3. The state of stress at a point in a continuum body is given by X 1.5 0 1.0 0 00 [a] 1.5 0 MPa where X is a non-zero value but has not been determined. If the body is made up of a brittle material that fractures along the plane of maximum principal stress and the critical tensile stress at which fracture occurs is 5 MPa, (a) what is the maximum value of X that the body can sustain without fracture? (b) if X were to reach the critical value, what would be the orientation of the fracture plane? Show the stress state on a properly oriented element.

3. The state of stress at a point in a continuum body is given by X 1.5 0 1.0 0 00 [a] 1.5 0 MPa where X is a non-zero value but has not been determined. If the body is made up of a brittle material that fractures along the plane of maximum principal stress and the critical tensile stress at which fracture occurs is 5 MPa, (a) what is the maximum value of X that the body can sustain without fracture? (b) if X were to reach the critical value, what would be the orientation of the fracture plane? Show the stress state on a properly oriented element.

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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For a given homogeneous, isotropic, linearly elastic material, E = 15e6 psi and v = 0.3. Solve for the shear modulus. 2.1.1 Homogeneous, isotropic, linearly elastic materials For specimens undergoing small deformations, the stress-strain diagram often ex- hibits a linear behavior. Although this is a very crude approximation to the behavior of actual materials, it is a convenient assumption that is often used for preliminary evaluation. A linear relationship between stress and strain can be expressed as 01 = E €1, (2.1) where the coefficient of proportionality, E, is called Young's modulus or modulus of elasticity. Since strains are non-dimensional quantities, this coefficient has the same units as stress quantities, i.e., Pa. This linear relationship is known as Hooke's law. The elongation of a bar in the direction of the applied stress is accompanied by a lateral contraction that is also proportional to the applied stress. The resulting defor- mations for this uniaxial state of stress…
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gauges system mounted at a point on a structural member that is subjected to multiaxial stresses, where we have the following readings: Ex = 6.686 x104 ;&, 3.0 x10-4; & = - 6.857 x10-5; Yxy = 2.580 x10-3; %3D %3D Determine the stress components if the member is made of an isotropic material with linear elastic behavior having the following elastic properties: Young's modulus E = 70 Gpa and Poisson's ratio v = 0.29; Select one: Ox = 70 Mpa; Oy = 50 Mpa; o, 3 30 Мра; Тҳу 35 Mра; %3D 25 Mpa; 0z = 30 Mpa; Txy = 70 Mpa; %3D Ох %3D 140 Мра; бу %3D Ox = 90 Mpa; oy = 50 Mpa; o, = 60 Mpa; Ty = 35 Mpa%3; Ox = 70 Mpa; oy = 50 Mpa; 0z = 30 Mpa; Txy = 70 Mpa; = 70 Mpa3; = 100 Mpa; Oy = 50 Mpa; 0z = 80 Mpa; Txy
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