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Problem 7 A force P of 80 kN is applied in the plane xy to the beam show on the figure. The material has a Young's modulus E = 200 GPa and a Poisson's ration v = 0.3. DO NOT CONSIDER THE CRACK FOR a) b) c) and d). a) Is this a plane stress, plane strain or full 3D stress problem? b) At points C (on neutral axis y = 0) and K (at y = -40 mm), calculate the stresses and draw a cube showing the stresses. USE A 3D CUBE. c) Compute and write the strain tensor at point C. d) Draw the 3D Mohr circle at point K. Indicate the magnitude of principal stresses and maximum shear stress. e) Calculate the maximum magnitude of the force P when a 16 mm crack is introduced at K. Consider a material with a fracture toughness of 77 MPa sqrt(m) . Axial stress: sigma = N/A A = 3200 mm^2 Bending stress: sigma = -My/I I = 1.7x10^6 mm^4 Shear stress: tau = V/(2I) * (80^2/4 - y^2) I = 1.7x10^6 mm^4 * dimensions for y in mm where N = axial force, V = shear force, M = bending moment, y = distance from the neutral axis.

          Problem 7
A force P of 80 kN is applied in the plane xy to the beam show on the figure. The material has a Young's modulus E = 200 GPa and a Poisson's ration v = 0.3. DO NOT CONSIDER THE CRACK FOR a) b) c) and d).
a) Is this a plane stress, plane strain or full 3D stress problem?
b) At points C (on neutral axis y = 0) and K (at y = -40 mm), calculate the stresses and draw a cube showing the stresses. USE A 3D CUBE.
c) Compute and write the strain tensor at point C.
d) Draw the 3D Mohr circle at point K. Indicate the magnitude of principal stresses and maximum shear stress.
e) Calculate the maximum magnitude of the force P when a 16 mm crack is introduced at K. Consider a material with a fracture toughness of 77 MPa sqrt(m) .
Axial stress: sigma = N/A A = 3200 mm^2 Bending stress: sigma = -My/I I = 1.7x10^6 mm^4
Shear stress: tau = V/(2I) * (80^2/4 - y^2) I = 1.7x10^6 mm^4 * dimensions for y in mm
where N = axial force, V = shear force, M = bending moment, y = distance from the neutral axis.

$Problem 7 A force P of 80 kN is applied in the plane xy to the beam show on the figure. The material has a Young's modulus E = 200 GPa and a Poisson's ration v = 0.3. DO NOT CONSIDER THE CRACK FOR a) b) c) and d). a) Is this a plane stress, plane strain or full 3D stress problem? b) At points C (on neutral axis y = 0) and K (at y = -40 mm), calculate the stresses and draw a cube showing the stresses. USE A 3D CUBE. c) Compute and write the strain tensor at point C. d) Draw the 3D Mohr circle at point K. Indicate the magnitude of principal stresses and maximum shear stress. e) Calculate the maximum magnitude of the force P when a 16 mm crack is introduced at K. Consider a material with a fracture toughness of 77 MPa sqrt(m) . Axial stress: sigma = N/A A = 3200 mm^2 Bending stress: sigma = -My/I I = 1.7x10^6 mm^4 Shear stress: tau = V/(2I) * (80^2/4 - y^2) I = 1.7x10^6 mm^4 * dimensions for y in mm where N = axial force, V = shear force, M = bending moment, y = distance from the neutral axis.$

Added by Michael M.

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