The state of strain at a point on a wrench has components E = 120(10-6), Ey = -180(10-6), Yzy= 150(10-6). Use Mohr's circle to solve the Part A problem. Determine the in-plane principal strains.
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- An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.A strain rosette (see figure) mounted on the surface of an automobile frame gives the following readings: gage A,310 × 10-6:gage B,180 × l0-6; and gage C. -160 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.An element of material in plain strain has the following strains: x = 0.001 and y = 0.0015. (a) Determine the strains for an element oriented at an angle = 250. (b) Find the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.
- The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?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.
- Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.Assume that the normal strains x and y , for an clement in plane stress (see figure) are measured with strain gages. (a) Obtain a formula for the normal strain x in the : direction in terms x , y and Poisson’s ratio v. (b) Obtain a formula for the dilatation L’ in terms of x , y and Poisson’s ratio v.Solve the preceding problem if the plate is made of aluminum with E = 72 GPa and Poisson’s ratio v = 0.33. The plate is loaded in biaxial stress with normal stress sx= 79 MPa, angle Ø = 18°, and the strain measured by the gage is e = 925 × 10-6.
- 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.An clement of material subjected to plane strain (see figure) has strains of x=280106 , y=420106 , and xy=150106 . Calculate the strains for an element oriented at an angle = 35°. Show these strains on a sketch of a properly oriented element.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.