The stress tensor at a Point is iven as lo 6 5 Determine the strain tensor at this Poi The stress tensor at a Point is iven as lo 6 5 Determine the strain tensor at this Poi
e tress tensor at a Point is iven as 6 5 Determine the strain tensor at this Point e tress tensor at a Point is iven as 6 5 Determine the strain tensor at this Point
5. (Stress tensor, principe stress - 20 points) The state of stress at a point in a material can be described by: 10 2 0 [T] 2 10 0MPa a. Compute the principle stresses and directions. As it is always a good idea to be able to find and correct your own mistakes, you are encouraged to use MATLAB, Maple, Mathematics, etc. to check your answers, but you still need to show all steps b. Compute the invariants of the...
For an isotropic material, (a) Calculate the components of the strain tensor and the stress tensor for the following set of given displacements for an isotropic material: Uj = - X1 , U2 = -V – X2, U3 = -V – X3 , E E E where o is a constant. (b) Check the equilibrium equations to see if they are satisfied for zero body forces. (c) Show the edge tractions on a diagram of the body0 S XL SL,0...
1. Consider the stress tensor T at a particular point in a xyz Cartesian coordinate system. (30 T = 10 (15 10 15 -35 0 ksi 0 40) The material has a modulus of elasticity equal to 10 psi and a Poisson's ratio of 0.3. The principal stresses are 51, 20, and -37 ksi. (A) Determine the nine elements of the strain tensor € (in/in). (B) Determine the largest principal shear stress (ksi). (C) Determine the Von Mises stress (ksi)....
5. The following state of strain has been measured by strain gages at a point on the surface of a crane hook: where strain gages (d. b, c) have θαー30°; θb--30°.0c-900. Determine the strain tensor components
2. If an engineering stress-strain curve shows a stress of 130ksi at a strain of 1890 , determine the true stress and strain at that point.
Question 2 The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: on 0, 0] [220 0 01 [0]= 0, 0, 0, = 0 80 50 MPa Loa 0 0 Lo 50 120] a. Calculate the strain tensor b. Calculate the characteristic equation for the three-dimensional state of strain. C. Calculate the principal strains at the point. d. Calculate the volumetric strain and the deviatoric strain invariants The material is linear elastic...
Question 1 The 3-dimensional state of strain at a material point in x, y, z coordinates is given by: Calculate the volumetric strain and the deviatoric strain invariants a. b. Calculate the mean stress and the deviatoric stress tensor. Calculate the characteristic equation of strain. Calculate the characteristic equation of stress. c. d. The material is linear elastic (E-210GPa, v-0.3) (18 marks) Question 1 The 3-dimensional state of strain at a material point in x, y, z coordinates is given...
4. The three-dimensional state of stress at a point is given by the stress tensor 12 8 101 [ou] = 8 3 4 10 4 7 The principal stresses and the principal directions at the point are given by the eigenvalues and the eigenvectors. I 0 Use the power method for determining value of the largest principal stress. Start with a column vector of ls, and carry out the first four iterations. Also check convergence after fourth iteration
Match the following label with the point on the stress-strain diagram Strain