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Question 3 It was found experimentally that a certain material does not change in volume when...
The state of stress at a point of an elastic solid is given in the x-y-z...
The state of stress at a point of an elastic solid is given in
the x-y-z coordinates by:
Question 2 The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: o. O40000 L0 80 230 ay 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...
need solution for milestones A Q1 Solid Mechanics 3 Assessment Task 1a - 2020 Milestone a...
need solution for milestones A Q1
Solid Mechanics 3 Assessment Task 1a - 2020 Milestone a Question 1. For each of the plane-stress conditions given below, construct a Mohr's circle of stress, find the principal stresses and the orientation of the principal axes relative to the xy axes and determine the stresses on an element, rotated in the x-y plane 60° counterclockwise from its original position: (a) dx = 200 MPa Oy - 300 MPa T .40 MPa (b) dx...
A cube made from an isotropic material whose sides are initially 200 mm is subjected to...
A cube made from an isotropic material whose sides are initially 200 mm is subjected to stresses of 100 MPa (tensile), 150 MPa (compressive) and 80 MPa (tensile) in the x-, y- and z- directions, respectively. Calculate the dimensional changes and the change in volume that results from the loading. The modulus of elasticity of the material is 50 GPa and poisson's ratio is o.3.
Question 1 The 3-dimensional state of strain at a material point in x, y, z coordinates is given ...
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...
Question 13 Define a homogeneous material Material has uniform properties throughout Material exhibits little or no...
Question 13 Define a homogeneous material Material has uniform properties throughout Material exhibits little or no yielding before failure. O Material exhibits little or no yielding before failure. O Material has temperature dependent refractive index. Question 14 Which of the following are true of ductile materials? Fails suddenly without warning, Can be subjected to large strains before failure May exhibit necking prior to failure Shows signs of failure prior to rupture Question 15 The ratio of shear stress to shear...
Question 15 (1 point) A material element is subjected to plane stress conditions. The stresses at...
Question 15 (1 point) A material element is subjected to plane stress conditions. The stresses at the point of interest are as follows (units of MPa are assumed): 0x =-87 Oy =36 Txy =-77 Determine the normal strain in the z-direction, Ex, in microstrain (to one decimal place). So if the value is 18.4 E-06, just enter "18.4". You may assume Young's modulus is 72 GPa and Poisson's ratio is 0.3 for this material.
(3) Elastic constants: (a) Consider a cube of isotropic material and show that the bulk modulus...
(3) Elastic constants: (a) Consider a cube of isotropic material and show that the bulk modulus Eq. (3.5) is related to Young's modulus Eq. (3.1) and Poisson's ratio Eq. (3.6) by K 3(1-2v) (b) What happens when v reaches its upper limit of 0.5? (4) Elastic constants: We have stated that the numerical value of Poisson's ratio is always between +0.5 and -1, but we have proven only the upper limit. Use Eq. (3.10) to argue why -1 is the...
For the following fiber and matrix material properties Fiber (F) Matrix 1 (M1)Matrix2 (M2) Elastic Modulus...
For the following fiber and matrix material properties Fiber (F) Matrix 1 (M1)Matrix2 (M2) Elastic Modulus Shear Modulus Poisson's Ratio Densitv 85 GPa 35 GPa 0.20 2500 kg/m 3.5 GPa 1.5 GPa 0.30 35 GPa 15 GPa 0.30 1200 kg/m3 1800 kg/m Use following fiber volume ratio values with 0.05 increment. Vf - (0,0.05, 0. 10, 0.15, 0.20, 0.25,..,1) 1. (25 pts.) Determine the fiber to composite load ratio (F/ ) vs. fiber volume ratio Vf) curves for F-M1 and...
Question 6 1 pts When a material doesn't change its strain perpendicular to the loading condition,...
