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
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
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
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...
Equation 3.5.10 is below We were unable to transcribe this image114 KINEMATICS OF 3.5.3 Infinitesimal Rotation Tensor e displacement gradient tensor can be expressed as the sum of a tensor and a skew symmetric tensor. We have where the symmetric part is similar to the infinitesimal strain tensor (and a when VuVoul << 1), and the skew symmetric part is known as the infinitesimal rotation tensor 3.i1 We note that there is no restriction placed on the magnitude of Vu...
5. The rectangular plate deforms as shown by the dashed lines. Determine the shear strain yrv at Point A Determine the shear strain yyrv, at Point A 0.01 in. 5 in. 0.02 in. 5 in. 0.02 in. -5 in. 5. The rectangular plate deforms as shown by the dashed lines. Determine the shear strain yrv at Point A Determine the shear strain yyrv, at Point A 0.01 in. 5 in. 0.02 in. 5 in. 0.02 in. -5 in.
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...
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)....
Problem1: Inertia tensor Four point masses are connected by massless rods as shown in the figure. TYL CL (a) Find inertia tensor (b) Determine a set of principal axes and the cor responding inertia tensor 2a 2a rm rn Problem1: Inertia tensor Four point masses are connected by massless rods as shown in the figure. TYL CL (a) Find inertia tensor (b) Determine a set of principal axes and the cor responding inertia tensor 2a 2a rm rn
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...
Algebraic Vectors in 3 Dimension iven OA(1.3, 5) iiii = (-2,4,-6) vectors 2 Express each vectors as a 3 Determine the opposite vector of oc - (4.-8 0 located e frontback, letnght, upperower standard unit vector form. oC 4. Determine the magnitude of each vector 5. Determine the unit vectors in 6 Express the following as a component form of loAl OA + 08-20で los) 10리 7. Determine 8. Point D is (1,2,3) and9 Point E if (3,5,7), determine by...