4. What are the maximum and minimum stresses for a circular hole in a plate subjected to pure shear? Where are they located? What is the full 3D stress tensor at these positions (in polar coordinates)? Hint: use a stress transformation and superposition. TV о T
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- During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.The stress tensor in MPa for a three-dimensional system for some x, y z axis system is 20 40 -301 40 30 25 -30 25 -10. (a) Confirm that one of the principal stresses is 65.333 MPa, hence find the other princinal stresses and the direction cosines of the planes on which they act. (b) Determine the maximum shear stress.What are the maximum and minimum stresses for a circular hole in a plate subjected to pure shear? Where are they located? What is the full 3D stress tensor at these positions (in polar coordinates)?
- The following stress condition is applied to a cubic material. Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa (a) Write the stress tensor (b) Find the maximum normal stress (c) Find the angle with respect to the x-axis at which the maximum normal stress is applied (d) Find the maximum shear stress (e) Determine the angle with respect to the x-axis at which the maximum shear stress is experiencedThe following stress condition is applied to a cubic material.Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa.(a) Write the stress tensor(b) Find the maximum shear stress(c) Determine the angle with respect to the x-axis at which the maximum shear stress is experiencedThe maximum principal stress in a material is 6 MPa. If the second invariant of the stress tensor is -4 MPa and the third invariant of the stress tensor is -48 (MPa)' find: (a) The remaining principal stresses (b) The normal and shear stresses on a plane, whose normal direction cosines are 0.6, 0.3 and 0.742 (c) The state of stress existing on the maximum shear plane (d) The unit vectors which define the plane in (c) relative to the principal directions.
- The three-dimensional state of stress at a point is given by 30 10 -10T [0]= 10 0 20 MN/m? %3D -10 20 The shear stress on the x-face in y-direction at the same point is then equal to (a) zero MN/m2 (c) 10 MN/m2 (b) -10 MN/m2 (d) 20 MN/m2For the given question and solution, Why is taux'y' after the 25 degree rotation = positive Rsin(phi) = 1.05MA instead of negative Rsin(phi) ? how can i determine the sign convention after rotation? i get mixed up with the sign convention of the shear stress after rotation.Show the following: (a) E E O = 0 leads to symmetry of stress tensor (i.e. o =o or o = o') F.F. -8)=, +u,; (b) E %3D ("n"n+"n+
- At a point in an elastic material under strain, the stresses on the three mutually perpendicular planes are as follows:A normal tensile stress of 60 N/mm^2and shear stress of 40 N/mm2 on one plane and a normal tensile force of 40 N/mm^2and a complimentary shear stress of 40 N/mm^2 on another plane. Find the following using Mohr circle only (take 5 N/mm2 = 1 cm)a. The principal stresses and principal planes.b. The maximum shear stress and its plane.c. The normal and shear stress on a plane inclined at an angle of 30Oto major principal plane.The three-dimensional state of stress at a point is given by 30 10 -10 [0]= 10 20 MN/m² -10 20 0 The shear stress on the x-face in y-direction at the same point is then equal to (a) zero MN/m2 (c) 10 MN/m (b) -10 MN/m² (d) 20 MN/m2 은 ㅇThe following stress condition is applied to a cubic material.Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa.(a) Write the stress tensor(b) Find the maximum normal stress(c) Find the angle with respect to the x- axis at which the maximum normal stress is applied(d) Find the maximum shear stress(e) Determine the angle with respect to the x-axis at which the maximum shear stress is experienced