) = x³y³ x104 w(x, y, z) = 0 (a) Determine all the strains in x-y-z coordinates at any point (x,y,z). (b) Is the body in plane strain? Explain why or why not. (c) Determine by a calculation whether or not compatibility holds for this strain field. (d) From (a) what is the strain tensor at the point (1,2,1)? (e) Compute the principal normal strains at the point (1,2,1). (f) What is the maximum shear strain at the point (1,2,1)? (g) If the shear modulus of the material is 80 MPa, find the difference between the two principal stresses.

Name: 2. The displacements, in meters, at an arbitrary point (x,y,z) in a g
Uploaded: 2024-03-20T06:56:55.000Z
Channel: Bartleby
Description: 2. The displacements, in meters, at an arbitrary point (x,y,z) in a given body are:x104v(x, y,z) = x³y³ x 10w(x, y,z)=0(a) Determine all the strains in x-y-z coordinates at any point (x,y,z).(b) Is the body in plane strain? Explain why or why not.(c

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

See similar textbooks

Similar questions

The 3-dimensional state of strain at a material point in x, y, z Q4 coordinates is given by: E ya [ε]=Ey Eyy - M E E 20 E יה = -120 0-150 0 0 0 -150 0 240 *10-6 (a) Calculate the volumetric strain and the deviatoric strain invariants (b) Calculate the mean stress and the deviatoric stress tensor (c) Write the characteristic equation of strain (d) Write the characteristic equation of stress The material is linear elastic (E=210GPa, v=0.3).
Find the solution set of each of the following equation/inequality. |x9|= 4x + 1
If n1 is an eigenvector for a strain tensor, show it is also a principal direction for the stress tensor
traction vector acting on a plane through the point whose unit normal is n=(1/3)e_1 + (2/3)e_2 -(2/3)e_3 component of this traction action perpendicular to the plane shear component of the traction on the plane principal stress values and directions of σ_ij maximum shear stress
6
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.
force in three dimensions is given by (a) F = FO(yx^ - xy^) (b) F= FO(yx^ + xy ^) where x^ and y^ are the cartesian basic vectors and F0 is a constant. Find if possible the corresponding potential energy
The state of stress at a point with respect to a Cartesian coordinates system 0x,x,x, is given by: [2 1 3 6,]=1 2 -2 3 -2 1 Determine: (a) the traction vector acting on a plane through the point whose unit normal is n= (1/3)e, + (2/3)e,-(2/3)e, the component of this traction acting perpendicular to the plane the shear component of traction on the plane (b) (c)
Given uAF=1.5/6.5i+2/6.5j−6/6.5k, uAE=−1/3i−2/3j−2/3k, uAG=2/7i+3/7j−6/7k, and magnitude of the force FAF=1083 N. Find the projection on line AE of the force in cable AF.
4.30 Given the following state of stress at a point in a continuum, [5x273 3x3 0 3x² 0 [0] = 0-21 MPa, -21 0 determine the body force vector such that the stress tensor corresponds to an equilibrium state.
Q5/ Find the directional derivative of f(x, y, z) = 3xy + 2xz2 + 8y2 At the point P(2,2,2) in the direction of a = [4,1,2]. %3D %3D
3.56. Check whether or not the following distribution of the state of strain satisfies the compatibility conditions: where k = 10-4. XX+XX₁X3 0 [E]=k|x² + x3 Kinematics of a Continuum 169 X₁ X1Xx3 X₁ X²