4. Show that Cp = as +45°. principal strain and shear strain
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- An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.An element of material in plain strain is subjected to shear strain xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 30°. (b) Determine the principal strains of the clement. Confirm the solution using Mohr’s circle for plane strain.1. Find the relationships between strain components in the polar coordinate and strain components in the rectangular coordinate.
- Tensile test specimens are extracted from the "X" and "y" directions of a rolled sheet of metal. "x" is the rolling direction, "y" is transverse to the rolling direction, and "z" is in the thickness direction. Both specimens were pulled to a longitudinal strain = 0.15 strain. For the sample in the x-direction, the width strain was measured to be ew= -0.0923 at that instant. For the sample in the y-direction, the width strain was measured to be gw=-0.1000 at that instant. The yield strength of the x-direction specimen was 50 kpsi and the yield strength of the y-direction specimen was 52 kpsi. Determine the strain ratio for the x direction tensile test specimen. Determine the strain ratio for the y-direction tensile test specimen. Determine the expected yield strength in the z-direction. Give your answer in units of kpsi (just the number). If the sheet is plastically deformed in equal biaxial tension (a, = 0, to the point where & = 0.15, calculate the strain, 6, that would be expected.The state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and Yxy = 275 x 10-6. (a) Use the strain transformation equations to determine the equivalent strain components on an element oriented at an angle of 0 = 30° counterclockwise from the original position. (b) Sketch the deformed element due to these strains within the x-y plane.3.For a body under three dimensional stress state, describe the procedure for obtaining the absolute maximum shearing stress at a given point. What is meant by strain transformation? Describe two procedures for obtaining stress form Mohr’s circle for strain.
- Q4. The triangular plate ABC is deformed into the shape shown by the dashed lines. If at A, EAB = 0.007, EAC = 0.015, and xy = 0.006 rad, determine the average normal strain along edge BC. 350 mm y A -Yxy 1 450 mm 1 B X (Note: Work show the SI units throughout the solution and the final result should be in SI units)The strain components, ex= 940 micro strain, ey= -360 micro strain and yxy=830micro strain are given for a point in body subjected to plane strain. Determine; a. Magnitude of the principal strains b. The direction of the principal strain axes c. The maximum in-plane shear strain. Confirm your answer by means of Mohr's circle of strain and determine the linear strain on an axis inclined at 20 degrees clockwise to the direction of eyQ.3) A structural member in plane strain has the following strains at a point: & 360 μ , E, = 230 µ, Ky = 150 µ (a) Determine the strains for an element oriented at an angle of 60° counter clockwise. (b) Determine the principal strains and the maximum shear strain using strain transformation equations. (c) Show the result of parts (a) and (b) via sketches of properly oriented elements. Ey Yxy 1 Ex
- A material is subjected to the following strain system,ex=200x10-6, ey=-56x10-6,yxy=230x10-6. Using graphical method, determine A. The principal strains B. The directions of principal strain axes C. The linear strain on an axis inclined at 50o counter clockwise to the direction of ex Given that young's modulus for the material is 207GN/m2 and the poisson's ratio is 0.27, determine the principal stressesIn uniaxial loading the poisson's ratio is 0.30 and the strain in the x- direction is 250 x 10^-6 . What is the strain in the z- direction? a. -7.5 x 10^-5 b. 9.5 x 10^-5 c. -8.5 x 10^-5 d. 7.5 x 10^-5 Show the answer with complete solutionFind strain