Question 6 1 pts When a material doesn't change its strain perpendicular to the loading condition, the material is said to exhibit: Fracture Toughness Plane Strain Plane Stress Crack Propagation Question 7 1 pts The sharper the fillet radius is on the geometry of the part, the the stress concentration factor will be and the the material will catastrophically fajl. lower, more likely higher, less likely higher, more likely lower, less likely Question 8 1 pts FCC metals experience a...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner radius a and outer radius b. The cylinder is subjected to an internal pressure pi, and is under plane stress conditions. In this case the displacement field is of interest is given by and the stress field of interest is given by C2 C2 where, with (E and v) denoting the Young's modulus and the Poisson's Ratio. EA EB Show that b2 b2 (b/a)2-1)...
The state of stress at a point of an elastic solid is given in
the x-y-z coordinates by:
Question 2 The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: o. O40000 L0 80 230 ay 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...
need solution for milestones A Q1
Solid Mechanics 3 Assessment Task 1a - 2020 Milestone a Question 1. For each of the plane-stress conditions given below, construct a Mohr's circle of stress, find the principal stresses and the orientation of the principal axes relative to the xy axes and determine the stresses on an element, rotated in the x-y plane 60° counterclockwise from its original position: (a) dx = 200 MPa Oy - 300 MPa T .40 MPa (b) dx...
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...
Question 13 Define a homogeneous material Material has uniform properties throughout Material exhibits little or no yielding before failure. O Material exhibits little or no yielding before failure. O Material has temperature dependent refractive index. Question 14 Which of the following are true of ductile materials? Fails suddenly without warning, Can be subjected to large strains before failure May exhibit necking prior to failure Shows signs of failure prior to rupture Question 15 The ratio of shear stress to shear...
Question 15 (1 point) A material element is subjected to plane stress conditions. The stresses at the point of interest are as follows (units of MPa are assumed): 0x =-87 Oy =36 Txy =-77 Determine the normal strain in the z-direction, Ex, in microstrain (to one decimal place). So if the value is 18.4 E-06, just enter "18.4". You may assume Young's modulus is 72 GPa and Poisson's ratio is 0.3 for this material.
(3) Elastic constants: (a) Consider a cube of isotropic material and show that the bulk modulus Eq. (3.5) is related to Young's modulus Eq. (3.1) and Poisson's ratio Eq. (3.6) by K 3(1-2v) (b) What happens when v reaches its upper limit of 0.5? (4) Elastic constants: We have stated that the numerical value of Poisson's ratio is always between +0.5 and -1, but we have proven only the upper limit. Use Eq. (3.10) to argue why -1 is the...
For the following fiber and matrix material properties Fiber (F) Matrix 1 (M1)Matrix2 (M2) Elastic Modulus Shear Modulus Poisson's Ratio Densitv 85 GPa 35 GPa 0.20 2500 kg/m 3.5 GPa 1.5 GPa 0.30 35 GPa 15 GPa 0.30 1200 kg/m3 1800 kg/m Use following fiber volume ratio values with 0.05 increment. Vf - (0,0.05, 0. 10, 0.15, 0.20, 0.25,..,1) 1. (25 pts.) Determine the fiber to composite load ratio (F/ ) vs. fiber volume ratio Vf) curves for F-M1 and...
Question 6 1 pts When a material doesn't change its strain perpendicular to the loading condition, the material is said to exhibit: Fracture Toughness Plane Strain Plane Stress Crack Propagation Question 7 1 pts The sharper the fillet radius is on the geometry of the part, the the stress concentration factor will be and the the material will catastrophically fajl. lower, more likely higher, less likely higher, more likely lower, less likely Question 8 1 pts FCC metals experience a...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner radius a and outer radius b. The cylinder is subjected to an internal pressure pi, and is under plane stress conditions. In this case the displacement field is of interest is given by and the stress field of interest is given by C2 C2 where, with (E and v) denoting the Young's modulus and the Poisson's Ratio. EA EB Show that b2 b2 (b/a)2-1)...
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